Fun(ctional) equation #2

Algebra Level 4

$2f(x)=f(xy)+f\left(\dfrac{x}{y}\right)$

If the above equation is true for all $x,y\in \mathbb{R}^{+}$ and $f(1)=0, f'(1)=1$ , then find the closed form of $f(1000)$ to 3 decimal places.