We present SUDAF (Sharing User-Defined Aggregate Functions), a declarative framework that allows users to formulate UDAFs as mathematical expressions and use them in SQL statements. SUDAF rewrites partial aggregates of UDAFs using built-in aggregate functions and supports efficient dynamic caching and reusing of partial aggregates. Our evaluation shows that using SUDAF on top of Spark SQL can lead from one to two orders of magnitude improvement in query execution times compared to the original Spark SQL.