A common model used in addressing today's overwhelming amounts of data is the OLAP Cube. The OLAP community has proposed several cube algebras, although a standard has still not been nominated. This study focuses on a recent addition to the cube algebras: the user-centric Cube Algebra Query Language (CAQL). The study aims to explore the optimization potential of this algebra by applying logical rewriting inspired by classic relational algebra and parallelism. The lack of standard algebra is often cited as a problem in such discussions. Thus, the significance of this work is that of strengthening the position of this algebra within the OLAP algebras by addressing implementation details. The modern open-source PostgreSQL relational engine is used to encode the CAQL abstraction. A query workload based on a well-known dataset is adopted, and CAQL and SQL implementations are compared. Finally, the quality of the query created is evaluated through the observed performance characteristics of the query. Results show strong improvements over the baseline case of the unoptimized query.