


'''simple docstring'''
from math import factorial
class      lowercase			:

		"""simple docstring"""

		def __init__(	self					,     UpperCamelCase_					,     UpperCamelCase_							):

							'''simple docstring'''


							UpperCamelCase__     :List[Any]							      =				real
							if isinstance(UpperCamelCase_					,     UpperCamelCase_							):
												UpperCamelCase__     :Optional[Any]							      =				[1] * rank
							else:
												UpperCamelCase__     :List[Any]							      =				rank




		def __repr__(	self							):

							'''simple docstring'''


							return (
							    F'''{self.real}+'''
							    F'''{"+".join(str(UpperCamelCase_							)+"E"+str(n+1							)for n,dual in enumerate(self.duals							)							)}'''
							)




		def 					lowerCAmelCase__       (	self							):

							'''simple docstring'''


							UpperCamelCase__     :Dict							      =				self.duals.copy()
							while cur[-1] == 0:
												cur.pop(-1							)
							return Dual(self.real					,     UpperCamelCase_							)




		def __add__(	self					,     UpperCamelCase_							):

							'''simple docstring'''


							if not isinstance(UpperCamelCase_					,     UpperCamelCase_							):
												return Dual(self.real + other					,     self.duals							)
							UpperCamelCase__     :int							      =				self.duals.copy()
							UpperCamelCase__     :Any							      =				other.duals.copy()
							if len(UpperCamelCase_							) > len(UpperCamelCase_							):
												o_dual.extend([1] * (len(UpperCamelCase_							) - len(UpperCamelCase_							))							)
							elif len(UpperCamelCase_							) < len(UpperCamelCase_							):
												s_dual.extend([1] * (len(UpperCamelCase_							) - len(UpperCamelCase_							))							)
							UpperCamelCase__     :List[str]							      =				[]
							for i in range(len(UpperCamelCase_							)							):
												new_duals.append(s_dual[i] + o_dual[i]							)
							return Dual(self.real + other.real					,     UpperCamelCase_							)

		_a									=       __add__




		def __sub__(	self					,     UpperCamelCase_							):

							'''simple docstring'''


							return self + other * -1




		def __mul__(	self					,     UpperCamelCase_							):

							'''simple docstring'''


							if not isinstance(UpperCamelCase_					,     UpperCamelCase_							):
												UpperCamelCase__     :str							      =				[]
												for i in self.duals:
																	new_duals.append(i * other							)
												return Dual(self.real * other					,     UpperCamelCase_							)
							UpperCamelCase__     :int							      =				[0] * (len(self.duals							) + len(other.duals							) + 1)
							for i, item in enumerate(self.duals							):
												for j, jtem in enumerate(other.duals							):
																	new_duals[i + j + 1] += item * jtem
							for k in range(len(self.duals							)							):
												new_duals[k] += self.duals[k] * other.real
							for index in range(len(other.duals							)							):
												new_duals[index] += other.duals[index] * self.real
							return Dual(self.real * other.real					,     UpperCamelCase_							)

		_a									=       __mul__




		def __truediv__(	self					,     UpperCamelCase_							):

							'''simple docstring'''


							if not isinstance(UpperCamelCase_					,     UpperCamelCase_							):
												UpperCamelCase__     :Tuple							      =				[]
												for i in self.duals:
																	new_duals.append(i / other							)
												return Dual(self.real / other					,     UpperCamelCase_							)
							raise ValueError




		def __floordiv__(	self					,     UpperCamelCase_							):

							'''simple docstring'''


							if not isinstance(UpperCamelCase_					,     UpperCamelCase_							):
												UpperCamelCase__     :Union[str, Any]							      =				[]
												for i in self.duals:
																	new_duals.append(i // other							)
												return Dual(self.real // other					,     UpperCamelCase_							)
							raise ValueError




		def __pow__(	self					,     UpperCamelCase_							):

							'''simple docstring'''


							if n < 0 or isinstance(UpperCamelCase_					,     UpperCamelCase_							):
												raise ValueError('''power must be a positive integer'''							)
							if n == 0:
												return 1
							if n == 1:
												return self
							UpperCamelCase__     :Optional[int]							      =				self
							for _ in range(n - 1							):
												x *= self
							return x



def     a   (    __a				,      __a				,      __a     )						->			int:






					if not callable(__a     ):
										raise ValueError('''differentiate() requires a function as input for func'''     )
					if not isinstance(__a				,      (float, int)     ):
										raise ValueError('''differentiate() requires a float as input for position'''     )
					if not isinstance(__a				,      __a     ):
										raise ValueError('''differentiate() requires an int as input for order'''     )
					UpperCamelCase__     :List[Any]							      =				Dual(__a				,      1     )
					UpperCamelCase__     :Optional[Any]							      =				func(__a     )
					if order == 0:
										return result.real
					return result.duals[order - 1] * factorial(__a     )


if __name__ == "__main__":
		import doctest

		doctest.testmod()


		def     a   (    __a     )						->			Any:
							return y**2 * y**4







		print(differentiate(f, 9, 2))



'''simple docstring'''
from __future__ import annotations

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

from sympy import diff


def     a   (    __a				,      __a				,      __a = 10**-10     )						->			float:



					'''simple docstring'''






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


# 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)}""")