
'''simple docstring'''







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A			) ->			float:

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

		return "".join(__A			)

	# matching characters
	_snake_case     		=	get_matched_characters(__A    ,       __A			)
	_snake_case     		=	get_matched_characters(__A    ,       __A			)
	_snake_case     		=	len(__A			)

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

	if not match_count:
		_snake_case     		=	0.0
	else:
		_snake_case     		=	(
		    1
		    / 3
		    * (
		        match_count / len(__A			)
		        + match_count / len(__A			)
		        + (match_count - transpositions) / match_count
		    )
		)

	# common prefix up to 4 characters
	_snake_case     		=	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"))



'''simple docstring'''







from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403







def        SCREAMING_SNAKE_CASE__			(     __A    ,       __A    ,       __A = "x"    ,       __A = 10**-10    ,       __A = 1    ,       ) ->			complex:
	_snake_case     		=	symbols(__A			)
	_snake_case     		=	lambdify(__A    ,       __A			)
	_snake_case     		=	lambdify(__A    ,       diff(__A    ,       __A			)			)

	_snake_case     		=	starting_point

	while True:
		if diff_function(__A			) != 0:
			_snake_case     		=	prev_guess - multiplicity * func(__A			) / diff_function(
			    __A			)
		else:
			raise ZeroDivisionError('Could not find root'			) from None

		# Precision is checked by comparing the difference of consecutive guesses
		if abs(next_guess - prev_guess			) < precision:
			return next_guess

		_snake_case     		=	next_guess


# 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
					# Find fourth Root of 5
					print(F'''The root of x**4 - 5 = 0 is {newton_raphson("x**4 -5", 0.4 +5J)}''')

					# Find value of e
					print(
					    "The root of log(y) - 1 = 0 is ",
					    F'''{newton_raphson("log(y) - 1", 2, variable="y")}''',
					)

					# Exponential Roots
					print(
					    "The root of exp(x) - 1 = 0 is",
					    F'''{newton_raphson("exp(x) - 1", 10, precision=0.005)}''',
					)

					# Find root of cos(x)
					print(F'''The root of cos(x) = 0 is {newton_raphson("cos(x)", 0)}''')

