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Automatic differentiation is an elegant technique for converting a computable function expressed as a program into a derivative-computing program with similar time complexity. It does not execute the original program as a black-box, nor does it expand the program into a mathematical formula, both of which would be counter-productive. By generalizing this technique, you can produce efficient algorithms for constraint satisfaction, optimization, and Bayesian inference on models specified as programs. This approach can be broadly described as compiling into a message-passing program.

See more at https://www.microsoft.com/en-us/research/video/from-automatic-differentiation-to-message-passing/