PURPOSE: To obtain a compilation system for outputting an optimized code from a source program by providing a means for converting a useless statement to an efficient statement or eliminating it.

CONSTITUTION: The information of a common partial formula for which a variable name and an operational form are the same and the value of a variable is not changed in a source program is detected and described in a partial formula table. First, (a+b) of a minimum unit is written in the partial formula table as the common partial formula. Then, since (a+b)*c becomes a common formula, it is written in the partial formula table. The formula 3 includes the partial formula of the formula 1 and the formula 2, however, since the partial formula 2 includes the partial formula 3, the formula 2 becomes a start in the formula 3. When the partial formula table is prepared by the procedure, assembling is performed based on it. Further, a substitution sentence is detected from the rear part of the source program, an unrequired formula is judged from various conditions and it is eliminated. Furthermore, the substitution sentence is detected from the source program and the variable name is replaced with the constant of the substitution sentence retrieved at first when the value of the variable is not changed.