International Mathematical Olympiad 2015 Problem 5

Let $\mathbb{R}$ be the set of real numbers. Determine all functions $f \colon \mathbb{R} \to \mathbb{R}$ satisfying the equation $$f \big (x + f (x + y) \big) + f (xy) = x + f (x + y) + yf (x)$$ for all real numbers $x$ and $y$.