run bench to get the actual performance of WHIR

[kunxian-xia]

We want to know the performance of WHIR for opening one multilinear polynomial with n variables where n ranges from 10 to 28.

num variables	opening proof size	opening time	committing time	number of hashes on verifier side

[yczhangsjtu]

Variables	Committing Time (ms)	Proving Time (ms)	Verification Hashes	Proof Size (Bytes)
10	1.36	2.68	237	31912
11	2.05	3.28	341	40248
12	2.94	6.53	493	49480
13	4.49	11.30	605	54536
14	4.99	12.95	740	59224
15	8.21	18.08	843	62632
16	8.80	30.60	1036	69368
17	13.82	44.37	1157	75352
18	20.53	68.38	1268	78120
19	40.35	102.29	1380	81560
20	63.63	153.70	1564	87144
21	202.33	367.83	1692	93128
22	371.10	609.17	1773	94936
23	811.78	1278.33	1887	98440
24	1330.16	2131.61	2052	102872
25	2981.23	4702.45	2171	107960
26	5122.47	7904.00	2246	109864
27	11674.42	18004.46	2371	113688
28	20534.79	31242.04	2541	118440

[chaosma]

Here are partial benchmark results on apple m3 max. When variables equal 27 or 28, the swap space might on and affect the benchmark time. Need a large memory server to run all parameters.

Reference: #10

Example:
cargo run --release --bin ceno_bench -- -m 3 -d 28

num_variables	num_polys	commit_time(ms)	open_time(ms)	num_verifier_hashes	proof_size(bytes)
10	1	4.80	3.90	232	32328
11	1	4.41	4.32	336	39224
12	1	3.58	5.24	502	49224
13	1	8.99	7.56	601	54696
14	1	5.53	8.43	734	59032
15	1	6.81	11.54	841	62856
16	1	9.68	18.19	1018	69400
17	1	16.02	28.32	1161	75192
18	1	16.43	39.86	1257	77768
19	1	39.10	63.80	1375	81400
20	1	63.31	106.76	1586	87944
21	1	121.19	215.62	1667	92328
22	1	227.03	398.07	1763	94616
23	1	493.85	721.97	1910	99176
24	1	894.40	1374.69	2056	103032
25	1	1973.32	2917.11	2143	107064
26	1	3745.77	5748.57	2246	109864
27	1	8381.26	12625.41	2361	113368
28	1	15748.18	27699.23	2552	118824
10	2	3.96	3.33	240	50920
11	2	5.46	3.97	333	58360
12	2	4.05	5.18	501	70984
13	2	7.60	7.20	603	77352
14	2	8.75	8.33	738	82040
15	2	10.44	10.00	838	84520
16	2	14.84	18.48	1048	92504
17	2	21.55	29.73	1150	96920
18	2	35.17	42.18	1271	99752
19	2	55.10	67.65	1360	102200
20	2	106.66	123.53	1564	108456
21	2	214.19	246.25	1680	113512
22	2	403.07	405.62	1783	115768
23	2	820.84	760.67	1888	118728
24	2	1485.23	1512.15	2054	122968
25	2	3339.17	3222.41	2164	127480
26	2	6399.66	6350.81	2272	130184
27	2	14216.17	13327.54	2344	132056
28	2	30634.29	28125.10	2519	136872
10	4	4.93	6.31	255	93160
11	4	7.11	4.35	329	102456
12	4	10.67	15.06	482	110856
13	4	11.00	7.80	624	122152
14	4	10.44	8.69	736	126296
15	4	14.73	10.08	847	130248
16	4	19.78	20.31	1036	136248
17	4	34.54	32.82	1162	140888
18	4	55.75	47.70	1260	142472
19	4	102.95	78.27	1372	145144
20	4	196.26	150.32	1558	150344
21	4	362.17	255.82	1688	155304
22	4	664.25	456.94	1791	157048
23	4	1418.58	937.69	1895	159464
24	4	2602.98	1834.63	2051	162808
25	4	6006.59	3773.56	2145	166360
26	4	11609.98	7363.70	2237	168040
27	4	26465.14	15911.85	2359	171000
28	4	133066.79	37068.30	2546	175624
10	8	7.23	5.41	236	150664
11	8	18.41	3.40	325	165176
12	8	13.46	5.77	507	198408
13	8	15.76	6.54	603	209384
14	8	21.80	8.72	714	212728
15	8	26.06	13.01	829	214440
16	8	34.30	20.07	1052	224824
17	8	58.25	42.73	1137	227256
18	8	95.79	64.34	1283	229352
19	8	172.38	98.26	1362	229944
20	8	357.05	173.87	1544	233896
21	8	655.29	320.42	1697	238664
22	8	1214.18	601.04	1773	238520
23	8	2703.05	1183.77	1904	240776
24	8	4959.81	2387.09	2059	243160
25	8	11372.06	4832.08	2167	246040
26	8	22154.31	9536.61	2236	245960
27	8	95331.64	24371.31	2361	247992