A method and system is described for optimizing a digital filter defined by coefficients that are multiplied by input data and accumulated to generate output data. A factorization set of candidate factors is compiled based on the coefficients. For each of the candidate factors, an optimized solution is generated. To generate the optimized solution, the candidate factor is applied to the coefficients and a working set of terms is compiled. Terms in the working set are converted to power-of-two representations and grouped with other terms that have a common partial sum, or multiple of the partial sum, within their respective power-of-two representations. A reduction set is compiled from the grouped terms and an order of application is selected based on optimization objectives. The reduction set is then applied to the working set of terms to generate the optimized solution, which is ranked and stored based on the optimization objectives.