

"""simple docstring"""




import math
from timeit import timeit
def   __SCREAMING_SNAKE_CASE		(		lowercase__ ):
					"""simple docstring"""
					A     =   0
					A     =   abs(lowercase__ )
					while True:
										A     =   n // 10
										digits += 1
										if n == 0:
															break
					return digits
def   __SCREAMING_SNAKE_CASE		(		lowercase__ ):
					"""simple docstring"""
					return 1 if n == 0 else math.floor(math.log(abs(lowercase__ )     ,				10 ) + 1 )
def   __SCREAMING_SNAKE_CASE		(		lowercase__ ):
					"""simple docstring"""
					return len(str(abs(lowercase__ ) ) )
def   __SCREAMING_SNAKE_CASE		(		):
					"""simple docstring"""
					from collections.abc import Callable

					def benchmark_a_function(lowercase__     ,				lowercase__ ) -> None:
										A     =   F"""{func.__name__}({value})"""
										A     =   timeit(F"""__main__.{call}"""     ,				setup="import __main__" )
										print(F"""{call}: {func(lowercase__ )} -- {timing} seconds""" )

					for value in (262_144, 1_125_899_906_842_624, 1_267_650_600_228_229_401_496_703_205_376):
										for func in (num_digits, num_digits_fast, num_digits_faster):
															benchmark_a_function(lowercase__     ,				lowercase__ )
										print()


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	benchmark()









"""simple docstring"""





import math as m


def   _snake_case    (    _snake_case					:      List[Any]			, _snake_case					:      Tuple			, _snake_case					:      Tuple=0.001      ):
      return (f(a + h      ) - f(a - h      )) / (2 * h)


def   _snake_case    (    _snake_case					:      int			, _snake_case					:      List[Any]=0			, _snake_case					:      Any=100			, _snake_case					:      Any=0.0001			, _snake_case					:      Optional[Any]=1E-6			, _snake_case					:      Any=False      ):
      lowerCAmelCase       :						Optional[Any]							= xa  # set the initial guess
      lowerCAmelCase       :						str							= [a]
      lowerCAmelCase       :						List[str]							= abs(f(_snake_case      )      )
      lowerCAmelCase       :						Dict							= lambda _snake_case      : calc_derivative(_snake_case			, _snake_case			, h=_snake_case      )  # noqa: E731  Derivative of f(x)
      for _ in range(_snake_case      ):
            if fa(_snake_case      ) == 0:
                  raise ValueError('''No converging solution found'''      )
            lowerCAmelCase       :						Tuple							= a - f(_snake_case      ) / fa(_snake_case      )  # Calculate the next estimate
            if logsteps:
                  steps.append(_snake_case      )
            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__		:  Any     					=					lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
 snake_case__					,  snake_case__					,  snake_case__		:  List[str]     					=					newton_raphson(
     f, xa=10, maxiter=1_000, 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}}}""")


