Catalyzes the epimerization a variety of hydrophobic dipeptides. Epimerase activity is highest with L-Ala-L-Tyr, and lower with L-Ala-L-Met, L-Ala-L-Phe, L-Tyr-L-Ala, L-Tyr-L-Met and L-Tyr-L-Trp (in vitro). Binds 1 Mg(2+) ion per subunit. Part of a large, functionally divergent protein family. Protein modeling and substrate docking was used to predict the substrate specificity, prior to biochemical analysis. Belongs to the mandelate racemase/muconate lactonizing enzyme family.