In an optimization apparatus embedded in a compiler apparatus that compiles a high-level language program to a machine language program, equivalence relations among a plurality of expressions are analyzed in a short time period by calculating an equivalent expression set group of each basic block, the equivalent expression set group being composed of equivalent expression sets with equivalence relations. Specifically, an equivalent expression set group at the entry point of a basic block is calculated from equivalent expression set groups at the exit points of basic blocks that precede the basic block, and then an equivalent expression set group at the exit point of the basic block is calculated from the equivalent expression set group at the entry point of the basic block. These calculations are repeated until there are no more changes to the equivalent expression set group at the exit point of any of the basic blocks.