Real root isolation for exp–log–arctan functions

We present a real root isolation procedure for univariate functions obtained by composition and rational operations from exp,log,arctan and real constants. The procedure was first introduced for exp–log functions in Strzeboński (2008). Here we extend the procedure to exp–log–arctan functions, describe computation with elementary constants in detail and discuss the complexity of the root isolation procedure for the general exp–log–arctan case as well as for the special case of sparse polynomials. We discuss implementation of the procedure and present empirical results.