We introduce the notion of a quantitatively pleasant action on $\mathbb{Z}^d$, and show how the polynomial walks can be used to exhibit the quantitative pleasantness of certain natural actions on $\mathbb{Z}^d$. As a consequence, we derive that for every set $A$ of positive density in $\mathbb{Z}^3$, there exists $k <= k(d(A))$ such that $\left\{xy-z^2 | (x,y,z) \in A-A\right\}$ contains $k\mathbb{Z}$. We also present an elementary proof of the following  result: given sets $E_1, E_2$ in $\mathbb{Z}$ of positive density there exists $k <= k(d(E_1),d(E_2))$ such that $(E_1 - E_1)(E_2 - E_2)$ contains $k\mathbb{Z}$.

Based on a joint work with Kamil Bulinski.