The purity of a function may be determined after examining the performance history of a function and analyzing the conditions under which the function behaves as pure. In some cases, a function may be classified as pure when any side effects are de minimis or are otherwise considered trivial. A control flow graph may also be traversed to identify conditions in which a side effect may occur as well as to classify the side effects as trivial or non-trivial. The function purity may be used to identify functions for memoization. In some embodiments, the purity analysis may be performed by a remote server and communicated to a client device, where the client device may memoize the function.