import math

def 							UpperCamelCase				(    lowerCAmelCase_       ,					lowerCAmelCase_   )		->						float:




       '''simple docstring'''






       return math.pow(lowerCAmelCase_       ,					2   ) - a

def 							UpperCamelCase				(    lowerCAmelCase_   )		->						float:




       '''simple docstring'''






       return 2 * x

def 							UpperCamelCase				(    lowerCAmelCase_   )		->						float:




       '''simple docstring'''






       _A=	2.0

       while start <= a:
              _A=	math.pow(lowerCAmelCase_       ,					2   )

       return start

def 							UpperCamelCase				(    lowerCAmelCase_       ,					lowerCAmelCase_ = 99_99       ,					lowerCAmelCase_ = 0.00_000_000_000_001   )		->						float:




       '''simple docstring'''






       if a < 0:
              raise ValueError('math domain error'   )

       _A=	get_initial_point(lowerCAmelCase_   )

       for _ in range(lowerCAmelCase_   ):
              _A=	value
              _A=	value - fx(lowerCAmelCase_       ,					lowerCAmelCase_   ) / fx_derivative(lowerCAmelCase_   )
              if abs(prev_value - value   ) < tolerance:
                     return value

       return value


if __name__ == "__main__":
      from doctest import testmod

      testmod()
import pickle
import unittest

import torch

from accelerate import Accelerator
from accelerate.state import AcceleratorState
from accelerate.test_utils import require_cpu





@require_cpu
class      lowerCAmelCase						(					unittest.TestCase			):



     def 			a__  (					self       ):
            _A=	torch.nn.Linear(10				,      10       )
            _A=	torch.optim.SGD(model.parameters()				,      0.1       )
            _A=	Accelerator()
            _A=	accelerator.prepare(lowerCAmelCase__       )
            try:
                   pickle.loads(pickle.dumps(lowerCAmelCase__       )       )
            except Exception as e:
                   self.fail(f"Accelerated optimizer pickling failed with {e}"       )
            AcceleratorState._reset_state()