The default is a balance between leaf count and number of digits. But the documentation page above gives an example of how to nudge the cost function away from specialised functions.
Hyperbolic functions aren't used as much but the same principle applies. Here the core identity is cosh^2(x) = sinh^2(x) = 1 so:
sinh(arccosh(x))
= sqrt(1 + cosh^2(arccosh(x))
= sqrt(1 + x^2)
The first time I looked at the comment above, there was a reply, a reply to that reply, and a reply to the reply to the reply.
Later I came back and this time there were no replies. Since HN won't let you delete a comment that has a reply the only ways a comment chain should be able to go away are (1) the participants delete them in reverse order, or (2) a moderator intervenes.
I came back again and the comments are back!
I wonder if this is related to another comment problem I've seen many times in the past few weeks? I'll be using the "next" or "prev" links on top level comments to move through the comment and will come to a point where that breaks. Next reaches a comment that it will not go past. Coming from below prev will also not go past that point. Examining the links, next and prev are pointing to a nonexistent comment.
1. Multiply the input by itself
2. Add 1
3. Take the square root. There is often a fast square root function available.
The above is a fairly simply sequence of SIMD instructions. You can even do it without SIMD if you want.
Compare this to sinh being (e^x - e^-x) / 2 (you can reduce this to one exponentiation in terms of e^2x but I digress) and arccosh being ln(x + sqrt(s^2 - 1)) and you have an exponentiation, subtraction, division, logarithm, addition, square root and a subtraction. Computers generally implement e^2 and logarithm using numerical method approximations (eg of a Taylor's series expansion).
"Simplify" is a very old term (>50y) in computer algebra. Its meaning has become kind of layered in that time.