Automated Discovery of Numerical Approximation Formulae via Genetic Programming

This paper describes the use of genetic programming to automate the discovery of numerical approximation formulae. The authors present results involving rediscovery of known approximations for Harmonic numbers and discovery of rational polynomial approximations for functions of one or more variables, the latter of which are compared to Padé approximations obtained through a symbolic mathematics package. For functions of a single variable, it is shown that evolved solutions can be considered superior to Padé approximations, which represent a powerful technique from numerical analysis, given certain tradeoffs between approximation cost and accuracy, while for functions of more than one variable, we are able to evolve rational polynomial approximations where no Padé approximation can be computed. Further, it is shown that evolved approximations can be refined through the evolution of approximations to their error function. Based on these results, we consider genetic programming to be a powerful and effective technique for the automated discovery of numerical approximation formulae