Add workflow to compare vm outputs for factorial on all layouts

[fmoletta]

Depends on #1651
Also Fixes:

• Recursive layout is now usable
• Add missing extra step when running in proof mode

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 97.68%. Comparing base (7566aa5) to head (0c727bb).

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #1653   +/-   ##
=======================================
  Coverage   97.68%   97.68%           
=======================================
  Files          91       91           
  Lines       37668    37689   +21     
=======================================
+ Hits        36796    36817   +21     
  Misses        872      872           

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[github-actions]

Benchmark Results for unmodified programs 🚀

Command	Mean [s]	Min [s]	Max [s]	Relative
base big_factorial	2.173 ± 0.025	2.133	2.215	1.00
head big_factorial	2.260 ± 0.053	2.198	2.364	1.04 ± 0.03

Command	Mean [s]	Min [s]	Max [s]	Relative
base big_fibonacci	2.238 ± 0.021	2.199	2.268	1.03 ± 0.02
head big_fibonacci	2.182 ± 0.045	2.132	2.284	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base blake2s_integration_benchmark	8.192 ± 0.311	7.937	9.026	1.00
head blake2s_integration_benchmark	8.538 ± 0.268	8.205	9.205	1.04 ± 0.05

Command	Mean [s]	Min [s]	Max [s]	Relative
base compare_arrays_200000	2.258 ± 0.077	2.195	2.469	1.00
head compare_arrays_200000	2.311 ± 0.023	2.274	2.345	1.02 ± 0.04

Command	Mean [s]	Min [s]	Max [s]	Relative
base dict_integration_benchmark	1.398 ± 0.016	1.371	1.422	1.00
head dict_integration_benchmark	1.458 ± 0.014	1.438	1.478	1.04 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base field_arithmetic_get_square_benchmark	1.273 ± 0.040	1.219	1.373	1.00
head field_arithmetic_get_square_benchmark	1.286 ± 0.016	1.256	1.311	1.01 ± 0.03

Command	Mean [s]	Min [s]	Max [s]	Relative
base integration_builtins	8.188 ± 0.126	8.012	8.413	1.00
head integration_builtins	8.486 ± 0.137	8.295	8.751	1.04 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base keccak_integration_benchmark	8.430 ± 0.130	8.271	8.633	1.00
head keccak_integration_benchmark	8.633 ± 0.196	8.443	9.050	1.02 ± 0.03

Command	Mean [s]	Min [s]	Max [s]	Relative
base linear_search	2.244 ± 0.023	2.215	2.288	1.00
head linear_search	2.293 ± 0.027	2.254	2.338	1.02 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_cmp_and_pow_integration_benchmark	1.507 ± 0.013	1.488	1.523	1.00
head math_cmp_and_pow_integration_benchmark	1.556 ± 0.011	1.544	1.574	1.03 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_integration_benchmark	1.385 ± 0.036	1.356	1.474	1.00
head math_integration_benchmark	1.409 ± 0.015	1.390	1.433	1.02 ± 0.03

Command	Mean [s]	Min [s]	Max [s]	Relative
base memory_integration_benchmark	1.221 ± 0.035	1.181	1.299	1.00
head memory_integration_benchmark	1.253 ± 0.015	1.236	1.288	1.03 ± 0.03

Command	Mean [s]	Min [s]	Max [s]	Relative
base operations_with_data_structures_benchmarks	1.556 ± 0.017	1.525	1.586	1.00
head operations_with_data_structures_benchmarks	1.581 ± 0.016	1.561	1.608	1.02 ± 0.02

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base pedersen	576.1 ± 7.2	566.5	586.2	1.00
head pedersen	578.9 ± 5.5	568.4	585.1	1.00 ± 0.02

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base poseidon_integration_benchmark	949.9 ± 10.8	931.3	967.8	1.00
head poseidon_integration_benchmark	973.9 ± 13.2	955.7	996.7	1.03 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base secp_integration_benchmark	1.825 ± 0.025	1.790	1.872	1.00
head secp_integration_benchmark	1.870 ± 0.039	1.818	1.933	1.03 ± 0.03

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base set_integration_benchmark	717.7 ± 2.7	711.9	720.6	1.01 ± 0.02
head set_integration_benchmark	711.8 ± 11.1	691.0	724.3	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base uint256_integration_benchmark	4.493 ± 0.079	4.394	4.630	1.00
head uint256_integration_benchmark	4.566 ± 0.055	4.504	4.695	1.02 ± 0.02

[pefontana]

Nice!
I will add the workflow to required