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We show that Automatic Differentiation (AD) operators can be provided in adynamic language without sacrificing numeric performance. To achieve this,general forward and reverse AD functions are added to a simple high-leveldynamic language, and support for them is included in an aggressive optimizingcompiler. Novel technical mechanisms are discussed, which have the ability tomigrate the AD transformations from run-time to compile-time. The resultingsystem, although only a research prototype, exhibits startlingly goodperformance. In fact, despite the potential inefficiencies entailed by supportof a functional-programming language and a first-class AD operator, performanceis competitive with the fastest available preprocessor-based Fortran ADsystems. On benchmarks involving nested use of the AD operators, it can evendramatically exceed their performance.

Efficient Implementation of a Higher-Order Language with Built-In AD