Maxima big float numbers have no set upper bound for the exponent. Try
using the function bfloat; example
(%i27) bfloat(cosh(2.0b9));
(%o27) 3.202385861076592b868588963
--Barton
>
> I want to numerically evaluate an expression obtained by Maxima (or
> any other CAS for that matter). Doing that I frequently hit on an
> expression that cannot be evaluated because it involves parts with
> extremely big numbers.