old_contents: import numpy
  
  from chainer.backends import cuda
  from chainer import function_node
  from chainer import utils
  from chainer.utils import type_check
  
  
  class Sqrt(function_node.FunctionNode):
  
      @property
      def label(self):
          return 'sqrt'
  
      def check_type_forward(self, in_types):
          type_check.expect(
              in_types.size() == 1,
              in_types[0].dtype.kind == 'f',
          )
  
      def forward(self, x):
          self.retain_outputs((0,))
          xp = cuda.get_array_module(*x)
          return utils.force_array(xp.sqrt(x[0], dtype=x[0].dtype)),
  
      def backward(self, indexes, grad_outputs):
          gx = self.get_retained_outputs()[0]
          gy = grad_outputs[0]
          return gy / (gx * 2.0),
  
  
  class RsqrtGPU(function_node.FunctionNode):
  
      @property
      def label(self):
          return 'rsqrt'
  
      def check_type_forward(self, in_types):
          type_check.expect(
              in_types.size() == 1,
              in_types[0].dtype.kind == 'f',
          )
  
      def forward_gpu(self, inputs):
          self.retain_inputs((0,))
          x, = inputs
          out = cuda.cupyx.rsqrt(x, dtype=x.dtype)
          return utils.force_array(out),
  
      def backward(self, indexes, grad_outputs):
          x, = self.get_retained_inputs()
          gy, = grad_outputs
          return gy * (x ** -1.5) * -0.5,
  
  
  def sqrt(x):
      """Elementwise square root function.
  
      .. math::
         y_i = \\sqrt x_i.
  
      If the value of :math:`x_i` is negative, it returns ``Nan`` for :math:`y_i`
      respect to underlying numpy and cupy specification.
  
      Args:
          x (~chainer.Variable): Input variable.
  
      Returns:
          ~chainer.Variable: Output variable.
      """
      return Sqrt().apply((x,))[0]
  
  
  def rsqrt(x):
      """Computes elementwise reciprocal of square root of input :math:`x_i`.
  
      .. math::
         y_i = {1 \\over \\sqrt x_i}.
  
      Args:
          x (~chainer.Variable): Input variable.
  
      Returns:
          ~chainer.Variable: Output variable.
  
      .. seealso:: :func:`~chainer.functions.sqrt`
      """
      xp = cuda.get_array_module(x)
      if xp is numpy:
          return 1.0 / sqrt(x)
  
      # CuPy provides `rsqrt` which is faster than `1.0 / sqrt(x)`.
      return RsqrtGPU().apply((x,))[0]
  
new_contents: import numpy
  
  from chainer.backends import cuda
  from chainer import function_node
  from chainer import utils
  from chainer.utils import type_check
  
  
  class Sqrt(function_node.FunctionNode):
  
      @property
      def label(self):
          return 'sqrt'
  
      def check_type_forward(self, in_types):
          type_check.expect(
              in_types.size() == 1,
              in_types[0].dtype.kind == 'f',
          )
  
      def forward(self, x):
          self.retain_outputs((0,))
          xp = cuda.get_array_module(*x)
          return utils.force_array(xp.sqrt(x[0], dtype=x[0].dtype)),
  
      def backward(self, indexes, grad_outputs):
          gx = self.get_retained_outputs()[0]
          gy = grad_outputs[0]
          return gy / (gx * 2.0),
  
  
  class RsqrtGPU(function_node.FunctionNode):
  
      @property
      def label(self):
          return 'rsqrt'
  
      def check_type_forward(self, in_types):
          type_check.expect(
              in_types.size() == 1,
              in_types[0].dtype.kind == 'f',
          )
  
      def forward_gpu(self, inputs):
          self.retain_outputs((0,))
          x, = inputs
          out = cuda.cupyx.rsqrt(x, dtype=x.dtype)
          return utils.force_array(out),
  
      def backward(self, indexes, grad_outputs):
          y, = self.get_retained_outputs()
          gy, = grad_outputs
          return gy * (y ** 3) * -0.5,
  
  
  def sqrt(x):
      """Elementwise square root function.
  
      .. math::
         y_i = \\sqrt x_i.
  
      If the value of :math:`x_i` is negative, it returns ``Nan`` for :math:`y_i`
      respect to underlying numpy and cupy specification.
  
      Args:
          x (~chainer.Variable): Input variable.
  
      Returns:
          ~chainer.Variable: Output variable.
      """
      return Sqrt().apply((x,))[0]
  
  
  def rsqrt(x):
      """Computes elementwise reciprocal of square root of input :math:`x_i`.
  
      .. math::
         y_i = {1 \\over \\sqrt x_i}.
  
      Args:
          x (~chainer.Variable): Input variable.
  
      Returns:
          ~chainer.Variable: Output variable.
  
      .. seealso:: :func:`~chainer.functions.sqrt`
      """
      xp = cuda.get_array_module(x)
      if xp is numpy:
          return 1.0 / sqrt(x)
  
      # CuPy provides `rsqrt` which is faster than `1.0 / sqrt(x)`.
      return RsqrtGPU().apply((x,))[0]
  
subject: simplify rsqrt