Systems and methods allow the use of algebra to optimize several queries at once by algebraically breaking them into pieces, interleaving them in the most efficient way and then computing the queries together. For instance, a user or application may have many queries to process. A computing device may handle each query sequentially. However, if the computing device handled the queries simultaneously and if they are presented at once, there are ways to algebraically optimize them together by interleaving the tasks required to execute each one and complete the entire batch more efficiently.