






import math

def      _lowerCamelCase	(						__A    :							int )      ->					List[str]:
    return math.sqrt(lowerCAmelCase__ ) * math.sqrt(lowerCAmelCase__ ) == num

def      _lowerCamelCase	(						__A    :							int )      ->					str:
    _UpperCAmelCase				:      Optional[Any]			  =				0
    _UpperCAmelCase				:      int			  =				n
    while left <= right:
        _UpperCAmelCase				:      List[Any]			  =				(left + right) // 2
        if mid**2 == n:
            return True
        elif mid**2 > n:
            _UpperCAmelCase				:      List[Any]			  =				mid - 1
        else:
            _UpperCAmelCase				:      List[Any]			  =				mid + 1
    return False


if __name__ == "__main__":
  import doctest

  doctest.testmod()












import math_equivalence  # From: git+https://github.com/hendrycks/math.git

import datasets


SCREAMING_SNAKE_CASE 							=						'\\n@article{hendrycksmath2021,\n  title={Measuring Mathematical Problem Solving With the MATH Dataset},\n  author={Dan Hendrycks\n    and Collin Burns\n    and Saurav Kadavath\n    and Akul Arora\n    and Steven Basart\n    and Eric Tang\n    and Dawn Song\n    and Jacob Steinhardt},\n  journal={arXiv preprint arXiv:2103.03874},\n  year={2021}\n}\n'


SCREAMING_SNAKE_CASE 							=						'\\nThis metric is used to assess performance on the Mathematics Aptitude Test of Heuristics (MATH) dataset.\nIt first canonicalizes the inputs (e.g., converting "1/2" to "\\frac{1}{2}") and then computes accuracy.\n'


SCREAMING_SNAKE_CASE 							=						R'\nCalculates accuracy after canonicalizing inputs.\n\nArgs:\n    predictions: list of predictions to score. Each prediction\n        is a string that contains natural language and LaTex.\n    references: list of reference for each prediction. Each\n        reference is a string that contains natural language\n        and LaTex.\nReturns:\n    accuracy: accuracy after canonicalizing inputs\n        (e.g., converting "1/2" to "\\frac{1}{2}")\n\nExamples:\n    >>> metric = datasets.load_metric("competition_math")\n    >>> results = metric.compute(references=["\\frac{1}{2}"], predictions=["1/2"])\n    >>> print(results)\n    {\'accuracy\': 1.0}\n'
@datasets.utils.file_utils.add_end_docstrings(_DESCRIPTION ,   _KWARGS_DESCRIPTION			)
class 							A_    (						datasets.Metric			):






 '''simple docstring'''




 def  snake_case__				(	self) ->		Optional[Any]:

     """simple docstring"""



     return datasets.MetricInfo(
         description=_DESCRIPTION							,  citation=_CITATION							,  inputs_description=_KWARGS_DESCRIPTION							,  features=datasets.Features(
             {
                 '''predictions''': datasets.Value('''string'''),
                 '''references''': datasets.Value('''string'''),
             })							,  homepage='''https://github.com/hendrycks/math'''							,  codebase_urls=['''https://github.com/hendrycks/math''']							,  )


 def  snake_case__				(	self							,  _A							,  _A) ->		Tuple:

     """simple docstring"""



     _UpperCAmelCase				:      Tuple			  =				0.0
     for i, j in zip(_A							,  _A):
         n_correct += 1.0 if math_equivalence.is_equiv(_A							,  _A) else 0.0
     _UpperCAmelCase				:      Tuple			  =				n_correct / len(_A)
     return {
         "accuracy": accuracy,
     }




