
"""simple docstring"""
from math import factorial






class      _UpperCAmelCase				:
    def __init__(    self						,    snake_case_						,    snake_case_     ):
      _snake_case     :						Dict						=   real
      if isinstance(UpperCamelCase__						,    UpperCamelCase__     ):
        _snake_case     :						int						=   [1] * rank
      else:
        _snake_case     :						Optional[Any]						=   rank
    def __repr__(    self     ):
      return (
          F'{self.real}+'
          F'{"+".join(str(UpperCamelCase__     )+"E"+str(n+1     )for n,dual in enumerate(self.duals     )     )}'
      )
    def 					lowerCamelCase__	(    self     ):
      _snake_case     :						Optional[Any]						=   self.duals.copy()
      while cur[-1] == 0:
        cur.pop(-1     )
      return Dual(self.real						,    UpperCamelCase__     )
    def __add__(    self						,    snake_case_     ):
      if not isinstance(UpperCamelCase__						,    UpperCamelCase__     ):
        return Dual(self.real + other						,    self.duals     )
      _snake_case     :						int						=   self.duals.copy()
      _snake_case     :						Dict						=   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__     ))     )
      _snake_case     :						Optional[Any]						=   []
      for i in range(len(UpperCamelCase__     )     ):
        new_duals.append(s_dual[i] + o_dual[i]     )
      return Dual(self.real + other.real						,    UpperCamelCase__     )

    __lowercase							: Tuple  =					__add__
    def __sub__(    self						,    snake_case_     ):
      return self + other * -1
    def __mul__(    self						,    snake_case_     ):
      if not isinstance(UpperCamelCase__						,    UpperCamelCase__     ):
        _snake_case     :						int						=   []
        for i in self.duals:
          new_duals.append(i * other     )
        return Dual(self.real * other						,    UpperCamelCase__     )
      _snake_case     :						Optional[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__     )

    __lowercase							: List[Any]  =					__mul__
    def __truediv__(    self						,    snake_case_     ):
      if not isinstance(UpperCamelCase__						,    UpperCamelCase__     ):
        _snake_case     :						Tuple						=   []
        for i in self.duals:
          new_duals.append(i / other     )
        return Dual(self.real / other						,    UpperCamelCase__     )
      raise ValueError
    def __floordiv__(    self						,    snake_case_     ):
      if not isinstance(UpperCamelCase__						,    UpperCamelCase__     ):
        _snake_case     :						Any						=   []
        for i in self.duals:
          new_duals.append(i // other     )
        return Dual(self.real // other						,    UpperCamelCase__     )
      raise ValueError


    def __pow__(    self						,    snake_case_     ):
      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
      _snake_case     :						Dict						=   self
      for _ in range(n - 1     ):
        x *= self
      return x


def 				a__   (   a   :				List[str]       ,     a   :				int       ,     a   :				List[str]		):

  """simple docstring"""







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


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    def 				a__   (   a   :				Union[str, Any]		):

      """simple docstring"""







      return y**2 * y**4



    print(differentiate(f, 9, 2))








"""simple docstring"""
from ...utils import (
    OptionalDependencyNotAvailable,
    is_torch_available,
    is_transformers_available,
    is_transformers_version,
)


try:
    if not (is_transformers_available() and is_torch_available() and is_transformers_version(""">=""", """4.25.0""")):
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    from ...utils.dummy_torch_and_transformers_objects import UnCLIPImageVariationPipeline, UnCLIPPipeline
else:
    from .pipeline_unclip import UnCLIPPipeline
    from .pipeline_unclip_image_variation import UnCLIPImageVariationPipeline
    from .text_proj import UnCLIPTextProjModel

