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What can we do to increase the precision of $\sinh x$ at $x \approx 0$?

I tried to use conjugation , but it gives me $e^{2x} - e^{-2x}$ which is again the subtraction of "similar" numbers at $x \approx 0$

Thank you

John Lennon
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    Have you found some problem with the $\sinh$ function provided by your computer/OS/language? I guarantee that the guys who wrote that function have a lot more expertise in this area than you or I. So, unless you have some very special needs, I would be inclined to just trust them. – bubba Sep 25 '13 at 00:59

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It is unlikely that $\sinh x$ is computed using the definition when $x\approx 0$, exactly to avoid subtraction cancellation.

Indeed, when $x\approx 0$ one uses the Taylor expansion $ \sinh x \approx x+x^3/6+x^5/120+O(x^7) $ or a better polynomial or rational function (Padé approximant), as for instance in http://www.doc.ic.ac.uk/~svb/CS/Lab/Minix%203/lib/math/sinh.c.

lhf
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