feat(hints): Add alternative hint string for nondet_bigint3

[fmoletta]

Description

Description of the pull request changes and motivation.

Checklist

• Linked to Github Issue
• Unit tests added
• Integration tests added.
• This change requires new documentation.
  • Documentation has been added/updated.
  • CHANGELOG has been updated.

[codecov]

Codecov Report

Merging #1071 (23accf8) into main (327ee7d) will not change coverage.
The diff coverage is 100.00%.

@@           Coverage Diff           @@
##             main    #1071   +/-   ##
=======================================
  Coverage   98.09%   98.09%           
=======================================
  Files          84       84           
  Lines       33837    33837           
=======================================
  Hits        33192    33192           
  Misses        645      645           

Impacted Files	Coverage Δ
...int_processor/builtin_hint_processor_definition.rs	98.99% <100.00%> (ø)

📣 We’re building smart automated test selection to slash your CI/CD build times. Learn more

[github-actions]

Benchmark Results for unmodified programs 🚀

Command	Mean [s]	Min [s]	Max [s]	Relative
base blake2s_integration_benchmark	3.689 ± 0.072	3.603	3.843	1.00
head blake2s_integration_benchmark	3.691 ± 0.050	3.647	3.776	1.00 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base compare_arrays_200000	4.388 ± 0.056	4.299	4.492	1.00 ± 0.02
head compare_arrays_200000	4.385 ± 0.037	4.344	4.459	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base dict_integration_benchmark	3.328 ± 0.026	3.295	3.381	1.00
head dict_integration_benchmark	3.366 ± 0.083	3.308	3.543	1.01 ± 0.03

Command	Mean [s]	Min [s]	Max [s]	Relative
base factorial_multirun	5.404 ± 0.082	5.302	5.563	1.00 ± 0.02
head factorial_multirun	5.390 ± 0.044	5.300	5.445	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base fibonacci_1000_multirun	4.334 ± 0.060	4.243	4.440	1.00
head fibonacci_1000_multirun	4.388 ± 0.103	4.262	4.570	1.01 ± 0.03

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base field_arithmetic_get_square_benchmark	154.9 ± 3.4	152.4	163.7	1.00
head field_arithmetic_get_square_benchmark	155.5 ± 4.9	148.9	162.8	1.00 ± 0.04

Command	Mean [s]	Min [s]	Max [s]	Relative
base integration_builtins	4.569 ± 0.686	4.197	6.476	1.00
head integration_builtins	4.915 ± 0.983	4.261	6.860	1.08 ± 0.27

Command	Mean [s]	Min [s]	Max [s]	Relative
base keccak_integration_benchmark	4.975 ± 1.031	4.035	6.320	1.22 ± 0.25
head keccak_integration_benchmark	4.073 ± 0.080	3.992	4.274	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base linear_search	4.510 ± 0.039	4.448	4.573	1.00
head linear_search	4.530 ± 0.072	4.464	4.677	1.00 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_cmp_and_pow_integration_benchmark	3.723 ± 0.042	3.663	3.798	1.00
head math_cmp_and_pow_integration_benchmark	3.769 ± 0.101	3.676	4.040	1.01 ± 0.03

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_integration_benchmark	3.394 ± 0.053	3.331	3.503	1.00
head math_integration_benchmark	3.423 ± 0.017	3.406	3.454	1.01 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base memory_integration_benchmark	3.030 ± 0.056	2.972	3.147	1.00
head memory_integration_benchmark	3.035 ± 0.021	2.994	3.065	1.00 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base operations_with_data_structures_benchmarks	2.983 ± 0.043	2.930	3.059	1.00 ± 0.02
head operations_with_data_structures_benchmarks	2.976 ± 0.032	2.942	3.059	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base pedersen	1.067 ± 0.080	1.013	1.288	1.03 ± 0.08
head pedersen	1.039 ± 0.014	1.016	1.058	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base poseidon_integration_benchmark	1.921 ± 0.026	1.877	1.958	1.01 ± 0.02
head poseidon_integration_benchmark	1.907 ± 0.023	1.876	1.948	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base secp_integration_benchmark	3.503 ± 0.028	3.450	3.542	1.00
head secp_integration_benchmark	3.508 ± 0.042	3.459	3.582	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base set_integration_benchmark	2.581 ± 0.039	2.542	2.664	1.00
head set_integration_benchmark	2.606 ± 0.031	2.563	2.650	1.01 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base uint256_integration_benchmark	5.056 ± 0.049	4.980	5.133	1.00
head uint256_integration_benchmark	5.091 ± 0.063	4.984	5.192	1.01 ± 0.02

[MegaRedHand]

Just a nitpick