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= "7abceef4b2ef94f67b69835bbeabbb2815d5820b" } + +num = "0.4.3" +lazy_static = "1.4" + +[dev-dependencies] +codspeed-criterion-compat = "2.7.2" +glob = "0.3.1" +libtest-mimic = "0.6.1" diff --git a/Makefile b/Makefile new file mode 100644 index 0000000..b592ed5 --- /dev/null +++ b/Makefile @@ -0,0 +1,20 @@ +WWW=${PWD}/target/www/ + +all: test nits docs + +test: + cargo nextest run --release + # nextest doesn't run doctests, so do it here + cargo test --doc --release + +nits: + @rustup component add clippy + cargo clippy --tests -- -D warnings + @rustup component add rustfmt + cargo fmt --check + +docs: + mkdir -p ${WWW} + cargo doc --no-deps --all-features + touch target/doc/.nojekyll # prevent github from trying to run jekyll + cp -r target/doc ${WWW}/docs diff --git a/src/lib.rs b/src/lib.rs new file mode 100644 index 0000000..51363df --- /dev/null +++ b/src/lib.rs @@ -0,0 +1,11 @@ +pub use egglog::*; +use std::sync::Arc; + +mod rational; +pub use rational::*; + +pub fn new_experimental_egraph() -> EGraph { + let mut egraph = EGraph::default(); + egraph.add_arcsort(Arc::new(RationalSort)).unwrap(); + egraph +} diff --git a/src/main.rs b/src/main.rs new file mode 100644 index 0000000..c89b901 --- /dev/null +++ b/src/main.rs @@ -0,0 +1,3 @@ +fn main() { + todo!(); +} diff --git a/src/rational.rs b/src/rational.rs new file mode 100644 index 0000000..31ce391 --- /dev/null +++ b/src/rational.rs @@ -0,0 +1,150 @@ +use egglog::ast::{Expr, GenericExpr, Symbol, DUMMY_SPAN}; +use egglog::sort::{FromSort, IntoSort, Sort}; +use lazy_static::lazy_static; +use num::integer::Roots; +use num::rational::Rational64; +use num::traits::{CheckedAdd, CheckedDiv, CheckedMul, CheckedSub, One, Signed, ToPrimitive, Zero}; +use std::any::Any; +use std::sync::{Arc, Mutex}; + +#[derive(Clone, Copy, Debug, PartialEq, Eq, Hash)] +struct R(Rational64); // orphan rule +use crate::{ast::Literal, util::IndexSet}; + +use super::*; + +lazy_static! { + static ref RATIONAL_SORT_NAME: Symbol = "Rational".into(); + static ref RATS: Mutex> = Default::default(); +} + +#[derive(Debug)] +pub struct RationalSort; + +impl Sort for RationalSort { + fn name(&self) -> Symbol { + *RATIONAL_SORT_NAME + } + + fn as_arc_any(self: Arc) -> Arc { + self + } + + #[rustfmt::skip] + fn register_primitives(self: Arc, eg: &mut TypeInfo) { + type Opt = Option; + + // TODO we can't have primitives take borrows just yet, since it + // requires returning a reference to the locked sort + add_primitives!(eg, "+" = |a: R, b: R| -> Opt { a.0.checked_add(&b.0).map(R) }); + add_primitives!(eg, "-" = |a: R, b: R| -> Opt { a.0.checked_sub(&b.0).map(R) }); + add_primitives!(eg, "*" = |a: R, b: R| -> Opt { a.0.checked_mul(&b.0).map(R) }); + add_primitives!(eg, "/" = |a: R, b: R| -> Opt { a.0.checked_div(&b.0).map(R) }); + + add_primitives!(eg, "min" = |a: R, b: R| -> R { R(a.0.min(b.0)) }); + add_primitives!(eg, "max" = |a: R, b: R| -> R { R(a.0.max(b.0)) }); + add_primitives!(eg, "neg" = |a: R| -> R { R(-a.0) }); + add_primitives!(eg, "abs" = |a: R| -> R { R(a.0.abs()) }); + add_primitives!(eg, "floor" = |a: R| -> R { R(a.0.floor()) }); + add_primitives!(eg, "ceil" = |a: R| -> R { R(a.0.ceil()) }); + add_primitives!(eg, "round" = |a: R| -> R { R(a.0.round()) }); + add_primitives!(eg, "rational" = |a: i64, b: i64| -> R { R(Rational64::new(a, b)) }); + add_primitives!(eg, "numer" = |a: R| -> i64 { *a.0.numer() }); + add_primitives!(eg, "denom" = |a: R| -> i64 { *a.0.denom() }); + + add_primitives!(eg, "to-f64" = |a: R| -> f64 { a.0.to_f64().unwrap() }); + + add_primitives!(eg, "pow" = |a: R, b: R| -> Option { + if a.0.is_zero() { + if b.0.is_positive() { + Some(R(Rational64::zero())) + } else { + None + } + } else if b.0.is_zero() { + Some(R(Rational64::one())) + } else if let Some(b) = b.0.to_i64() { + if let Ok(b) = usize::try_from(b) { + num::traits::checked_pow(a.0, b).map(R) + } else { + // TODO handle negative powers + None + } + } else { + None + } + }); + add_primitives!(eg, "log" = |a: R| -> Option { + if a.0.is_one() { + Some(R(Rational64::zero())) + } else { + todo!() + } + }); + add_primitives!(eg, "sqrt" = |a: R| -> Option { + if a.0.numer().is_positive() && a.0.denom().is_positive() { + let s1 = a.0.numer().sqrt(); + let s2 = a.0.denom().sqrt(); + let is_perfect = &(s1 * s1) == a.0.numer() && &(s2 * s2) == a.0.denom(); + if is_perfect { + Some(R(Rational64::new(s1, s2))) + } else { + None + } + } else { + None + } + }); + add_primitives!(eg, "cbrt" = |a: R| -> Option { + if a.0.is_one() { + Some(R(Rational64::one())) + } else { + todo!() + } + }); + + add_primitives!(eg, "<" = |a: R, b: R| -> Opt { if a.0 < b.0 {Some(())} else {None} }); + add_primitives!(eg, ">" = |a: R, b: R| -> Opt { if a.0 > b.0 {Some(())} else {None} }); + add_primitives!(eg, "<=" = |a: R, b: R| -> Opt { if a.0 <= b.0 {Some(())} else {None} }); + add_primitives!(eg, ">=" = |a: R, b: R| -> Opt { if a.0 >= b.0 {Some(())} else {None} }); + } + + fn make_expr(&self, _egraph: &egglog::EGraph, value: Value) -> (usize, Expr) { + #[cfg(debug_assertions)] + debug_assert_eq!(value.tag, self.name()); + + let rat = R::load(self, &value); + let numer = *rat.0.numer(); + let denom = *rat.0.denom(); + ( + 1, + Expr::call_no_span( + "rational", + vec![ + GenericExpr::Lit(DUMMY_SPAN.clone(), Literal::Int(numer)), + GenericExpr::Lit(DUMMY_SPAN.clone(), Literal::Int(denom)), + ], + ), + ) + } +} + +impl FromSort for R { + type Sort = RationalSort; + fn load(_sort: &Self::Sort, value: &Value) -> Self { + let i = value.bits as usize; + *RATS.lock().unwrap().get_index(i).unwrap() + } +} + +impl IntoSort for R { + type Sort = RationalSort; + fn store(self, _sort: &Self::Sort) -> Option { + let (i, _) = RATS.lock().unwrap().insert_full(self); + Some(Value { + #[cfg(debug_assertions)] + tag: RationalSort.name(), + bits: i as u64, + }) + } +} diff --git a/tests/before-proofs.egg b/tests/before-proofs.egg new file mode 100644 index 0000000..3becdbb --- /dev/null +++ b/tests/before-proofs.egg @@ -0,0 +1,32 @@ +(datatype Math + (Add Math Math) + (Sub Math Math) + (Const Rational) + (Var String)) + +(rewrite (Add a b) (Add (Add a b) (Const (rational 0 1)))) + +(rewrite (Add a b) (Add b a)) + + +(rewrite (Add a (Add b c)) + (Add (Add a b) c)) + +(let two (rational 2 1)) +(let start1 (Add (Var "x") (Const two))) +;; add original proofs + +(run 3) + + +(check (!= (Var "x") (Const two))) +(check (= (Add (Var "x") (Const two)) + (Add (Const two) (Var "x")))) + +(let zero (Const (rational 0 1))) +(let addx2 (Add (Var "x") (Const two))) +(let addx20 (Add addx2 zero)) +(let addzerofront (Add (Add zero (Var "x")) (Const two))) + +(check (= addx2 + addx20)) diff --git a/tests/files.rs b/tests/files.rs new file mode 100644 index 0000000..21daa0e --- /dev/null +++ b/tests/files.rs @@ -0,0 +1,131 @@ +use std::path::PathBuf; + +use egglog_experimental::*; +use libtest_mimic::Trial; + +#[derive(Clone)] +struct Run { + path: PathBuf, + resugar: bool, +} + +impl Run { + fn run(&self) { + let program = std::fs::read_to_string(&self.path) + .unwrap_or_else(|err| panic!("Couldn't read {:?}: {:?}", self.path, err)); + + if !self.resugar { + self.test_program( + self.path.to_str().map(String::from), + &program, + "Top level error", + ); + } else { + let mut egraph = new_experimental_egraph(); + egraph.run_mode = RunMode::ShowDesugaredEgglog; + egraph.set_reserved_symbol("__".into()); + let desugared_str = egraph + .parse_and_run_program(self.path.to_str().map(String::from), &program) + .unwrap() + .join("\n"); + + self.test_program( + None, + &desugared_str, + "ERROR after parse, to_string, and parse again.", + ); + } + } + + fn test_program(&self, filename: Option, program: &str, message: &str) { + let mut egraph = new_experimental_egraph(); + egraph.set_reserved_symbol("___".into()); + match egraph.parse_and_run_program(filename, program) { + Ok(msgs) => { + if self.should_fail() { + panic!( + "Program should have failed! Instead, logged:\n {}", + msgs.join("\n") + ); + } else { + for msg in msgs { + println!(" {}", msg); + } + // Test graphviz dot generation + let mut serialized = egraph.serialize(SerializeConfig { + max_functions: Some(40), + max_calls_per_function: Some(40), + ..Default::default() + }); + serialized.to_dot(); + // Also try splitting and inlining + serialized.split_classes(|id, _| egraph.from_node_id(id).is_primitive()); + serialized.inline_leaves(); + serialized.to_dot(); + } + } + Err(err) => { + if !self.should_fail() { + panic!("{}: {err}", message) + } + } + }; + } + + fn into_trial(self) -> Trial { + let name = self.name().to_string(); + Trial::test(name, move || { + self.run(); + Ok(()) + }) + } + + fn name(&self) -> impl std::fmt::Display + '_ { + struct Wrapper<'a>(&'a Run); + impl std::fmt::Display for Wrapper<'_> { + fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { + let stem = self.0.path.file_stem().unwrap(); + let stem_str = stem.to_string_lossy().replace(['.', '-', ' '], "_"); + write!(f, "{stem_str}")?; + if self.0.resugar { + write!(f, "_resugar")?; + } + Ok(()) + } + } + Wrapper(self) + } + + fn should_fail(&self) -> bool { + self.path.to_string_lossy().contains("fail-typecheck") + } +} + +fn generate_tests(glob: &str) -> Vec { + let mut trials = vec![]; + let mut push_trial = |run: Run| trials.push(run.into_trial()); + + for entry in glob::glob(glob).unwrap() { + let run = Run { + path: entry.unwrap().clone(), + resugar: false, + }; + let should_fail = run.should_fail(); + + push_trial(run.clone()); + if !should_fail { + push_trial(Run { + resugar: true, + ..run.clone() + }); + } + } + + trials +} + +fn main() { + let args = libtest_mimic::Arguments::from_args(); + let tests = generate_tests("tests/**/*.egg"); + libtest_mimic::run(&args, tests).exit(); +} diff --git a/tests/herbie-tutorial.egg b/tests/herbie-tutorial.egg new file mode 100644 index 0000000..2c2b8db --- /dev/null +++ b/tests/herbie-tutorial.egg @@ -0,0 +1,137 @@ +(datatype Math + (Num Rational) + (Var String) + (Add Math Math) + (Div Math Math) + (Mul Math Math)) + +(let zero (Num (rational 0 1))) +(let one (Num (rational 1 1))) +(let two (Num (rational 2 1))) + +(rewrite (Add a b) (Add b a)) +(rewrite (Add a zero) a) +(rewrite (Add (Num r1) (Num r2)) + (Num (+ r1 r2))) + +(let one-two (Add one two)) + +(push) +(run 1) +;; yay, constant folding works +(check (= one-two (Num (rational 3 1)))) +;; also, commutativity works +(check (= (Add two one) one-two)) +(pop) + +(push) +;; rule is like rewrite, but more general +;; the following rule doesn't union (Num r) with the result: +(rule ((Num r)) + ((union one (Div (Num r) (Num r))))) +;; uh oh, division by zero! +(run 1) + +(pop) + +;; we need to detect when things are non-zero +(function lower-bound (Math) Rational :merge (max old new)) +(function upper-bound (Math) Rational :merge (min old new)) + +(rule ((Num r)) + ((set (lower-bound (Num r)) r) + (set (upper-bound (Num r)) r))) +(rule ((= e (Add a b)) (= x (lower-bound a)) (= y (lower-bound b))) + ((set (lower-bound e) (+ x y)))) +(rule ((= e (Add a b)) (= x (upper-bound a)) (= y (upper-bound b))) + ((set (upper-bound e) (+ x y)))) +(rule ((= e (Mul a b))) + ((set (lower-bound e) + (min (* (lower-bound a) (lower-bound b)) + (min (* (lower-bound a) (upper-bound b)) + (min (* (upper-bound a) (lower-bound b)) + (* (upper-bound a) (upper-bound b)))))) + (set (upper-bound e) + (max (* (lower-bound a) (lower-bound b)) + (max (* (lower-bound a) (upper-bound b)) + (max (* (upper-bound a) (lower-bound b)) + (* (upper-bound a) (upper-bound b)))))))) + +(rule ((= e (Add a b)) + (> (lower-bound e) (rational 0 1))) + ((union one (Div (Add a b) (Add a b))))) + +(let x (Var "x")) +(let x1 (Add x one)) + +(push) +(set (lower-bound x) (rational 0 1)) +(set (upper-bound x) (rational 1 1)) + +(run 3) + +(query-extract (lower-bound x1)) +(query-extract (upper-bound x1)) +(check (= one (Div x1 x1))) + +(pop) + + +;; Set the variable x to a particular input value 200/201 +(set (lower-bound x) (rational 200 201)) +(set (upper-bound x) (rational 200 201)) + +(run 3) + +(query-extract (lower-bound x1)) +(query-extract (upper-bound x1)) + +(function true-value (Math) f64) + +(rule ((= (to-f64 (lower-bound e)) + (to-f64 (upper-bound e)))) + ((set (true-value e) + (to-f64 (lower-bound e))))) + +(run 1) +(query-extract (true-value x1)) + +(function best-error (Math) f64 :merge new :default (to-f64 (rational 10000 1))) + +(rule ((Num n)) + ((set (best-error (Num n)) (to-f64 n)))) +(rule ((Add a b)) ((best-error (Add a b)))) + +;; finally, the mega rule for finding more accurate programs +(rule ((= expr (Add a b)) + (= (best-error a) va) + (= (best-error b) vb) + (= true-v (true-value (Add a b))) + (= computed (+ va vb)) + (< (abs (- computed true-v)) + (best-error (Add a b)))) + ((set (best-error (Add a b)) computed))) + + + +(push) + +(let target + (Add + (Add (Num (rational 1 100)) (Num (rational 1 100))) + (Num (rational -2 100)))) + +(run 1) + +;; set a default +(best-error target) +;; error is bad, constant folding hasn't fired enough +(query-extract (best-error target)) + +(run 1) + +;; error is good, constant folding has fired enough +(query-extract (best-error target)) + + +(pop) \ No newline at end of file diff --git a/tests/herbie.egg b/tests/herbie.egg new file mode 100644 index 0000000..6b19c31 --- /dev/null +++ b/tests/herbie.egg @@ -0,0 +1,570 @@ +;; Implements part of the simplification layer of herbie in egglog🫡 + +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; +;; +;; Datatypes + +(datatype Math + ; Ground terms + (Num Rational) + (Var String) + + ; Custom ops + (Const String) + (Unary String Math) + ; unneeded for now + ; (Binary String Math Math) + + ; Constant-folding ops + (Add Math Math) + (Sub Math Math) + (Mul Math Math) + (Div Math Math) + (Pow Math Math) + (Neg Math) + (Sqrt Math) + (Cbrt Math) ; cube root + (Fabs Math) + (Ceil Math) + (Floor Math) + (Round Math) + (Log Math)) + +(let r-zero (rational 0 1)) +(let r-one (rational 1 1)) +(let r-two (rational 2 1)) +(let zero (Num r-zero)) +(let one (Num r-one)) +(let two (Num r-two)) +(let three (Num (rational 3 1))) +(let neg-one (Neg one)) + +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; +;; +;; Analyses +;; -------- +;; This example has three analyses: +;; an interval analysis consisting of a hi and lo component +;; and a non-zero analysis. +;; The non-zero analysis is built off the interval analysis (in order to prove +;; that rewrites are sound, even if some parts of an expr can't be const-evaled) + +; TODO: unbounded intervals? +(function hi (Math) Rational :merge (min old new)) +(function lo (Math) Rational :merge (max old new)) +(relation non-zero (Math)) + +;; First, constant folding! +;; We don't need an explicit constant folding analysis, we can just union +;; with nums when we can + +; Cases +(rewrite (Add (Num a) (Num b)) (Num (+ a b))) +(rewrite (Sub (Num a) (Num b)) (Num (- a b))) +(rewrite (Mul (Num a) (Num b)) (Num (* a b))) +(rewrite (Div (Num a) denom) (Num (/ a b)) :when ((= denom (Num b)) (non-zero denom))) +(rewrite (Pow (Num a) (Num b)) (Num res) :when ((= res (pow a b)))) +(rewrite (Neg (Num a)) (Num (neg a))) +;; TODO unimplemented +;; (rewrite (Sqrt (Num a)) (Num res) :when ((= res (sqrt a)))) +;; (rewrite (Cbrt (Num a)) (Num res) :when ((= res (cbrt a)))) +(rewrite (Fabs (Num a)) (Num (abs a))) +(rewrite (Ceil (Num a)) (Num (ceil a))) +(rewrite (Floor (Num a)) (Num (floor a))) +(rewrite (Round (Num a)) (Num (round a))) +(rewrite (Log (Num a)) (Num res) :when ((= res (log a)))) + +;; To check if something is zero, we check that zero is not contained in the +;; interval. There are two possible (overlapping!) cases: +;; - There exists a lo interval, in which case it must be larger than 0 +;; - There exists a hi interval, in which case it must be smaller than 0 +;; This assumes that intervals are well-formed: lo <= hi at all times. +(rule ((= l (lo e)) + (> l r-zero)) + ((non-zero e))) +(rule ((= h (hi e)) + (< h r-zero)) + ((non-zero e))) + +(rule ((= e (Num ve))) + ((set (lo e) ve) + (set (hi e) ve))) + +;; The interval analyses are similar to the constant-folding analysis, +;; except we have to take the lower/upper bound of the results we get +(rule ((= e (Add a b)) + (= la (lo a)) + (= lb (lo b))) + ((set (lo e) (+ la lb)))) +(rule ((= e (Add a b)) + (= ha (hi a)) + (= hb (hi b))) + ((set (hi e) (+ ha hb)))) + +(rule ((= e (Sub a b)) + (= la (lo a)) + (= ha (hi a)) + (= lb (lo b)) + (= hb (hi b))) + ((set (lo e) + (min (min (- la lb) (- la hb)) + (min (- ha lb) (- ha hb)))) + (set (hi e) + (max (max (- la lb) (- la hb)) + (max (- ha lb) (- ha hb)))))) + +(rule ((= e (Mul a b)) + (= la (lo a)) + (= ha (hi a)) + (= lb (lo b)) + (= hb (hi b))) + ((set (lo e) + (min (min (* la lb) (* la hb)) + (min (* ha lb) (* ha hb)))) + (set (hi e) + (max (max (* la lb) (* la hb)) + (max (* ha lb) (* ha hb)))))) + +(rule ((= e (Div a b)) + (= la (lo a)) + (= ha (hi a)) + (= lb (lo b)) + (= hb (hi b))) + ((set (lo e) + (min (min (/ la lb) (/ la hb)) + (min (/ ha lb) (/ ha hb)))) + (set (hi e) + (max (max (/ la lb) (/ la hb)) + (max (/ ha lb) (/ ha hb)))))) + +; TODO: Pow + +(rule ((= e (Neg a)) + (= la (lo a)) + (= ha (hi a))) + ((set (lo e) (neg ha)) + (set (hi e) (neg la)))) + +; TODO: Sqrt +; TODO: Cbrt + +(rule ((= e (Fabs a)) + (= la (lo a)) + (= ha (hi a))) + ((set (lo e) (min (abs la) (abs ha))) + (set (hi e) (max (abs la) (abs ha))))) + +(rule ((= e (Ceil a)) + (= la (lo a))) + ((set (lo e) (ceil la)))) +(rule ((= e (Ceil a)) + (= ha (hi a))) + ((set (hi e) (ceil ha)))) + +(rule ((= e (Floor a)) + (= la (lo a))) + ((set (lo e) (floor la)))) +(rule ((= e (Floor a)) + (= ha (hi a))) + ((set (hi e) (floor ha)))) + +(rule ((= e (Round a)) + (= la (lo a))) + ((set (lo e) (round la)))) +(rule ((= e (Round a)) + (= ha (hi a))) + ((set (hi e) (round ha)))) + +; TODO: Log + +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; +;; +;; Rewrites +;; -------- +;; These rewrites were compiled from src/syntax/rules.rkt in the herbie repo, +;; using all rewrites in the `simplify` rewrite group. + +;; Commutativity +(rewrite (Add a b) (Add b a)) +(rewrite (Mul a b) (Mul b a)) + +;; Associativity +(rewrite (Add a (Add b c)) (Add (Add a b) c)) +(rewrite (Add (Add a b) c) (Add a (Add b c))) +(rewrite (Add a (Sub b c)) (Sub (Add a b) c)) +(rewrite (Add (Sub a b) c) (Sub a (Sub b c))) +(rewrite (Sub a (Add b c)) (Sub (Sub a b) c)) +(rewrite (Sub (Add a b) c) (Add a (Sub b c))) +(rewrite (Sub (Sub a b) c) (Sub a (Add b c))) +(rewrite (Sub a (Sub b c)) (Add (Sub a b) c)) +(rewrite (Mul a (Mul b c)) (Mul (Mul a b) c)) +(rewrite (Mul (Mul a b) c) (Mul a (Mul b c))) +(rewrite (Mul a (Div b c)) (Div (Mul a b) c)) +(rewrite (Mul (Div a b) c) (Div (Mul a c) b)) +(rewrite (Div a (Mul b c)) (Div (Div a b) c)) +(rewrite (Div (Mul b c) a) (Div b (Div a c)) :when ((non-zero c))) +(rewrite (Div a (Div b c)) (Mul (Div a b) c) :when ((non-zero c))) +(rewrite (Div (Div b c) a) (Div b (Mul a c)) :when ((non-zero a))) + +;; Counting +(rewrite (Add x x) (Mul two x)) + +;; Distributivity +(rewrite (Mul a (Add b c)) (Add (Mul a b) (Mul a c))) +(rewrite (Mul a (Add b c)) (Add (Mul b a) (Mul c a))) +(rewrite (Add (Mul a b) (Mul a c)) (Mul a (Add b c))) +(rewrite (Sub (Mul a b) (Mul a c)) (Mul a (Sub b c))) +(rewrite (Add (Mul b a) (Mul c a)) (Mul a (Add b c))) +(rewrite (Sub (Mul b a) (Mul c a)) (Mul a (Sub b c))) +(rewrite (Add (Mul b a) a) (Mul (Add b one) a)) +(rewrite (Add a (Mul c a)) (Mul (Add c one) a)) + +(rewrite (Neg (Mul a b)) (Mul (Neg a) b)) +(rewrite (Neg (Mul a b)) (Mul a (Neg b))) +(rewrite (Mul (Neg a) b) (Neg (Mul a b))) +(rewrite (Mul a (Neg b)) (Neg (Mul a b))) +(rewrite (Neg (Add a b)) (Add (Neg a) (Neg b))) +(rewrite (Add (Neg a) (Neg b)) (Neg (Add a b))) +(rewrite (Div (Neg a) b) (Neg (Div a b))) +(rewrite (Neg (Div a b)) (Div (Neg a) b)) + +(rewrite (Sub a (Mul (Neg b) c)) (Add a (Mul b c))) +(rewrite (Sub a (Mul b c)) (Add a (Mul (Neg b) c))) + +;; Difference of squares +(rewrite (Mul (Mul a b) (Mul a b)) (Mul (Mul a a) (Mul b b))) +(rewrite (Mul (Mul a a) (Mul b b)) (Mul (Mul a b) (Mul a b))) +(rewrite (Sub (Mul a a) (Mul b b)) (Mul (Add a b) (Sub a b))) +(rewrite (Sub (Mul a a) one) (Mul (Add a one) (Sub a one))) +(rewrite (Add (Mul a a) (Neg one)) (Mul (Add a one) (Sub a one))) +(rewrite (Pow a b) (Mul (Pow a (Div b two)) (Pow a (Div b two)))) +(rewrite (Mul (Pow a b) (Pow a b)) (Pow a (Mul two b))) + +;; Identity +;; This isn't subsumed by const folding since this can return results +;; even if we can't evaluate a precise value for x +(rewrite (Div one (Div one x)) + x + :when ((non-zero x))) +(rewrite (Mul x (Div one x)) + one + :when ((non-zero x))) +(rewrite (Mul (Div one x) x) + one + :when ((non-zero x))) + +(rewrite (Sub x x) zero) +(rewrite (Div x x) one + :when ((non-zero x))) +(rewrite (Div zero x) zero + :when ((non-zero x))) +(rewrite (Mul zero x) zero) +(rewrite (Mul x zero) zero) + +(rewrite (Add zero x) x) +(rewrite (Add x zero) x) +(rewrite (Sub zero x) (Neg x)) +(rewrite (Sub x zero) x) +(rewrite (Neg (Neg x)) x) +(rewrite (Mul one x) x) +(rewrite (Mul x one) x) +(rewrite (Div x one) x) +(rewrite (Mul neg-one x) (Neg x)) + +(rewrite (Sub a b) (Add a (Neg b))) +(rewrite (Add a (Neg b)) (Sub a b)) +(rewrite (Neg x) (Sub zero x)) +(rewrite (Neg x) (Mul neg-one x)) + +(rewrite (Div x y) (Mul x (Div one y))) +(rewrite (Mul x (Div one y)) (Div x y)) +(rewrite (Div x y) (Div one (Div y x)) + :when ((non-zero x) + (non-zero y))) + +; FIXME: this rule can't be expressed in its full generality; +; we can't express the general rule x -> 1/x since +; we can't quantify over Math yet +; for now we just apply it to vars +; it's also p slow lmao +(rewrite (Var x) (Mul one (Var x))) + +;; Fractions +(rewrite (Div (Sub a b) c) (Sub (Div a c) (Div b c))) +(rewrite (Div (Mul a b) (Mul c d)) (Mul (Div a c) (Div b d))) + +;; Square root +(rewrite (Mul (Sqrt x) (Sqrt x)) x) +(rewrite (Sqrt (Mul x x)) (Fabs x)) + +(rewrite (Mul (Neg x) (Neg x)) (Mul x x)) +(rewrite (Mul (Fabs x) (Fabs x)) (Mul x x)) + +;; Absolute values +(rewrite (Fabs (Fabs x)) (Fabs x)) +(rewrite (Fabs (Sub a b)) (Fabs (Sub b a))) +(rewrite (Fabs (Neg x)) (Fabs x)) +(rewrite (Fabs (Mul x x)) (Mul x x)) +(rewrite (Fabs (Mul a b)) (Mul (Fabs a) (Fabs b))) +(rewrite (Fabs (Div a b)) (Div (Fabs a) (Fabs b))) + +;; Cube root +(rewrite (Pow (Cbrt x) three) x) +(rewrite (Cbrt (Pow x three)) x) +(rewrite (Mul (Mul (Cbrt x) (Cbrt x)) (Cbrt x)) x) +(rewrite (Mul (Cbrt x) (Mul (Cbrt x) (Cbrt x))) x) +(rewrite (Pow (Neg x) three) (Neg (Pow x three))) + +(rewrite (Pow (Mul x y) three) + (Mul (Pow x three) (Pow y three))) +(rewrite (Pow (Div x y) three) + (Div (Pow x three) (Pow y three))) + +(rewrite (Pow x three) (Mul x (Mul x x))) +; FIXME: this rewrite is slow and has the potential to blow up the egraph +; this is bc this rule and the second-to-last difference of squares rule +; have some cyclic behavior goin on +; the last identity rule compounds this behavior +(rewrite (Mul x (Mul x x)) (Pow x three)) + +;; Exponentials +(rewrite (Unary "exp" (Log x)) x) +(rewrite (Log (Unary "exp" x)) x) + +(rewrite (Unary "exp" zero) one) +(rewrite (Unary "exp" one) (Const "E")) +;; (rewrite one (Unary "exp" zero)) +(rewrite (Const "E") (Unary "exp" one)) + +(rewrite (Unary "exp" (Add a b)) (Mul (Unary "exp" a) (Unary "exp" b))) +(rewrite (Unary "exp" (Sub a b)) (Div (Unary "exp" a) (Unary "exp" b))) +(rewrite (Unary "exp" (Neg a)) (Div one (Unary "exp" a))) + +(rewrite (Mul (Unary "exp" a) (Unary "exp" b)) (Unary "exp" (Add a b))) +(rewrite (Div one (Unary "exp" a)) (Unary "exp" (Neg a))) +(rewrite (Div (Unary "exp" a) (Unary "exp" b)) (Unary "exp" (Sub a b))) +(rewrite (Unary "exp" (Mul a b)) (Pow (Unary "exp" a) b)) +(rewrite (Unary "exp" (Div a two)) (Sqrt (Unary "exp" a))) +(rewrite (Unary "exp" (Div a three)) (Cbrt (Unary "exp" a))) +(rewrite (Unary "exp" (Mul a two)) (Mul (Unary "exp" a) (Unary "exp" a))) +(rewrite (Unary "exp" (Mul a three)) (Pow (Unary "exp" a) three)) + +;; Powers +(rewrite (Pow a neg-one) (Div one a)) +(rewrite (Pow a one) a) + +; 0^0 is undefined +(rewrite (Pow a zero) one :when ((non-zero a))) +(rewrite (Pow one a) one) + +(rewrite (Unary "Exp" (Mul (Log a) b)) (Pow a b)) +(rewrite (Mul (Pow a b) a) (Pow a (Add b one))) +(rewrite (Pow a (Num (rational 1 2))) (Sqrt a)) +(rewrite (Pow a two) (Mul a a)) +(rewrite (Pow a (Num (rational 1 3))) (Cbrt a)) +(rewrite (Pow a three) (Mul (Mul a a) a)) + +; 0^0 is undefined +(rewrite (Pow zero a) zero :when ((non-zero a))) + +;; Logarithms +(rewrite (Log (Mul a b)) (Add (Log a) (Log b))) +(rewrite (Log (Div a b)) (Sub (Log a) (Log b))) +(rewrite (Log (Div one a)) (Neg (Log a))) +(rewrite (Log (Pow a b)) (Mul b (Log a))) +(rewrite (Log (Const "E")) one) + +;; Trigonometry +(rewrite (Add (Mul (Unary "cos" a) (Unary "cos" a)) (Mul (Unary "sin" a) (Unary "sin" a))) + one) +(rewrite (Sub one (Mul (Unary "cos" a) (Unary "cos" a))) + (Mul (Unary "sin" a) (Unary "sin" a))) +(rewrite (Sub one (Mul (Unary "sin" a) (Unary "sin" a))) + (Mul (Unary "cos" a) (Unary "cos" a))) +(rewrite (Add (Mul (Unary "cos" a) (Unary "cos" a)) (Num (rational -1 1))) + (Neg (Mul (Unary "sin" a) (Unary "sin" a)))) +(rewrite (Add (Mul (Unary "sin" a) (Unary "sin" a)) (Num (rational -1 1))) + (Neg (Mul (Unary "cos" a) (Unary "cos" a)))) +(rewrite (Sub (Mul (Unary "cos" a) (Unary "cos" a)) one) + (Neg (Mul (Unary "sin" a) (Unary "sin" a)))) +(rewrite (Sub (Mul (Unary "sin" a) (Unary "sin" a)) one) + (Neg (Mul (Unary "cos" a) (Unary "cos" a)))) +(rewrite (Unary "sin" (Div (Const "PI") (Num (rational 6 1)))) + (Num (rational 1 2))) +(rewrite (Unary "sin" (Div (Const "PI") (Num (rational 4 1)))) + (Div (Sqrt two) two)) +(rewrite (Unary "sin" (Div (Const "PI") three)) + (Div (Sqrt three) two)) +(rewrite (Unary "sin" (Div (Const "PI") two)) + one) +(rewrite (Unary "sin" (Const "PI")) + zero) +(rewrite (Unary "sin" (Add x (Const "PI"))) + (Neg (Unary "sin" x))) +(rewrite (Unary "sin" (Add x (Div (Const "PI") two))) + (Unary "cos" x)) +(rewrite (Unary "cos" (Div (Const "PI") (Num (rational 6 1)))) + (Div (Sqrt three) two)) +(rewrite (Unary "cos" (Div (Const "PI") (Num (rational 4 1)))) + (Div (Sqrt two) two)) +(rewrite (Unary "cos" (Div (Const "PI") three)) + (Num (rational 1 2))) +(rewrite (Unary "cos" (Div (Const "PI") two)) + zero) +(rewrite (Unary "cos" (Const "PI")) + (Num (rational -1 1))) +(rewrite (Unary "cos" (Add x (Const "PI"))) + (Neg (Unary "cos" x))) +(rewrite (Unary "cos" (Add x (Div (Const "PI") two))) + (Neg (Unary "sin" x))) +(rewrite (Unary "tan" (Div (Const "PI") (Num (rational 6 1)))) + (Div one (Sqrt three))) +(rewrite (Unary "tan" (Div (Const "PI") (Num (rational 4 1)))) + one) +(rewrite (Unary "tan" (Div (Const "PI") three)) + (Sqrt three)) +(rewrite (Unary "tan" (Const "PI")) + zero) +(rewrite (Unary "tan" (Add x (Const "PI"))) + (Unary "tan" x)) +(rewrite (Unary "tan" (Add x (Div (Const "PI") two))) + (Div neg-one (Unary "tan" x))) +(rewrite (Div (Unary "sin" a) (Add one (Unary "cos" a))) + (Unary "tan" (Div a two))) +(rewrite (Div (Neg (Unary "sin" a)) (Add one (Unary "cos" a))) + (Unary "tan" (Div (Neg a) two))) +(rewrite (Div (Sub one (Unary "cos" a)) (Unary "sin" a)) + (Unary "tan" (Div a two))) +(rewrite (Div (Sub one (Unary "cos" a)) (Neg (Unary "sin" a))) + (Unary "tan" (Div (Neg a) two))) +(rewrite (Div (Add (Unary "sin" a) (Unary "sin" b)) (Add (Unary "cos" a) (Unary "cos" b))) + (Unary "tan" (Div (Add a b) two))) +(rewrite (Div (Sub (Unary "sin" a) (Unary "sin" b)) (Add (Unary "cos" a) (Unary "cos" b))) + (Unary "tan" (Div (Sub a b) two))) + +(rewrite (Unary "sin" zero) zero) +(rewrite (Unary "cos" zero) one) +(rewrite (Unary "tan" zero) zero) + +(rewrite (Unary "sin" (Neg x)) (Neg (Unary "sin" x))) +(rewrite (Unary "cos" (Neg x)) (Unary "cos" x)) +(rewrite (Unary "tan" (Neg x)) (Neg (Unary "cos" x))) + +; Hyperbolics +(rewrite (Unary "sinh" x) (Div (Sub (Unary "exp" x) (Unary "exp" (Neg x))) two)) +(rewrite (Unary "cosh" x) (Div (Add (Unary "exp" x) (Unary "exp" (Neg x))) two)) +(rewrite (Unary "tanh" x) (Div (Sub (Unary "exp" x) (Unary "exp" (Neg x))) (Add (Unary "exp" x) (Unary "exp" (Neg x))))) +(rewrite (Unary "tanh" x) (Div (Sub (Unary "exp" (Mul two x)) one) (Add (Unary "exp" (Mul two x)) one))) +(rewrite (Unary "tanh" x) (Div (Sub one (Unary "exp" (Mul (Num (rational -2 1)) x))) (Add one (Unary "exp" (Mul (Num (rational -2 1)) x))))) +(rewrite (Sub (Mul (Unary "cosh" x) (Unary "cosh" x)) (Mul (Unary "sinh" x) (Unary "sinh" x))) one) +(rewrite (Add (Unary "cosh" x) (Unary "sinh" x)) (Unary "exp" x)) +(rewrite (Sub (Unary "cosh" x) (Unary "sinh" x)) (Unary "exp" (Neg x))) + +;; Unimplemented: misc. rewrites (conditionals, specialized numerical fns) + +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; +;; +;; Testing +;; ------- +;; In actuality, herbie would be responsible for plugging exprs in here. +;; For our purposes, we take some test cases from herbie +;; (src/core/simplify.rkt) + +(push) +(let e (Add one zero)) +(run 1) +(check (= e one)) +(pop) + +(push) +(let five (Num (rational 5 1))) +(let six (Num (rational 6 1))) +(let e2 (Add one five)) +(run 1) +(check (= e2 six)) +(pop) + +(let x (Var "x")) + +(push) +(let e3 (Add x zero)) +(run 1) +(check (= e3 x)) +(pop) + +(push) +(let e4 (Sub x zero)) +(run 1) +(check (= e4 x)) +(pop) + +(push) + +(let e5 (Mul x one)) +(run 1) +(check (= e5 x)) +(pop) + +(push) + +(let e6 (Div x one)) +(run 1) +(check (= e6 x)) +(pop) + +(push) + +(let e7 (Sub (Mul one x) (Mul (Add x one) one))) +(run 3) +(check (= e7 (Num (rational -1 1)))) +(pop) + +(push) + +(let e8 (Sub (Add x one) x)) +(run 4) +(check (= e8 one)) +(pop) + +(push) + +(let e9 (Sub (Add x one) one)) +(run 4) +(check (= e9 x)) +(pop) + +(push) + +(set (lo x) r-one) +(let e10 (Div (Mul x three) x)) +(run 3) +(check (= e10 three)) +(pop) + +(push) + +(let e11 (Sub (Mul (Sqrt (Add x one)) (Sqrt (Add x one))) (Mul (Sqrt x) (Sqrt x)))) +(run 5) +(check (= one e11)) +(pop) + +(push) +(let e12 (Add (Num (rational 1 5)) (Num (rational 3 10)))) +(run 1) +(check (= e12 (Num (rational 1 2)))) +(pop) + +(push) +(let e13 (Unary "cos" (Const "PI"))) +(run 1) +(check (= e13 (Num (rational -1 1)))) +(pop) + +(push) +(let sqrt5 (Sqrt (Num (rational 5 1)))) +(let e14 + (Div one (Sub (Div (Add one sqrt5) two) (Div (Sub one sqrt5) two)))) +(let tgt (Div one sqrt5)) +(run 6) +(check (= e14 tgt)) +(pop) \ No newline at end of file diff --git a/tests/interval.egg b/tests/interval.egg new file mode 100644 index 0000000..2c82611 --- /dev/null +++ b/tests/interval.egg @@ -0,0 +1,31 @@ +(datatype Math + (Num Rational) + (Var String) + (Mul Math Math)) + +(function hi (Math) Rational :merge (min old new)) +(function lo (Math) Rational :merge (max old new)) + +(rule ((= mul (Mul a b))) + ((set (lo mul) + (min (min (* (lo a) (lo b)) (* (lo a) (hi b))) + (min (* (hi a) (lo b)) (* (hi a) (hi b))))))) + +(let x (Var "x")) +(let e (Mul x x)) + +(set (lo x) (rational -10 1)) +(set (hi x) (rational 10 1)) + +(run 1) + +(check (= (lo e) (rational -100 1))) + +(rule ((= mul (Mul a a))) + ((set (lo mul) (* (lo a) (lo a))))) + +(run 1) +(check (= (lo e) (rational 100 1))) + +;; testing extraction of rationals +(query-extract (lo e)) diff --git a/tests/math-microbenchmark.egg b/tests/math-microbenchmark.egg new file mode 100644 index 0000000..328c974 --- /dev/null +++ b/tests/math-microbenchmark.egg @@ -0,0 +1,73 @@ +(datatype Math + (Diff Math Math) + (Integral Math Math) + + (Add Math Math) + (Sub Math Math) + (Mul Math Math) + (Div Math Math) + (Pow Math Math) + (Ln Math) + (Sqrt Math) + + (Sin Math) + (Cos Math) + + (Const Rational) + (Var String)) + +(rewrite (Add a b) (Add b a)) +(rewrite (Mul a b) (Mul b a)) +(rewrite (Add a (Add b c)) (Add (Add a b) c)) +(rewrite (Mul a (Mul b c)) (Mul (Mul a b) c)) + +(rewrite (Sub a b) (Add a (Mul (Const (rational -1 1)) b))) +;; (rewrite (Div a b) (Mul a (Pow b (Const (rational -1 1)))) :when ((is-not-zero b))) + +(rewrite (Add a (Const (rational 0 1))) a) +(rewrite (Mul a (Const (rational 0 1))) (Const (rational 0 1))) +(rewrite (Mul a (Const (rational 1 1))) a) + +(rewrite (Sub a a) (Const (rational 0 1))) + +(rewrite (Mul a (Add b c)) (Add (Mul a b) (Mul a c))) +(rewrite (Add (Mul a b) (Mul a c)) (Mul a (Add b c))) + +(rewrite (Mul (Pow a b) (Pow a c)) (Pow a (Add b c))) +(rewrite (Pow x (Const (rational 1 1))) x) +(rewrite (Pow x (Const (rational 2 1))) (Mul x x)) + +(rewrite (Diff x (Add a b)) (Add (Diff x a) (Diff x b))) +(rewrite (Diff x (Mul a b)) (Add (Mul a (Diff x b)) (Mul b (Diff x a)))) + +(rewrite (Diff x (Sin x)) (Cos x)) +(rewrite (Diff x (Cos x)) (Mul (Const (rational -1 1)) (Sin x))) + +(rewrite (Integral (Const (rational 1 1)) x) x) +(rewrite (Integral (Cos x) x) (Sin x)) +(rewrite (Integral (Sin x) x) (Mul (Const (rational -1 1)) (Cos x))) +(rewrite (Integral (Add f g) x) (Add (Integral f x) (Integral g x))) +(rewrite (Integral (Sub f g) x) (Sub (Integral f x) (Integral g x))) +(rewrite (Integral (Mul a b) x) +(Sub (Mul a (Integral b x)) + (Integral (Mul (Diff x a) (Integral b x)) x))) +(Integral (Ln (Var "x")) (Var "x")) +(Integral (Add (Var "x") (Cos (Var "x"))) (Var "x")) +(Integral (Mul (Cos (Var "x")) (Var "x")) (Var "x")) +(Diff (Var "x") (Add (Const (rational 1 1)) (Mul (Const (rational 2 1)) (Var "x")))) +(Diff (Var "x") (Sub (Pow (Var "x") (Const (rational 3 1))) (Mul (Const (rational 7 1)) (Pow (Var "x") (Const (rational 2 1)))))) +(Add (Mul (Var "y") (Add (Var "x") (Var "y"))) (Sub (Add (Var "x") (Const (rational 2 1))) (Add (Var "x") (Var "x")))) +(Div (Const (rational 1 1)) + (Sub (Div (Add (Const (rational 1 1)) + (Sqrt (Var "five"))) + (Const (rational 2 1))) + (Div (Sub (Const (rational 1 1)) + (Sqrt (Var "five"))) + (Const (rational 2 1))))) +(run 11) +(print-size Add) +(print-size Mul) + +(print-size) + +(print-stats) \ No newline at end of file diff --git a/tests/math.egg b/tests/math.egg new file mode 100644 index 0000000..127b054 --- /dev/null +++ b/tests/math.egg @@ -0,0 +1,144 @@ +(datatype Math + (Diff Math Math) + (Integral Math Math) + + (Add Math Math) + (Sub Math Math) + (Mul Math Math) + (Div Math Math) + (Pow Math Math) + (Ln Math) + (Sqrt Math) + + (Sin Math) + (Cos Math) + + (Const Rational) + (Var String)) + +(relation MathU (Math)) +(rule ((= e (Diff x y))) ((MathU e))) +(rule ((= e (Integral x y))) ((MathU e))) +(rule ((= e (Add x y))) ((MathU e))) +(rule ((= e (Sub x y))) ((MathU e))) +(rule ((= e (Mul x y))) ((MathU e))) +(rule ((= e (Div x y))) ((MathU e))) +(rule ((= e (Pow x y))) ((MathU e))) +(rule ((= e (Ln x))) ((MathU e))) +(rule ((= e (Sqrt x))) ((MathU e))) +(rule ((= e (Sin x))) ((MathU e))) +(rule ((= e (Cos x))) ((MathU e))) +(rule ((= e (Const x))) ((MathU e))) +(rule ((= e (Var x))) ((MathU e))) + +(relation evals-to (Math Rational)) + +(rule ((= e (Const c))) ((evals-to e c))) +(rule ((= e (Add a b)) (evals-to a va) (evals-to b vb)) + ((evals-to e (+ va vb)))) +(rule ((= e (Sub a b)) (evals-to a va) (evals-to b vb)) + ((evals-to e (- va vb)))) +(rule ((= e (Mul a b)) (evals-to a va) (evals-to b vb)) + ((evals-to e (* va vb)))) +(rule ((= e (Div a b)) (evals-to a va) (evals-to b vb) (!= vb (rational 0 1))) + ((evals-to e (/ va vb)))) +(rule ((evals-to x vx)) ((union x (Const vx)))) + +(relation is-const (Math)) +(rule ((evals-to a va)) ((is-const a))) + +(relation is-sym (Math)) +(rule ((= e (Var s))) ((is-sym e))) + +(relation is-not-zero (Math)) +(rule ((evals-to x vx) + (!= vx (rational 0 1))) + ((is-not-zero x))) + +(relation is-const-or-distinct-var-demand (Math Math)) +(relation is-const-or-distinct-var (Math Math)) +(rule ((is-const-or-distinct-var-demand v w) + (is-const v)) + ((is-const-or-distinct-var v w))) +(rule ((is-const-or-distinct-var-demand v w) + (= v (Var vv)) + (= w (Var vw)) + (!= vv vw)) + ((is-const-or-distinct-var v w))) + +(rewrite (Add a b) (Add b a)) +(rewrite (Mul a b) (Mul b a)) +(rewrite (Add a (Add b c)) (Add (Add a b) c)) +(rewrite (Mul a (Mul b c)) (Mul (Mul a b) c)) + +(rewrite (Sub a b) (Add a (Mul (Const (rational -1 1)) b))) +(rewrite (Div a b) (Mul a (Pow b (Const (rational -1 1)))) :when ((is-not-zero b))) + +(rewrite (Add a (Const (rational 0 1))) a) +(rewrite (Mul a (Const (rational 0 1))) (Const (rational 0 1))) +(rewrite (Mul a (Const (rational 1 1))) a) + +;; NOTE: these two rules are different from math.rs, as math.rs does pruning +(rule ((MathU a) (!= a (Const (rational 0 1)))) ((union a (Add a (Const (rational 0 1)))))) +(rule ((MathU a) (!= a (Const (rational 1 1)))) ((union a (Mul a (Const (rational 1 1)))))) + +(rewrite (Sub a a) (Const (rational 0 1))) +(rewrite (Div a a) (Const (rational 1 1)) :when ((is-not-zero a))) + +(rewrite (Mul a (Add b c)) (Add (Mul a b) (Mul a c))) +(rewrite (Add (Mul a b) (Mul a c)) (Mul a (Add b c))) + +(rewrite (Mul (Pow a b) (Pow a c)) (Pow a (Add b c))) +(rewrite (Pow x (Const (rational 0 1))) (Const (rational 1 1)) :when ((is-not-zero x))) +(rewrite (Pow x (Const (rational 1 1))) x) +(rewrite (Pow x (Const (rational 2 1))) (Mul x x)) +(rewrite (Pow x (Const (rational -1 1))) (Div (Const (rational 1 1)) x) :when ((is-not-zero x))) +(rewrite (Mul x (Div (Const (rational 1 1)) x)) (Const (rational 1 1)) :when ((is-not-zero x))) + +(rewrite (Diff x x) (Const (rational 1 1)) :when ((is-sym x))) +(rule ((= e (Diff x c)) + (is-sym x)) + ((is-const-or-distinct-var-demand c x))) +(rewrite (Diff x c) (Const (rational 0 1)) :when ((is-sym x) (is-const-or-distinct-var c x))) + +(rewrite (Diff x (Add a b)) (Add (Diff x a) (Diff x b))) +(rewrite (Diff x (Mul a b)) (Add (Mul a (Diff x b)) (Mul b (Diff x a)))) + +(rewrite (Diff x (Sin x)) (Cos x)) +(rewrite (Diff x (Cos x)) (Mul (Const (rational -1 1)) (Sin x))) + +(rewrite (Diff x (Ln x)) (Div (Const (rational 1 1)) x) :when ((is-not-zero x))) + +(rewrite (Diff x (Pow f g)) + (Mul (Pow f g) + (Add (Mul (Diff x f) (Div g f)) + (Mul (Diff x g) (Ln f)))) + :when ((is-not-zero f) + (is-not-zero g))) + +(rewrite (Integral (Const (rational 1 1)) x) x) +(rewrite (Integral (Pow x c) x) + (Div (Pow x (Add c (Const (rational 1 1)))) (Add c (Const (rational 1 1)))) + :when ((is-const c))) +(rewrite (Integral (Cos x) x) (Sin x)) +(rewrite (Integral (Sin x) x) (Mul (Const (rational -1 1)) (Cos x))) +(rewrite (Integral (Add f g) x) (Add (Integral f x) (Integral g x))) +(rewrite (Integral (Sub f g) x) (Sub (Integral f x) (Integral g x))) +(rewrite (Integral (Mul a b) x) + (Sub (Mul a (Integral b x)) + (Integral (Mul (Diff x a) (Integral b x)) x))) + + +(let start-expr2 (Add (Const (rational 1 1)) + (Sub (Var "a") + (Mul (Sub (Const (rational 2 1)) + (Const (rational 1 1))) + (Var "a"))))) + +(run 6) + +(let end-expr2 (Const (rational 1 1))) + +(check (= start-expr2 end-expr2)) + +(query-extract start-expr2) \ No newline at end of file diff --git a/tests/python_array_optimize.egg b/tests/python_array_optimize.egg new file mode 100644 index 0000000..0e2b1bb --- /dev/null +++ b/tests/python_array_optimize.egg @@ -0,0 +1,1569 @@ +;; created by `python python/tests/test_array_api.py` +(push 1) +(sort DType) +(function DType_float64 () DType) +(let %__expr_2565664028803046192 (DType_float64)) +(sort Boolean) +(function DType___eq__ (DType DType) Boolean) +(sort NDArray) +(function NDArray_dtype (NDArray) DType) +(function assume_isfinite (NDArray) NDArray) +(sort TupleInt) +(function assume_shape (NDArray TupleInt) NDArray) +(function assume_dtype (NDArray DType) NDArray) +(function NDArray_var (String) NDArray :cost 200) +(sort Int) +(sort Vec_Int (Vec Int)) +(function TupleInt_from_vec (Vec_Int) TupleInt) +(function Int___init__ (i64) Int) +(DType___eq__ %__expr_2565664028803046192 (NDArray_dtype (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") %__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))))) +(ruleset array_api_ruleset) +(function i-Int__-Int_i (Int Int) Int) +(rewrite (i-Int__-Int_i i _) i :ruleset array_api_ruleset) +(function TupleInt_single (Int) TupleInt) +(sort UnstableFn_Int_Int (UnstableFn (Int) Int)) +(function TupleInt___init__ (Int UnstableFn_Int_Int) TupleInt :unextractable) +(rewrite (TupleInt_single i) (TupleInt___init__ (Int___init__ 1) (unstable-fn "i-Int__-Int_i" i)) :ruleset array_api_ruleset) +(function i-Int_i (Int) Int) +(rewrite (i-Int_i i) i :ruleset array_api_ruleset) +(function TupleInt_range (Int) TupleInt) +(rewrite (TupleInt_range stop) (TupleInt___init__ stop (unstable-fn "i-Int_i")) :ruleset array_api_ruleset) +(function index_vec_int (Vec_Int Int) Int) +(rewrite (TupleInt_from_vec vec) (TupleInt___init__ (Int___init__ (vec-length vec)) (unstable-fn "index_vec_int" vec)) :ruleset array_api_ruleset) +(function Int_if_ (Boolean Int Int) Int) +(function Int___lt__ (Int Int) Boolean) +(function TupleInt_length (TupleInt) Int) +(function TupleInt___getitem__ (TupleInt Int) Int) +(function Int___sub__ (Int Int) Int) +(function other-TupleInt_self-TupleInt_i-Int__Int_if___Int___lt___i__TupleInt_length_self____TupleInt___getitem___self_i___TupleInt___getitem___other__Int___sub___i__TupleInt_length_self____ (TupleInt TupleInt Int) Int) +(rewrite (other-TupleInt_self-TupleInt_i-Int__Int_if___Int___lt___i__TupleInt_length_self____TupleInt___getitem___self_i___TupleInt___getitem___other__Int___sub___i__TupleInt_length_self____ other self i) (Int_if_ (Int___lt__ i (TupleInt_length self)) (TupleInt___getitem__ self i) (TupleInt___getitem__ other (Int___sub__ i (TupleInt_length self)))) :ruleset array_api_ruleset) +(function TupleInt___add__ (TupleInt TupleInt) TupleInt) +(function Int___add__ (Int Int) Int) +(rewrite (TupleInt___add__ self other) (TupleInt___init__ (Int___add__ (TupleInt_length self) (TupleInt_length other)) (unstable-fn "other-TupleInt_self-TupleInt_i-Int__Int_if___Int___lt___i__TupleInt_length_self____TupleInt___getitem___self_i___TupleInt___getitem___other__Int___sub___i__TupleInt_length_self____" other self)) :ruleset array_api_ruleset) +(function Boolean___or__ (Boolean Boolean) Boolean) +(function Int___eq__ (Int Int) Boolean) +(function i-Int_acc-Boolean_j-Int__Boolean___or___acc__Int___eq___i_j__ (Int Boolean Int) Boolean) +(rewrite (i-Int_acc-Boolean_j-Int__Boolean___or___acc__Int___eq___i_j__ i acc j) (Boolean___or__ acc (Int___eq__ i j)) :ruleset array_api_ruleset) +(function TupleInt_contains (TupleInt Int) Boolean) +(sort UnstableFn_Boolean_Boolean_Int (UnstableFn (Boolean Int) Boolean)) +(function TupleInt_fold_boolean (TupleInt Boolean UnstableFn_Boolean_Boolean_Int) Boolean) +(function FALSE () Boolean) +(rewrite (TupleInt_contains self i) (TupleInt_fold_boolean self (FALSE) (unstable-fn "i-Int_acc-Boolean_j-Int__Boolean___or___acc__Int___eq___i_j__" i)) :ruleset array_api_ruleset) +(function f-UnstableFn_Int_Int_self-TupleInt_i-Int__unstable-app_f__TupleInt___getitem___self_i__ (UnstableFn_Int_Int TupleInt Int) Int) +(rewrite (f-UnstableFn_Int_Int_self-TupleInt_i-Int__unstable-app_f__TupleInt___getitem___self_i__ f self i) (unstable-app f (TupleInt___getitem__ self i)) :ruleset array_api_ruleset) +(function TupleInt_map (TupleInt UnstableFn_Int_Int) TupleInt :cost 100) +(rewrite (TupleInt_map self f) (TupleInt___init__ (TupleInt_length self) (unstable-fn "f-UnstableFn_Int_Int_self-TupleInt_i-Int__unstable-app_f__TupleInt___getitem___self_i__" f self)) :ruleset array_api_ruleset) +(function NDArray_size (NDArray) Int) +(sort UnstableFn_Int_Int_Int (UnstableFn (Int Int) Int)) +(function TupleInt_fold (TupleInt Int UnstableFn_Int_Int_Int) Int) +(function NDArray_shape (NDArray) TupleInt) +(function Int___mul__ (Int Int) Int) +(rewrite (NDArray_size x) (TupleInt_fold (NDArray_shape x) (Int___init__ 1) (unstable-fn "Int___mul__")) :ruleset array_api_ruleset) +(function unique_values (NDArray) NDArray) +(sort TupleValue) +(function NDArray_vector (TupleValue) NDArray) +(sort Value) +(function possible_values (Value) TupleValue) +(function NDArray_index (NDArray TupleInt) Value) +(function ALL_INDICES () TupleInt) +(rewrite (unique_values a) (NDArray_vector (possible_values (NDArray_index a (ALL_INDICES)))) :ruleset array_api_ruleset) +(function Value_isfinite (Value) Boolean) +(function Value_int (Int) Value) +(function TRUE () Boolean) +(rewrite (Value_isfinite (Value_int i)) (TRUE) :ruleset array_api_ruleset) +(function Value_bool (Boolean) Value) +(rewrite (Value_isfinite (Value_bool b)) (TRUE) :ruleset array_api_ruleset) +(sort Float) +(function Value_float (Float) Value) +(function Float___init__ (f64) Float :cost 3) +(rewrite (Value_isfinite (Value_float (Float___init__ f))) (TRUE) :when ((!