
'''simple docstring'''







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

import datasets


_lowercase :  int    							=       "\\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"


_lowercase :  Union[str, Any]    							=       "\\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"


_lowercase :  Tuple    							=       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  lowerCAmelCase__   (  datasets.Metric     ):






					def 	_snake_case    (   self		):


											"""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				,							__SCREAMING_SNAKE_CASE				,							__SCREAMING_SNAKE_CASE		):


											"""simple docstring"""





											lowercase_	:     int													=       0.0
											for i, j in zip(__SCREAMING_SNAKE_CASE				,							__SCREAMING_SNAKE_CASE		):
																	n_correct += 1.0 if math_equivalence.is_equiv(__SCREAMING_SNAKE_CASE				,							__SCREAMING_SNAKE_CASE		) else 0.0
											lowercase_	:     Union[str, Any]													=       n_correct / len(__SCREAMING_SNAKE_CASE		)
											return {
											    "accuracy": accuracy,
											}





'''simple docstring'''







from math import isqrt, loga
def 					snake_case_		(				__SCREAMING_SNAKE_CASE					: int							):



						"""simple docstring"""





						lowercase_	:     Any													=       [True] * max_number
						for i in range(2      ,      isqrt(max_number - 1							) + 1							):
												if is_prime[i]:
																		for j in range(i**2      ,      __SCREAMING_SNAKE_CASE      ,      __SCREAMING_SNAKE_CASE							):
																								lowercase_	:     Optional[Any]													=       False

						return [i for i in range(2      ,      __SCREAMING_SNAKE_CASE							) if is_prime[i]]
def 					snake_case_		(				__SCREAMING_SNAKE_CASE					: int = 800800      ,      __SCREAMING_SNAKE_CASE					: int = 800800							):



						"""simple docstring"""





						lowercase_	:     Union[str, Any]													=       degree * loga(__SCREAMING_SNAKE_CASE							)
						lowercase_	:     Any													=       int(__SCREAMING_SNAKE_CASE							)
						lowercase_	:     Optional[Any]													=       calculate_prime_numbers(__SCREAMING_SNAKE_CASE							)

						lowercase_	:     Optional[Any]													=       0
						lowercase_	:     List[Any]													=       0
						lowercase_	:     Union[str, Any]													=       len(__SCREAMING_SNAKE_CASE							) - 1
						while left < right:
												while (
												    prime_numbers[right] * loga(prime_numbers[left]							)
												    + prime_numbers[left] * loga(prime_numbers[right]							)
												    > upper_bound
												):
																		right -= 1
												hybrid_integers_count += right - left
												left += 1

						return hybrid_integers_count


if __name__ == "__main__":
							print(f"""{solution() = }""")



