Best practices for when exp() fails to exclude zero?

[Ryan Gibson]

Hi,

I have a bit of a strange situation with a function of the form f(exp(g(x))) where

1. f is a monotonic bounded function
2. g diverges to infinity near the edges of an integration domain

I'm finding that exp() behaves a bit strangely for large inputs (perhaps when the radius of the interval gets too close in magnitude to the midpoint). For instance,

In such cases, I would hopefully get a tight interval near the x->infty limit of f(x). However, due to the centering around zero, I just get an indeterminate result instead.

I was going to hack in a priori bounds in my handling of f(exp(g(x))) via comparisons on x, but wanted to see if you all had a better idea. Increasing the precision doesn't actually appear to help in my case since it just shifts the issue slightly closer to the edge of the integration domain.

Thanks so much,

Ryan