Is it possible to pick up the value $\log^2 x<y<x$ to get this expressions simuletansionally
$$\sum_{d\leq y}\left \{ \frac{x}{d} \right \}\leqslant \frac{y}{\log^{3} y}?$$
$$\sum_{d\leq y}\left \{ \frac{x+y}{d} \right \}\leqslant \frac{y}{\log^{3} y}?$$