N-body simulation is a classic application in high-performance computing. Although compiler optimizations designed for other classics such as matrix multiplication and FFT were well developed, the ones designed for $N$-body problems have been little studied. Hand optimizations for $N$-body solvers are thus rampant. To remedy this complication, we design a domain-specific language (DSL) embedded in Python for describing $N$-body problems and develop a DSL compiler that exploits the symmetric nature of $N$-body problems. It brings efficient code comparably with hand-written code.