For positive integers $\hspace{.06 in}m_{\hspace{.02 in}0}\hspace{.02 in},n_0\hspace{.02 in},m_1,n_1\:$, $\;$ how difficult is it to decide whether $$\exp\left(\hspace{-0.03 in}\frac{m_{\hspace{.02 in}0}}{n_0}\hspace{-0.04 in}\right)-\frac{m_1}{n_1}$$
is positive or negative? $\;$ In particular, can that be decided in polynomial time?
(A consequence of the Lindemann-Weierstrass Theorem is that the above expression won't be zero.)
If it could be done efficiently, then that would give a way around the
table-maker's dilemma for the exponential and natural log functions.