In mathematics and computer algebra, automatic differentiation, also called algorithmic differentiation, computational differentiation, and differentiation arithmetic is a set of techniques to evaluate the partial derivative of a function specified by a computer program. Automatic differentiation enables the simultaneous computation of the numerical values of arbitrarily complex functions and their derivatives using only the function itself; no symbolic derivative is required. Auto-differentiation is thus neither numeric nor symbolic, nor is it a combination of both. In contrast to the more traditional numerical methods based on finite differences, auto-differentiation is 'in theory' exact, and in comparison to symbolic algorithms, it is computationally inexpensive.