import numpy as np
import math

# Create random input and output data
x = np.linspace(-math.pi, math.pi, 2000)
y = np.sin(x)

# Randomly initialize weights
a = np.random.randn()
b = np.random.randn()
c = np.random.randn()
d = np.random.randn()

learning_rate = 1e-6
for t in range(5000):
    # Forward pass, compute predicted y
    # y = a + b * x + c * x^2 + d * x^3
    y_pred = a + b * x + c * (x**2) + d * (x**3)

    # Compute and print loss
    loss = np.square(y_pred - y).sum()
    if t % 100 == 99:
        print("Epoch: {} Loss: {}.".format(t, loss))

    # Backprop to compute gradients of a, b, c, d with respect to loss
    grad_y_pred = 2.0 * (y_pred - y)
    grad_a = grad_y_pred.sum()
    grad_b = (grad_y_pred * x).sum()
    grad_c = (grad_y_pred * x**2).sum()
    grad_d = (grad_y_pred * x**3).sum()

    # Update weights
    a -= learning_rate * grad_a
    b -= learning_rate * grad_b
    c -= learning_rate * grad_c
    d -= learning_rate * grad_d

print("Result: f(x) = {} + {} * x + {} * x**2 + {} * x**3".format(a, b, c, d))
