Let $E \subseteq \mathbb R^n$ be closed. We consider the expansion $\mathfrak R = (\mathbb R,+,\cdot,E)$ of the real field by the set $E$. In this talk, we will prove that if $\mathfrak R$ is d-minimal, then for each $p \in \mathbb N$ there is a $C^p$ function $f \colon \mathbb R^n \to \mathbb R$ definable in $\mathfrak R$ such that $E = \{ x \in \mathbb R^n : f(x) = 0\}$.