

import random

class  a     :


						def __init__(				self  ,    A_  ,    A_		):







										'''simple docstring'''


										_UpperCAmelCase				:						List[str]       						=			x
										_UpperCAmelCase				:						Dict       						=			y


						def 				_UpperCAmelCase (				self		):







										'''simple docstring'''


										return (self.x**2 + self.y**2) <= 1





						@classmethod
						def 				_UpperCAmelCase (				cls		):







										'''simple docstring'''


										return cls(x=random.random()  ,    y=random.random()		)







def 							__SCREAMING_SNAKE_CASE							( lowerCAmelCase:     int       )      ->				float:
				if number_of_simulations < 1:
								raise ValueError("At least one simulation is necessary to estimate PI."       )

				_UpperCAmelCase				:						Any       						=			0
				for _ in range(lowerCAmelCase       ):
								_UpperCAmelCase				:						Tuple       						=			Point.random_unit_square()

								if random_point.is_in_unit_circle():
												number_in_unit_circle += 1

				return 4 * number_in_unit_circle / number_of_simulations


if __name__ == "__main__":
					# import doctest

					# doctest.testmod()
					from math import pi

					SCREAMING_SNAKE_CASE_						=					'Please enter the desired number of Monte Carlo simulations: '
					SCREAMING_SNAKE_CASE_						=					estimate_pi(int(input(prompt).strip()))
					print(F'''An estimate of PI is {my_pi} with an error of {abs(my_pi - pi)}''')






import math as m







def   lowerCamelCase(      a__		,a__		,a__=0.001):
				return (f(a + h) - f(a - h)) / (2 * h)







def   lowerCamelCase(      a__		,a__=0		,a__=100		,a__=0.0001		,a__=1e-6		,a__=False):
				_SCREAMING_SNAKE_CASE	     =xa  # set the initial guess
				_SCREAMING_SNAKE_CASE	     =[a]
				_SCREAMING_SNAKE_CASE	     =abs(f(a__))
				_SCREAMING_SNAKE_CASE	     =lambda a__: calc_derivative(a__		,a__		,h=a__)  # noqa: E731  Derivative of f(x)
				for _ in range(a__):
								if fa(a__) == 0:
												raise ValueError('''No converging solution found''')
								_SCREAMING_SNAKE_CASE	     =a - f(a__) / fa(a__)  # Calculate the next estimate
								if logsteps:
												steps.append(a__)
								if error < maxerror:
												break
				else:
								raise ValueError('''Iteration limit reached, no converging solution found''')
				if logsteps:
								# If logstep is true, then log intermediate steps
								return a, error, steps
				return a, error


if __name__ == "__main__":
							from matplotlib import pyplot as plt

							snake_case_  :	Tuple							  =							lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
							snake_case_  , snake_case_  , snake_case_  :	str							  =							newton_raphson(
							    f, xa=10, maxiter=10_00, step=1e-6, logsteps=True
							)
							plt.plot([abs(f(x)) for x in steps])
							plt.xlabel('''step''')
							plt.ylabel('''error''')
							plt.show()
							print(f"""solution = {{{solution:f}}}, error = {{{error:f}}}""")