This invention determines whether two circuit models have equivalent functionality. The method allows very fast comparison between two circuits taking advantage of previous work done. Whenever an apparatus associated with the method solves a problem, it stores information that learned during the solution of the problem, in a database. If the apparatus is presented with a new problem of determining equivalence between two portions of two circuits, it checks if it has seen sub-circuits similar to either of the two pieces before. If it has, it uses the knowledge cached during the previous checks to make the new check easier. Checking equivalence of two circuit models involves checking equivalence of many pairs of sub-parts. Even when the subsequent comparisons involve different circuits, it is possible to take advantage of the information acquired during previous equivalence checks.