> Hmm, do we have problems as we get close to -1 or 1 where the outputs of
> the two forms might diverge?

Well, I did some minor testing with that with input x around nextafter(1, -1);
There are a minor imprecision when comparing directly with
sinh(atanh(x)) and cosh(atanh(x)).
  * On 32-bits floats, for such x the error is about 10^-4
  * On 64-bits floats, for such x the error is about 10^-7
  * On 80-bits floats, for such x the error is about 10^-9

here are the code that I used for the test: https://pastebin.com/JzYZyigQ

I can create a testcase based on this if needed :-)

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