If one is adding probabilities as log probabilities lp and lq so that $lsum =\max(lp,lq)+\log(1+\exp(-|lp-lq|))$ it would be nice to have a slightly less computationally expensive correction to the max term. I known that $\log(1+x) = x-x^2/2+x^3/3-x^4/4$ etc. However firstly that's not great for x=1 and also I would think there was more that could be done since $x = \exp(-|a|)$. Reasonable ranges of a are from 0 to 10. Any thoughts?
2026-04-03 00:54:46.1775177686
Approximation for $\log( 1+\exp(-|a|) )$ with $a \in \Re$
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