feat(hints): Add alternative string for hint EC_DOUBLE_ASSIGN_NEW_X

[fmoletta]

TITLE

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 #1083 (0c6b521) into main (e756edd) will increase coverage by 0.00%.
The diff coverage is 100.00%.

@@           Coverage Diff           @@
##             main    #1083   +/-   ##
=======================================
  Coverage   98.10%   98.10%           
=======================================
  Files          84       84           
  Lines       34150    34161   +11     
=======================================
+ Hits        33504    33515   +11     
  Misses        646      646           

Impacted Files	Coverage Δ
...int_processor/builtin_hint_processor_definition.rs	99.02% <100.00%> (+0.01%)	⬆️
..._processor/builtin_hint_processor/secp/ec_utils.rs	99.54% <100.00%> (+<0.01%)	⬆️

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[github-actions]

Benchmark Results for unmodified programs 🚀

Command	Mean [s]	Min [s]	Max [s]	Relative
base blake2s_integration_benchmark	2.476 ± 0.032	2.451	2.558	1.00
head blake2s_integration_benchmark	2.481 ± 0.029	2.443	2.552	1.00 ± 0.02

Command	Mean [s]	Min [s]	Max [s]	Relative
base compare_arrays_200000	3.047 ± 0.033	3.011	3.111	1.01 ± 0.01
head compare_arrays_200000	3.028 ± 0.015	3.014	3.056	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base dict_integration_benchmark	2.404 ± 0.012	2.387	2.430	1.00 ± 0.01
head dict_integration_benchmark	2.393 ± 0.005	2.386	2.403	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base factorial_multirun	3.742 ± 0.020	3.715	3.776	1.00 ± 0.01
head factorial_multirun	3.738 ± 0.040	3.710	3.841	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base fibonacci_1000_multirun	3.007 ± 0.041	2.952	3.080	1.01 ± 0.01
head fibonacci_1000_multirun	2.972 ± 0.016	2.951	2.992	1.00

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base field_arithmetic_get_square_benchmark	129.5 ± 1.1	128.2	131.7	1.01 ± 0.01
head field_arithmetic_get_square_benchmark	128.1 ± 1.1	127.2	131.0	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base integration_builtins	2.916 ± 0.020	2.896	2.961	1.00
head integration_builtins	2.922 ± 0.010	2.910	2.941	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base keccak_integration_benchmark	2.639 ± 0.007	2.629	2.654	1.00
head keccak_integration_benchmark	2.648 ± 0.011	2.634	2.670	1.00 ± 0.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base linear_search	3.148 ± 0.017	3.131	3.179	1.00 ± 0.01
head linear_search	3.141 ± 0.015	3.130	3.177	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_cmp_and_pow_integration_benchmark	2.667 ± 0.016	2.649	2.698	1.01 ± 0.01
head math_cmp_and_pow_integration_benchmark	2.653 ± 0.008	2.640	2.664	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base math_integration_benchmark	2.471 ± 0.009	2.462	2.485	1.00 ± 0.01
head math_integration_benchmark	2.465 ± 0.017	2.452	2.511	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base memory_integration_benchmark	2.138 ± 0.049	2.110	2.273	1.00 ± 0.03
head memory_integration_benchmark	2.130 ± 0.030	2.109	2.211	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base operations_with_data_structures_benchmarks	2.211 ± 0.042	2.187	2.328	1.00 ± 0.02
head operations_with_data_structures_benchmarks	2.202 ± 0.031	2.178	2.280	1.00

Command	Mean [ms]	Min [ms]	Max [ms]	Relative
base pedersen	775.4 ± 6.1	770.7	791.7	1.00 ± 0.01
head pedersen	772.8 ± 1.9	769.4	775.5	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base poseidon_integration_benchmark	1.499 ± 0.010	1.485	1.518	1.00
head poseidon_integration_benchmark	1.505 ± 0.011	1.496	1.531	1.00 ± 0.01

Command	Mean [s]	Min [s]	Max [s]	Relative
base secp_integration_benchmark	2.344 ± 0.006	2.335	2.355	1.00 ± 0.01
head secp_integration_benchmark	2.342 ± 0.014	2.328	2.376	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base set_integration_benchmark	1.687 ± 0.012	1.676	1.718	1.00 ± 0.01
head set_integration_benchmark	1.680 ± 0.005	1.674	1.688	1.00

Command	Mean [s]	Min [s]	Max [s]	Relative
base uint256_integration_benchmark	3.891 ± 0.012	3.876	3.915	1.00 ± 0.00
head uint256_integration_benchmark	3.886 ± 0.010	3.875	3.902	1.00