# Let's see why we use (predictions - targets) ** 2
pred = np.array([0.8, 0.2, 0.9, 0.1])
target = np.array([1.0, 0.0, 1.0, 0.0])

differences = pred - target
squared_differences = differences ** 2

print("Understanding squared error:")
print(f"Predictions: {pred}")
print(f"Targets:     {target}")
print(f"Differences: {differences}")
print(f"Squared:     {squared_differences}")
print(f"Mean squared error: {np.mean(squared_differences):.4f}")

# Why not just absolute difference?
abs_differences = np.abs(differences)
print(f"\nComparison:")
print(f"Absolute differences: {abs_differences}")
print(f"Squared differences:  {squared_differences}")
print("Squared errors penalize large mistakes more heavily!")