





'''simple docstring'''


from __future__ import annotations

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

from sympy import diff







def  _lowerCamelCase	(__lowerCamelCase	:  str       ,	__lowerCamelCase	:  float | Decimal       ,	__lowerCamelCase	:  float = 10**-10  ) ->     float:
			a__	 =			a
			while True:
						a__	 =			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)}""")










"""simple docstring"""



def 						__lowercase	(  snake_case_    :    str							,snake_case_    :    str		)  ->float:



    '''simple docstring'''







    def get_matched_characters(snake_case_    :    str							,snake_case_    :    str		) -> str:
        __A       :		Any							=	[]
        __A       :		Any							=	min(len(_stra		)							,len(_stra		)		) // 2
        for i, l in enumerate(_stra		):
            __A       :		Dict							=	int(max(0							,i - limit		)		)
            __A       :		Tuple							=	int(min(i + limit + 1							,len(_stra		)		)		)
            if l in _stra[left:right]:
                matched.append(snake_case_		)
                __A       :		Any							=	F"""{_stra[0:_stra.index(snake_case_		)]} {_stra[_stra.index(snake_case_		) + 1:]}"""

        return "".join(snake_case_		)

    # matching characters
    __A       :		int							=	get_matched_characters(snake_case_							,snake_case_		)
    __A       :		Tuple							=	get_matched_characters(snake_case_							,snake_case_		)
    __A       :		str							=	len(snake_case_		)

    # transposition
    __A       :		Dict							=	(
        len([(ca, ca) for ca, ca in zip(snake_case_							,snake_case_		) if ca != ca]		) // 2
    )

    if not match_count:
        __A       :		List[str]							=	0.0
    else:
        __A       :		Tuple							=	(
            1
            / 3
            * (
                match_count / len(snake_case_		)
                + match_count / len(snake_case_		)
                + (match_count - transpositions) / match_count
            )
        )

    # common prefix up to 4 characters
    __A       :		Tuple							=	0
    for ca, ca in zip(stra[:4]							,stra[:4]		):
        if ca == ca:
            prefix_len += 1
        else:
            break

    return jaro + 0.1 * prefix_len * (1 - jaro)


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       print(jaro_winkler("""hello""", """world"""))




