Mxyzptlk: An efficient, native C++ differentiation engine

Mxyzptlk was among the earliest implementations of a differentiation engine reported in the literature [1,2]. It was created with an eye to enabling accelerator related computations, especially within the realm of perturbation theories. Such computations are supported by (1) a one-to-one correspondence between original mathematical abstractions and the data types and operations used to implement them and (2) accurate computation of high order derivatives. To this day, mxyzptlk distinguishes itself by being among the few available implementations that takes full advantage of the native operator overloading capabilities of their implementation language. Recently, significant efforts were expanded in modernizing mxyzptlk, both architecturally and algorithmically, resulting in substantially improved performance, maintainability and usability. We present an overview of the mxyzptlk internals and summarize current capabilities and performance.