# Difference between Erf functions

I was evaluating some integrals and got, as part of the result, a ratio between a number and $\operatorname{erf}(c1^{c2} c3)-\operatorname{erf}(c1^{-c2} c3)$

Unfortunately, $c1^{c2} c3$ is a large number and so this difference becomes $0$, giving me a ratio of $c4/0$.

If I separately evaluate the integrals numerically, I can get the correct result, but this makes everything very slow...

Is there a way to force Mathematica to evaluate Erf in a different way? Is there a nice approximation of Erf for very large and very small numbers?

In such a case, this is what the two-argument form of Erf[] is intended for:
With[{p = N[2*^3], q = N[1*^2]}, {Erf[q] - Erf[p], Erf[p, q]}]

Similar "arbitrary limits" functionality is also available for special functions like Gamma[], GammaRegularized[], Beta[], BetaRegularized[], MarcumQ[]...