Update the custom hint example

[d-roak]

Update the custom hint example

Description

• Added custom_hint_example to workspace
• Removed local Cargo.lock
• Fixed the example

Checklist

• Linked to Github Issue (Update the custom hint example #1235)
• Unit tests added
• Integration tests added.
• This change requires new documentation.
  • Documentation has been added/updated.
  • CHANGELOG has been updated.

[codecov]

Codecov Report

Merging #1258 (b99dc2c) into main (6680f38) will not change coverage.
The diff coverage is n/a.

@@           Coverage Diff           @@
##             main    #1258   +/-   ##
=======================================
  Coverage   97.60%   97.60%           
=======================================
  Files          89       89           
  Lines       36335    36335           
=======================================
  Hits        35466    35466           
  Misses        869      869           

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[github-actions]

Benchmark Results for unmodified programs 🚀

Command	Mean [s]	Min [s]	Max [s]	Relative
base blake2s_integration_benchmark	11.111 ± 0.086	11.000	11.271	1.00
head blake2s_integration_benchmark	11.121 ± 0.087	11.039	11.352	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base compare_arrays_200000	3.940 ± 0.057	3.885	4.059	1.01 ± 0.02
head compare_arrays_200000	3.916 ± 0.045	3.869	4.030	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base dict_integration_benchmark	2.573 ± 0.013	2.558	2.602	1.00 ± 0.01
head dict_integration_benchmark	2.567 ± 0.013	2.550	2.588	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base factorial_multirun	4.113 ± 0.039	4.083	4.219	1.00
head factorial_multirun	4.134 ± 0.028	4.096	4.180	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base fibonacci_1000_multirun	3.499 ± 0.023	3.476	3.545	1.00 ± 0.01
head fibonacci_1000_multirun	3.491 ± 0.016	3.472	3.525	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base field_arithmetic_get_square_benchmark	1.924 ± 0.007	1.911	1.934	1.00
head field_arithmetic_get_square_benchmark	1.935 ± 0.027	1.913	2.004	1.01 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base integration_builtins	9.811 ± 0.119	9.624	9.999	1.00
head integration_builtins	9.820 ± 0.119	9.620	10.014	1.00 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base keccak_integration_benchmark	11.428 ± 0.255	11.182	12.072	1.02 ± 0.02
head keccak_integration_benchmark	11.222 ± 0.064	11.154	11.350	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base linear_search	3.915 ± 0.019	3.891	3.945	1.00 ± 0.01
head linear_search	3.903 ± 0.015	3.875	3.926	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_cmp_and_pow_integration_benchmark	2.813 ± 0.015	2.791	2.843	1.00 ± 0.01
head math_cmp_and_pow_integration_benchmark	2.812 ± 0.016	2.792	2.844	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_integration_benchmark	2.559 ± 0.019	2.540	2.594	1.00
head math_integration_benchmark	2.571 ± 0.033	2.546	2.659	1.00 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base memory_integration_benchmark	2.246 ± 0.029	2.228	2.323	1.00
head memory_integration_benchmark	2.247 ± 0.031	2.228	2.335	1.00 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base operations_with_data_structures_benchmarks	2.536 ± 0.019	2.518	2.578	1.00 ± 0.02
head operations_with_data_structures_benchmarks	2.528 ± 0.036	2.510	2.629	1.00

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base pedersen	878.0 ± 6.1	872.8	891.9	1.00 ± 0.01
head pedersen	877.7 ± 3.7	873.4	886.0	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base poseidon_integration_benchmark	1.587 ± 0.004	1.580	1.593	1.00 ± 0.00
head poseidon_integration_benchmark	1.583 ± 0.007	1.576	1.600	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base secp_integration_benchmark	2.970 ± 0.019	2.955	3.016	1.00 ± 0.01
head secp_integration_benchmark	2.969 ± 0.022	2.951	3.027	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base set_integration_benchmark	1.548 ± 0.014	1.527	1.577	1.00 ± 0.01
head set_integration_benchmark	1.547 ± 0.008	1.533	1.558	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base uint256_integration_benchmark	7.122 ± 0.162	7.047	7.579	1.01 ± 0.03
head uint256_integration_benchmark	7.083 ± 0.072	7.033	7.252	1.00