I am trying to compute the following expression numerically stable:
$$ \log \left(\frac{5 e^{a+b}+3 e^a+3 e^b-3}{-e^{a+b}+e^a+e^b+7}\right) \text{ for }a,b\in\mathbb{R} $$
I have attempted simplifying it but found nothing solving the problem of having to evaluate an exponential, sum up, and then evaluating the logarithm.