= Logarithmic inversion of a Gaussian divided by its argument
{title2=$e^{-x^2}/x=\epsilon,\quad x=\sqrt L-\frac{\log L}{4\sqrt L}+\cdots$}
For $\epsilon\downarrow0$, put $L=\log(1/\epsilon)$. Taking a <logarithm> gives $x^2+\log x=L$, first implying $x\sim\sqrt L$. Substitution of $x=\sqrt L+d$ gives $2\sqrt L\,d+\tfrac12\log L$ at first correction order. Hence $d=-(\log L)/(4\sqrt L)$; substituting back and using the <derivative> of $x^2+\log x$ bounds the remaining root error by $O((\log L)^2/L^{3/2})$.
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