We prove that an associative algebra $A$ has minimal rank if and only if the Alder -- Strassen bound is also tight for the multiplicative complexity of $A$, that is, the multiplicative complexity of $A$ is $2 \dim A - t_A$ where $t_A$ denotes the number of maximal two sided ideals of $A$. This generalizes a result by E. Feig who proved this for division algebras. Furthermore, we show that if $A$ is local or super basic, then every optimal quadratic computation for $A$ is almost bilinear.