# Computing Derivatives of Computer Programs.

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## Abstract

Automatic differentiation is introduced as a powerful technique to compute derivatives of functions given in the form of a computer program in a high-level programming language such as Fortran, C or C++. In contrast to traditional approaches such as handcoding of analytic expressions, numerical approximation by divided differences, or manipulation of symbolic algebraic expressions by computer algebra systems, automatic differentiation offers the following substantial benefits: it is accurate up to machine precision, efficient in terms of computational cost, applicable to a 1-line formula as well as to a 100,000-line code, and can be produced with minimal human effort.