= f NaN)) :ruleset array_api_ruleset) +(function isfinite (NDArray) NDArray) +(sort OptionalIntOrTuple) +(function sum (NDArray OptionalIntOrTuple) NDArray) +(function OptionalIntOrTuple_none () OptionalIntOrTuple) +(function NDArray_scalar (Value) NDArray) +(rewrite (isfinite (sum arr (OptionalIntOrTuple_none))) (NDArray_scalar (Value_bool (Value_isfinite (NDArray_index arr (ALL_INDICES))))) :ruleset array_api_ruleset) +(function assume_value_one_of (NDArray TupleValue) NDArray) +(rewrite (NDArray_shape (assume_value_one_of x vs)) (NDArray_shape x) :ruleset array_api_ruleset) +(rewrite (NDArray_dtype (assume_value_one_of x vs)) (NDArray_dtype x) :ruleset array_api_ruleset) +(rule ((= v (NDArray_index (assume_value_one_of x vs) idx))) + ((union v (NDArray_index x idx)) + (union (possible_values v) vs)) + :ruleset array_api_ruleset ) +(rewrite (NDArray_shape (assume_isfinite x)) (NDArray_shape x) :ruleset array_api_ruleset) +(rewrite (NDArray_dtype (assume_isfinite x)) (NDArray_dtype x) :ruleset array_api_ruleset) +(rewrite (NDArray_index (assume_isfinite x) ti) (NDArray_index x ti) :ruleset array_api_ruleset) +(rewrite (Value_isfinite (NDArray_index (assume_isfinite x) ti)) (TRUE) :ruleset array_api_ruleset) +(rewrite (NDArray_shape (assume_shape x shape)) shape :ruleset array_api_ruleset) +(rewrite (NDArray_dtype (assume_shape x shape)) (NDArray_dtype x) :ruleset array_api_ruleset) +(rewrite (NDArray_index (assume_shape x shape) idx) (NDArray_index x idx) :ruleset array_api_ruleset) +(rewrite (NDArray_dtype (assume_dtype x dtype)) dtype :ruleset array_api_ruleset) +(rewrite (NDArray_shape (assume_dtype x dtype)) (NDArray_shape x) :ruleset array_api_ruleset) +(rewrite (NDArray_index (assume_dtype x dtype) idx) (NDArray_index x idx) :ruleset array_api_ruleset) +(sort IndexKey) +(function NDArray___getitem__ (NDArray IndexKey) NDArray) +(function IndexKey_int (Int) IndexKey) +(rewrite (NDArray___getitem__ x (IndexKey_int i)) (NDArray_scalar (NDArray_index x (TupleInt_single i))) :ruleset array_api_ruleset) +(sort OptionalBool) +(function reshape (NDArray TupleInt OptionalBool) NDArray) +(rule ((= __a (reshape x shape copy))) + ((NDArray_shape x) + (TupleInt_length (NDArray_shape x))) + :ruleset array_api_ruleset ) +(rule ((reshape x shape copy)) + ((TupleInt_length shape) + (TupleInt___getitem__ shape (Int___init__ 0))) + :ruleset array_api_ruleset ) +(rewrite (reshape x shape copy) x :when ((= (TupleInt_length (NDArray_shape x)) (Int___init__ 1)) (= (TupleInt_length shape) (Int___init__ 1)) (= (TupleInt___getitem__ shape (Int___init__ 0)) (Int___init__ -1))) :ruleset array_api_ruleset) +(function TupleValue_length (TupleValue) Int) +(rewrite (NDArray_shape (NDArray_vector vs)) (TupleInt_single (TupleValue_length vs)) :ruleset array_api_ruleset) +(function Value_dtype (Value) DType) +(function TupleValue___getitem__ (TupleValue Int) Value) +(rewrite (NDArray_dtype (NDArray_vector vs)) (Value_dtype (TupleValue___getitem__ vs (Int___init__ 0))) :ruleset array_api_ruleset) +(rewrite (NDArray_index (NDArray_vector vs) ti) (TupleValue___getitem__ vs (TupleInt___getitem__ ti (Int___init__ 0))) :ruleset array_api_ruleset) +(function TupleInt_EMPTY () TupleInt) +(rewrite (NDArray_shape (NDArray_scalar v)) (TupleInt_EMPTY) :ruleset array_api_ruleset) +(rewrite (NDArray_dtype (NDArray_scalar v)) (Value_dtype v) :ruleset array_api_ruleset) +(rewrite (NDArray_index (NDArray_scalar v) (TupleInt_EMPTY)) v :ruleset array_api_ruleset) +(function any (NDArray) NDArray) +(function TupleValue_includes (TupleValue Value) Boolean) +(function Value_to_truthy_value (Value) Value) +(rewrite (any x) (NDArray_scalar (Value_bool (TupleValue_includes (possible_values (Value_to_truthy_value (NDArray_index x (ALL_INDICES)))) (Value_bool (TRUE))))) :ruleset array_api_ruleset) +(function NDArray___lt__ (NDArray NDArray) NDArray) +(function Value___lt__ (Value Value) Value) +(function broadcast_index (TupleInt TupleInt TupleInt) TupleInt) +(function broadcast_shapes (TupleInt TupleInt) TupleInt) +(rewrite (NDArray_index (NDArray___lt__ x y) idx) (Value___lt__ (NDArray_index x (broadcast_index (NDArray_shape x) (broadcast_shapes (NDArray_shape x) (NDArray_shape y)) idx)) (NDArray_index y (broadcast_index (NDArray_shape y) (broadcast_shapes (NDArray_shape x) (NDArray_shape y)) idx))) :ruleset array_api_ruleset) +(function NDArray___truediv__ (NDArray NDArray) NDArray) +(function Value___truediv__ (Value Value) Value) +(rewrite (NDArray_index (NDArray___truediv__ x y) idx) (Value___truediv__ (NDArray_index x (broadcast_index (NDArray_shape x) (broadcast_shapes (NDArray_shape x) (NDArray_shape y)) idx)) (NDArray_index y (broadcast_index (NDArray_shape y) (broadcast_shapes (NDArray_shape x) (NDArray_shape y)) idx))) :ruleset array_api_ruleset) +(rewrite (NDArray_index (NDArray_scalar v) idx) v :ruleset array_api_ruleset) +(function astype (NDArray DType) NDArray) +(function Value_astype (Value DType) Value) +(rewrite (NDArray_index (astype x dtype) idx) (Value_astype (NDArray_index x idx) dtype) :ruleset array_api_ruleset) +(relation greater_zero (Value)) +(sort TupleNDArray) +(function TupleNDArray___getitem__ (TupleNDArray Int) NDArray) +(function unique_counts (NDArray) TupleNDArray) +(rule ((= v (NDArray_index (TupleNDArray___getitem__ (unique_counts x) (Int___init__ 1)) idx))) + ((greater_zero v)) + :ruleset array_api_ruleset ) +(rule ((greater_zero v) + (= v1 (Value_astype v dtype))) + ((greater_zero v1)) + :ruleset array_api_ruleset ) +(rule ((= v (Value_float (Float___init__ f))) + (> f 0.0)) + ((greater_zero v)) + :ruleset array_api_ruleset ) +(rule ((= v (Value_int (Int___init__ i))) + (> i 0)) + ((greater_zero v)) + :ruleset array_api_ruleset ) +(rule ((greater_zero v) + (greater_zero v1) + (= v2 (Value___truediv__ v v1))) + ((greater_zero v2)) + :ruleset array_api_ruleset ) +(rule ((greater_zero v) + (= v1 (Value___lt__ v (Value_int (Int___init__ 0))))) + ((union v1 (Value_bool (FALSE)))) + :ruleset array_api_ruleset ) +(function TupleValue___init__ (Value) TupleValue) +(rewrite (possible_values (Value_bool b)) (TupleValue___init__ (Value_bool b)) :ruleset array_api_ruleset) +(rule ((= v1 (Value_astype v dtype)) + (greater_zero v)) + ((greater_zero v1)) + :ruleset array_api_ruleset ) +(function TupleNDArray_length (TupleNDArray) Int) +(function svd (NDArray Boolean) TupleNDArray) +(rewrite (TupleNDArray_length (svd x full_matrices)) (Int___init__ 3) :ruleset array_api_ruleset) +(function unique_inverse (NDArray) TupleNDArray) +(rewrite (TupleNDArray_length (unique_inverse x)) (Int___init__ 2) :ruleset array_api_ruleset) +(rewrite (TupleNDArray___getitem__ (unique_inverse x) (Int___init__ 0)) (unique_values x) :ruleset array_api_ruleset) +(function ndarray-abs (NDArray) NDArray) +(function Float_abs (Float) Float) +(rewrite (ndarray-abs (NDArray_scalar (Value_float f))) (NDArray_scalar (Value_float (Float_abs f))) :ruleset array_api_ruleset) +(rewrite (TupleNDArray_length (unique_counts x)) (Int___init__ 2) :ruleset array_api_ruleset) +(rewrite (sum (TupleNDArray___getitem__ (unique_counts x) (Int___init__ 1)) (OptionalIntOrTuple_none)) (NDArray_scalar (Value_int (NDArray_size x))) :ruleset array_api_ruleset) +(rewrite (sum (astype (TupleNDArray___getitem__ (unique_counts x) (Int___init__ 1)) dtype) (OptionalIntOrTuple_none)) (astype (NDArray_scalar (Value_int (NDArray_size x))) dtype) :ruleset array_api_ruleset) +(rewrite (NDArray_dtype (astype x dtype)) dtype :ruleset array_api_ruleset) +(rewrite (astype (NDArray_scalar (Value_int (Int___init__ i))) %__expr_2565664028803046192) (NDArray_scalar (Value_float (Float___init__ (to-f64 i)))) :ruleset array_api_ruleset) +(sort OptionalInt) +(function concat (TupleNDArray OptionalInt) NDArray) +(function TupleNDArray___init__ (NDArray) TupleNDArray) +(function OptionalInt_none () OptionalInt) +(rewrite (concat (TupleNDArray___init__ x) (OptionalInt_none)) x :ruleset array_api_ruleset) +(rewrite (unique_values (unique_values x)) (unique_values x) :ruleset array_api_ruleset) +(rewrite (sum (NDArray___truediv__ x (NDArray_scalar v)) (OptionalIntOrTuple_none)) (NDArray___truediv__ (sum x (OptionalIntOrTuple_none)) (NDArray_scalar v)) :ruleset array_api_ruleset) +(function NDArray_ndim (NDArray) Int) +(sort OptionalDType) +(sort OptionalDevice) +(function asarray (NDArray OptionalDType OptionalBool OptionalDevice) NDArray) +(function OptionalDevice_none () OptionalDevice) +(rewrite (NDArray_ndim (asarray a d ob (OptionalDevice_none))) (NDArray_ndim a) :ruleset array_api_ruleset) +(function OptionalDType_none () OptionalDType) +(function OptionalBool_none () OptionalBool) +(rewrite (asarray a (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none)) a :ruleset array_api_ruleset) +(function TupleNDArray___add__ (TupleNDArray TupleNDArray) TupleNDArray) +(function TupleNDArray_EMPTY () TupleNDArray) +(rewrite (TupleNDArray___add__ ti (TupleNDArray_EMPTY)) ti :ruleset array_api_ruleset) +(rewrite (TupleNDArray_length (TupleNDArray___init__ n)) (Int___init__ 1) :ruleset array_api_ruleset) +(rewrite (TupleNDArray_length (TupleNDArray___add__ ti ti2)) (Int___add__ (TupleNDArray_length ti) (TupleNDArray_length ti2)) :ruleset array_api_ruleset) +(sort UnstableFn_Value_TupleInt (UnstableFn (TupleInt) Value)) +(function NDArray___init__ (TupleInt DType UnstableFn_Value_TupleInt) NDArray) +(rewrite (NDArray_shape (NDArray___init__ shape dtype idx_fn)) shape :ruleset array_api_ruleset) +(rewrite (NDArray_dtype (NDArray___init__ shape dtype idx_fn)) dtype :ruleset array_api_ruleset) +(rewrite (NDArray_ndim x) (TupleInt_length (NDArray_shape x)) :ruleset array_api_ruleset) +(function NDArray_to_value (NDArray) Value) +(rewrite (NDArray_to_value x) (NDArray_index x (TupleInt_EMPTY)) :ruleset array_api_ruleset) +(rewrite (NDArray___truediv__ (NDArray_scalar (Value_float f)) (NDArray_scalar (Value_float f))) (NDArray_scalar (Value_float (Float___init__ 1.0))) :ruleset array_api_ruleset) +(function NDArray___sub__ (NDArray NDArray) NDArray) +(rewrite (NDArray___sub__ (NDArray_scalar (Value_float f)) (NDArray_scalar (Value_float f))) (NDArray_scalar (Value_float (Float___init__ 0.0))) :ruleset array_api_ruleset) +(function NDArray___gt__ (NDArray NDArray) NDArray) +(rewrite (NDArray___gt__ (NDArray_scalar (Value_float (Float___init__ fi1))) (NDArray_scalar (Value_float (Float___init__ fi2)))) (NDArray_scalar (Value_bool (TRUE))) :when ((> fi1 fi2)) :ruleset array_api_ruleset) +(rewrite (NDArray___gt__ (NDArray_scalar (Value_float (Float___init__ fi1))) (NDArray_scalar (Value_float (Float___init__ fi2)))) (NDArray_scalar (Value_bool (FALSE))) :when ((<= fi1 fi2)) :ruleset array_api_ruleset) +(function NDArray_T (NDArray) NDArray) +(rewrite (NDArray_T (NDArray_T x)) x :ruleset array_api_ruleset) +(function TupleValue___add__ (TupleValue TupleValue) TupleValue) +(function TupleValue_EMPTY () TupleValue) +(rewrite (TupleValue___add__ ti (TupleValue_EMPTY)) ti :ruleset array_api_ruleset) +(rewrite (TupleValue_length (TupleValue_EMPTY)) (Int___init__ 0) :ruleset array_api_ruleset) +(rewrite (TupleValue_length (TupleValue___init__ v)) (Int___init__ 1) :ruleset array_api_ruleset) +(rewrite (TupleValue_length (TupleValue___add__ ti ti2)) (Int___add__ (TupleValue_length ti) (TupleValue_length ti2)) :ruleset array_api_ruleset) +(rewrite (TupleValue___getitem__ (TupleValue___init__ v) (Int___init__ 0)) v :ruleset array_api_ruleset) +(rewrite (TupleValue___getitem__ (TupleValue___add__ (TupleValue___init__ v) ti) (Int___init__ 0)) v :ruleset array_api_ruleset) +(rule ((= v (TupleValue___getitem__ (TupleValue___add__ (TupleValue___init__ v2) ti) (Int___init__ k))) + (> k 0)) + ((union v (TupleValue___getitem__ ti (Int___init__ (- k 1))))) + :ruleset array_api_ruleset ) +(rewrite (TupleValue_includes (TupleValue_EMPTY) v) (FALSE) :ruleset array_api_ruleset) +(rewrite (TupleValue_includes (TupleValue___init__ v) v) (TRUE) :ruleset array_api_ruleset) +(rewrite (TupleValue_includes (TupleValue___init__ v) v2) (FALSE) :when ((!= v v2)) :ruleset array_api_ruleset) +(rewrite (TupleValue_includes (TupleValue___add__ ti ti2) v) (Boolean___or__ (TupleValue_includes ti v) (TupleValue_includes ti2 v)) :ruleset array_api_ruleset) +(function DType_int64 () DType) +(rewrite (Value_dtype (Value_int i)) (DType_int64) :ruleset array_api_ruleset) +(rewrite (Value_dtype (Value_float f)) %__expr_2565664028803046192 :ruleset array_api_ruleset) +(function DType_bool () DType) +(rewrite (Value_dtype (Value_bool b)) (DType_bool) :ruleset array_api_ruleset) +(function Value_to_bool (Value) Boolean) +(rewrite (Value_to_bool (Value_bool b)) b :ruleset array_api_ruleset) +(function Value_to_int (Value) Int) +(rewrite (Value_to_int (Value_int i)) i :ruleset array_api_ruleset) +(rewrite (Value_to_truthy_value (Value_bool b)) (Value_bool b) :ruleset array_api_ruleset) +(sort IsDtypeKind) +(function isdtype (DType IsDtypeKind) Boolean) +(function DType_float32 () DType) +(function IsDtypeKind_string (String) IsDtypeKind) +(rewrite (isdtype (DType_float32) (IsDtypeKind_string "integral")) (FALSE) :ruleset array_api_ruleset) +(rewrite (isdtype %__expr_2565664028803046192 (IsDtypeKind_string "integral")) (FALSE) :ruleset array_api_ruleset) +(function DType_object () DType) +(rewrite (isdtype (DType_object) (IsDtypeKind_string "integral")) (FALSE) :ruleset array_api_ruleset) +(rewrite (isdtype (DType_int64) (IsDtypeKind_string "integral")) (TRUE) :ruleset array_api_ruleset) +(function DType_int32 () DType) +(rewrite (isdtype (DType_int32) (IsDtypeKind_string "integral")) (TRUE) :ruleset array_api_ruleset) +(rewrite (isdtype (DType_float32) (IsDtypeKind_string "real floating")) (TRUE) :ruleset array_api_ruleset) +(rewrite (isdtype %__expr_2565664028803046192 (IsDtypeKind_string "real floating")) (TRUE) :ruleset array_api_ruleset) +(rewrite (isdtype (DType_object) (IsDtypeKind_string "real floating")) (FALSE) :ruleset array_api_ruleset) +(rewrite (isdtype (DType_int64) (IsDtypeKind_string "real floating")) (FALSE) :ruleset array_api_ruleset) +(rewrite (isdtype (DType_int32) (IsDtypeKind_string "real floating")) (FALSE) :ruleset array_api_ruleset) +(rewrite (isdtype (DType_float32) (IsDtypeKind_string "complex floating")) (FALSE) :ruleset array_api_ruleset) +(rewrite (isdtype %__expr_2565664028803046192 (IsDtypeKind_string "complex floating")) (FALSE) :ruleset array_api_ruleset) +(rewrite (isdtype (DType_object) (IsDtypeKind_string "complex floating")) (FALSE) :ruleset array_api_ruleset) +(rewrite (isdtype (DType_int64) (IsDtypeKind_string "complex floating")) (FALSE) :ruleset array_api_ruleset) +(rewrite (isdtype (DType_int32) (IsDtypeKind_string "complex floating")) (FALSE) :ruleset array_api_ruleset) +(function IsDtypeKind_NULL () IsDtypeKind) +(rewrite (isdtype d (IsDtypeKind_NULL)) (FALSE) :ruleset array_api_ruleset) +(function IsDtypeKind_dtype (DType) IsDtypeKind) +(rewrite (isdtype d (IsDtypeKind_dtype d)) (TRUE) :ruleset array_api_ruleset) +(function IsDtypeKind___or__ (IsDtypeKind IsDtypeKind) IsDtypeKind :cost 10) +(rewrite (isdtype d (IsDtypeKind___or__ k1 k2)) (Boolean___or__ (isdtype d k1) (isdtype d k2)) :ruleset array_api_ruleset) +(rewrite (IsDtypeKind___or__ k1 (IsDtypeKind_NULL)) k1 :ruleset array_api_ruleset) +(rewrite (DType___eq__ %__expr_2565664028803046192 %__expr_2565664028803046192) (TRUE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ %__expr_2565664028803046192 (DType_float32)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ %__expr_2565664028803046192 (DType_int32)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ %__expr_2565664028803046192 (DType_int64)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ %__expr_2565664028803046192 (DType_object)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_float32) %__expr_2565664028803046192) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_float32) (DType_float32)) (TRUE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_float32) (DType_int32)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_float32) (DType_int64)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_float32) (DType_object)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_int32) %__expr_2565664028803046192) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_int32) (DType_float32)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_int32) (DType_int32)) (TRUE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_int32) (DType_int64)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_int32) (DType_object)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_int64) %__expr_2565664028803046192) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_int64) (DType_float32)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_int64) (DType_int32)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_int64) (DType_int64)) (TRUE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_int64) (DType_object)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_object) %__expr_2565664028803046192) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_object) (DType_float32)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_object) (DType_int32)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_object) (DType_int64)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_object) (DType_object)) (TRUE) :ruleset array_api_ruleset) +(function idx_fn-UnstableFn_Int_Int_i-Int__unstable-app_idx_fn__Int___add___i__Int___init___1___ (UnstableFn_Int_Int Int) Int) +(rewrite (idx_fn-UnstableFn_Int_Int_i-Int__unstable-app_idx_fn__Int___add___i__Int___init___1___ idx_fn i) (unstable-app idx_fn (Int___add__ i (Int___init__ 1))) :ruleset array_api_ruleset) +(rewrite (TupleInt_length (TupleInt___init__ i idx_fn)) i :ruleset array_api_ruleset) +(rewrite (TupleInt___getitem__ (TupleInt___init__ i idx_fn) i2) (unstable-app idx_fn i2) :ruleset array_api_ruleset) +(rewrite (index_vec_int vs (Int___init__ k)) (vec-get vs k) :when ((> (vec-length vs) k)) :ruleset array_api_ruleset) +(rewrite (TupleInt_fold (TupleInt___init__ (Int___init__ 0) idx_fn) i f) i :ruleset array_api_ruleset) +(rewrite (TupleInt_fold (TupleInt___init__ (Int___init__ k) idx_fn) i f) (unstable-app f (TupleInt_fold (TupleInt___init__ (Int___init__ (- k 1)) (unstable-fn "idx_fn-UnstableFn_Int_Int_i-Int__unstable-app_idx_fn__Int___add___i__Int___init___1___" idx_fn)) i f) (unstable-app idx_fn (Int___init__ 0))) :when ((!= k 0)) :ruleset array_api_ruleset) +(rewrite (TupleInt_fold_boolean (TupleInt___init__ (Int___init__ 0) idx_fn) b bool_f) b :ruleset array_api_ruleset) +(rewrite (TupleInt_fold_boolean (TupleInt___init__ (Int___init__ k) idx_fn) b bool_f) (unstable-app bool_f (TupleInt_fold_boolean (TupleInt___init__ (Int___init__ (- k 1)) (unstable-fn "idx_fn-UnstableFn_Int_Int_i-Int__unstable-app_idx_fn__Int___add___i__Int___init___1___" idx_fn)) b bool_f) (unstable-app idx_fn (Int___init__ 0))) :when ((!= k 0)) :ruleset array_api_ruleset) +(sort UnstableFn_Boolean_Int (UnstableFn (Int) Boolean)) +(function TupleInt_filter (TupleInt UnstableFn_Boolean_Int) TupleInt :cost 100) +(rewrite (TupleInt_filter (TupleInt___init__ (Int___init__ 0) idx_fn) filter_f) (TupleInt___init__ (Int___init__ 0) idx_fn) :ruleset array_api_ruleset) +(function TupleInt_if_ (Boolean TupleInt TupleInt) TupleInt) +(rewrite (TupleInt_filter (TupleInt___init__ (Int___init__ k) idx_fn) filter_f) (TupleInt_if_ (unstable-app filter_f (unstable-app idx_fn (Int___init__ k))) (TupleInt___add__ 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(IsDtypeKind___or__ (IsDtypeKind_string "real floating") (IsDtypeKind___or__ (IsDtypeKind_string "complex floating") (IsDtypeKind_NULL))))) 0) +(TupleInt_length (NDArray_shape (asarray (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") %__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none)))) +(run-schedule (saturate (run array_api_ruleset))) +(extract (Int_i64 (TupleInt_length (NDArray_shape (asarray (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") %__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none))))) 0) +(TupleInt_length (NDArray_shape (asarray (reshape (asarray (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int 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(asarray (asarray (reshape (asarray (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (OptionalDType_none) (OptionalBool_none) %__expr_-3674731718720096444) (TupleInt_from_vec (vec-of (Int___init__ -1))) %__expr_-4122594143565222517) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444))) (OptionalInt_none))))) 0) +(let %__expr_-8664633617851008504 (unique_inverse (asarray (reshape (asarray (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (OptionalDType_none) (OptionalBool_none) %__expr_-3674731718720096444) (TupleInt_from_vec (vec-of (Int___init__ -1))) %__expr_-4122594143565222517) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444))) +(let %__expr_-8475266842302933511 (NDArray_shape (asarray (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") %__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none)))) +(let %__expr_-6765600943420531488 (Value_int (Int___init__ 2))) +(let %__expr_-5200143055942215294 (asarray (reshape (asarray (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (OptionalDType_none) (OptionalBool_none) %__expr_-3674731718720096444) (TupleInt_from_vec (vec-of (Int___init__ -1))) %__expr_-4122594143565222517) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444)) +(let %__expr_-8613124149453883591 (asarray (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") %__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none))) +(let %__expr_-622493510873225930 (Value_int (Int___init__ 1))) +(let %__expr_-3283806677371465170 (NDArray_scalar %__expr_478758938070675600)) +(let %__expr_-2704792733181451377 (TupleNDArray___getitem__ %__expr_-8664633617851008504 %__expr_3300329792522185471)) +(sort MultiAxisIndexKeyItem) +(sort Slice) +(function MultiAxisIndexKeyItem_slice (Slice) MultiAxisIndexKeyItem) +(function Slice___init__ (OptionalInt OptionalInt OptionalInt) Slice) +(let %__expr_-8637348939342624324 (MultiAxisIndexKeyItem_slice (Slice___init__ (OptionalInt_none) (OptionalInt_none) (OptionalInt_none)))) +(sort IntOrTuple) +(function OptionalIntOrTuple_some (IntOrTuple) OptionalIntOrTuple) +(function IntOrTuple_int (Int) IntOrTuple) +(let %__expr_1913846200346632608 (OptionalIntOrTuple_some (IntOrTuple_int %__expr_-7942988945600443502))) +(let %__expr_6185990579165616281 (FALSE)) +(let %__expr_-1113027338580586528 (unique_values (concat (TupleNDArray___init__ (unique_values (asarray (asarray (reshape (asarray (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (OptionalDType_none) (OptionalBool_none) %__expr_-3674731718720096444) (TupleInt_from_vec (vec-of (Int___init__ -1))) %__expr_-4122594143565222517) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444))) (OptionalInt_none)))) +(sort MultiAxisIndexKey) +(function IndexKey_multi_axis (MultiAxisIndexKey) IndexKey) +(sort Vec_MultiAxisIndexKeyItem (Vec MultiAxisIndexKeyItem)) +(function MultiAxisIndexKey_from_vec (Vec_MultiAxisIndexKeyItem) MultiAxisIndexKey) +(function MultiAxisIndexKeyItem_int (Int) MultiAxisIndexKeyItem) +(let %__expr_7180621784385959982 (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_int %__expr_3300329792522185471) %__expr_-8637348939342624324)))) +(let %__expr_-4323225966908438009 (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_int %__expr_-7942988945600443502) %__expr_-8637348939342624324)))) +(let %__expr_483064111004974365 (Float___init__ 1.0)) +(let %__expr_-143818766793636568 (OptionalInt_none)) +(function NDArray___setitem__ (NDArray IndexKey NDArray) NDArray) +(function zeros (TupleInt OptionalDType OptionalDevice) NDArray) +(function OptionalDType_some (DType) OptionalDType) +(sort Device) +(function OptionalDevice_some (Device) OptionalDevice) +(function NDArray_device (NDArray) Device) +(function mean (NDArray OptionalIntOrTuple Boolean) NDArray) +(function IndexKey_ndarray (NDArray) IndexKey) +(function NDArray___eq__ (NDArray NDArray) NDArray) +(let %__expr_7843526591494960327 (NDArray___setitem__ (NDArray___setitem__ (NDArray___setitem__ (zeros (TupleInt_from_vec (vec-of (TupleInt___getitem__ (NDArray_shape (TupleNDArray___getitem__ (unique_inverse (asarray (reshape (asarray (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (OptionalDType_none) (OptionalBool_none) %__expr_-3674731718720096444) (TupleInt_from_vec (vec-of (Int___init__ -1))) %__expr_-4122594143565222517) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444)) %__expr_-7942988945600443502)) %__expr_-7942988945600443502) (TupleInt___getitem__ (NDArray_shape (asarray (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") %__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none))) (Int___init__ 1)))) (OptionalDType_some (NDArray_dtype (asarray (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") %__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none)))) (OptionalDevice_some (NDArray_device %__expr_-8613124149453883591))) %__expr_-4323225966908438009 (mean (NDArray___getitem__ %__expr_-8613124149453883591 (IndexKey_ndarray (NDArray___eq__ %__expr_-2704792733181451377 %__expr_-3283806677371465170))) %__expr_1913846200346632608 %__expr_6185990579165616281)) %__expr_7180621784385959982 (mean (NDArray___getitem__ %__expr_-8613124149453883591 (IndexKey_ndarray (NDArray___eq__ %__expr_-2704792733181451377 (NDArray_scalar %__expr_-622493510873225930)))) %__expr_1913846200346632608 %__expr_6185990579165616281)) (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_int %__expr_2305922367412063525) %__expr_-8637348939342624324))) (mean (NDArray___getitem__ %__expr_-8613124149453883591 (IndexKey_ndarray (NDArray___eq__ %__expr_-2704792733181451377 (NDArray_scalar %__expr_-6765600943420531488)))) %__expr_1913846200346632608 %__expr_6185990579165616281))) +(let %__expr_-954298076671303615 (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_int %__expr_2305922367412063525) %__expr_-8637348939342624324)))) +(function std (NDArray OptionalIntOrTuple) NDArray) +(function OptionalInt_some (Int) OptionalInt) +(let %__expr_3049932803880609425 (std (concat (TupleNDArray___add__ (TupleNDArray___init__ (NDArray___sub__ (NDArray___getitem__ %__expr_-8613124149453883591 (IndexKey_ndarray (NDArray___eq__ %__expr_-5200143055942215294 (NDArray___getitem__ %__expr_-1113027338580586528 (IndexKey_int %__expr_-7942988945600443502))))) (NDArray___getitem__ %__expr_7843526591494960327 %__expr_-4323225966908438009))) (TupleNDArray___add__ (TupleNDArray___init__ (NDArray___sub__ (NDArray___getitem__ %__expr_-8613124149453883591 (IndexKey_ndarray (NDArray___eq__ %__expr_-5200143055942215294 (NDArray___getitem__ %__expr_-1113027338580586528 (IndexKey_int %__expr_3300329792522185471))))) (NDArray___getitem__ %__expr_7843526591494960327 %__expr_7180621784385959982))) (TupleNDArray___init__ (NDArray___sub__ (NDArray___getitem__ %__expr_-8613124149453883591 (IndexKey_ndarray (NDArray___eq__ %__expr_-5200143055942215294 (NDArray___getitem__ %__expr_-1113027338580586528 (IndexKey_int %__expr_2305922367412063525))))) (NDArray___getitem__ %__expr_7843526591494960327 %__expr_-954298076671303615))))) (OptionalInt_some %__expr_-7942988945600443502)) %__expr_1913846200346632608)) +(let %__expr_-671931098406187877 (concat (TupleNDArray___add__ (TupleNDArray___init__ (NDArray___sub__ (NDArray___getitem__ %__expr_-8613124149453883591 (IndexKey_ndarray (NDArray___eq__ %__expr_-5200143055942215294 (NDArray___getitem__ %__expr_-1113027338580586528 (IndexKey_int %__expr_-7942988945600443502))))) (NDArray___getitem__ %__expr_7843526591494960327 %__expr_-4323225966908438009))) (TupleNDArray___add__ (TupleNDArray___init__ (NDArray___sub__ (NDArray___getitem__ %__expr_-8613124149453883591 (IndexKey_ndarray (NDArray___eq__ %__expr_-5200143055942215294 (NDArray___getitem__ %__expr_-1113027338580586528 (IndexKey_int %__expr_3300329792522185471))))) (NDArray___getitem__ %__expr_7843526591494960327 %__expr_7180621784385959982))) (TupleNDArray___init__ (NDArray___sub__ (NDArray___getitem__ %__expr_-8613124149453883591 (IndexKey_ndarray (NDArray___eq__ %__expr_-5200143055942215294 (NDArray___getitem__ %__expr_-1113027338580586528 (IndexKey_int %__expr_2305922367412063525))))) (NDArray___getitem__ %__expr_7843526591494960327 %__expr_-954298076671303615))))) (OptionalInt_some %__expr_-7942988945600443502))) +(function NDArray___mul__ (NDArray NDArray) NDArray) +(function ndarray-sqrt (NDArray) NDArray) +(TupleNDArray_length (svd (NDArray___mul__ (ndarray-sqrt (asarray (NDArray_scalar (Value_float (Float___truediv__ %__expr_483064111004974365 (Float_from_int (Int___sub__ (TupleInt___getitem__ (NDArray_shape (asarray (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") %__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none))) (Int___init__ 0)) (TupleInt___getitem__ (NDArray_shape (unique_values (concat (TupleNDArray___init__ (unique_values (asarray (asarray (reshape (asarray (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (OptionalDType_none) (OptionalBool_none) %__expr_-3674731718720096444) (TupleInt_from_vec (vec-of (Int___init__ -1))) %__expr_-4122594143565222517) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444))) (OptionalInt_none)))) %__expr_-7942988945600443502)))))) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444)) (NDArray___truediv__ %__expr_-671931098406187877 (NDArray___setitem__ %__expr_3049932803880609425 (IndexKey_ndarray (NDArray___eq__ %__expr_3049932803880609425 %__expr_-3283806677371465170)) (NDArray_scalar (Value_float (Float___init__ 1.0)))))) %__expr_6185990579165616281)) +(run-schedule (saturate (run array_api_ruleset))) +(extract (Int_i64 (TupleNDArray_length (svd (NDArray___mul__ (ndarray-sqrt (asarray (NDArray_scalar (Value_float (Float___truediv__ %__expr_483064111004974365 (Float_from_int (Int___sub__ (TupleInt___getitem__ (NDArray_shape (asarray (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") %__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none))) (Int___init__ 0)) (TupleInt___getitem__ (NDArray_shape (unique_values (concat (TupleNDArray___init__ (unique_values (asarray (asarray (reshape (asarray (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (OptionalDType_none) (OptionalBool_none) %__expr_-3674731718720096444) (TupleInt_from_vec (vec-of (Int___init__ -1))) %__expr_-4122594143565222517) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444))) (OptionalInt_none)))) %__expr_-7942988945600443502)))))) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444)) (NDArray___truediv__ %__expr_-671931098406187877 (NDArray___setitem__ %__expr_3049932803880609425 (IndexKey_ndarray (NDArray___eq__ %__expr_3049932803880609425 %__expr_-3283806677371465170)) (NDArray_scalar (Value_float (Float___init__ 1.0)))))) %__expr_6185990579165616281))) 0) +(Int___eq__ (TupleInt___getitem__ (NDArray_shape (unique_values (concat (TupleNDArray___init__ (unique_values (asarray (asarray (reshape (asarray (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (OptionalDType_none) (OptionalBool_none) %__expr_-3674731718720096444) (TupleInt_from_vec (vec-of (Int___init__ -1))) %__expr_-4122594143565222517) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444))) (OptionalInt_none)))) %__expr_-7942988945600443502) %__expr_3300329792522185471) +(run-schedule (saturate (run array_api_ruleset))) +(extract (Boolean_bool (Int___eq__ (TupleInt___getitem__ (NDArray_shape (unique_values (concat (TupleNDArray___init__ (unique_values (asarray (asarray (reshape (asarray (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (OptionalDType_none) (OptionalBool_none) %__expr_-3674731718720096444) (TupleInt_from_vec (vec-of (Int___init__ -1))) %__expr_-4122594143565222517) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444))) (OptionalInt_none)))) %__expr_-7942988945600443502) %__expr_3300329792522185471)) 0) +(let %__expr_-1459297673498492435 (Slice___init__ %__expr_-143818766793636568 (OptionalInt_some (Value_to_int (NDArray_to_value (sum (astype (NDArray___gt__ (TupleNDArray___getitem__ (svd (NDArray___mul__ (ndarray-sqrt (asarray (NDArray_scalar (Value_float (Float___truediv__ %__expr_483064111004974365 (Float_from_int (Int___sub__ (TupleInt___getitem__ (NDArray_shape (asarray (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") %__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none))) (Int___init__ 0)) (TupleInt___getitem__ (NDArray_shape (unique_values (concat (TupleNDArray___init__ (unique_values (asarray (asarray (reshape (asarray (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (OptionalDType_none) (OptionalBool_none) %__expr_-3674731718720096444) (TupleInt_from_vec (vec-of (Int___init__ -1))) %__expr_-4122594143565222517) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444))) (OptionalInt_none)))) %__expr_-7942988945600443502)))))) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444)) (NDArray___truediv__ %__expr_-671931098406187877 (NDArray___setitem__ %__expr_3049932803880609425 (IndexKey_ndarray (NDArray___eq__ %__expr_3049932803880609425 %__expr_-3283806677371465170)) (NDArray_scalar (Value_float (Float___init__ 1.0)))))) %__expr_6185990579165616281) %__expr_3300329792522185471) (NDArray_scalar (Value_float (Float___init__ 0.0001)))) (DType_int32)) (OptionalIntOrTuple_none))))) %__expr_-143818766793636568)) +(let %__expr_-5540247018246576406 (NDArray___truediv__ (astype (TupleNDArray___getitem__ (unique_counts (asarray (reshape (asarray (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (OptionalDType_none) (OptionalBool_none) %__expr_-3674731718720096444) (TupleInt_from_vec (vec-of (Int___init__ -1))) %__expr_-4122594143565222517) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444)) %__expr_3300329792522185471) (NDArray_dtype (asarray (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") %__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none)))) (NDArray_scalar (Value_float (Float___init__ 150.0))))) +(let %__expr_-4744074158064860754 (TupleNDArray___getitem__ (svd (NDArray___mul__ (ndarray-sqrt (asarray (NDArray_scalar (Value_float (Float___truediv__ %__expr_483064111004974365 (Float_from_int (Int___sub__ (TupleInt___getitem__ (NDArray_shape (asarray (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") %__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none))) (Int___init__ 0)) (TupleInt___getitem__ (NDArray_shape (unique_values (concat (TupleNDArray___init__ (unique_values (asarray (asarray (reshape (asarray (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (OptionalDType_none) (OptionalBool_none) %__expr_-3674731718720096444) (TupleInt_from_vec (vec-of (Int___init__ -1))) %__expr_-4122594143565222517) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444))) (OptionalInt_none)))) %__expr_-7942988945600443502)))))) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444)) (NDArray___truediv__ %__expr_-671931098406187877 (NDArray___setitem__ %__expr_3049932803880609425 (IndexKey_ndarray (NDArray___eq__ %__expr_3049932803880609425 %__expr_-3283806677371465170)) (NDArray_scalar (Value_float (Float___init__ 1.0)))))) %__expr_6185990579165616281) %__expr_3300329792522185471)) +(let %__expr_2307122782736907488 (NDArray___setitem__ %__expr_3049932803880609425 (IndexKey_ndarray (NDArray___eq__ %__expr_3049932803880609425 %__expr_-3283806677371465170)) (NDArray_scalar (Value_float (Float___init__ 1.0))))) +(let %__expr_4799320818084596281 (svd (NDArray___mul__ (ndarray-sqrt (asarray (NDArray_scalar (Value_float (Float___truediv__ %__expr_483064111004974365 (Float_from_int (Int___sub__ (TupleInt___getitem__ (NDArray_shape (asarray (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") %__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none))) (Int___init__ 0)) (TupleInt___getitem__ (NDArray_shape (unique_values (concat (TupleNDArray___init__ (unique_values (asarray (asarray (reshape (asarray (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (OptionalDType_none) (OptionalBool_none) %__expr_-3674731718720096444) (TupleInt_from_vec (vec-of (Int___init__ -1))) %__expr_-4122594143565222517) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444))) (OptionalInt_none)))) %__expr_-7942988945600443502)))))) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444)) (NDArray___truediv__ %__expr_-671931098406187877 (NDArray___setitem__ %__expr_3049932803880609425 (IndexKey_ndarray (NDArray___eq__ %__expr_3049932803880609425 %__expr_-3283806677371465170)) (NDArray_scalar (Value_float (Float___init__ 1.0)))))) %__expr_6185990579165616281)) +(function NDArray___matmul__ (NDArray NDArray) NDArray) +(function IndexKey_slice (Slice) IndexKey) +(TupleNDArray_length (svd (NDArray___matmul__ (NDArray_T (NDArray___mul__ (ndarray-sqrt (NDArray___mul__ (NDArray___mul__ (NDArray_scalar (Value_int (TupleInt___getitem__ (NDArray_shape (asarray (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") %__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none))) (Int___init__ 0)))) %__expr_-5540247018246576406) (NDArray_scalar (Value_float (Float___truediv__ %__expr_483064111004974365 (Float_from_int (Int___sub__ (TupleInt___getitem__ (NDArray_shape (unique_values (concat (TupleNDArray___init__ (unique_values (asarray (asarray (reshape (asarray (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (OptionalDType_none) (OptionalBool_none) %__expr_-3674731718720096444) (TupleInt_from_vec (vec-of (Int___init__ -1))) %__expr_-4122594143565222517) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444))) (OptionalInt_none)))) %__expr_-7942988945600443502) %__expr_3300329792522185471))))))) (NDArray_T (NDArray___sub__ %__expr_7843526591494960327 (NDArray___matmul__ %__expr_-5540247018246576406 %__expr_7843526591494960327))))) (NDArray___truediv__ (NDArray_T (NDArray___truediv__ (NDArray___getitem__ (TupleNDArray___getitem__ %__expr_4799320818084596281 %__expr_2305922367412063525) (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_slice %__expr_-1459297673498492435) %__expr_-8637348939342624324)))) %__expr_2307122782736907488)) (NDArray___getitem__ %__expr_-4744074158064860754 (IndexKey_slice %__expr_-1459297673498492435)))) %__expr_6185990579165616281)) +(run-schedule (saturate (run array_api_ruleset))) +(extract (Int_i64 (TupleNDArray_length (svd (NDArray___matmul__ (NDArray_T (NDArray___mul__ (ndarray-sqrt (NDArray___mul__ (NDArray___mul__ (NDArray_scalar (Value_int (TupleInt___getitem__ (NDArray_shape (asarray (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") %__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none))) (Int___init__ 0)))) %__expr_-5540247018246576406) (NDArray_scalar (Value_float (Float___truediv__ %__expr_483064111004974365 (Float_from_int (Int___sub__ (TupleInt___getitem__ (NDArray_shape (unique_values (concat (TupleNDArray___init__ (unique_values (asarray (asarray (reshape (asarray (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (OptionalDType_none) (OptionalBool_none) %__expr_-3674731718720096444) (TupleInt_from_vec (vec-of (Int___init__ -1))) %__expr_-4122594143565222517) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444))) (OptionalInt_none)))) %__expr_-7942988945600443502) %__expr_3300329792522185471))))))) (NDArray_T (NDArray___sub__ %__expr_7843526591494960327 (NDArray___matmul__ %__expr_-5540247018246576406 %__expr_7843526591494960327))))) (NDArray___truediv__ (NDArray_T (NDArray___truediv__ (NDArray___getitem__ (TupleNDArray___getitem__ %__expr_4799320818084596281 %__expr_2305922367412063525) (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_slice %__expr_-1459297673498492435) %__expr_-8637348939342624324)))) %__expr_2307122782736907488)) (NDArray___getitem__ %__expr_-4744074158064860754 (IndexKey_slice %__expr_-1459297673498492435)))) %__expr_6185990579165616281))) 0) +(TupleInt_length (NDArray_shape (unique_values (concat (TupleNDArray___init__ (unique_values 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(TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (OptionalDType_none) (OptionalBool_none) %__expr_-3674731718720096444) (TupleInt_from_vec (vec-of (Int___init__ -1))) %__expr_-4122594143565222517) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444))) (OptionalInt_none)))))) 0) +(Int___eq__ (Int___mul__ %__expr_3300329792522185471 (TupleInt___getitem__ (NDArray_shape (unique_values (concat (TupleNDArray___init__ (unique_values (asarray (asarray (reshape (asarray (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (OptionalDType_none) (OptionalBool_none) %__expr_-3674731718720096444) (TupleInt_from_vec (vec-of (Int___init__ -1))) %__expr_-4122594143565222517) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444))) (OptionalInt_none)))) %__expr_-7942988945600443502)) %__expr_2305922367412063525) +(run-schedule (saturate (run array_api_ruleset))) +(extract (Boolean_bool (Int___eq__ (Int___mul__ %__expr_3300329792522185471 (TupleInt___getitem__ (NDArray_shape (unique_values (concat (TupleNDArray___init__ (unique_values (asarray (asarray (reshape (asarray (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) 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%__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none))) (Int___init__ 0))) 0) +(Int___eq__ (NDArray_ndim (asarray (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") %__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none))) (Int___init__ 1)) +(run-schedule (saturate (run array_api_ruleset))) +(extract (Boolean_bool (Int___eq__ (NDArray_ndim (asarray (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") %__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none))) (Int___init__ 1))) 0) +(Int___ge__ (NDArray_ndim (asarray (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") %__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) 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(OptionalDevice_none))) (Int___init__ 1)) (Int___init__ 1))) 0) +(TupleInt_length (NDArray_shape (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") %__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))))) +(run-schedule (saturate (run array_api_ruleset))) +(extract (Int_i64 (TupleInt_length (NDArray_shape (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") %__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4)))))))) 0) +(let %__expr_-7766708656681124433 (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") %__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4)))))) +(Int___eq__ (TupleInt___getitem__ (NDArray_shape (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") %__expr_2565664028803046192) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4)))))) %__expr_3300329792522185471) (TupleInt___getitem__ (NDArray_shape 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array_api_ruleset) +(sort TupleInt) +(function TupleInt_single (Int) TupleInt) +(sort UnstableFn_Int_Int (UnstableFn (Int) Int)) +(function TupleInt___init__ (Int UnstableFn_Int_Int) TupleInt :unextractable) +(function Int___init__ (i64) Int) +(rewrite (TupleInt_single i) (TupleInt___init__ (Int___init__ 1) (unstable-fn "i-Int__-Int_i" i)) :ruleset array_api_ruleset) +(function i-Int_i (Int) Int) +(rewrite (i-Int_i i) i :ruleset array_api_ruleset) +(function TupleInt_range (Int) TupleInt) +(rewrite (TupleInt_range stop) (TupleInt___init__ stop (unstable-fn "i-Int_i")) :ruleset array_api_ruleset) +(sort Vec_Int (Vec Int)) +(function TupleInt_from_vec (Vec_Int) TupleInt) +(function index_vec_int (Vec_Int Int) Int) +(rewrite (TupleInt_from_vec vec) (TupleInt___init__ (Int___init__ (vec-length vec)) (unstable-fn "index_vec_int" vec)) :ruleset array_api_ruleset) +(sort Boolean) +(function Int_if_ (Boolean Int Int) Int) +(function Int___lt__ (Int Int) Boolean) +(function TupleInt_length (TupleInt) Int) +(function TupleInt___getitem__ (TupleInt Int) Int) +(function Int___sub__ (Int Int) Int) +(function other-TupleInt_self-TupleInt_i-Int__Int_if___Int___lt___i__TupleInt_length_self____TupleInt___getitem___self_i___TupleInt___getitem___other__Int___sub___i__TupleInt_length_self____ (TupleInt TupleInt Int) Int) +(rewrite (other-TupleInt_self-TupleInt_i-Int__Int_if___Int___lt___i__TupleInt_length_self____TupleInt___getitem___self_i___TupleInt___getitem___other__Int___sub___i__TupleInt_length_self____ other self i) (Int_if_ (Int___lt__ i (TupleInt_length self)) (TupleInt___getitem__ self i) (TupleInt___getitem__ other (Int___sub__ i (TupleInt_length self)))) :ruleset array_api_ruleset) +(function TupleInt___add__ (TupleInt TupleInt) TupleInt) +(function Int___add__ (Int Int) Int) +(rewrite (TupleInt___add__ self other) (TupleInt___init__ (Int___add__ (TupleInt_length self) (TupleInt_length other)) (unstable-fn "other-TupleInt_self-TupleInt_i-Int__Int_if___Int___lt___i__TupleInt_length_self____TupleInt___getitem___self_i___TupleInt___getitem___other__Int___sub___i__TupleInt_length_self____" other self)) :ruleset array_api_ruleset) +(function Boolean___or__ (Boolean Boolean) Boolean) +(function Int___eq__ (Int Int) Boolean) +(function i-Int_acc-Boolean_j-Int__Boolean___or___acc__Int___eq___i_j__ (Int Boolean Int) Boolean) +(rewrite (i-Int_acc-Boolean_j-Int__Boolean___or___acc__Int___eq___i_j__ i acc j) (Boolean___or__ acc (Int___eq__ i j)) :ruleset array_api_ruleset) +(function TupleInt_contains (TupleInt Int) Boolean) +(sort UnstableFn_Boolean_Boolean_Int (UnstableFn (Boolean Int) Boolean)) +(function TupleInt_fold_boolean (TupleInt Boolean UnstableFn_Boolean_Boolean_Int) Boolean) +(function FALSE () Boolean) +(rewrite (TupleInt_contains self i) (TupleInt_fold_boolean self (FALSE) (unstable-fn "i-Int_acc-Boolean_j-Int__Boolean___or___acc__Int___eq___i_j__" i)) :ruleset array_api_ruleset) +(function f-UnstableFn_Int_Int_self-TupleInt_i-Int__unstable-app_f__TupleInt___getitem___self_i__ (UnstableFn_Int_Int TupleInt Int) Int) +(rewrite (f-UnstableFn_Int_Int_self-TupleInt_i-Int__unstable-app_f__TupleInt___getitem___self_i__ f self i) (unstable-app f (TupleInt___getitem__ self i)) :ruleset array_api_ruleset) +(function TupleInt_map (TupleInt UnstableFn_Int_Int) TupleInt :cost 100) +(rewrite (TupleInt_map self f) (TupleInt___init__ (TupleInt_length self) (unstable-fn "f-UnstableFn_Int_Int_self-TupleInt_i-Int__unstable-app_f__TupleInt___getitem___self_i__" f self)) :ruleset array_api_ruleset) +(sort NDArray) +(function NDArray_size (NDArray) Int) +(sort UnstableFn_Int_Int_Int (UnstableFn (Int Int) Int)) +(function TupleInt_fold (TupleInt Int UnstableFn_Int_Int_Int) Int) +(function NDArray_shape (NDArray) TupleInt) +(function Int___mul__ (Int Int) Int) +(rewrite (NDArray_size x) (TupleInt_fold (NDArray_shape x) (Int___init__ 1) (unstable-fn "Int___mul__")) :ruleset array_api_ruleset) +(function unique_values (NDArray) NDArray) +(sort TupleValue) +(function NDArray_vector (TupleValue) NDArray) +(sort Value) +(function possible_values (Value) TupleValue) +(function NDArray_index (NDArray TupleInt) Value) +(function ALL_INDICES () TupleInt) +(rewrite (unique_values a) (NDArray_vector (possible_values (NDArray_index a (ALL_INDICES)))) :ruleset array_api_ruleset) +(function Value_isfinite (Value) Boolean) +(function Value_int (Int) Value) +(function TRUE () Boolean) +(rewrite (Value_isfinite (Value_int i)) (TRUE) :ruleset array_api_ruleset) +(function Value_bool (Boolean) Value) +(rewrite (Value_isfinite (Value_bool b)) (TRUE) :ruleset array_api_ruleset) +(sort Float) +(function Value_float (Float) Value) +(function Float___init__ (f64) Float :cost 3) +(rewrite (Value_isfinite (Value_float (Float___init__ f))) (TRUE) :when ((!