

from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean



def        lowerCAmelCase__				(						SCREAMING_SNAKE_CASE_:				Any   )      ->   List[str]:




				'''simple docstring'''





				def is_in_circle(SCREAMING_SNAKE_CASE_:				Tuple						,							SCREAMING_SNAKE_CASE_:				Optional[int]   ) -> bool:
								A__          =      sqrt((x**2) + (y**2)   )
								# Our circle has a radius of 1, so a distance
								# greater than 1 would land outside the circle.
								return distance_from_centre <= 1

				# The proportion of guesses that landed in the circle
				A__          =      mean(
				    int(is_in_circle(uniform(-1.0						,							1.0   )						,							uniform(-1.0						,							1.0   )   )   )
				    for _ in range(SCREAMING_SNAKE_CASE_   )   )
				# The ratio of the area for circle to square is pi/4.
				A__          =      proportion * 4
				print(F'The estimated value of pi is {pi_estimate}'   )
				print(F'The numpy value of pi is {pi}'   )
				print(F'The total error is {abs(pi - pi_estimate   )}'   )



def        lowerCAmelCase__				(						SCREAMING_SNAKE_CASE_:				int						,							SCREAMING_SNAKE_CASE_:				Tuple						,							SCREAMING_SNAKE_CASE_:				int = 0.0						,							SCREAMING_SNAKE_CASE_:				Tuple = 1.0						,							)      ->   List[Any]:




				'''simple docstring'''





				return mean(
				    function_to_integrate(uniform(SCREAMING_SNAKE_CASE_						,							SCREAMING_SNAKE_CASE_   )   ) for _ in range(SCREAMING_SNAKE_CASE_   )   ) * (max_value - min_value)



def        lowerCAmelCase__				(						SCREAMING_SNAKE_CASE_:				List[str]						,							SCREAMING_SNAKE_CASE_:				Optional[int] = 0.0						,							SCREAMING_SNAKE_CASE_:				str = 1.0   )      ->   int:




				'''simple docstring'''





				def identity_function(SCREAMING_SNAKE_CASE_:				int   ) -> float:
								return x

				A__          =      area_under_curve_estimator(
				    SCREAMING_SNAKE_CASE_						,							SCREAMING_SNAKE_CASE_						,							SCREAMING_SNAKE_CASE_						,							SCREAMING_SNAKE_CASE_   )
				A__          =      (max_value * max_value - min_value * min_value) / 2

				print("******************"   )
				print(F'Estimating area under y=x where x varies from {min_value} to {max_value}'   )
				print(F'Estimated value is {estimated_value}'   )
				print(F'Expected value is {expected_value}'   )
				print(F'Total error is {abs(estimated_value - expected_value   )}'   )
				print("******************"   )



def        lowerCAmelCase__				(						SCREAMING_SNAKE_CASE_:				str   )      ->   List[Any]:




				'''simple docstring'''





				def function_to_integrate(SCREAMING_SNAKE_CASE_:				Tuple   ) -> float:
								return sqrt(4.0 - x * x   )

				A__          =      area_under_curve_estimator(
				    SCREAMING_SNAKE_CASE_						,							SCREAMING_SNAKE_CASE_						,							0.0						,							2.0   )

				print("******************"   )
				print("Estimating pi using area_under_curve_estimator"   )
				print(F'Estimated value is {estimated_value}'   )
				print(F'Expected value is {pi}'   )
				print(F'Total error is {abs(estimated_value - pi   )}'   )
				print("******************"   )


if __name__ == "__main__":
	import doctest

	doctest.testmod()







import math

import tensorflow as tf
from packaging import version




def 		lowerCAmelCase_ (						lowerCamelCase ):
				__magic_name__						:						str										=tf.convert_to_tensor(lowerCamelCase )
				__magic_name__						:						List[str]										=0.5 * (1.0 + tf.math.erf(x / tf.cast(tf.sqrt(2.0 )						,  x.dtype ) ))

				return x * cdf




def 		lowerCAmelCase_ (						lowerCamelCase ):
				__magic_name__						:						str										=tf.convert_to_tensor(lowerCamelCase )
				__magic_name__						:						Optional[Any]										=tf.cast(math.pi						,  x.dtype )
				__magic_name__						:						int										=tf.cast(0.0_4_4_7_1_5						,  x.dtype )
				__magic_name__						:						Tuple										=0.5 * (1.0 + tf.tanh(tf.sqrt(2.0 / pi ) * (x + coeff * tf.pow(lowerCamelCase						,  3 )) ))

				return x * cdf




def 		lowerCAmelCase_ (						lowerCamelCase ):
				__magic_name__						:						Any										=tf.convert_to_tensor(lowerCamelCase )

				return x * tf.tanh(tf.math.softplus(lowerCamelCase ) )




def 		lowerCAmelCase_ (						lowerCamelCase ):
				__magic_name__						:						Optional[Any]										=tf.convert_to_tensor(lowerCamelCase )
				__magic_name__						:						Union[str, Any]										=tf.cast(0.0_4_4_7_1_5						,  x.dtype )
				__magic_name__						:						Tuple										=tf.cast(0.7_9_7_8_8_4_5_6_0_8						,  x.dtype )

				return 0.5 * x * (1.0 + tf.tanh(x * coeffa * (1.0 + coeffa * x * x) ))




def 		lowerCAmelCase_ (						lowerCamelCase ):
				__magic_name__						:						List[str]										=tf.convert_to_tensor(lowerCamelCase )
				__magic_name__						:						Dict										=tf.cast(1.7_0_2						,  x.dtype )
				return x * tf.math.sigmoid(coeff * x )




def 		lowerCAmelCase_ (						lowerCamelCase ):
				return tf.clip_by_value(_gelu(lowerCamelCase )						,  -10						,  10 )




def 		lowerCAmelCase_ (						lowerCamelCase						,  lowerCamelCase=-1 ):
				__magic_name__					,			__magic_name__						:						List[Any]										=tf.split(lowerCamelCase						,  2						,  axis=lowerCamelCase )
				return a * tf.math.sigmoid(lowerCamelCase )


if version.parse(tf.version.VERSION) >= version.parse("2.4"):




							def 		lowerCAmelCase_ (						lowerCamelCase ):
											return tf.keras.activations.gelu(lowerCamelCase						,  approximate=lowerCamelCase )

							UpperCAmelCase_		:					List[str]          =  tf.keras.activations.gelu



							UpperCAmelCase_		:					Dict          =  approximate_gelu_wrap
else:
							UpperCAmelCase_		:					Dict          =  _gelu
							UpperCAmelCase_		:					str          =  _gelu_new


UpperCAmelCase_		:					Any          =  {
    "gelu": gelu,
    "gelu_10": gelu_aa,
    "gelu_fast": gelu_fast,
    "gelu_new": gelu_new,
    "glu": glu,
    "mish": mish,
    "quick_gelu": quick_gelu,
    "relu": tf.keras.activations.relu,
    "sigmoid": tf.keras.activations.sigmoid,
    "silu": tf.keras.activations.swish,
    "swish": tf.keras.activations.swish,
    "tanh": tf.keras.activations.tanh,
}




def 		lowerCAmelCase_ (						lowerCamelCase ):
				if activation_string in ACTaFN:
								return ACTaFN[activation_string]
				else:
								raise KeyError(F"function {activation_string} not found in ACT2FN mapping {list(ACTaFN.keys() )}" )




