


from sklearn.metrics import mean_squared_error

import datasets


snake_case							: Optional[Any]      =   '\\n@article{scikit-learn,\n title={Scikit-learn: Machine Learning in {P}ython},\n author={Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V.\n         and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P.\n         and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and\n         Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E.},\n journal={Journal of Machine Learning Research},\n volume={12},\n pages={2825--2830},\n year={2011}\n}\n'

snake_case							: List[Any]      =   '\\nMean Squared Error(MSE) is the average of the square of difference between the predicted\nand actual values.\n'


snake_case							: int      =   '\nArgs:\n    predictions: array-like of shape (n_samples,) or (n_samples, n_outputs)\n        Estimated target values.\n    references: array-like of shape (n_samples,) or (n_samples, n_outputs)\n        Ground truth (correct) target values.\n    sample_weight: array-like of shape (n_samples,), default=None\n        Sample weights.\n    multioutput: {"raw_values", "uniform_average"} or array-like of shape (n_outputs,), default="uniform_average"\n        Defines aggregating of multiple output values. Array-like value defines weights used to average errors.\n\n        "raw_values" : Returns a full set of errors in case of multioutput input.\n\n        "uniform_average" : Errors of all outputs are averaged with uniform weight.\n\n    squared : bool, default=True\n        If True returns MSE value, if False returns RMSE (Root Mean Squared Error) value.\n\nReturns:\n    mse : mean squared error.\nExamples:\n\n    >>> mse_metric = datasets.load_metric("mse")\n    >>> predictions = [2.5, 0.0, 2, 8]\n    >>> references = [3, -0.5, 2, 7]\n    >>> results = mse_metric.compute(predictions=predictions, references=references)\n    >>> print(results)\n    {\'mse\': 0.375}\n    >>> rmse_result = mse_metric.compute(predictions=predictions, references=references, squared=False)\n    >>> print(rmse_result)\n    {\'mse\': 0.6123724356957945}\n\n    If you\'re using multi-dimensional lists, then set the config as follows :\n\n    >>> mse_metric = datasets.load_metric("mse", "multilist")\n    >>> predictions = [[0.5, 1], [-1, 1], [7, -6]]\n    >>> references = [[0, 2], [-1, 2], [8, -5]]\n    >>> results = mse_metric.compute(predictions=predictions, references=references)\n    >>> print(results)\n    {\'mse\': 0.7083333333333334}\n    >>> results = mse_metric.compute(predictions=predictions, references=references, multioutput=\'raw_values\')\n    >>> print(results) # doctest: +NORMALIZE_WHITESPACE\n    {\'mse\': array([0.41666667, 1. ])}\n'







@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION			,		_KWARGS_DESCRIPTION   )
class  snake_case_     (datasets.Metric   ):
					def 				lowerCamelCase__(   self     :Optional[Any]   )      ->					Optional[Any]:
												return datasets.MetricInfo(
												    description=_DESCRIPTION    ,citation=_CITATION    ,inputs_description=_KWARGS_DESCRIPTION    ,features=datasets.Features(self._get_feature_types()   )    ,reference_urls=[
												        'https://scikit-learn.org/stable/modules/generated/sklearn.metrics.mean_squared_error.html'
												    ]    ,)
					def 				lowerCamelCase__(   self     :Dict   )      ->					List[Any]:
												if self.config_name == "multilist":
																			return {
																			    "predictions": datasets.Sequence(datasets.Value('float'   )   ),
																			    "references": datasets.Sequence(datasets.Value('float'   )   ),
																			}
												else:
																			return {
																			    "predictions": datasets.Value('float'   ),
																			    "references": datasets.Value('float'   ),
																			}



					def 				lowerCamelCase__(   self     :Optional[Any]    ,__snake_case     :Tuple    ,__snake_case     :Any    ,__snake_case     :Optional[int]=None    ,__snake_case     :List[str]="uniform_average"    ,__snake_case     :List[Any]=True   )      ->					Tuple:
												a__    =  mean_squared_error(
												    __A    ,__A    ,sample_weight=__A    ,multioutput=__A    ,squared=__A   )

												return {"mse": mse}








from decimal import Decimal, getcontext
from math import ceil, factorial






def 							__lowercase     (				__lowerCAmelCase							:       int     ):

							if not isinstance(__lowerCAmelCase      ,					__lowerCAmelCase     ):
														raise TypeError('Undefined for non-integers'     )
							elif precision < 1:
														raise ValueError('Undefined for non-natural numbers'     )

							a__    =  precision
							a__    =  ceil(precision / 1_4     )
							a__    =  4_2_6_8_8_0 * Decimal(1_0_0_0_5     ).sqrt()
							a__    =  1
							a__    =  1_3_5_9_1_4_0_9
							a__    =  Decimal(__lowerCAmelCase     )
							for k in range(1      ,					__lowerCAmelCase     ):
														a__    =  factorial(6 * k     ) // (factorial(3 * k     ) * factorial(__lowerCAmelCase     ) ** 3)
														linear_term += 5_4_5_1_4_0_1_3_4
														exponential_term *= -2_6_2_5_3_7_4_1_2_6_4_0_7_6_8_0_0_0
														partial_sum += Decimal(multinomial_term * linear_term     ) / exponential_term
							return str(constant_term / partial_sum     )[:-1]


if __name__ == "__main__":
						snake_case							: Tuple      =   50
						print(f"""The first {n} digits of pi is: {pi(n)}""")




