This paper presents new methods of detecting missed arithmetic optimization opportunities for C compilers by random testing. For each iteration of random testing, two equivalent programs are generated, where the arithmetic expressions in the second program are more optimized in the C program level. By comparing the two assembly codes compiled from the two C programs, lack of optimization on either of the programs is detected. This method is further extended for detecting erroneous or insufficient optimization involving volatile variables. Two random programs differing only on the initial values for volatile variables are generated, and the resulting assembly codes are compared. Random test systems implemented based on the proposed methods have detected missed optimization opportunities on several compilers, including the latest development versions of GCC-5.0.0 and LLVM/Clang-3.6.