Zygote and ForwardDiff give different results for gradient of NonlinearSolve

**Describe the bug 🐞**

I'm getting different results from Zygote and ForwardDiff for the gradient of a simple NonlinearSolve. 

```julia
julia> using Zygote, SciMLSensitivity, NonlinearSolve, ForwardDiff

julia> function h(x,p)
           x .^2 .- p
       end
h (generic function with 1 method)

julia> r(p) = solve(NonlinearProblem(h, [1.0], p), Broyden()).u[1]
r (generic function with 1 method)

julia> r([4.0])
1.9999999999999938

julia> Zygote.gradient(r, [4.0])
([0.4999999962747082],)

julia> ForwardDiff.gradient(r, [4.0])
1-element Vector{Float64}:
 0.2500000000000008

```



**Environment (please complete the following information):**

  - Output of `using Pkg; Pkg.status()`

```julia
(jl_7Hg3KM) pkg> st
Status `/tmp/jl_7Hg3KM/Project.toml`
  [f6369f11] ForwardDiff v1.0.1
  [8913a72c] NonlinearSolve v4.8.0
  [1ed8b502] SciMLSensitivity v7.81.0
  [e88e6eb3] Zygote v0.7.7

```

  - Output of `using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)`

```julia
(jl_7Hg3KM) pkg> st -m
Status `/tmp/jl_7Hg3KM/Manifest.toml`
  [47edcb42] ADTypes v1.14.0
  [621f4979] AbstractFFTs v1.5.0
  [7d9f7c33] Accessors v0.1.42
  [79e6a3ab] Adapt v4.3.0
  [66dad0bd] AliasTables v1.1.3
  [4fba245c] ArrayInterface v7.19.0
  [4c555306] ArrayLayouts v1.11.1
  [a9b6321e] Atomix v1.1.1
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [70df07ce] BracketingNonlinearSolve v1.2.0
  [fa961155] CEnum v0.5.0
  [2a0fbf3d] CPUSummary v0.2.6
  [7057c7e9] Cassette v0.3.14
  [082447d4] ChainRules v1.72.3
  [d360d2e6] ChainRulesCore v1.25.1
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.16.0
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [187b0558] ConstructionBase v1.5.8
  [adafc99b] CpuId v0.3.1
  [a8cc5b0e] Crayons v4.1.1
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.22
  [e2d170a0] DataValueInterfaces v1.0.0
  [2b5f629d] DiffEqBase v6.174.0
  [459566f4] DiffEqCallbacks v4.6.0
  [77a26b50] DiffEqNoiseProcess v5.24.1
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
⌅ [a0c0ee7d] DifferentiationInterface v0.6.54
  [31c24e10] Distributions v0.25.120
  [ffbed154] DocStringExtensions v0.9.4
  [4e289a0a] EnumX v1.0.5
  [7da242da] Enzyme v0.13.44
  [f151be2c] EnzymeCore v0.8.8
  [e2ba6199] ExprTools v0.1.10
  [55351af7] ExproniconLite v0.10.14
  [7034ab61] FastBroadcast v0.3.5
  [9aa1b823] FastClosures v0.3.2
  [a4df4552] FastPower v1.1.2
  [1a297f60] FillArrays v1.13.0
  [6a86dc24] FiniteDiff v2.27.0
  [f6369f11] ForwardDiff v1.0.1
  [f62d2435] FunctionProperties v0.1.2
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [d9f16b24] Functors v0.5.2
  [46192b85] GPUArraysCore v0.2.0
  [61eb1bfa] GPUCompiler v1.5.0
  [076d061b] HashArrayMappedTries v0.2.0
  [34004b35] HypergeometricFunctions v0.3.28
  [7869d1d1] IRTools v0.4.14
  [615f187c] IfElse v0.1.1
  [3587e190] InverseFunctions v0.1.17
  [92d709cd] IrrationalConstants v0.2.4
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.7.0
  [ae98c720] Jieko v0.2.1
  [63c18a36] KernelAbstractions v0.9.34
  [ba0b0d4f] Krylov v0.10.1
  [929cbde3] LLVM v9.4.0
  [b964fa9f] LaTeXStrings v1.4.0
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.6.1
  [87fe0de2] LineSearch v0.1.4
  [d3d80556] LineSearches v7.3.0
  [7ed4a6bd] LinearSolve v3.14.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [1914dd2f] MacroTools v0.5.16
  [d125e4d3] ManualMemory v0.1.8
  [bb5d69b7] MaybeInplace v0.1.4
  [e1d29d7a] Missings v1.2.0
  [2e0e35c7] Moshi v0.3.5
  [46d2c3a1] MuladdMacro v0.2.4
  [d41bc354] NLSolversBase v7.9.1
  [872c559c] NNlib v0.9.30
  [77ba4419] NaNMath v1.1.3
  [8913a72c] NonlinearSolve v4.8.0
  [be0214bd] NonlinearSolveBase v1.9.0
  [5959db7a] NonlinearSolveFirstOrder v1.5.0
  [9a2c21bd] NonlinearSolveQuasiNewton v1.5.0
  [26075421] NonlinearSolveSpectralMethods v1.2.0
  [d8793406] ObjectFile v0.4.4
  [429524aa] Optim v1.12.0
  [3bd65402] Optimisers v0.4.6
  [bac558e1] OrderedCollections v1.8.0
  [bbf590c4] OrdinaryDiffEqCore v1.26.0
  [90014a1f] PDMats v0.11.35
  [d96e819e] Parameters v0.12.3
  [e409e4f3] PoissonRandom v0.4.4
  [f517fe37] Polyester v0.7.17
  [1d0040c9] PolyesterWeave v0.2.2
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.27
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [08abe8d2] PrettyTables v2.4.0
  [43287f4e] PtrArrays v1.3.0
  [1fd47b50] QuadGK v2.11.2
  [74087812] Random123 v1.7.1
  [e6cf234a] RandomNumbers v1.6.0
  [c1ae055f] RealDot v0.1.0
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.33.0
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.1
  [ae5879a3] ResettableStacks v1.1.1
  [37e2e3b7] ReverseDiff v1.16.1
  [79098fc4] Rmath v0.8.0
  [7e49a35a] RuntimeGeneratedFunctions v0.5.14
  [94e857df] SIMDTypes v0.1.0
  [0bca4576] SciMLBase v2.92.0
  [19f34311] SciMLJacobianOperators v0.1.5
⌅ [c0aeaf25] SciMLOperators v0.4.0
  [1ed8b502] SciMLSensitivity v7.81.0
  [53ae85a6] SciMLStructures v1.7.0
  [7e506255] ScopedValues v1.3.0
  [6c6a2e73] Scratch v1.2.1
  [efcf1570] Setfield v1.1.2
  [727e6d20] SimpleNonlinearSolve v2.5.0
  [ce78b400] SimpleUnPack v1.1.0
  [a2af1166] SortingAlgorithms v1.2.1
  [dc90abb0] SparseInverseSubset v0.1.2
  [0a514795] SparseMatrixColorings v0.4.19
  [276daf66] SpecialFunctions v2.5.1
  [aedffcd0] Static v1.2.0
  [0d7ed370] StaticArrayInterface v1.8.0
  [90137ffa] StaticArrays v1.9.13
  [1e83bf80] StaticArraysCore v1.4.3
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.7.0
  [2913bbd2] StatsBase v0.34.5
  [4c63d2b9] StatsFuns v1.5.0
  [7792a7ef] StrideArraysCore v0.5.7
  [892a3eda] StringManipulation v0.4.1
  [09ab397b] StructArrays v0.7.1
  [53d494c1] StructIO v0.3.1
  [2efcf032] SymbolicIndexingInterface v0.3.40
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
  [8290d209] ThreadingUtilities v0.5.3
  [a759f4b9] TimerOutputs v0.5.28
  [9f7883ad] Tracker v0.2.38
  [e689c965] Tracy v0.1.4
  [781d530d] TruncatedStacktraces v1.4.0
  [3a884ed6] UnPack v1.0.2
  [013be700] UnsafeAtomics v0.3.0
  [e88e6eb3] Zygote v0.7.7
  [700de1a5] ZygoteRules v0.2.7
  [7cc45869] Enzyme_jll v0.0.180+0
  [1d5cc7b8] IntelOpenMP_jll v2025.0.4+0
  [dad2f222] LLVMExtra_jll v0.0.36+0
  [ad6e5548] LibTracyClient_jll v0.9.1+6
  [856f044c] MKL_jll v2025.0.1+1
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [f50d1b31] Rmath_jll v0.5.1+0
  [1317d2d5] oneTBB_jll v2022.0.0+0
  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 v1.11.0
  [ade2ca70] Dates v1.11.0
  [8ba89e20] Distributed v1.11.0
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching v1.11.0
  [9fa8497b] Future v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.11.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.11.0
  [de0858da] Printf v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [deac9b47] LibCURL_jll v8.6.0+0
  [e37daf67] LibGit2_jll v1.7.2+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.6+0
  [14a3606d] MozillaCACerts_jll v2023.12.12
  [4536629a] OpenBLAS_jll v0.3.27+1
  [05823500] OpenLibm_jll v0.8.1+2
  [bea87d4a] SuiteSparse_jll v7.7.0+0
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.11.0+0
  [8e850ede] nghttp2_jll v1.59.0+0
  [3f19e933] p7zip_jll v17.4.0+2

