We present efficient operators for the fast multipole method (FMM) based on totally symmetric and traceless Cartesian multipole tensors, which have been designed to translate well into computer code. Using the traceless tensor form significantly reduces memory usage and network communication traffic for large-scale applications in molecular dynamics and astrophysics. We have also developed a software generator that symbolically produces, verifies, and optimizes code for the FMM operators. The

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... nerator can easily produce different forms of the operators more suitable to specific applications. In realistic tests of biophysical simulations we observe a 20% speed-up, demonstrating the efficiency and improved performance of these routines compared to non-traceless tensor operators.