Here's the (pedantically-worked) example with reverse-mode:

Program:

  y = g(x) = x^3
  z = f(y) = cuberoot(y)

Want: dz/dx

Reverse-mode autodiff:

  // Forward pass
  y = g(0) = 0^3         = 0      g'(0) = 3 x^2                           = 0
  z = f(0) = cuberoot(0) = 0      f'(0) = (1/3) / cuberoot(y^2) = (1/3)/0 = Inf

  // Reverse pass
  dz/dy = f'(0)                   = Inf
  dz/dx = dz/dy * g'(0) = Inf * 0 = NaN