I have a practical application where it would be useful to have a fast way to compute the approximate value of $\log (- \log x)$, for $0 < x < 1$, to maybe two decimal digits of precision. (This may be inexact, since the range is $-\infty$ to $\infty$.)
2026-04-12 14:10:02.1776003002
Is there a fast, reasonable way to compute the approximate value of $\log(- \log x)$?
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