Toward a Better Sine Wave

In a previous paper, we showed that genetic programming can be used to evolve approximations to functions which, given certain trade-offs between cost and error, are superior to Padé approximations, which represent a generalization of Taylor series and a powerful technique from numerical analysis. In the present paper, we present an extension to this work which allows existing Padé approximations to be used to bootstrap the evolutionary process. Specifically, we use program trees corresponding to existing Padé approximations to seed the initial GP population; this allows for the evolution of approximations which are much more accurate in approximating certain combinations of function and interval. We illustrate the effectiveness of this approach by evolving approximations to the function sin(x) over the interval [0,π/2] which build upon and significantly improve some of the most efficient Padé approximations to that function.