1  import math
 2  import random as _random
 3  
 4  
 5  def sigmoid(x: float) -> float:
 6      return 1 / (1 + math.exp(-x))
 7  
 8  
 9  def sigmoid_prime(x: float) -> float:
10      return sigmoid(x) * (1 - sigmoid(x))
11  
12  
13  def random():
14      return _random.random() * 2 - 1