Separable Asymptotic Cost of Evaluating Elementary Functions

The computational cost, in the bit model of computation, of the evaluation of a real function f(x) in a point x is analyzed, when the number d of correct digits of the result increases asymptotically. We want to study how the cost depends on x also when x approaches a critical point for the function f. We investigate yhe hypotheses under which it is possible to give upper bounds on the cost as functions of "separated variables" d and x, that is as products of the two functions, each of one variable. We examine in particular the case of elementary functions.