= f NaN)) :ruleset array_api_ruleset) +(function isfinite (NDArray) NDArray) +(sort OptionalIntOrTuple) +(function sum (NDArray OptionalIntOrTuple) NDArray) +(function OptionalIntOrTuple_none () OptionalIntOrTuple) +(function NDArray_scalar (Value) NDArray) +(rewrite (isfinite (sum arr (OptionalIntOrTuple_none))) (NDArray_scalar (Value_bool (Value_isfinite (NDArray_index arr (ALL_INDICES))))) :ruleset array_api_ruleset) +(function assume_value_one_of (NDArray TupleValue) NDArray) +(rewrite (NDArray_shape (assume_value_one_of x vs)) (NDArray_shape x) :ruleset array_api_ruleset) +(sort DType) +(function NDArray_dtype (NDArray) DType) +(rewrite (NDArray_dtype (assume_value_one_of x vs)) (NDArray_dtype x) :ruleset array_api_ruleset) +(rule ((= v (NDArray_index (assume_value_one_of x vs) idx))) + ((union v (NDArray_index x idx)) + (union (possible_values v) vs)) + :ruleset array_api_ruleset ) +(function assume_isfinite (NDArray) NDArray) +(rewrite (NDArray_shape (assume_isfinite x)) (NDArray_shape x) :ruleset array_api_ruleset) +(rewrite (NDArray_dtype (assume_isfinite x)) (NDArray_dtype x) :ruleset array_api_ruleset) +(rewrite (NDArray_index (assume_isfinite x) ti) (NDArray_index x ti) :ruleset array_api_ruleset) +(rewrite (Value_isfinite (NDArray_index (assume_isfinite x) ti)) (TRUE) :ruleset array_api_ruleset) +(function assume_shape (NDArray TupleInt) NDArray) +(rewrite (NDArray_shape (assume_shape x shape)) shape :ruleset array_api_ruleset) +(rewrite (NDArray_dtype (assume_shape x shape)) (NDArray_dtype x) :ruleset array_api_ruleset) +(rewrite (NDArray_index (assume_shape x shape) idx) (NDArray_index x idx) :ruleset array_api_ruleset) +(function assume_dtype (NDArray DType) NDArray) +(rewrite (NDArray_dtype (assume_dtype x dtype)) dtype :ruleset array_api_ruleset) +(rewrite (NDArray_shape (assume_dtype x dtype)) (NDArray_shape x) :ruleset array_api_ruleset) +(rewrite (NDArray_index (assume_dtype x dtype) idx) (NDArray_index x idx) :ruleset array_api_ruleset) +(sort IndexKey) +(function NDArray___getitem__ (NDArray IndexKey) NDArray) +(function IndexKey_int (Int) IndexKey) +(rewrite (NDArray___getitem__ x (IndexKey_int i)) (NDArray_scalar (NDArray_index x (TupleInt_single i))) :ruleset array_api_ruleset) +(sort OptionalBool) +(function reshape (NDArray TupleInt OptionalBool) NDArray) +(rule ((= __a (reshape x shape copy))) + ((NDArray_shape x) + (TupleInt_length (NDArray_shape x))) + :ruleset array_api_ruleset ) +(rule ((reshape x shape copy)) + ((TupleInt_length shape) + (TupleInt___getitem__ shape (Int___init__ 0))) + :ruleset array_api_ruleset ) +(rewrite (reshape x shape copy) x :when ((= (TupleInt_length (NDArray_shape x)) (Int___init__ 1)) (= (TupleInt_length shape) (Int___init__ 1)) (= (TupleInt___getitem__ shape (Int___init__ 0)) (Int___init__ -1))) :ruleset array_api_ruleset) +(function TupleValue_length (TupleValue) Int) +(rewrite (NDArray_shape (NDArray_vector vs)) (TupleInt_single (TupleValue_length vs)) :ruleset array_api_ruleset) +(function Value_dtype (Value) DType) +(function TupleValue___getitem__ (TupleValue Int) Value) +(rewrite (NDArray_dtype (NDArray_vector vs)) (Value_dtype (TupleValue___getitem__ vs (Int___init__ 0))) :ruleset array_api_ruleset) +(rewrite (NDArray_index (NDArray_vector vs) ti) (TupleValue___getitem__ vs (TupleInt___getitem__ ti (Int___init__ 0))) :ruleset array_api_ruleset) +(function TupleInt_EMPTY () TupleInt) +(rewrite (NDArray_shape (NDArray_scalar v)) (TupleInt_EMPTY) :ruleset array_api_ruleset) +(rewrite (NDArray_dtype (NDArray_scalar v)) (Value_dtype v) :ruleset array_api_ruleset) +(rewrite (NDArray_index (NDArray_scalar v) (TupleInt_EMPTY)) v :ruleset array_api_ruleset) +(function any (NDArray) NDArray) +(function TupleValue_includes (TupleValue Value) Boolean) +(function Value_to_truthy_value (Value) Value) +(rewrite (any x) (NDArray_scalar (Value_bool (TupleValue_includes (possible_values (Value_to_truthy_value (NDArray_index x (ALL_INDICES)))) (Value_bool (TRUE))))) :ruleset array_api_ruleset) +(function NDArray___lt__ (NDArray NDArray) NDArray) +(function Value___lt__ (Value Value) Value) +(function broadcast_index (TupleInt TupleInt TupleInt) TupleInt) +(function broadcast_shapes (TupleInt TupleInt) TupleInt) +(rewrite (NDArray_index (NDArray___lt__ x y) idx) (Value___lt__ (NDArray_index x (broadcast_index (NDArray_shape x) (broadcast_shapes (NDArray_shape x) (NDArray_shape y)) idx)) (NDArray_index y (broadcast_index (NDArray_shape y) (broadcast_shapes (NDArray_shape x) (NDArray_shape y)) idx))) :ruleset array_api_ruleset) +(function NDArray___truediv__ (NDArray NDArray) NDArray) +(function Value___truediv__ (Value Value) Value) +(rewrite (NDArray_index (NDArray___truediv__ x y) idx) (Value___truediv__ (NDArray_index x (broadcast_index (NDArray_shape x) (broadcast_shapes (NDArray_shape x) (NDArray_shape y)) idx)) (NDArray_index y (broadcast_index (NDArray_shape y) (broadcast_shapes (NDArray_shape x) (NDArray_shape y)) idx))) :ruleset array_api_ruleset) +(rewrite (NDArray_index (NDArray_scalar v) idx) v :ruleset array_api_ruleset) +(function astype (NDArray DType) NDArray) +(function Value_astype (Value DType) Value) +(rewrite (NDArray_index (astype x dtype) idx) (Value_astype (NDArray_index x idx) dtype) :ruleset array_api_ruleset) +(relation greater_zero (Value)) +(sort TupleNDArray) +(function TupleNDArray___getitem__ (TupleNDArray Int) NDArray) +(function unique_counts (NDArray) TupleNDArray) +(rule ((= v (NDArray_index (TupleNDArray___getitem__ (unique_counts x) (Int___init__ 1)) idx))) + ((greater_zero v)) + :ruleset array_api_ruleset ) +(rule ((greater_zero v) + (= v1 (Value_astype v dtype))) + ((greater_zero v1)) + :ruleset array_api_ruleset ) +(rule ((= v (Value_float (Float___init__ f))) + (> f 0.0)) + ((greater_zero v)) + :ruleset array_api_ruleset ) +(rule ((= v (Value_int (Int___init__ i))) + (> i 0)) + ((greater_zero v)) + :ruleset array_api_ruleset ) +(rule ((greater_zero v) + (greater_zero v1) + (= v2 (Value___truediv__ v v1))) + ((greater_zero v2)) + :ruleset array_api_ruleset ) +(rule ((greater_zero v) + (= v1 (Value___lt__ v (Value_int (Int___init__ 0))))) + ((union v1 (Value_bool (FALSE)))) + :ruleset array_api_ruleset ) +(function TupleValue___init__ (Value) TupleValue) +(rewrite (possible_values (Value_bool b)) (TupleValue___init__ (Value_bool b)) :ruleset array_api_ruleset) +(rule ((= v1 (Value_astype v dtype)) + (greater_zero v)) + ((greater_zero v1)) + :ruleset array_api_ruleset ) +(function TupleNDArray_length (TupleNDArray) Int) +(function svd (NDArray Boolean) TupleNDArray) +(rewrite (TupleNDArray_length (svd x full_matrices)) (Int___init__ 3) :ruleset array_api_ruleset) +(function unique_inverse (NDArray) TupleNDArray) +(rewrite (TupleNDArray_length (unique_inverse x)) (Int___init__ 2) :ruleset array_api_ruleset) +(rewrite (TupleNDArray___getitem__ (unique_inverse x) (Int___init__ 0)) (unique_values x) :ruleset array_api_ruleset) +(function ndarray-abs (NDArray) NDArray) +(function Float_abs (Float) Float) +(rewrite (ndarray-abs (NDArray_scalar (Value_float f))) (NDArray_scalar (Value_float (Float_abs f))) :ruleset array_api_ruleset) +(rewrite (TupleNDArray_length (unique_counts x)) (Int___init__ 2) :ruleset array_api_ruleset) +(rewrite (sum (TupleNDArray___getitem__ (unique_counts x) (Int___init__ 1)) (OptionalIntOrTuple_none)) (NDArray_scalar (Value_int (NDArray_size x))) :ruleset array_api_ruleset) +(rewrite (sum (astype (TupleNDArray___getitem__ (unique_counts x) (Int___init__ 1)) dtype) (OptionalIntOrTuple_none)) (astype (NDArray_scalar (Value_int (NDArray_size x))) dtype) :ruleset array_api_ruleset) +(rewrite (NDArray_dtype (astype x dtype)) dtype :ruleset array_api_ruleset) +(function DType_float64 () DType) +(rewrite (astype (NDArray_scalar (Value_int (Int___init__ i))) (DType_float64)) (NDArray_scalar (Value_float (Float___init__ (to-f64 i)))) :ruleset array_api_ruleset) +(sort OptionalInt) +(function concat (TupleNDArray OptionalInt) NDArray) +(function TupleNDArray___init__ (NDArray) TupleNDArray) +(function OptionalInt_none () OptionalInt) +(rewrite (concat (TupleNDArray___init__ x) (OptionalInt_none)) x :ruleset array_api_ruleset) +(rewrite (unique_values (unique_values x)) (unique_values x) :ruleset array_api_ruleset) +(rewrite (sum (NDArray___truediv__ x (NDArray_scalar v)) (OptionalIntOrTuple_none)) (NDArray___truediv__ (sum x (OptionalIntOrTuple_none)) (NDArray_scalar v)) :ruleset array_api_ruleset) +(function NDArray_ndim (NDArray) Int) +(sort OptionalDType) +(sort OptionalDevice) +(function asarray (NDArray OptionalDType OptionalBool OptionalDevice) NDArray) +(function OptionalDevice_none () OptionalDevice) +(rewrite (NDArray_ndim (asarray a d ob (OptionalDevice_none))) (NDArray_ndim a) :ruleset array_api_ruleset) +(function OptionalDType_none () OptionalDType) +(function OptionalBool_none () OptionalBool) +(rewrite (asarray a (OptionalDType_none) (OptionalBool_none) (OptionalDevice_none)) a :ruleset array_api_ruleset) +(function TupleNDArray___add__ (TupleNDArray TupleNDArray) TupleNDArray) +(function TupleNDArray_EMPTY () TupleNDArray) +(rewrite (TupleNDArray___add__ ti (TupleNDArray_EMPTY)) ti :ruleset array_api_ruleset) +(rewrite (TupleNDArray_length (TupleNDArray___init__ n)) (Int___init__ 1) :ruleset array_api_ruleset) +(rewrite (TupleNDArray_length (TupleNDArray___add__ ti ti2)) (Int___add__ (TupleNDArray_length ti) (TupleNDArray_length ti2)) :ruleset array_api_ruleset) +(sort UnstableFn_Value_TupleInt (UnstableFn (TupleInt) Value)) +(function NDArray___init__ (TupleInt DType UnstableFn_Value_TupleInt) NDArray) +(rewrite (NDArray_shape (NDArray___init__ shape dtype idx_fn)) shape :ruleset array_api_ruleset) +(rewrite (NDArray_dtype (NDArray___init__ shape dtype idx_fn)) dtype :ruleset array_api_ruleset) +(rewrite (NDArray_ndim x) (TupleInt_length (NDArray_shape x)) :ruleset array_api_ruleset) +(function NDArray_to_value (NDArray) Value) +(rewrite (NDArray_to_value x) (NDArray_index x (TupleInt_EMPTY)) :ruleset array_api_ruleset) +(rewrite (NDArray___truediv__ (NDArray_scalar (Value_float f)) (NDArray_scalar (Value_float f))) (NDArray_scalar (Value_float (Float___init__ 1.0))) :ruleset array_api_ruleset) +(function NDArray___sub__ (NDArray NDArray) NDArray) +(rewrite (NDArray___sub__ (NDArray_scalar (Value_float f)) (NDArray_scalar (Value_float f))) (NDArray_scalar (Value_float (Float___init__ 0.0))) :ruleset array_api_ruleset) +(function NDArray___gt__ (NDArray NDArray) NDArray) +(rewrite (NDArray___gt__ (NDArray_scalar (Value_float (Float___init__ fi1))) (NDArray_scalar (Value_float (Float___init__ fi2)))) (NDArray_scalar (Value_bool (TRUE))) :when ((> fi1 fi2)) :ruleset array_api_ruleset) +(rewrite (NDArray___gt__ (NDArray_scalar (Value_float (Float___init__ fi1))) (NDArray_scalar (Value_float (Float___init__ fi2)))) (NDArray_scalar (Value_bool (FALSE))) :when ((<= fi1 fi2)) :ruleset array_api_ruleset) +(function NDArray_T (NDArray) NDArray) +(rewrite (NDArray_T (NDArray_T x)) x :ruleset array_api_ruleset) +(function TupleValue___add__ (TupleValue TupleValue) TupleValue) +(function TupleValue_EMPTY () TupleValue) +(rewrite (TupleValue___add__ ti (TupleValue_EMPTY)) ti :ruleset array_api_ruleset) +(rewrite (TupleValue_length (TupleValue_EMPTY)) (Int___init__ 0) :ruleset array_api_ruleset) +(rewrite (TupleValue_length (TupleValue___init__ v)) (Int___init__ 1) :ruleset array_api_ruleset) +(rewrite (TupleValue_length (TupleValue___add__ ti ti2)) (Int___add__ (TupleValue_length ti) (TupleValue_length ti2)) :ruleset array_api_ruleset) +(rewrite (TupleValue___getitem__ (TupleValue___init__ v) (Int___init__ 0)) v :ruleset array_api_ruleset) +(rewrite (TupleValue___getitem__ (TupleValue___add__ (TupleValue___init__ v) ti) (Int___init__ 0)) v :ruleset array_api_ruleset) +(rule ((= v (TupleValue___getitem__ (TupleValue___add__ (TupleValue___init__ v2) ti) (Int___init__ k))) + (> k 0)) + ((union v (TupleValue___getitem__ ti (Int___init__ (- k 1))))) + :ruleset array_api_ruleset ) +(rewrite (TupleValue_includes (TupleValue_EMPTY) v) (FALSE) :ruleset array_api_ruleset) +(rewrite (TupleValue_includes (TupleValue___init__ v) v) (TRUE) :ruleset array_api_ruleset) +(rewrite (TupleValue_includes (TupleValue___init__ v) v2) (FALSE) :when ((!= v v2)) :ruleset array_api_ruleset) +(rewrite (TupleValue_includes (TupleValue___add__ ti ti2) v) (Boolean___or__ (TupleValue_includes ti v) (TupleValue_includes ti2 v)) :ruleset array_api_ruleset) +(function DType_int64 () DType) +(rewrite (Value_dtype (Value_int i)) (DType_int64) :ruleset array_api_ruleset) +(rewrite (Value_dtype (Value_float f)) (DType_float64) :ruleset array_api_ruleset) +(function DType_bool () DType) +(rewrite (Value_dtype (Value_bool b)) (DType_bool) :ruleset array_api_ruleset) +(function Value_to_bool (Value) Boolean) +(rewrite (Value_to_bool (Value_bool b)) b :ruleset array_api_ruleset) +(function Value_to_int (Value) Int) +(rewrite (Value_to_int (Value_int i)) i :ruleset array_api_ruleset) +(rewrite (Value_to_truthy_value (Value_bool b)) (Value_bool b) :ruleset array_api_ruleset) +(sort IsDtypeKind) +(function isdtype (DType IsDtypeKind) Boolean) +(function DType_float32 () DType) +(function IsDtypeKind_string (String) IsDtypeKind) +(rewrite (isdtype (DType_float32) (IsDtypeKind_string "integral")) (FALSE) :ruleset array_api_ruleset) +(rewrite (isdtype (DType_float64) (IsDtypeKind_string "integral")) (FALSE) :ruleset array_api_ruleset) +(function DType_object () DType) +(rewrite (isdtype (DType_object) (IsDtypeKind_string "integral")) (FALSE) :ruleset array_api_ruleset) +(rewrite (isdtype (DType_int64) (IsDtypeKind_string "integral")) (TRUE) :ruleset array_api_ruleset) +(function DType_int32 () DType) +(rewrite (isdtype (DType_int32) (IsDtypeKind_string "integral")) (TRUE) :ruleset array_api_ruleset) +(rewrite (isdtype (DType_float32) (IsDtypeKind_string "real floating")) (TRUE) :ruleset array_api_ruleset) +(rewrite (isdtype (DType_float64) (IsDtypeKind_string "real floating")) (TRUE) :ruleset array_api_ruleset) +(rewrite (isdtype (DType_object) (IsDtypeKind_string "real floating")) (FALSE) :ruleset array_api_ruleset) +(rewrite (isdtype (DType_int64) (IsDtypeKind_string "real floating")) (FALSE) :ruleset array_api_ruleset) +(rewrite (isdtype (DType_int32) (IsDtypeKind_string "real floating")) (FALSE) :ruleset array_api_ruleset) +(rewrite (isdtype (DType_float32) (IsDtypeKind_string "complex floating")) (FALSE) :ruleset array_api_ruleset) +(rewrite (isdtype (DType_float64) (IsDtypeKind_string "complex floating")) (FALSE) :ruleset array_api_ruleset) +(rewrite (isdtype (DType_object) (IsDtypeKind_string "complex floating")) (FALSE) :ruleset array_api_ruleset) +(rewrite (isdtype (DType_int64) (IsDtypeKind_string "complex floating")) (FALSE) :ruleset array_api_ruleset) +(rewrite (isdtype (DType_int32) (IsDtypeKind_string "complex floating")) (FALSE) :ruleset array_api_ruleset) +(function IsDtypeKind_NULL () IsDtypeKind) +(rewrite (isdtype d (IsDtypeKind_NULL)) (FALSE) :ruleset array_api_ruleset) +(function IsDtypeKind_dtype (DType) IsDtypeKind) +(rewrite (isdtype d (IsDtypeKind_dtype d)) (TRUE) :ruleset array_api_ruleset) +(function IsDtypeKind___or__ (IsDtypeKind IsDtypeKind) IsDtypeKind :cost 10) +(rewrite (isdtype d (IsDtypeKind___or__ k1 k2)) (Boolean___or__ (isdtype d k1) (isdtype d k2)) :ruleset array_api_ruleset) +(rewrite (IsDtypeKind___or__ k1 (IsDtypeKind_NULL)) k1 :ruleset array_api_ruleset) +(function DType___eq__ (DType DType) Boolean) +(rewrite (DType___eq__ (DType_float64) (DType_float64)) (TRUE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_float64) (DType_float32)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_float64) (DType_int32)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_float64) (DType_int64)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_float64) (DType_object)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_float32) (DType_float64)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_float32) (DType_float32)) (TRUE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_float32) (DType_int32)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_float32) (DType_int64)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_float32) (DType_object)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_int32) (DType_float64)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_int32) (DType_float32)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_int32) (DType_int32)) (TRUE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_int32) (DType_int64)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_int32) (DType_object)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_int64) (DType_float64)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_int64) (DType_float32)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_int64) (DType_int32)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_int64) (DType_int64)) (TRUE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_int64) (DType_object)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_object) (DType_float64)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_object) (DType_float32)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_object) (DType_int32)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_object) (DType_int64)) (FALSE) :ruleset array_api_ruleset) +(rewrite (DType___eq__ (DType_object) (DType_object)) (TRUE) :ruleset array_api_ruleset) +(function idx_fn-UnstableFn_Int_Int_i-Int__unstable-app_idx_fn__Int___add___i__Int___init___1___ (UnstableFn_Int_Int Int) Int) +(rewrite (idx_fn-UnstableFn_Int_Int_i-Int__unstable-app_idx_fn__Int___add___i__Int___init___1___ idx_fn i) (unstable-app idx_fn (Int___add__ i (Int___init__ 1))) :ruleset array_api_ruleset) +(rewrite (TupleInt_length (TupleInt___init__ i idx_fn)) i :ruleset array_api_ruleset) +(rewrite (TupleInt___getitem__ (TupleInt___init__ i idx_fn) i2) (unstable-app idx_fn i2) :ruleset array_api_ruleset) +(rewrite (index_vec_int vs (Int___init__ k)) (vec-get vs k) :when ((> (vec-length vs) k)) :ruleset array_api_ruleset) +(rewrite (TupleInt_fold (TupleInt___init__ (Int___init__ 0) idx_fn) i f) i :ruleset array_api_ruleset) +(rewrite (TupleInt_fold (TupleInt___init__ (Int___init__ k) idx_fn) i f) (unstable-app f (TupleInt_fold (TupleInt___init__ (Int___init__ (- k 1)) (unstable-fn "idx_fn-UnstableFn_Int_Int_i-Int__unstable-app_idx_fn__Int___add___i__Int___init___1___" idx_fn)) i f) (unstable-app idx_fn (Int___init__ 0))) :when ((!= k 0)) :ruleset array_api_ruleset) +(rewrite (TupleInt_fold_boolean (TupleInt___init__ (Int___init__ 0) idx_fn) b bool_f) b :ruleset array_api_ruleset) +(rewrite (TupleInt_fold_boolean (TupleInt___init__ (Int___init__ k) idx_fn) b bool_f) (unstable-app bool_f (TupleInt_fold_boolean (TupleInt___init__ (Int___init__ (- k 1)) (unstable-fn "idx_fn-UnstableFn_Int_Int_i-Int__unstable-app_idx_fn__Int___add___i__Int___init___1___" idx_fn)) b bool_f) (unstable-app idx_fn (Int___init__ 0))) :when ((!= k 0)) :ruleset array_api_ruleset) +(sort UnstableFn_Boolean_Int (UnstableFn (Int) Boolean)) +(function TupleInt_filter (TupleInt UnstableFn_Boolean_Int) TupleInt :cost 100) +(rewrite (TupleInt_filter (TupleInt___init__ (Int___init__ 0) idx_fn) filter_f) (TupleInt___init__ (Int___init__ 0) idx_fn) :ruleset array_api_ruleset) +(function TupleInt_if_ (Boolean TupleInt TupleInt) TupleInt) +(rewrite (TupleInt_filter (TupleInt___init__ (Int___init__ k) idx_fn) filter_f) (TupleInt_if_ (unstable-app filter_f (unstable-app idx_fn (Int___init__ k))) (TupleInt___add__ (TupleInt_single (unstable-app idx_fn (Int___init__ k))) (TupleInt_filter (TupleInt___init__ (Int___init__ (- k 1)) (unstable-fn "idx_fn-UnstableFn_Int_Int_i-Int__unstable-app_idx_fn__Int___add___i__Int___init___1___" idx_fn)) filter_f)) (TupleInt_filter (TupleInt___init__ (Int___init__ (- k 1)) (unstable-fn "idx_fn-UnstableFn_Int_Int_i-Int__unstable-app_idx_fn__Int___add___i__Int___init___1___" idx_fn)) filter_f)) :when ((!= k 0)) :ruleset array_api_ruleset) +(function bottom_indexing (Int) Int) +(rewrite (TupleInt_EMPTY) (TupleInt___init__ (Int___init__ 0) (unstable-fn "bottom_indexing")) :ruleset array_api_ruleset) +(rewrite (TupleInt_if_ (TRUE) ti ti2) ti :ruleset array_api_ruleset) +(rewrite (TupleInt_if_ (FALSE) ti ti2) ti2 :ruleset array_api_ruleset) +(rewrite (Float_abs (Float___init__ f)) (Float___init__ f) :when ((>= f 0.0)) :ruleset array_api_ruleset) +(rewrite (Float_abs (Float___init__ f)) (Float___init__ (neg f)) :when ((< f 0.0)) :ruleset array_api_ruleset) +(function Float_rational (Rational) Float :cost 2) +(rewrite (Float___init__ f) (Float_rational (rational (to-i64 f) 1)) :when ((= (to-f64 (to-i64 f)) f)) :ruleset array_api_ruleset) +(function Float_from_int (Int) Float) +(rewrite (Float_from_int (Int___init__ i)) (Float_rational (rational i 1)) :ruleset array_api_ruleset) +(function Float___add__ (Float Float) Float) +(rewrite (Float___add__ (Float___init__ f) (Float___init__ f2)) (Float___init__ (+ f f2)) :ruleset array_api_ruleset) +(function Float___sub__ (Float Float) Float) +(rewrite (Float___sub__ (Float___init__ f) (Float___init__ f2)) (Float___init__ (- f f2)) :ruleset array_api_ruleset) +(function Float___mul__ (Float Float) Float) +(rewrite (Float___mul__ (Float___init__ f) (Float___init__ f2)) (Float___init__ (* f f2)) :ruleset array_api_ruleset) +(function Float___truediv__ (Float Float) Float) +(rewrite (Float___truediv__ (Float_rational r) (Float_rational r1)) (Float_rational (/ r r1)) :ruleset array_api_ruleset) +(rewrite (Float___add__ (Float_rational r) (Float_rational r1)) (Float_rational (+ r r1)) :ruleset array_api_ruleset) +(rewrite (Float___sub__ (Float_rational r) (Float_rational r1)) (Float_rational (- r r1)) :ruleset array_api_ruleset) +(rewrite (Float___mul__ (Float_rational r) (Float_rational r1)) (Float_rational (* r r1)) :ruleset array_api_ruleset) +(rewrite (Int___eq__ (Int___init__ i) (Int___init__ i)) (TRUE) :ruleset array_api_ruleset) +(rule ((= r (Int___eq__ (Int___init__ i) (Int___init__ j))) + (!