




'''simple docstring'''






from collections.abc import Callable

lowercase	:      Optional[Any]       	=       Callable[[float], float]  # type alias for a real -> real function




def 		a_( lowerCamelCase   ,				lowerCamelCase   ,				lowerCamelCase   ,				)				->float:






       '''simple docstring'''




       lowercase  :		List[str]						=      float(lowerCamelCase      )
       while True:
              try:
                     lowercase  :		Dict						=      prev_guess - function(lowerCamelCase      ) / derivative(lowerCamelCase      )
              except ZeroDivisionError:
                     raise ZeroDivisionError('''Could not find root'''      ) from None
              if abs(prev_guess - next_guess      ) < 10**-5:
                     return next_guess
              lowercase  :		Union[str, Any]						=      next_guess




def 		a_( lowerCamelCase      )				->float:






       '''simple docstring'''




       return (x**3) - (2 * x) - 5




def 		a_( lowerCamelCase      )				->float:






       '''simple docstring'''




       return 3 * (x**2) - 2


if __name__ == "__main__":
      print(newton(f, fa, 3))










'''simple docstring'''






import math
from timeit import timeit




def 		a_( lowerCamelCase      )				->int:






       '''simple docstring'''




       lowercase  :		Dict						=      0
       lowercase  :		Union[str, Any]						=      abs(lowerCamelCase      )
       while True:
              lowercase  :		List[Any]						=      n // 10
              digits += 1
              if n == 0:
                     break
       return digits




def 		a_( lowerCamelCase      )				->int:






       '''simple docstring'''




       return 1 if n == 0 else math.floor(math.log(abs(lowerCamelCase      )   ,				10      ) + 1      )




def 		a_( lowerCamelCase      )				->int:






       '''simple docstring'''




       return len(str(abs(lowerCamelCase      )      )      )




def 		a_( )				->None:






       '''simple docstring'''




       from collections.abc import Callable

       def benchmark_a_function(lowerCamelCase   ,				lowerCamelCase      ) -> None:
              lowercase  :		str						=      f"""{func.__name__}({value})"""
              lowercase  :		Optional[Any]						=      timeit(f"""__main__.{call}"""   ,				setup='''import __main__'''      )
              print(f"""{call}: {func(lowerCamelCase      )} -- {timing} seconds"""      )

       for value in (26_2144, 1125_8999_0684_2624, 126_7650_6002_2822_9401_4967_0320_5376):
              for func in (num_digits, num_digits_fast, num_digits_faster):
                     benchmark_a_function(lowerCamelCase   ,				lowerCamelCase      )
              print()


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      benchmark()




