sinh not too accurate for numbers approaching -1 or 1

[jrus]

I left a comment on the relevant pull request, but I figured I should make a separate issue, in case nobody sees that one. Ping @pavpanchekha.

A 5th degree Taylor expansion for sinh, as currently used by mathjs, isn’t very accurate when you get away from zero. For instance, with x = 0.99, it has an error of ~1.87e-4 (according to Wolfram Alpha).

As an alternative, you could use the degree 17 Taylor expansion the way the GNU Scientific Library does for the range [-1, 1], or you could e.g. use a Chebyshev series expansion.

Also, it probably makes sense to defer to the native Math.sinh function if it is defined. (Part of ECMAScript 6.)

[josdejong]

Thanks for bringing this up! Would you be interested in improving the current implementation?

[pavpanchekha]

Hi @jrus, and thanks for bringing up this problem. I'll look into using Chebyshev series, and try to figure out how to avoid the problem in the future.

[josdejong]

Thanks @pavpanchekha

[cukejianya]

See if #555 solves this problem. @josdejong @jrus

[josdejong]

I've fixed this in the develop branch by using ES6 Math functions when available, and if not, falling back on a simple implementation using exp (nothing fancy). This means that in practice you may see some inaccuracy issues on old versions of node (v0.10, v0.12).