= i j)) + ((union r (FALSE))) + :ruleset array_api_ruleset ) +(function Int___ge__ (Int Int) Boolean) +(rewrite (Int___ge__ (Int___init__ i) (Int___init__ i)) (TRUE) :ruleset array_api_ruleset) +(rule ((= r (Int___ge__ (Int___init__ i) (Int___init__ j))) + (> i j)) + ((union r (TRUE))) + :ruleset array_api_ruleset ) +(rule ((= r (Int___ge__ (Int___init__ i) (Int___init__ j))) + (< i j)) + ((union r (FALSE))) + :ruleset array_api_ruleset ) +(rewrite (Int___lt__ (Int___init__ i) (Int___init__ i)) (FALSE) :ruleset array_api_ruleset) +(rule ((= r (Int___lt__ (Int___init__ i) (Int___init__ j))) + (< i j)) + ((union r (TRUE))) + :ruleset array_api_ruleset ) +(rule ((= r (Int___lt__ (Int___init__ i) (Int___init__ j))) + (> i j)) + ((union r (FALSE))) + :ruleset array_api_ruleset ) +(function Int___gt__ (Int Int) Boolean) +(rewrite (Int___gt__ (Int___init__ i) (Int___init__ i)) (FALSE) :ruleset array_api_ruleset) +(rule ((= r (Int___gt__ (Int___init__ i) (Int___init__ j))) + (> i j)) + ((union r (TRUE))) + :ruleset array_api_ruleset ) +(rule ((= r (Int___gt__ (Int___init__ i) (Int___init__ j))) + (< i j)) + ((union r (FALSE))) + :ruleset array_api_ruleset ) +(function Int_i64 (Int) i64) +(rule ((= o (Int___init__ j))) + ((set (Int_i64 o) j)) + :ruleset array_api_ruleset ) +(rewrite (Int___add__ (Int___init__ i) (Int___init__ j)) (Int___init__ (+ i j)) :ruleset array_api_ruleset) +(rewrite (Int___sub__ (Int___init__ i) (Int___init__ j)) (Int___init__ (- i j)) :ruleset array_api_ruleset) +(rewrite (Int___mul__ (Int___init__ i) (Int___init__ j)) (Int___init__ (* i j)) :ruleset array_api_ruleset) +(function Int___truediv__ (Int Int) Int) +(rewrite (Int___truediv__ (Int___init__ i) (Int___init__ j)) (Int___init__ (/ i j)) :ruleset array_api_ruleset) +(function Int___mod__ (Int Int) Int) +(rewrite (Int___mod__ (Int___init__ i) (Int___init__ j)) (Int___init__ (% i j)) :ruleset array_api_ruleset) +(function Int___and__ (Int Int) Int) +(rewrite (Int___and__ (Int___init__ i) (Int___init__ j)) (Int___init__ (& i j)) :ruleset array_api_ruleset) +(function Int___or__ (Int Int) Int) +(rewrite (Int___or__ (Int___init__ i) (Int___init__ j)) (Int___init__ (| i j)) :ruleset array_api_ruleset) +(function Int___xor__ (Int Int) Int) +(rewrite (Int___xor__ (Int___init__ i) (Int___init__ j)) (Int___init__ (^ i j)) :ruleset array_api_ruleset) +(function Int___lshift__ (Int Int) Int) +(rewrite (Int___lshift__ (Int___init__ i) (Int___init__ j)) (Int___init__ (<< i j)) :ruleset array_api_ruleset) +(function Int___rshift__ (Int Int) Int) +(rewrite (Int___rshift__ (Int___init__ i) (Int___init__ j)) (Int___init__ (>> i j)) :ruleset array_api_ruleset) +(function Int___invert__ (Int) Int) +(rewrite (Int___invert__ (Int___init__ i)) (Int___init__ (not-i64 i)) :ruleset array_api_ruleset) +(rewrite (Int_if_ (TRUE) o b) o :ruleset array_api_ruleset) +(rewrite (Int_if_ (FALSE) o b) b :ruleset array_api_ruleset) +(function Boolean_bool (Boolean) bool) +(rule ((= x (TRUE))) + ((set (Boolean_bool x) true)) + :ruleset array_api_ruleset ) +(rule ((= x (FALSE))) + ((set (Boolean_bool x) false)) + :ruleset array_api_ruleset ) +(rewrite (Boolean___or__ (TRUE) x) (TRUE) :ruleset array_api_ruleset) +(rewrite (Boolean___or__ (FALSE) x) x :ruleset array_api_ruleset) +(function Boolean___and__ (Boolean Boolean) Boolean) +(rewrite (Boolean___and__ (TRUE) x) x :ruleset array_api_ruleset) +(rewrite (Boolean___and__ (FALSE) x) (FALSE) :ruleset array_api_ruleset) +(function Boolean_if_int (Boolean Int Int) Int) +(rewrite (Boolean_if_int (TRUE) i j) i :ruleset array_api_ruleset) +(rewrite (Boolean_if_int (FALSE) i j) j :ruleset array_api_ruleset) +(function Boolean___invert__ (Boolean) Boolean) +(rewrite (Boolean___invert__ (TRUE)) (FALSE) :ruleset array_api_ruleset) +(rewrite (Boolean___invert__ (FALSE)) (TRUE) :ruleset array_api_ruleset) +(ruleset ruleset_5033605696) +(function NDArray___eq__ (NDArray NDArray) NDArray) +(rewrite (NDArray___eq__ (TupleNDArray___getitem__ (unique_inverse x) (Int___init__ 1)) (NDArray_scalar (Value_int i))) (NDArray___eq__ x (NDArray_scalar (NDArray_index (unique_values x) (TupleInt_from_vec (vec-of i))))) :subsume :ruleset ruleset_5033605696) +(function count_values (NDArray NDArray) TupleValue :unextractable) +(rewrite (TupleNDArray___getitem__ (unique_counts x) (Int___init__ 1)) (NDArray_vector (count_values x (unique_values x))) :subsume :ruleset ruleset_5033605696) +(rewrite (count_values x (NDArray_vector (TupleValue___add__ (TupleValue___init__ v) tv))) (TupleValue___add__ (TupleValue___init__ (NDArray_to_value (sum (NDArray___eq__ x (NDArray_scalar v)) (OptionalIntOrTuple_none)))) (count_values x (NDArray_vector tv))) :subsume :ruleset ruleset_5033605696) +(rewrite (count_values x (NDArray_vector (TupleValue___init__ v))) (TupleValue___init__ (NDArray_to_value (sum (NDArray___eq__ x (NDArray_scalar v)) (OptionalIntOrTuple_none)))) :subsume :ruleset ruleset_5033605696) +(function std (NDArray OptionalIntOrTuple) NDArray) +(sort IntOrTuple) +(function OptionalIntOrTuple_some (IntOrTuple) OptionalIntOrTuple) +(function IntOrTuple_int (Int) IntOrTuple) +(function ndarray-sqrt (NDArray) NDArray) +(function mean (NDArray OptionalIntOrTuple Boolean) NDArray) +(function square (NDArray) NDArray) +(rewrite (std x (OptionalIntOrTuple_some (IntOrTuple_int i))) (ndarray-sqrt (mean (square (NDArray___sub__ x (mean x (OptionalIntOrTuple_some (IntOrTuple_int i)) (TRUE)))) (OptionalIntOrTuple_some (IntOrTuple_int i)) (FALSE))) :subsume :ruleset ruleset_5033605696) +(rewrite (mean x (OptionalIntOrTuple_some (IntOrTuple_int i)) (FALSE)) (NDArray___truediv__ (sum x (OptionalIntOrTuple_some (IntOrTuple_int i))) (NDArray_scalar (Value_int (TupleInt___getitem__ (NDArray_shape x) i)))) :subsume :ruleset ruleset_5033605696) +(function expand_dims (NDArray Int) NDArray) +(rewrite (mean x (OptionalIntOrTuple_some (IntOrTuple_int i)) (TRUE)) (expand_dims (NDArray___truediv__ (sum x (OptionalIntOrTuple_some (IntOrTuple_int i))) (NDArray_scalar (Value_int (TupleInt___getitem__ (NDArray_shape x) i)))) i) :subsume :ruleset ruleset_5033605696) +(let %__expr_-4122594143565222517 (OptionalBool_none)) +(let %__expr_-3674731718720096444 (OptionalDevice_none)) +(let %__expr_2091604061025500396 (OptionalDType_none)) +(function NDArray_var (String) NDArray :cost 200) +(let %__expr_-5200143055942215294 (asarray (reshape (asarray (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444) (TupleInt_from_vec (vec-of (Int___init__ -1))) %__expr_-4122594143565222517) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444)) +(let %__expr_3300329792522185471 (Int___init__ 1)) +(let %__expr_-7942988945600443502 (Int___init__ 0)) +(let %__expr_2407075622821899710 (TupleInt___getitem__ (NDArray_shape (unique_values (concat (TupleNDArray___init__ (unique_values (asarray %__expr_-5200143055942215294 %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444))) (OptionalInt_none)))) %__expr_-7942988945600443502)) +(let %__expr_-143818766793636568 (OptionalInt_none)) +(let %__expr_2305922367412063525 (Int___init__ 2)) +(let %__expr_-1113027338580586528 (unique_values (concat (TupleNDArray___init__ (unique_values (asarray %__expr_-5200143055942215294 %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444))) (OptionalInt_none)))) +(let %__expr_4326809257670680665 (IndexKey_int %__expr_-7942988945600443502)) +(let %__expr_-6932009612334166206 (TupleInt___getitem__ (NDArray_shape (asarray (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") (DType_float64)) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444)) %__expr_-7942988945600443502)) +(sort MultiAxisIndexKey) +(function IndexKey_multi_axis (MultiAxisIndexKey) IndexKey) +(sort MultiAxisIndexKeyItem) +(sort Vec_MultiAxisIndexKeyItem (Vec MultiAxisIndexKeyItem)) +(function MultiAxisIndexKey_from_vec (Vec_MultiAxisIndexKeyItem) MultiAxisIndexKey) +(function MultiAxisIndexKeyItem_int (Int) MultiAxisIndexKeyItem) +(sort Slice) +(function MultiAxisIndexKeyItem_slice (Slice) MultiAxisIndexKeyItem) +(function Slice___init__ (OptionalInt OptionalInt OptionalInt) Slice) +(let %__expr_-954298076671303615 (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_int %__expr_2305922367412063525) (MultiAxisIndexKeyItem_slice (Slice___init__ %__expr_-143818766793636568 %__expr_-143818766793636568 %__expr_-143818766793636568)))))) +(let %__expr_483064111004974365 (Float___init__ 1.0)) +(let %__expr_-3520630818915629594 (Int___init__ 150)) +(let %__expr_-6765600943420531488 (Value_int (Int___init__ 2))) +(let %__expr_-622493510873225930 (Value_int (Int___init__ 1))) +(let %__expr_478758938070675600 (Value_int (Int___init__ 0))) +(let %__expr_-8664633617851008504 (unique_inverse %__expr_-5200143055942215294)) +(let %__expr_-8613124149453883591 (asarray (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") (DType_float64)) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444)) +(let %__expr_-8637348939342624324 (MultiAxisIndexKeyItem_slice (Slice___init__ %__expr_-143818766793636568 %__expr_-143818766793636568 %__expr_-143818766793636568))) +(let %__expr_-2704792733181451377 (TupleNDArray___getitem__ %__expr_-8664633617851008504 %__expr_3300329792522185471)) +(let %__expr_1913846200346632608 (OptionalIntOrTuple_some (IntOrTuple_int %__expr_-7942988945600443502))) +(let %__expr_6185990579165616281 (FALSE)) +(function NDArray___setitem__ (NDArray IndexKey NDArray) NDArray) +(function zeros (TupleInt OptionalDType OptionalDevice) NDArray) +(function OptionalDType_some (DType) OptionalDType) +(sort Device) +(function OptionalDevice_some (Device) OptionalDevice) +(function NDArray_device (NDArray) Device) +(function IndexKey_ndarray (NDArray) IndexKey) +(let %__expr_7843526591494960327 (NDArray___setitem__ (NDArray___setitem__ (NDArray___setitem__ (zeros (TupleInt_from_vec (vec-of (TupleInt___getitem__ (NDArray_shape (TupleNDArray___getitem__ %__expr_-8664633617851008504 %__expr_-7942988945600443502)) %__expr_-7942988945600443502) (TupleInt___getitem__ (NDArray_shape (asarray (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") (DType_float64)) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444)) %__expr_3300329792522185471))) (OptionalDType_some (NDArray_dtype %__expr_-8613124149453883591)) (OptionalDevice_some (NDArray_device %__expr_-8613124149453883591))) (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_int %__expr_-7942988945600443502) %__expr_-8637348939342624324))) (mean (NDArray___getitem__ %__expr_-8613124149453883591 (IndexKey_ndarray (NDArray___eq__ %__expr_-2704792733181451377 (NDArray_scalar %__expr_478758938070675600)))) %__expr_1913846200346632608 %__expr_6185990579165616281)) (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_int %__expr_3300329792522185471) %__expr_-8637348939342624324))) (mean (NDArray___getitem__ %__expr_-8613124149453883591 (IndexKey_ndarray (NDArray___eq__ %__expr_-2704792733181451377 (NDArray_scalar %__expr_-622493510873225930)))) %__expr_1913846200346632608 %__expr_6185990579165616281)) %__expr_-954298076671303615 (mean (NDArray___getitem__ %__expr_-8613124149453883591 (IndexKey_ndarray (NDArray___eq__ %__expr_-2704792733181451377 (NDArray_scalar %__expr_-6765600943420531488)))) %__expr_1913846200346632608 %__expr_6185990579165616281))) +(let %__expr_7180621784385959982 (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_int %__expr_3300329792522185471) %__expr_-8637348939342624324)))) +(let %__expr_-3283806677371465170 (NDArray_scalar %__expr_478758938070675600)) +(let %__expr_-4323225966908438009 (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_int %__expr_-7942988945600443502) %__expr_-8637348939342624324)))) +(let %__expr_-8475266842302933511 (NDArray_shape (asarray (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") (DType_float64)) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444))) +(function OptionalInt_some (Int) OptionalInt) +(let %__expr_3049932803880609425 (std (concat (TupleNDArray___add__ (TupleNDArray___init__ (NDArray___sub__ (NDArray___getitem__ %__expr_-8613124149453883591 (IndexKey_ndarray (NDArray___eq__ %__expr_-5200143055942215294 (NDArray___getitem__ %__expr_-1113027338580586528 %__expr_4326809257670680665)))) (NDArray___getitem__ %__expr_7843526591494960327 %__expr_-4323225966908438009))) (TupleNDArray___add__ (TupleNDArray___init__ (NDArray___sub__ (NDArray___getitem__ %__expr_-8613124149453883591 (IndexKey_ndarray (NDArray___eq__ %__expr_-5200143055942215294 (NDArray___getitem__ %__expr_-1113027338580586528 (IndexKey_int %__expr_3300329792522185471))))) (NDArray___getitem__ %__expr_7843526591494960327 %__expr_7180621784385959982))) (TupleNDArray___init__ (NDArray___sub__ (NDArray___getitem__ %__expr_-8613124149453883591 (IndexKey_ndarray (NDArray___eq__ %__expr_-5200143055942215294 (NDArray___getitem__ %__expr_-1113027338580586528 (IndexKey_int %__expr_2305922367412063525))))) (NDArray___getitem__ %__expr_7843526591494960327 %__expr_-954298076671303615))))) (OptionalInt_some %__expr_-7942988945600443502)) %__expr_1913846200346632608)) +(let %__expr_-671931098406187877 (concat (TupleNDArray___add__ (TupleNDArray___init__ (NDArray___sub__ (NDArray___getitem__ %__expr_-8613124149453883591 (IndexKey_ndarray (NDArray___eq__ %__expr_-5200143055942215294 (NDArray___getitem__ %__expr_-1113027338580586528 %__expr_4326809257670680665)))) (NDArray___getitem__ %__expr_7843526591494960327 %__expr_-4323225966908438009))) (TupleNDArray___add__ (TupleNDArray___init__ (NDArray___sub__ (NDArray___getitem__ %__expr_-8613124149453883591 (IndexKey_ndarray (NDArray___eq__ %__expr_-5200143055942215294 (NDArray___getitem__ %__expr_-1113027338580586528 (IndexKey_int %__expr_3300329792522185471))))) (NDArray___getitem__ %__expr_7843526591494960327 %__expr_7180621784385959982))) (TupleNDArray___init__ (NDArray___sub__ (NDArray___getitem__ %__expr_-8613124149453883591 (IndexKey_ndarray (NDArray___eq__ %__expr_-5200143055942215294 (NDArray___getitem__ %__expr_-1113027338580586528 (IndexKey_int %__expr_2305922367412063525))))) (NDArray___getitem__ %__expr_7843526591494960327 %__expr_-954298076671303615))))) (OptionalInt_some %__expr_-7942988945600443502))) +(function NDArray___mul__ (NDArray NDArray) NDArray) +(let %__expr_-1459297673498492435 (Slice___init__ %__expr_-143818766793636568 (OptionalInt_some (Value_to_int (NDArray_to_value (sum (astype (NDArray___gt__ (TupleNDArray___getitem__ (svd (NDArray___mul__ (ndarray-sqrt (asarray (NDArray_scalar (Value_float (Float___truediv__ %__expr_483064111004974365 (Float_from_int (Int___sub__ %__expr_-6932009612334166206 %__expr_2407075622821899710))))) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444)) (NDArray___truediv__ %__expr_-671931098406187877 (NDArray___setitem__ %__expr_3049932803880609425 (IndexKey_ndarray (NDArray___eq__ %__expr_3049932803880609425 %__expr_-3283806677371465170)) (NDArray_scalar (Value_float (Float___init__ 1.0)))))) %__expr_6185990579165616281) %__expr_3300329792522185471) (NDArray_scalar (Value_float (Float___init__ 0.0001)))) (DType_int32)) (OptionalIntOrTuple_none))))) %__expr_-143818766793636568)) +(let %__expr_4799320818084596281 (svd (NDArray___mul__ (ndarray-sqrt (asarray (NDArray_scalar (Value_float (Float___truediv__ %__expr_483064111004974365 (Float_from_int (Int___sub__ %__expr_-6932009612334166206 %__expr_2407075622821899710))))) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444)) (NDArray___truediv__ %__expr_-671931098406187877 (NDArray___setitem__ %__expr_3049932803880609425 (IndexKey_ndarray (NDArray___eq__ %__expr_3049932803880609425 %__expr_-3283806677371465170)) (NDArray_scalar (Value_float (Float___init__ 1.0)))))) %__expr_6185990579165616281)) +(let %__expr_-4744074158064860754 (TupleNDArray___getitem__ (svd (NDArray___mul__ (ndarray-sqrt (asarray (NDArray_scalar (Value_float (Float___truediv__ %__expr_483064111004974365 (Float_from_int (Int___sub__ %__expr_-6932009612334166206 %__expr_2407075622821899710))))) %__expr_2091604061025500396 %__expr_-4122594143565222517 %__expr_-3674731718720096444)) (NDArray___truediv__ %__expr_-671931098406187877 (NDArray___setitem__ %__expr_3049932803880609425 (IndexKey_ndarray (NDArray___eq__ %__expr_3049932803880609425 %__expr_-3283806677371465170)) (NDArray_scalar (Value_float (Float___init__ 1.0)))))) %__expr_6185990579165616281) %__expr_3300329792522185471)) +(let %__expr_2307122782736907488 (NDArray___setitem__ %__expr_3049932803880609425 (IndexKey_ndarray (NDArray___eq__ %__expr_3049932803880609425 %__expr_-3283806677371465170)) (NDArray_scalar (Value_float (Float___init__ 1.0))))) +(function NDArray___matmul__ (NDArray NDArray) NDArray) +(function IndexKey_slice (Slice) IndexKey) +(let %__expr_270530672567316052 (TupleNDArray___getitem__ (svd (NDArray___matmul__ (NDArray_T (NDArray___mul__ (ndarray-sqrt (NDArray___mul__ (NDArray___mul__ (NDArray_scalar (Value_int %__expr_-6932009612334166206)) (NDArray___truediv__ (astype (TupleNDArray___getitem__ (unique_counts %__expr_-5200143055942215294) %__expr_3300329792522185471) (NDArray_dtype %__expr_-8613124149453883591)) (NDArray_scalar (Value_float (Float___init__ 150.0))))) (NDArray_scalar (Value_float (Float___truediv__ %__expr_483064111004974365 (Float_from_int (Int___sub__ %__expr_2407075622821899710 %__expr_3300329792522185471))))))) (NDArray_T (NDArray___sub__ %__expr_7843526591494960327 (NDArray___matmul__ (NDArray___truediv__ (astype (TupleNDArray___getitem__ (unique_counts %__expr_-5200143055942215294) %__expr_3300329792522185471) (NDArray_dtype %__expr_-8613124149453883591)) (NDArray_scalar (Value_float (Float___init__ 150.0)))) %__expr_7843526591494960327))))) (NDArray___truediv__ (NDArray_T (NDArray___truediv__ (NDArray___getitem__ (TupleNDArray___getitem__ %__expr_4799320818084596281 %__expr_2305922367412063525) (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_slice %__expr_-1459297673498492435) %__expr_-8637348939342624324)))) %__expr_2307122782736907488)) (NDArray___getitem__ %__expr_-4744074158064860754 (IndexKey_slice %__expr_-1459297673498492435)))) %__expr_6185990579165616281) %__expr_3300329792522185471)) +(let %__expr_-5540247018246576406 (NDArray___truediv__ (astype (TupleNDArray___getitem__ (unique_counts %__expr_-5200143055942215294) %__expr_3300329792522185471) (NDArray_dtype %__expr_-8613124149453883591)) (NDArray_scalar (Value_float (Float___init__ 150.0))))) +(let %__expr_-5933626871507061239 (svd (NDArray___matmul__ (NDArray_T (NDArray___mul__ (ndarray-sqrt (NDArray___mul__ (NDArray___mul__ (NDArray_scalar (Value_int %__expr_-6932009612334166206)) (NDArray___truediv__ (astype (TupleNDArray___getitem__ (unique_counts %__expr_-5200143055942215294) %__expr_3300329792522185471) (NDArray_dtype %__expr_-8613124149453883591)) (NDArray_scalar (Value_float (Float___init__ 150.0))))) (NDArray_scalar (Value_float (Float___truediv__ %__expr_483064111004974365 (Float_from_int (Int___sub__ %__expr_2407075622821899710 %__expr_3300329792522185471))))))) (NDArray_T (NDArray___sub__ %__expr_7843526591494960327 (NDArray___matmul__ (NDArray___truediv__ (astype (TupleNDArray___getitem__ (unique_counts %__expr_-5200143055942215294) %__expr_3300329792522185471) (NDArray_dtype %__expr_-8613124149453883591)) (NDArray_scalar (Value_float (Float___init__ 150.0)))) %__expr_7843526591494960327))))) (NDArray___truediv__ (NDArray_T (NDArray___truediv__ (NDArray___getitem__ (TupleNDArray___getitem__ %__expr_4799320818084596281 %__expr_2305922367412063525) (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_slice %__expr_-1459297673498492435) %__expr_-8637348939342624324)))) %__expr_2307122782736907488)) (NDArray___getitem__ %__expr_-4744074158064860754 (IndexKey_slice %__expr_-1459297673498492435)))) %__expr_6185990579165616281)) +(let %__expr_-4180228001421012884 (NDArray_scalar (Value_float (Float___init__ 0.0001)))) +(let %__expr_-3501279694271260104 (DType_int32)) +(let %__expr_5981948135265815040 (OptionalIntOrTuple_none)) +(let %__expr_2917853313867759590 (NDArray_dtype %__expr_-8613124149453883591)) +(let %__expr_-5161099022452562755 (NDArray___matmul__ (NDArray___truediv__ (astype (TupleNDArray___getitem__ (unique_counts %__expr_-5200143055942215294) %__expr_3300329792522185471) (NDArray_dtype %__expr_-8613124149453883591)) (NDArray_scalar (Value_float (Float___init__ 150.0)))) %__expr_7843526591494960327)) +(let %__expr_7947521701427986423 (NDArray___truediv__ (NDArray_T (NDArray___truediv__ (NDArray___getitem__ (TupleNDArray___getitem__ %__expr_4799320818084596281 %__expr_2305922367412063525) (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_slice %__expr_-1459297673498492435) %__expr_-8637348939342624324)))) %__expr_2307122782736907488)) (NDArray___getitem__ %__expr_-4744074158064860754 (IndexKey_slice %__expr_-1459297673498492435)))) +(simplify (saturate (seq (run array_api_ruleset) (run ruleset_5033605696))) (NDArray___getitem__ (NDArray___matmul__ (NDArray___sub__ %__expr_-8613124149453883591 %__expr_-5161099022452562755) (NDArray___matmul__ %__expr_7947521701427986423 (NDArray___getitem__ (NDArray_T (TupleNDArray___getitem__ %__expr_-5933626871507061239 %__expr_2305922367412063525)) (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of %__expr_-8637348939342624324 (MultiAxisIndexKeyItem_slice (Slice___init__ %__expr_-143818766793636568 (OptionalInt_some (Value_to_int (NDArray_to_value (sum (astype (NDArray___gt__ %__expr_270530672567316052 (NDArray___mul__ %__expr_-4180228001421012884 (NDArray___getitem__ %__expr_270530672567316052 %__expr_4326809257670680665))) %__expr_-3501279694271260104) %__expr_5981948135265815040)))) %__expr_-143818766793636568)))))))) (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of %__expr_-8637348939342624324 (MultiAxisIndexKeyItem_slice (Slice___init__ %__expr_-143818766793636568 (OptionalInt_some %__expr_2305922367412063525) %__expr_-143818766793636568))))))) +(let %__expr_978886785202701864 (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") (DType_float64)) (TupleInt_from_vec (vec-of %__expr_-3520630818915629594 (Int___init__ 4)))))) +(let %__expr_3826936542596060759 (Int___init__ 4)) +(let %__expr_-8607724285922497289 (NDArray___getitem__ %__expr_978886785202701864 (IndexKey_ndarray (NDArray___eq__ (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of %__expr_-3520630818915629594))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (NDArray_scalar %__expr_-622493510873225930))))) +(let %__expr_8779256037532389381 (NDArray___getitem__ %__expr_978886785202701864 (IndexKey_ndarray (NDArray___eq__ (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of %__expr_-3520630818915629594))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) %__expr_-3283806677371465170)))) +(let %__expr_2565664028803046192 (DType_float64)) +(let %__expr_3562727526135681919 (NDArray___getitem__ %__expr_978886785202701864 (IndexKey_ndarray (NDArray___eq__ (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of %__expr_-3520630818915629594))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (NDArray_scalar %__expr_-6765600943420531488))))) +(let %__expr_5127641217187406832 (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of %__expr_-3520630818915629594))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2))))))) +(let %__expr_-5874110021677832412 (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_int %__expr_-7942988945600443502) %__expr_-8637348939342624324)))) +(let %__expr_2924140249920978521 (NDArray___setitem__ (NDArray___setitem__ (NDArray___setitem__ (zeros (TupleInt_from_vec (vec-of (Int___init__ 3) %__expr_3826936542596060759)) (OptionalDType_some %__expr_2565664028803046192) (OptionalDevice_some (NDArray_device %__expr_978886785202701864))) %__expr_-5874110021677832412 (NDArray___truediv__ (sum %__expr_8779256037532389381 %__expr_1913846200346632608) (NDArray_scalar (Value_int (TupleInt___getitem__ (NDArray_shape %__expr_8779256037532389381) %__expr_-7942988945600443502))))) (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_int %__expr_3300329792522185471) %__expr_-8637348939342624324))) (NDArray___truediv__ (sum %__expr_-8607724285922497289 %__expr_1913846200346632608) (NDArray_scalar (Value_int (TupleInt___getitem__ (NDArray_shape %__expr_-8607724285922497289) %__expr_-7942988945600443502))))) (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_int %__expr_2305922367412063525) %__expr_-8637348939342624324))) (NDArray___truediv__ (sum %__expr_3562727526135681919 %__expr_1913846200346632608) (NDArray_scalar (Value_int (TupleInt___getitem__ (NDArray_shape %__expr_3562727526135681919) %__expr_-7942988945600443502)))))) +(let %__expr_8582344284568866371 (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_int %__expr_2305922367412063525) %__expr_-8637348939342624324)))) +(let %__expr_-3132706819403651174 (concat (TupleNDArray___add__ (TupleNDArray___init__ (NDArray___sub__ %__expr_8779256037532389381 (NDArray___getitem__ %__expr_2924140249920978521 %__expr_-5874110021677832412))) (TupleNDArray___add__ (TupleNDArray___init__ (NDArray___sub__ %__expr_-8607724285922497289 (NDArray___getitem__ %__expr_2924140249920978521 (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_int %__expr_3300329792522185471) %__expr_-8637348939342624324)))))) (TupleNDArray___init__ (NDArray___sub__ %__expr_3562727526135681919 (NDArray___getitem__ %__expr_2924140249920978521 %__expr_8582344284568866371))))) (OptionalInt_some %__expr_-7942988945600443502))) +(let %__expr_755766186975356825 (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_int %__expr_3300329792522185471) %__expr_-8637348939342624324)))) +(let %__expr_1540266631570115279 (NDArray___eq__ (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of %__expr_-3520630818915629594))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (NDArray_scalar %__expr_-622493510873225930))) +(let %__expr_7382830492167037887 (square (NDArray___sub__ %__expr_-3132706819403651174 (expand_dims (NDArray___truediv__ (sum %__expr_-3132706819403651174 %__expr_1913846200346632608) (NDArray_scalar (Value_int (TupleInt___getitem__ (NDArray_shape %__expr_-3132706819403651174) %__expr_-7942988945600443502)))) %__expr_-7942988945600443502)))) +(let %__expr_-8085216922850384227 1) +(let %__expr_-6293504624159906607 (ndarray-sqrt (NDArray___truediv__ (sum %__expr_7382830492167037887 %__expr_1913846200346632608) (NDArray_scalar (Value_int (TupleInt___getitem__ (NDArray_shape %__expr_7382830492167037887) %__expr_-7942988945600443502)))))) +(let %__expr_6749312899897339687 (Slice___init__ %__expr_-143818766793636568 (OptionalInt_some (Value_to_int (NDArray_to_value (sum (astype (NDArray___gt__ (TupleNDArray___getitem__ (svd (NDArray___mul__ (ndarray-sqrt (NDArray_scalar (Value_float (Float_rational (rational %__expr_-8085216922850384227 147))))) (NDArray___truediv__ %__expr_-3132706819403651174 (NDArray___setitem__ %__expr_-6293504624159906607 (IndexKey_ndarray (NDArray___eq__ %__expr_-6293504624159906607 %__expr_-3283806677371465170)) (NDArray_scalar (Value_float (Float_rational (rational %__expr_-8085216922850384227 %__expr_-8085216922850384227))))))) %__expr_6185990579165616281) %__expr_3300329792522185471) %__expr_-4180228001421012884) %__expr_-3501279694271260104) %__expr_5981948135265815040)))) %__expr_-143818766793636568)) +(let %__expr_-5507881356079575778 (TupleNDArray___getitem__ (svd (NDArray___mul__ (ndarray-sqrt (NDArray_scalar (Value_float (Float_rational (rational %__expr_-8085216922850384227 147))))) (NDArray___truediv__ %__expr_-3132706819403651174 (NDArray___setitem__ %__expr_-6293504624159906607 (IndexKey_ndarray (NDArray___eq__ %__expr_-6293504624159906607 %__expr_-3283806677371465170)) (NDArray_scalar (Value_float (Float_rational (rational %__expr_-8085216922850384227 %__expr_-8085216922850384227))))))) %__expr_6185990579165616281) %__expr_3300329792522185471)) +(let %__expr_-649824781713772813 (NDArray___eq__ (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of %__expr_-3520630818915629594))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) %__expr_-3283806677371465170)) +(let %__expr_-7715872950595615314 (svd (NDArray___mul__ (ndarray-sqrt (NDArray_scalar (Value_float (Float_rational (rational %__expr_-8085216922850384227 147))))) (NDArray___truediv__ %__expr_-3132706819403651174 (NDArray___setitem__ %__expr_-6293504624159906607 (IndexKey_ndarray (NDArray___eq__ %__expr_-6293504624159906607 %__expr_-3283806677371465170)) (NDArray_scalar (Value_float (Float_rational (rational %__expr_-8085216922850384227 %__expr_-8085216922850384227))))))) %__expr_6185990579165616281)) +(let %__expr_-3823036485969157667 150) +(let %__expr_-5209865760313326585 (NDArray___truediv__ (astype (NDArray_vector (TupleValue___add__ (TupleValue___init__ (NDArray_to_value (sum %__expr_-649824781713772813 %__expr_5981948135265815040))) (TupleValue___add__ (TupleValue___init__ (NDArray_to_value (sum %__expr_1540266631570115279 %__expr_5981948135265815040))) (TupleValue___init__ (NDArray_to_value (sum (NDArray___eq__ (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of %__expr_-3520630818915629594))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (NDArray_scalar %__expr_-6765600943420531488)) %__expr_5981948135265815040)))))) %__expr_2565664028803046192) (NDArray_scalar (Value_float (Float_rational (rational %__expr_-3823036485969157667 %__expr_-8085216922850384227)))))) +(let %__expr_3134672938439589730 (NDArray___setitem__ %__expr_-6293504624159906607 (IndexKey_ndarray (NDArray___eq__ %__expr_-6293504624159906607 %__expr_-3283806677371465170)) (NDArray_scalar (Value_float (Float_rational (rational %__expr_-8085216922850384227 %__expr_-8085216922850384227)))))) +(let %__expr_2615935926139764667 (TupleNDArray___getitem__ (svd (NDArray___matmul__ (NDArray_T (NDArray___mul__ (ndarray-sqrt (NDArray___mul__ (NDArray___mul__ (NDArray_scalar (Value_int %__expr_-3520630818915629594)) %__expr_-5209865760313326585) (NDArray_scalar (Value_float (Float_rational (rational %__expr_-8085216922850384227 2)))))) (NDArray_T (NDArray___sub__ %__expr_2924140249920978521 (NDArray___matmul__ %__expr_-5209865760313326585 %__expr_2924140249920978521))))) (NDArray___truediv__ (NDArray_T (NDArray___truediv__ (NDArray___getitem__ (TupleNDArray___getitem__ %__expr_-7715872950595615314 %__expr_2305922367412063525) (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_slice %__expr_6749312899897339687) %__expr_-8637348939342624324)))) %__expr_3134672938439589730)) (NDArray___getitem__ %__expr_-5507881356079575778 (IndexKey_slice %__expr_6749312899897339687)))) %__expr_6185990579165616281) %__expr_3300329792522185471)) +(let %__expr_-3749619018425312853 2) +(let %__expr_-4464433185064523998 (svd (NDArray___matmul__ (NDArray_T (NDArray___mul__ (ndarray-sqrt (NDArray___mul__ (NDArray___mul__ (NDArray_scalar (Value_int %__expr_-3520630818915629594)) %__expr_-5209865760313326585) (NDArray_scalar (Value_float (Float_rational (rational %__expr_-8085216922850384227 2)))))) (NDArray_T (NDArray___sub__ %__expr_2924140249920978521 (NDArray___matmul__ %__expr_-5209865760313326585 %__expr_2924140249920978521))))) (NDArray___truediv__ (NDArray_T (NDArray___truediv__ (NDArray___getitem__ (TupleNDArray___getitem__ %__expr_-7715872950595615314 %__expr_2305922367412063525) (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_slice %__expr_6749312899897339687) %__expr_-8637348939342624324)))) %__expr_3134672938439589730)) (NDArray___getitem__ %__expr_-5507881356079575778 (IndexKey_slice %__expr_6749312899897339687)))) %__expr_6185990579165616281)) +(let %__expr_8528844779137627870 (NDArray___eq__ (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of %__expr_-3520630818915629594))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) (NDArray_scalar %__expr_-6765600943420531488))) +(let %__expr_4447619498771141281 (NDArray___matmul__ %__expr_-5209865760313326585 %__expr_2924140249920978521)) +(let %__expr_-2753571644920605745 (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))) +(let %__expr_3259058749987290790 (assume_dtype (NDArray_var "y") (DType_int64))) +(let %__expr_-6562228218073754698 (NDArray___truediv__ (NDArray_T (NDArray___truediv__ (NDArray___getitem__ (TupleNDArray___getitem__ %__expr_-7715872950595615314 %__expr_2305922367412063525) (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of (MultiAxisIndexKeyItem_slice %__expr_6749312899897339687) %__expr_-8637348939342624324)))) %__expr_3134672938439589730)) (NDArray___getitem__ %__expr_-5507881356079575778 (IndexKey_slice %__expr_6749312899897339687)))) +(let %__expr_-1580149342035447281 0) +(sort Program) +(function Program_compile (Program i64) Unit :default ()) +(function ndarray_function_two_program (NDArray NDArray NDArray) Program) +(Program_compile (ndarray_function_two_program (NDArray___getitem__ (NDArray___matmul__ (NDArray___sub__ %__expr_978886785202701864 %__expr_4447619498771141281) (NDArray___matmul__ %__expr_-6562228218073754698 (NDArray___getitem__ (NDArray_T (TupleNDArray___getitem__ %__expr_-4464433185064523998 %__expr_2305922367412063525)) (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of %__expr_-8637348939342624324 (MultiAxisIndexKeyItem_slice (Slice___init__ %__expr_-143818766793636568 (OptionalInt_some (Value_to_int (NDArray_to_value (sum (astype (NDArray___gt__ %__expr_2615935926139764667 (NDArray___mul__ %__expr_-4180228001421012884 (NDArray___getitem__ %__expr_2615935926139764667 %__expr_4326809257670680665))) %__expr_-3501279694271260104) %__expr_5981948135265815040)))) %__expr_-143818766793636568)))))))) (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of %__expr_-8637348939342624324 (MultiAxisIndexKeyItem_slice (Slice___init__ %__expr_-143818766793636568 (OptionalInt_some %__expr_2305922367412063525) %__expr_-143818766793636568)))))) (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") (DType_float64)) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2))))))) %__expr_-1580149342035447281) +(ruleset array_api_program_gen_ruleset) +(function Program_function_two (Program Program Program String) Program) +(function ndarray_program (NDArray) Program) +(rewrite (ndarray_function_two_program res l r) (Program_function_two (ndarray_program res) (ndarray_program l) (ndarray_program r) "__fn") :ruleset array_api_program_gen_ruleset) +(function Program___init__ (String bool) Program) +(rewrite (ndarray_program (NDArray_var s)) (Program___init__ s true) :ruleset array_api_program_gen_ruleset) +(function Program_statement (Program Program) Program :unextractable) +(function Program___add__ (Program Program) Program) +(function dtype_program (DType) Program) +(rewrite (ndarray_program (assume_dtype z dtype)) (Program_statement (ndarray_program z) (Program___add__ (Program___add__ (Program___add__ (Program___init__ "assert " false) (ndarray_program z)) (Program___init__ ".dtype == " false)) (dtype_program dtype))) :ruleset array_api_program_gen_ruleset) +(function tuple_int_program (TupleInt) Program) +(rewrite (ndarray_program (assume_shape z ti)) (Program_statement (ndarray_program z) (Program___add__ (Program___add__ (Program___add__ (Program___init__ "assert " false) (ndarray_program z)) (Program___init__ ".shape == " false)) (tuple_int_program ti))) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (assume_isfinite z)) (Program_statement (ndarray_program z) (Program___add__ (Program___add__ (Program___init__ "assert np.all(np.isfinite(" false) (ndarray_program z)) (Program___init__ "))" false))) :ruleset array_api_program_gen_ruleset) +(function tuple_value_program (TupleValue) Program) +(rewrite (ndarray_program (assume_value_one_of z tv)) (Program_statement (ndarray_program z) (Program___add__ (Program___add__ (Program___add__ (Program___add__ (Program___init__ "assert set(np.unique(" false) (ndarray_program z)) (Program___init__ ")) == set(" false)) (tuple_value_program tv)) (Program___init__ ")" false))) :ruleset array_api_program_gen_ruleset) +(function Program_assign (Program) Program) +(rewrite (ndarray_program (reshape y ti ob)) (Program_assign (Program___add__ (Program___add__ (Program___add__ (ndarray_program y) (Program___init__ ".reshape(" false)) (tuple_int_program ti)) (Program___init__ ")" false))) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (astype y dtype)) (Program_assign (Program___add__ (Program___add__ (Program___add__ (ndarray_program y) (Program___init__ ".astype(" false)) (dtype_program dtype)) (Program___init__ ")" false))) :ruleset array_api_program_gen_ruleset) +(function tuple_ndarray_program (TupleNDArray) Program) +(rewrite (tuple_ndarray_program (unique_counts x)) (Program_assign (Program___add__ (Program___add__ (Program___init__ "np.unique(" false) (ndarray_program x)) (Program___init__ ", return_counts=True)" false))) :ruleset array_api_program_gen_ruleset) +(rewrite (tuple_ndarray_program (unique_inverse x)) (Program_assign (Program___add__ (Program___add__ (Program___init__ "np.unique(" false) (ndarray_program x)) (Program___init__ ", return_inverse=True)" false))) :ruleset array_api_program_gen_ruleset) +(function int_program (Int) Program) +(rewrite (ndarray_program (TupleNDArray___getitem__ tnd i)) (Program___add__ (Program___add__ (Program___add__ (tuple_ndarray_program tnd) (Program___init__ "[" false)) (int_program i)) (Program___init__ "]" false)) :ruleset array_api_program_gen_ruleset) +(function value_program (Value) Program) +(rewrite (ndarray_program (NDArray_scalar v)) (Program___add__ (Program___add__ (Program___init__ "np.array(" false) (value_program v)) (Program___init__ ")" false)) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (zeros ti %__expr_2091604061025500396 optional_device_)) (Program_assign (Program___add__ (Program___add__ (Program___init__ "np.zeros(" false) (tuple_int_program ti)) (Program___init__ ")" false))) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (zeros ti (OptionalDType_some dtype) optional_device_)) (Program_assign (Program___add__ (Program___add__ (Program___add__ (Program___add__ (Program___init__ "np.zeros(" false) (tuple_int_program ti)) (Program___init__ ", dtype=" false)) (dtype_program dtype)) (Program___init__ ")" false))) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (unique_values x)) (Program_assign (Program___add__ (Program___add__ (Program___init__ "np.unique(" false) (ndarray_program x)) (Program___init__ ")" false))) :ruleset array_api_program_gen_ruleset) +(function NDArray___add__ (NDArray NDArray) NDArray) +(rewrite (ndarray_program (NDArray___add__ x y)) (Program_assign (Program___add__ (Program___add__ (ndarray_program x) (Program___init__ " + " false)) (ndarray_program y))) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (NDArray___sub__ x y)) (Program_assign (Program___add__ (Program___add__ (ndarray_program x) (Program___init__ " - " false)) (ndarray_program y))) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (NDArray___mul__ x y)) (Program_assign (Program___add__ (Program___add__ (ndarray_program x) (Program___init__ " * " false)) (ndarray_program y))) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (NDArray___truediv__ x y)) (Program_assign (Program___add__ (Program___add__ (ndarray_program x) (Program___init__ " / " false)) (ndarray_program y))) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (NDArray___lt__ x y)) (Program_assign (Program___add__ (Program___add__ (ndarray_program x) (Program___init__ " < " false)) (ndarray_program y))) :ruleset array_api_program_gen_ruleset) +(function NDArray___le__ (NDArray NDArray) NDArray) +(rewrite (ndarray_program (NDArray___le__ x y)) (Program_assign (Program___add__ (Program___add__ (ndarray_program x) (Program___init__ " <= " false)) (ndarray_program y))) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (NDArray___gt__ x y)) (Program_assign (Program___add__ (Program___add__ (ndarray_program x) (Program___init__ " > " false)) (ndarray_program y))) :ruleset array_api_program_gen_ruleset) +(function NDArray___ge__ (NDArray NDArray) NDArray) +(rewrite (ndarray_program (NDArray___ge__ x y)) (Program_assign (Program___add__ (Program___add__ (ndarray_program x) (Program___init__ " >= " false)) (ndarray_program y))) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (NDArray___eq__ x y)) (Program_assign (Program___add__ (Program___add__ (ndarray_program x) (Program___init__ " == " false)) (ndarray_program y))) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (NDArray___matmul__ x y)) (Program_assign (Program___add__ (Program___add__ (ndarray_program x) (Program___init__ " @ " false)) (ndarray_program y))) :ruleset array_api_program_gen_ruleset) +(function NDArray___mod__ (NDArray NDArray) NDArray) +(rewrite (ndarray_program (NDArray___mod__ x y)) (Program_assign (Program___add__ (Program___add__ (ndarray_program x) (Program___init__ " % " false)) (ndarray_program y))) :ruleset array_api_program_gen_ruleset) +(function NDArray___and__ (NDArray NDArray) NDArray) +(rewrite (ndarray_program (NDArray___and__ x y)) (Program_assign (Program___add__ (Program___add__ (ndarray_program x) (Program___init__ " & " false)) (ndarray_program y))) :ruleset array_api_program_gen_ruleset) +(function NDArray___or__ (NDArray NDArray) NDArray) +(rewrite (ndarray_program (NDArray___or__ x y)) (Program_assign (Program___add__ (Program___add__ (ndarray_program x) (Program___init__ " | " false)) (ndarray_program y))) :ruleset array_api_program_gen_ruleset) +(function NDArray___xor__ (NDArray NDArray) NDArray) +(rewrite (ndarray_program (NDArray___xor__ x y)) (Program_assign (Program___add__ (Program___add__ (ndarray_program x) (Program___init__ " ^ " false)) (ndarray_program y))) :ruleset array_api_program_gen_ruleset) +(function NDArray___lshift__ (NDArray NDArray) NDArray) +(rewrite (ndarray_program (NDArray___lshift__ x y)) (Program_assign (Program___add__ (Program___add__ (ndarray_program x) (Program___init__ " << " false)) (ndarray_program y))) :ruleset array_api_program_gen_ruleset) +(function NDArray___rshift__ (NDArray NDArray) NDArray) +(rewrite (ndarray_program (NDArray___rshift__ x y)) (Program_assign (Program___add__ (Program___add__ (ndarray_program x) (Program___init__ " >> " false)) (ndarray_program y))) :ruleset array_api_program_gen_ruleset) +(function NDArray___floordiv__ (NDArray NDArray) NDArray) +(rewrite (ndarray_program (NDArray___floordiv__ x y)) (Program_assign (Program___add__ (Program___add__ (ndarray_program x) (Program___init__ " // " false)) (ndarray_program y))) :ruleset array_api_program_gen_ruleset) +(function NDArray___pow__ (NDArray NDArray) NDArray) +(rewrite (ndarray_program (NDArray___pow__ x y)) (Program_assign (Program___add__ (Program___add__ (ndarray_program x) (Program___init__ " ** " false)) (ndarray_program y))) :ruleset array_api_program_gen_ruleset) +(function index_key_program (IndexKey) Program) +(rewrite (ndarray_program (NDArray___setitem__ x idx y)) (Program_statement (Program_assign (ndarray_program x)) (Program___add__ (Program___add__ (Program___add__ (Program___add__ (Program_assign (ndarray_program x)) (Program___init__ "[" false)) (index_key_program idx)) (Program___init__ "] = " false)) (ndarray_program y))) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (NDArray___getitem__ x idx)) (Program___add__ (Program___add__ (Program___add__ (ndarray_program x) (Program___init__ "[" false)) (index_key_program idx)) (Program___init__ "]" false)) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (square x)) (Program_assign (Program___add__ (Program___add__ (Program___init__ "np.square(" false) (ndarray_program x)) (Program___init__ ")" false))) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (expand_dims x i)) (Program_assign (Program___add__ (Program___add__ (Program___add__ (Program___add__ (Program___init__ "np.expand_dims(" false) (ndarray_program x)) (Program___init__ ", " false)) (int_program i)) (Program___init__ ")" false))) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (mean x %__expr_5981948135265815040 %__expr_6185990579165616281)) (Program_assign (Program___add__ (Program___add__ (Program___init__ "np.mean(" false) (ndarray_program x)) (Program___init__ ")" false))) :ruleset array_api_program_gen_ruleset) +(function int_or_tuple_program (IntOrTuple) Program) +(rewrite (ndarray_program (mean x (OptionalIntOrTuple_some int_or_tuple_) %__expr_6185990579165616281)) (Program_assign (Program___add__ (Program___add__ (Program___add__ (Program___add__ (Program___init__ "np.mean(" false) (ndarray_program x)) (Program___init__ ", axis=" false)) (int_or_tuple_program int_or_tuple_)) (Program___init__ ")" false))) :ruleset array_api_program_gen_ruleset) +(rewrite 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(ndarray_program (NDArray_vector tv)) (Program___add__ (Program___add__ (Program___init__ "np.array(" false) (tuple_value_program tv)) (Program___init__ ")" false)) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (std x %__expr_5981948135265815040)) (Program_assign (Program___add__ (Program___add__ (Program___init__ "np.std(" false) (ndarray_program x)) (Program___init__ ")" false))) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (std x (OptionalIntOrTuple_some int_or_tuple_))) (Program_assign (Program___add__ (Program___add__ (Program___add__ (Program___add__ (Program___init__ "np.std(" false) (ndarray_program x)) (Program___init__ ", axis=" false)) (int_or_tuple_program int_or_tuple_)) (Program___init__ ")" false))) :ruleset array_api_program_gen_ruleset) +(rewrite (tuple_ndarray_program (svd x (TRUE))) (Program_assign (Program___add__ (Program___add__ (Program___init__ "np.linalg.svd(" false) (ndarray_program x)) (Program___init__ ")" false))) :ruleset array_api_program_gen_ruleset) +(rewrite (tuple_ndarray_program (svd x %__expr_6185990579165616281)) (Program_assign (Program___add__ (Program___add__ (Program___init__ "np.linalg.svd(" false) (ndarray_program x)) (Program___init__ ", full_matrices=False)" false))) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (ndarray-sqrt x)) (Program_assign (Program___add__ (Program___add__ (Program___init__ "np.sqrt(" false) (ndarray_program x)) (Program___init__ ")" false))) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (NDArray_T x)) (Program___add__ (ndarray_program x) (Program___init__ ".T" false)) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (sum x (OptionalIntOrTuple_none))) (Program_assign (Program___add__ (Program___add__ (Program___init__ "np.sum(" false) (ndarray_program x)) (Program___init__ ")" false))) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (sum x (OptionalIntOrTuple_some int_or_tuple_))) (Program_assign (Program___add__ (Program___add__ (Program___add__ (Program___add__ (Program___init__ "np.sum(" false) (ndarray_program x)) (Program___init__ ", axis=" false)) (int_or_tuple_program int_or_tuple_)) (Program___init__ ")" false))) :ruleset array_api_program_gen_ruleset) +(rewrite (tuple_int_program (NDArray_shape x)) (Program___add__ (ndarray_program x) (Program___init__ ".shape" false)) :ruleset array_api_program_gen_ruleset) +(rewrite (ndarray_program (ndarray-abs x)) (Program_assign (Program___add__ (Program___add__ (Program___init__ "np.abs(" false) (ndarray_program x)) (Program___init__ ")" false))) :ruleset array_api_program_gen_ruleset) +(function optional_int_or_tuple_program (OptionalIntOrTuple) Program) +(rewrite (optional_int_or_tuple_program (OptionalIntOrTuple_some it)) (int_or_tuple_program it) :ruleset array_api_program_gen_ruleset) +(rewrite (optional_int_or_tuple_program %__expr_5981948135265815040) (Program___init__ "None" false) :ruleset array_api_program_gen_ruleset) +(rewrite (int_or_tuple_program (IntOrTuple_int x)) (int_program x) :ruleset array_api_program_gen_ruleset) +(function IntOrTuple_tuple (TupleInt) IntOrTuple) +(rewrite (int_or_tuple_program (IntOrTuple_tuple t)) (tuple_int_program t) :ruleset array_api_program_gen_ruleset) +(function IndexKey_ELLIPSIS () IndexKey) +(rewrite (index_key_program (IndexKey_ELLIPSIS)) (Program___init__ "..." false) :ruleset array_api_program_gen_ruleset) +(rewrite (index_key_program (IndexKey_int i)) (int_program i) :ruleset array_api_program_gen_ruleset) +(function slice_program (Slice) Program) +(rewrite (index_key_program (IndexKey_slice s)) (slice_program s) :ruleset array_api_program_gen_ruleset) +(function multi_axis_index_key_program (MultiAxisIndexKey) Program) +(rewrite (index_key_program (IndexKey_multi_axis key)) (multi_axis_index_key_program key) :ruleset array_api_program_gen_ruleset) +(rewrite (index_key_program (IndexKey_ndarray a)) (ndarray_program a) :ruleset array_api_program_gen_ruleset) +(sort UnstableFn_MultiAxisIndexKeyItem_Int (UnstableFn (Int) MultiAxisIndexKeyItem)) +(function idx_fn-UnstableFn_MultiAxisIndexKeyItem_Int_i-Int__unstable-app_idx_fn__Int___add___i__Int___init___1___ (UnstableFn_MultiAxisIndexKeyItem_Int Int) MultiAxisIndexKeyItem) +(rewrite (idx_fn-UnstableFn_MultiAxisIndexKeyItem_Int_i-Int__unstable-app_idx_fn__Int___add___i__Int___init___1___ idx_fn i) (unstable-app idx_fn (Int___add__ i (Int___init__ 1))) :ruleset array_api_program_gen_ruleset) +(function MultiAxisIndexKey___init__ (Int UnstableFn_MultiAxisIndexKeyItem_Int) MultiAxisIndexKey) +(rewrite (multi_axis_index_key_program (MultiAxisIndexKey___init__ %__expr_-7942988945600443502 idx_fn)) (Program___init__ "" false) :ruleset array_api_program_gen_ruleset) +(function multi_axis_index_key_item_program (MultiAxisIndexKeyItem) Program) +(rewrite (multi_axis_index_key_program (MultiAxisIndexKey___init__ (Int___init__ k) idx_fn)) (Program___add__ 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(Program___add__ p1 p2)) + (= (Program_parent p1) p) + (!