Recently, M.\ Kompatscher proved that for each finite supernilpotent algebra $A$ in a congruence modular variety, there is a polynomial time algorithm to solve polynomial equations over this algebra. Let $\mu$ be the maximal arity of the fundamental operations of $A$, and let
\[ d := |A|^{\log_2 (\mu) + \log_2 (|A|) + 1}. \]
Applying a method that G.\ K{\'a}rolyi and C.\ Szab\'{o} had used to solve equations over finite nilpotent rings, we show that for $A$,
there is $c \in \N$ such that a solution of every equation in $n$ variablescan be found by testing at most $c n^{d}$ (instead of all $|A|^n$ possible) assignments to the variables. We also consider systems of equations over such algebras.
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