
def      UpperCamelCase   (       __lowerCamelCase	:					Tuple							,   __lowerCamelCase	:					Dict							,   __lowerCamelCase	:					Union[str, Any]=False       ):

       if isinstance(__lowerCamelCase							,   __lowerCamelCase       ) and isinstance(__lowerCamelCase							,   __lowerCamelCase       ):
              snake_case			:  str     							= len(set_a.intersection(__lowerCamelCase       )       )

              if alternative_union:
                     snake_case			:  int     							= len(__lowerCamelCase       ) + len(__lowerCamelCase       )
              else:
                     snake_case			:  List[str]     							= len(set_a.union(__lowerCamelCase       )       )

              return intersection / union

       if isinstance(__lowerCamelCase							,   (list, tuple)       ) and isinstance(__lowerCamelCase							,   (list, tuple)       ):
              snake_case			:  int     							= [element for element in set_a if element in set_b]

              if alternative_union:
                     snake_case			:  Optional[int]     							= len(__lowerCamelCase       ) + len(__lowerCamelCase       )
                     return len(__lowerCamelCase       ) / union
              else:
                     snake_case			:  Any     							= set_a + [element for element in set_b if element not in set_a]
                     return len(__lowerCamelCase       ) / len(__lowerCamelCase       )

              return len(__lowerCamelCase       ) / len(__lowerCamelCase       )
       return None


if __name__ == "__main__":
   __lowerCamelCase				=			{"""a""", """b""", """c""", """d""", """e"""}
   __lowerCamelCase				=			{"""c""", """d""", """e""", """f""", """h""", """i"""}
   print(jaccard_similarity(set_a, set_b))







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

import datasets


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


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


__lowerCamelCase				=			R"""
Calculates accuracy after canonicalizing inputs.

Args:
    predictions: list of predictions to score. Each prediction
        is a string that contains natural language and LaTex.
    references: list of reference for each prediction. Each
        reference is a string that contains natural language
        and LaTex.
Returns:
    accuracy: accuracy after canonicalizing inputs
        (e.g., converting \"1/2\" to \"\\frac{1}{2}\")

Examples:
    >>> metric = datasets.load_metric(\"competition_math\")
    >>> results = metric.compute(references=[\"\\frac{1}{2}\"], predictions=[\"1/2\"])
    >>> print(results)
    {'accuracy': 1.0}
"""






@datasets.utils.file_utils.add_end_docstrings(_DESCRIPTION			,_KWARGS_DESCRIPTION					)
class     UpperCAmelCase						(		datasets.Metric					):



   def 							_SCREAMING_SNAKE_CASE  (self						:   Optional[int]					)						->      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 							_SCREAMING_SNAKE_CASE  (self						:   Optional[int]       ,		snake_case__						:   str       ,		snake_case__						:   List[Any]					)						->      Optional[Any]:


          '''simple docstring'''


          snake_case			:  Optional[int]     							= 0.0
          for i, j in zip(snake_case__       ,		snake_case__					):
                 n_correct += 1.0 if math_equivalence.is_equiv(snake_case__       ,		snake_case__					) else 0.0
          snake_case			:  Optional[int]     							= n_correct / len(snake_case__					)
          return {
              "accuracy": accuracy,
          }