= (Program_parent p2) p) + (= s1 (Program_statements p1)) + (= i (Program_next_sym p1))) + ((set (Program_statements p) s1) + (set (Program_next_sym p) i)) + :ruleset program_gen_ruleset ) +(rule ((= p (Program___add__ p1 p2)) + (= (Program_parent p2) p) + (!= (Program_parent p1) p) + (= s2 (Program_statements p2)) + (= i (Program_next_sym p2))) + ((set (Program_statements p) s2) + (set (Program_next_sym p) i)) + :ruleset program_gen_ruleset ) +(rule ((= p (Program_assign p1)) + (Program_compile p i)) + ((set (Program_parent p1) p) + (set (Program_is_identifer p) true)) + :ruleset program_gen_ruleset ) +(rule ((= p (Program_assign p1)) + (Program_compile p i) + (= (Program_parent p1) p)) + ((Program_compile p1 i)) + :ruleset program_gen_ruleset ) +(rule ((= p (Program_assign p1)) + (= (Program_parent p1) p) + (= s1 (Program_statements p1)) + (= i (Program_next_sym p1)) + (= s2 (Program_expr p1)) + (= (Program_is_identifer p1) false)) + ((set (Program_statements p) (+ s1 (+ "_" (to-string i)) " = " s2 " +")) + (set (Program_expr p) (+ "_" (to-string i))) + (set (Program_next_sym p) (+ i %__expr_-8085216922850384227))) + :ruleset program_gen_ruleset ) +(rule ((= p (Program_assign p1)) + (!= (Program_parent p1) p) + (Program_compile p i) + (= s2 (Program_expr p1)) + (= (Program_is_identifer p1) false)) + ((set (Program_statements p) (+ (+ "_" (to-string i)) " = " s2 " +")) + (set (Program_expr p) (+ "_" (to-string i))) + (set (Program_next_sym p) (+ i %__expr_-8085216922850384227))) + :ruleset program_gen_ruleset ) +(rule ((= p (Program_assign p1)) + (= (Program_parent p1) p) + (= s1 (Program_statements p1)) + (= i (Program_next_sym p1)) + (= s2 (Program_expr p1)) + (= (Program_is_identifer p1) true)) + ((set (Program_statements p) s1) + (set (Program_expr p) s2) + (set (Program_next_sym p) i)) + :ruleset program_gen_ruleset ) +(rule ((= p (Program_assign p1)) + (!= (Program_parent p1) p) + (Program_compile p i) + (= s2 (Program_expr p1)) + (= (Program_is_identifer p1) true)) + ((set (Program_statements p) "") + (set (Program_expr p) s2) + (set (Program_next_sym p) i)) + :ruleset program_gen_ruleset ) +(rule ((= p (Program_function_two p1 p2 p3 s1)) + (Program_compile p i)) + ((set (Program_parent p2) p) + (set (Program_parent p3) p) + (set (Program_parent p1) p) + (Program_compile p2 i) + (Program_compile p3 i) + (Program_compile p1 i) + (set (Program_is_identifer p) true)) + :ruleset program_gen_ruleset ) +(rule ((= p (Program_function_two p1 p2 p3 s1)) + (Program_compile p i) + (= s2 (Program_expr p1)) + (= s3 (Program_statements p1)) + (= s4 (Program_expr p2)) + (= s5 (Program_expr p3))) + ((set (Program_statements p) (+ "def " s1 "(" s4 ", " s5 "): + " (replace s3 " +" " + ") "return " s2 " +")) + (set (Program_next_sym p) i) + (set (Program_expr p) s1)) + :ruleset program_gen_ruleset ) +(run-schedule (seq (saturate (run array_api_program_gen_ruleset)) (saturate (run program_gen_ruleset)))) +(let %__expr_-116196252424162806 (assume_dtype (NDArray_var "X") (DType_float64))) +(extract (Program_statements (ndarray_function_two_program (NDArray___getitem__ (NDArray___matmul__ (NDArray___sub__ %__expr_978886785202701864 %__expr_4447619498771141281) (NDArray___matmul__ %__expr_-6562228218073754698 (NDArray___getitem__ (NDArray_T (TupleNDArray___getitem__ %__expr_-4464433185064523998 %__expr_2305922367412063525)) (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of %__expr_-8637348939342624324 (MultiAxisIndexKeyItem_slice (Slice___init__ %__expr_-143818766793636568 (OptionalInt_some (Value_to_int (NDArray_to_value (sum (astype (NDArray___gt__ %__expr_2615935926139764667 (NDArray___mul__ %__expr_-4180228001421012884 (NDArray___getitem__ %__expr_2615935926139764667 %__expr_4326809257670680665))) %__expr_-3501279694271260104) %__expr_5981948135265815040)))) %__expr_-143818766793636568)))))))) (IndexKey_multi_axis (MultiAxisIndexKey_from_vec (vec-of %__expr_-8637348939342624324 (MultiAxisIndexKeyItem_slice (Slice___init__ %__expr_-143818766793636568 (OptionalInt_some %__expr_2305922367412063525) %__expr_-143818766793636568)))))) (assume_isfinite (assume_shape (assume_dtype (NDArray_var "X") (DType_float64)) (TupleInt_from_vec (vec-of (Int___init__ 150) (Int___init__ 4))))) (assume_value_one_of (assume_shape (assume_dtype (NDArray_var "y") (DType_int64)) (TupleInt_from_vec (vec-of (Int___init__ 150)))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 0))) (TupleValue___add__ (TupleValue___init__ (Value_int (Int___init__ 1))) (TupleValue___init__ (Value_int (Int___init__ 2)))))))) 0) diff --git a/tests/rational.egg b/tests/rational.egg new file mode 100644 index 0000000..af7cae7 --- /dev/null +++ b/tests/rational.egg @@ -0,0 +1,14 @@ +; Test that can run rule matching on rational + +(datatype Pretty + (pretty-str String) + (pretty-rational Rational)) + +; This will fail with `Unbound variable x in primitive computation` currently: +; (rewrite (pretty-rational (rational x y)) (pretty-str (+ (to-string x) "/" (to-string y)))) + +(rewrite (pretty-rational r) (pretty-str (+ (to-string (numer r)) "/" (to-string (denom r))))) + +(let z (pretty-rational (rational 1 2))) +(run 1) +(check (= z (pretty-str "1/2"))) diff --git a/tests/repro-unsound-htutorial.egg b/tests/repro-unsound-htutorial.egg new file mode 100644 index 0000000..fcf1031 --- /dev/null +++ b/tests/repro-unsound-htutorial.egg @@ -0,0 +1,16 @@ +(datatype Math + (Num Rational) + (Var String) + (Add Math Math) + (Div Math Math) + (Mul Math Math)) + +(let z (Var "z")) + +(Add (Var "x") (Var "y")) + +(rewrite (Add a z) a) + +(run 2) + +(fail (check (= (Var "x") (Add (Var "x") (Var "y"))))) \ No newline at end of file diff --git a/tests/repro-unsound.egg b/tests/repro-unsound.egg new file mode 100644 index 0000000..a3127af --- /dev/null +++ b/tests/repro-unsound.egg @@ -0,0 +1,63 @@ + +(datatype HerbieType (Type String)) +(datatype Math (Num HerbieType Rational) (Var HerbieType String) (Fma HerbieType Math Math Math) (If HerbieType Math Math Math) (Less HerbieType Math Math) (LessEq HerbieType Math Math) (Greater HerbieType Math Math) (GreaterEq HerbieType Math Math) (Eq HerbieType Math Math) (NotEq HerbieType Math Math) (Add HerbieType Math Math) (Sub HerbieType Math Math) (Mul HerbieType Math Math) (Div HerbieType Math Math) (Pow HerbieType Math Math) (Atan2 HerbieType Math Math) (Hypot HerbieType Math Math) (And HerbieType Math Math) (Or HerbieType Math Math) (Not HerbieType Math) (Neg HerbieType Math) (Sqrt HerbieType Math) (Cbrt HerbieType Math) (Fabs HerbieType Math) (Ceil HerbieType Math) (Floor HerbieType Math) (Round HerbieType Math) (Log HerbieType Math) (Exp HerbieType Math) (Sin HerbieType Math) (Cos HerbieType Math) (Tan HerbieType Math) (Atan HerbieType Math) (Asin HerbieType Math) (Acos HerbieType Math) (Expm1 HerbieType Math) (Log1p HerbieType Math) (Sinh HerbieType Math) (Cosh HerbieType Math) (Tanh HerbieType Math) (PI HerbieType) (E HerbieType) (INFINITY HerbieType) (TRUE HerbieType) (FALSE HerbieType)) +(let r-zero (rational 0 1)) +(let r-one (rational 1 1)) +(let r-two (rational 2 1)) +(let r-three (rational 3 1)) +(let r-four (rational 4 1)) +(let r-neg-one (rational -1 1)) +(relation universe (Math HerbieType)) +(rule ((= t (Expm1 ty a))) ((universe t ty))) +(rewrite (Mul ty a b) (Mul ty b a)) + +(rewrite (Sub ty x x) (Num ty r-zero)) + +(rewrite (Mul ty x (Num ty r-one)) x) + +(rewrite (Div ty x (Num ty r-one)) x) + +(rewrite (Neg ty x) (Sub ty (Num ty r-zero) x)) + +(rewrite (Neg ty x) (Mul ty (Num ty r-neg-one) x)) + +(rule ((universe t ty)) ((union t (Mul ty (Num ty r-one) t)))) + +(rewrite (Div ty (Sub ty a b) c) + (Sub ty (Div ty a c) (Div ty b c))) + + +(rewrite (Div ty (Mul ty a b) (Mul ty c d)) ;; not defined if c or d is zero + (Mul ty (Div ty a c) (Div ty b d))) + + +;; errors if a or b errors +(rewrite (Add ty a b) + (If ty + (NotEq ty (Sub ty a b) (Num ty r-zero)) ;; errors if a or b errors + (Div ty + (Sub ty (Mul ty a a) (Mul ty b b)) + (Sub ty a b)) + (Add ty a b))) + + +(rewrite (Sub ty (Div ty a b) (Div ty c d)) ;; errors when b = 0 or d = 0 + (Div ty (Sub ty (Mul ty a d) (Mul ty b c)) + (Mul ty b d))) ;; errors when b = 0 or d = 0 + + +(rewrite (Sub ty (Mul ty x y) z) + (Fma ty x y (Neg ty z))) + + +(rewrite (Expm1 ty x) + (Sub ty (Exp ty x) (Num ty r-one))) + + + + +(let eggvar1 (Div (Type "binary64") (Expm1 (Type "binary64") (Add (Type "binary64") (Var (Type "binary64") "h0") (Var (Type "binary64") "h0"))) (Expm1 (Type "binary64") (Var (Type "binary64") "h0")))) + +(run 10) + +(check (= (Num ty n) (Num ty m)) (!= n m)) diff --git a/tests/stresstest_large_expr.egg b/tests/stresstest_large_expr.egg new file mode 100644 index 0000000..63ddaa4 --- /dev/null +++ b/tests/stresstest_large_expr.egg @@ -0,0 +1,440 @@ +;; Old version of python array optimization that does not include CSE with let statements +;; serves as a benchmark for adding large expressions to egglog +(ruleset array_api_ruleset) +(sort Int) +(function cast_Callable__Int__Int___Int___lambda_i_____i_ (Int Int) Int) +(rewrite (cast_Callable__Int__Int___Int___lambda_i_____i_ __var__i __var___) __var__i :ruleset array_api_ruleset) +(sort TupleInt) +(function TupleInt_single (Int) TupleInt) +(sort UnstableFn_Int_Int (UnstableFn (Int) Int)) +(function TupleInt___init__ (Int UnstableFn_Int_Int) TupleInt) +(function Int___init__ (i64) Int) +(rewrite (TupleInt_single __var__i) (TupleInt___init__ (Int___init__ 1) (unstable-fn "cast_Callable__Int__Int___Int___lambda_i_____i_" __var__i)) :ruleset array_api_ruleset) +(function cast_Callable__Int___Int___lambda_i__i_ (Int) Int) +(rewrite (cast_Callable__Int___Int___lambda_i__i_ __var__i) __var__i :ruleset array_api_ruleset) +(function TupleInt_range (Int) TupleInt) +(rewrite (TupleInt_range __var__stop) (TupleInt___init__ __var__stop (unstable-fn "cast_Callable__Int___Int___lambda_i__i_")) :ruleset array_api_ruleset) +(sort Vec_Int (Vec Int)) +(function TupleInt_from_vec (Vec_Int) TupleInt) +(function index_vec_int (Vec_Int Int) Int) +(rewrite (TupleInt_from_vec __var__vec) (TupleInt___init__ (Int___init__ (vec-length __var__vec)) (unstable-fn "index_vec_int" __var__vec)) :ruleset array_api_ruleset) +(function cast_Callable__TupleInt__TupleInt__Int___Int___lambda_other__self__i__Int_if__i_<_self_length____self_i___other_i_-_self_length_____ (TupleInt TupleInt Int) Int) +(sort Boolean) +(function Int_if_ (Boolean Int Int) Int) +(function Int___lt__ (Int Int) Boolean) +(function TupleInt_length (TupleInt) Int) +(function TupleInt___getitem__ (TupleInt Int) Int) +(function Int___sub__ (Int Int) Int) +(rewrite (cast_Callable__TupleInt__TupleInt__Int___Int___lambda_other__self__i__Int_if__i_<_self_length____self_i___other_i_-_self_length_____ __var__other __var__self __var__i) (Int_if_ (Int___lt__ __var__i (TupleInt_length __var__self)) (TupleInt___getitem__ __var__self __var__i) (TupleInt___getitem__ __var__other (Int___sub__ __var__i (TupleInt_length __var__self)))) :ruleset array_api_ruleset) +(function TupleInt___add__ (TupleInt TupleInt) TupleInt) +(function Int___add__ (Int Int) Int) +(rewrite (TupleInt___add__ __var__self __var__other) (TupleInt___init__ (Int___add__ (TupleInt_length __var__self) (TupleInt_length __var__other)) (unstable-fn "cast_Callable__TupleInt__TupleInt__Int___Int___lambda_other__self__i__Int_if__i_<_self_length____self_i___other_i_-_self_length_____" __var__other __var__self)) :ruleset array_api_ruleset) +(function cast_Callable__Int__Boolean__Int___Boolean___lambda_i__acc__j__acc_|__i_==_j__ (Int Boolean Int) Boolean) +(function Boolean___or__ (Boolean Boolean) Boolean) +(function Int___eq__ (Int Int) Boolean) +(rewrite (cast_Callable__Int__Boolean__Int___Boolean___lambda_i__acc__j__acc_|__i_==_j__ __var__i __var__acc __var__j) (Boolean___or__ __var__acc (Int___eq__ __var__i __var__j)) :ruleset array_api_ruleset) +(function TupleInt_contains (TupleInt Int) Boolean) +(sort UnstableFn_Boolean_Boolean_Int (UnstableFn (Boolean Int) Boolean)) +(function TupleInt_fold_boolean (TupleInt Boolean UnstableFn_Boolean_Boolean_Int) Boolean) +(function FALSE () Boolean) +(rewrite (TupleInt_contains __var__self __var__i) (TupleInt_fold_boolean __var__self (FALSE) (unstable-fn "cast_Callable__Int__Boolean__Int___Boolean___lambda_i__acc__j__acc_|__i_==_j__" __var__i)) :ruleset array_api_ruleset) +(sort NDArray) +(function NDArray_size (NDArray) Int) +(sort UnstableFn_Int_Int_Int (UnstableFn (Int Int) Int)) +(function TupleInt_fold (TupleInt Int UnstableFn_Int_Int_Int) Int) +(function NDArray_shape (NDArray) TupleInt) +(function Int___mul__ (Int Int) Int) +(rewrite (NDArray_size __var__x) (TupleInt_fold (NDArray_shape __var__x) (Int___init__ 1) (unstable-fn "Int___mul__")) :ruleset array_api_ruleset) +(function unique_values (NDArray) NDArray) +(sort TupleValue) +(function NDArray_vector (TupleValue) NDArray) +(sort Value) +(function possible_values (Value) TupleValue) +(function NDArray_index (NDArray TupleInt) Value) +(function ALL_INDICES () TupleInt) +(rewrite (unique_values __var__a) (NDArray_vector (possible_values (NDArray_index __var__a (ALL_INDICES)))) :ruleset array_api_ruleset) +(function Value_isfinite (Value) Boolean) +(function Value_int (Int) Value) +(function TRUE () Boolean) +(rewrite (Value_isfinite (Value_int __var__i)) (TRUE) :ruleset array_api_ruleset) +(function Value_bool (Boolean) Value) +(rewrite (Value_isfinite (Value_bool __var__b)) (TRUE) :ruleset array_api_ruleset) +(sort Float) +(function Value_float (Float) Value) +(function Float___init__ (f64) Float :cost 3) +(rewrite (Value_isfinite (Value_float (Float___init__ __var__f))) (TRUE) :when ((!= __var__f NaN)) :ruleset array_api_ruleset) +(function isfinite (NDArray) NDArray) +(sort OptionalIntOrTuple) +(function sum (NDArray OptionalIntOrTuple) NDArray) +(function OptionalIntOrTuple_none () OptionalIntOrTuple) +(function NDArray_scalar (Value) NDArray) +(rewrite (isfinite (sum __var__arr (OptionalIntOrTuple_none))) (NDArray_scalar (Value_bool (Value_isfinite (NDArray_index __var__arr (ALL_INDICES))))) :ruleset array_api_ruleset) +(function assume_value_one_of (NDArray TupleValue) NDArray) +(rewrite (NDArray_shape (assume_value_one_of __var__x __var__vs)) (NDArray_shape __var__x) :ruleset array_api_ruleset) +(sort DType) +(function NDArray_dtype (NDArray) DType) +(rewrite (NDArray_dtype (assume_value_one_of __var__x __var__vs)) (NDArray_dtype __var__x) :ruleset array_api_ruleset) +(rule ((= __var__v (NDArray_index (assume_value_one_of __var__x __var__vs) __var__idx))) + ((union __var__v (NDArray_index __var__x __var__idx)) + (union (possible_values __var__v) __var__vs)) + :ruleset array_api_ruleset ) +(function assume_isfinite (NDArray) NDArray) +(rewrite (NDArray_shape (assume_isfinite __var__x)) (NDArray_shape __var__x) :ruleset array_api_ruleset) +(rewrite (NDArray_dtype (assume_isfinite __var__x)) (NDArray_dtype __var__x) :ruleset array_api_ruleset) +(rewrite (NDArray_index (assume_isfinite __var__x) __var__ti) (NDArray_index __var__x __var__ti) :ruleset array_api_ruleset) +(rewrite (Value_isfinite (NDArray_index (assume_isfinite __var__x) __var__ti)) (TRUE) :ruleset array_api_ruleset) +(function assume_shape (NDArray TupleInt) NDArray) +(rewrite (NDArray_shape (assume_shape __var__x __var__shape)) __var__shape :ruleset array_api_ruleset) +(rewrite (NDArray_dtype (assume_shape __var__x __var__shape)) (NDArray_dtype __var__x) :ruleset array_api_ruleset) +(rewrite (NDArray_index (assume_shape __var__x __var__shape) __var__idx) (NDArray_index __var__x __var__idx) :ruleset array_api_ruleset) +(function assume_dtype (NDArray DType) NDArray) +(rewrite (NDArray_dtype (assume_dtype __var__x __var__dtype)) __var__dtype :ruleset array_api_ruleset) +(rewrite (NDArray_shape (assume_dtype __var__x __var__dtype)) (NDArray_shape __var__x) :ruleset array_api_ruleset) +(rewrite (NDArray_index (assume_dtype __var__x __var__dtype) __var__idx) (NDArray_index __var__x __var__idx) :ruleset array_api_ruleset) +(sort IndexKey) +(function NDArray___getitem__ (NDArray IndexKey) NDArray) +(function IndexKey_int (Int) IndexKey) +(rewrite (NDArray___getitem__ __var__x (IndexKey_int __var__i)) (NDArray_scalar (NDArray_index __var__x (TupleInt_single __var__i))) :ruleset array_api_ruleset) +(sort OptionalBool) +(function reshape (NDArray TupleInt OptionalBool) NDArray) +(rule ((= __a (reshape __var__x __var__shape __var__copy))) + ((NDArray_shape __var__x) + (TupleInt_length (NDArray_shape __var__x))) + :ruleset array_api_ruleset ) +(rule ((reshape __var__x __var__shape __var__copy)) + ((TupleInt_length __var__shape) + (TupleInt___getitem__ __var__shape (Int___init__ 0))) + :ruleset array_api_ruleset ) +(rewrite (reshape __var__x __var__shape __var__copy) __var__x :when ((= (TupleInt_length (NDArray_shape __var__x)) (Int___init__ 1)) (= (TupleInt_length __var__shape) (Int___init__ 1)) (= (TupleInt___getitem__ __var__shape (Int___init__ 0)) (Int___init__ -1))) :ruleset array_api_ruleset) +(function TupleValue_length (TupleValue) Int) +(rewrite (NDArray_shape (NDArray_vector __var__vs)) (TupleInt_single (TupleValue_length __var__vs)) :ruleset array_api_ruleset) +(function Value_dtype (Value) DType) +(function TupleValue___getitem__ (TupleValue Int) Value) +(rewrite (NDArray_dtype (NDArray_vector __var__vs)) (Value_dtype (TupleValue___getitem__ __var__vs (Int___init__ 0))) :ruleset array_api_ruleset) +(rewrite (NDArray_index (NDArray_vector __var__vs) __var__ti) (TupleValue___getitem__ __var__vs (TupleInt___getitem__ __var__ti (Int___init__ 0))) :ruleset array_api_ruleset) +(function TupleInt_EMPTY () TupleInt) +(rewrite (NDArray_shape (NDArray_scalar __var__v)) (TupleInt_EMPTY) :ruleset array_api_ruleset) +(rewrite (NDArray_dtype (NDArray_scalar __var__v)) (Value_dtype __var__v) :ruleset array_api_ruleset) +(rewrite (NDArray_index (NDArray_scalar __var__v) (TupleInt_EMPTY)) __var__v :ruleset array_api_ruleset) +(function any (NDArray) NDArray) +(function TupleValue_includes (TupleValue Value) Boolean) +(function Value_to_truthy_value (Value) Value) +(rewrite (any __var__x) (NDArray_scalar (Value_bool (TupleValue_includes (possible_values (Value_to_truthy_value (NDArray_index __var__x (ALL_INDICES)))) (Value_bool (TRUE))))) :ruleset array_api_ruleset) +(function NDArray___lt__ (NDArray NDArray) NDArray) +(function Value___lt__ (Value Value) Value) +(function broadcast_index (TupleInt TupleInt TupleInt) TupleInt) +(function broadcast_shapes (TupleInt TupleInt) TupleInt) +(rewrite (NDArray_index (NDArray___lt__ __var__x __var__y) __var__idx) (Value___lt__ (NDArray_index __var__x (broadcast_index (NDArray_shape __var__x) (broadcast_shapes (NDArray_shape __var__x) (NDArray_shape __var__y)) __var__idx)) (NDArray_index __var__y (broadcast_index (NDArray_shape __var__y) (broadcast_shapes (NDArray_shape __var__x) (NDArray_shape __var__y)) __var__idx))) :ruleset array_api_ruleset) +(function NDArray___truediv__ (NDArray NDArray) NDArray) +(function Value___truediv__ (Value Value) Value) +(rewrite (NDArray_index (NDArray___truediv__ __var__x __var__y) __var__idx) (Value___truediv__ (NDArray_index __var__x (broadcast_index (NDArray_shape __var__x) (broadcast_shapes (NDArray_shape __var__x) (NDArray_shape __var__y)) __var__idx)) (NDArray_index __var__y (broadcast_index (NDArray_shape __var__y) (broadcast_shapes (NDArray_shape __var__x) (NDArray_shape __var__y)) __var__idx))) :ruleset array_api_ruleset) +(rewrite (NDArray_index (NDArray_scalar __var__v) __var__idx) __var__v :ruleset array_api_ruleset) +(function astype (NDArray DType) NDArray) +(function Value_astype (Value DType) Value) +(rewrite (NDArray_index (astype __var__x __var__dtype) __var__idx) (Value_astype (NDArray_index __var__x __var__idx) __var__dtype) :ruleset array_api_ruleset) +(relation greater_zero (Value)) +(sort TupleNDArray) +(function 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(Value_bool (FALSE)))) + :ruleset array_api_ruleset ) +(function TupleValue___init__ (Value) TupleValue) +(rewrite (possible_values (Value_bool __var__b)) (TupleValue___init__ (Value_bool __var__b)) :ruleset array_api_ruleset) +(rule ((= __var__v1 (Value_astype __var__v __var__dtype)) + (greater_zero __var__v)) + ((greater_zero __var__v1)) + :ruleset array_api_ruleset ) +(function TupleNDArray_length (TupleNDArray) Int) +(function svd (NDArray Boolean) TupleNDArray) +(rewrite (TupleNDArray_length (svd __var__x __var__full_matrices)) (Int___init__ 3) :ruleset array_api_ruleset) +(function unique_inverse (NDArray) TupleNDArray) +(rewrite (TupleNDArray_length (unique_inverse __var__x)) (Int___init__ 2) :ruleset array_api_ruleset) +(rewrite (TupleNDArray___getitem__ (unique_inverse __var__x) (Int___init__ 0)) (unique_values __var__x) :ruleset array_api_ruleset) +(function ndarray-abs (NDArray) NDArray) +(function Float_abs (Float) Float) +(rewrite (ndarray-abs (NDArray_scalar (Value_float 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