```

  - Output of `versioninfo()`

```julia
julia> versioninfo()
Julia Version 1.11.3
Commit d63adeda50d (2025-01-21 19:42 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 16 × AMD Ryzen 7 6800U with Radeon Graphics
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 16 virtual cores)

```
@ChrisRackauckas @DhairyaLGandhi 

These lines: https://github.com/SciML/SciMLSensitivity.jl/blob/a5290392febeb4c54f817239e5fbad600e319f0e/src/concrete_solve.jl#L1805-L1819

end up essentially adding `dp` to itself in this case. `Δtunables` ends up just being `dp` which then gets added to `dp`.  I have a feeling that if `Δ.prob.p` is empty `Δp` should be as well? But that's not what happens. 


	dp, Δtunables = if isscimlstructure(p)
	Δp = setproperties(dp, to_nt(Δ.prob.p))
	Δtunables, _, _ = canonicalize(Tunable(), Δp)
	dp, _, _ = canonicalize(Tunable(), dp)
	dp, Δtunables
	elseif isfunctor(p)
	dp, _ = Functors.functor(dp)
	Δtunables, _ = Functors.functor(Δ.prob.p)
	dp, Δtunables
	else
	dp, Δ.prob.p
	end
	end

	dp = Zygote.accum(dp, (isnothing(Δtunables) \|\| isempty(Δtunables)) ? nothing : Δtunables)

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Zygote and ForwardDiff give different results for gradient of NonlinearSolve #1210

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Zygote and ForwardDiff give different results for gradient of NonlinearSolve #1210

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