I think it is well known that floating-point numbers have their limitations. How would the IEEE 754 floating-point system know when to use L'Hôpital's rule? I

I think it is well known that floating-point numbers have their limitations. How would the IEEE 754 floating-point system know when to use L'Hôpital's rule? If you know there is a singularity (0 / 0 or inf / inf) then you don't have to use floating-point; use calculus instead. Edit: What I want to say is that this is not a problem of floating-point number (not C or C++ either). It works _as intended_. Trying to increase the precision for evaluating (exp(x) - 1) / x at x = 0 is like beating a dead horse. Instead, a robust approach would be to expand (exp(x) - 1) / x at x = 0 as a Taylor series for very small x: 1 + x/2 + x^2/6 + x^3/24 + x^4/120 + O(x^5)