The paper has been presented at the 12th International Conference on Applications of
Computer Algebra, Varna, Bulgaria, June, 2006.To get guaranteed machine enclosures of a special function f(x),
an upper bound ε(f) of the relative error is needed, where ε(f) itself depends
on the error bounds ε(app); ε(eval) of the approximation and evaluation error
respectively. The approximation function g(x) ≈ f(x) is a rational function
(Remez algorithm), and with sufficiently high polynomial degrees ε(app)
becomes...