




"""simple docstring"""







def 							lowercase					(snake_case__   : int = 3      ,       snake_case__   : int = 7      ,       snake_case__   : int = 1_000_000 )     ->  int:


				'''simple docstring'''






				lowerCAmelCase  =				0
				lowerCAmelCase  =				1

				for current_denominator in range(1      ,       limit + 1 ):
								lowerCAmelCase  =				current_denominator * numerator // denominator
								if current_denominator % denominator == 0:
												current_numerator -= 1
								if current_numerator * max_denominator > current_denominator * max_numerator:
												lowerCAmelCase  =				current_numerator
												lowerCAmelCase  =				current_denominator
				return max_numerator


if __name__ == "__main__":
		print(solution(numerator=3, denominator=7, limit=1_0_0_0_0_0_0))











"""simple docstring"""







from __future__ import annotations

from decimal import Decimal
from math import *  # noqa: F403

from sympy import diff





def 							lowercase					(snake_case__   : str      ,       snake_case__   : float | Decimal      ,       snake_case__   : float = 10**-10 )     ->  float:


				'''simple docstring'''






				lowerCAmelCase  =				a
				while True:
								lowerCAmelCase  =				Decimal(snake_case__ ) - (
								    Decimal(eval(snake_case__ ) ) / Decimal(eval(str(diff(snake_case__ ) ) ) )  # noqa: S307
								)
								# This number dictates the accuracy of the answer
								if abs(eval(snake_case__ ) ) < precision:  # noqa: S307
												return float(snake_case__ )


# Let's Execute
if __name__ == "__main__":
		# Find root of trigonometric function
		# Find value of pi
		print(f"""The root of sin(x) = 0 is {newton_raphson("sin(x)", 2)}""")
		# Find root of polynomial
		print(f"""The root of x**2 - 5*x + 2 = 0 is {newton_raphson("x**2 - 5*x + 2", 0.4)}""")
		# Find Square Root of 5
		print(f"""The root of log(x) - 1 = 0 is {newton_raphson("log(x) - 1", 2)}""")
		# Exponential Roots
		print(f"""The root of exp(x) - 1 = 0 is {newton_raphson("exp(x) - 1", 0)}""")





