Torture tests: what do they mean?

[Manolo Sobrino]

(05-18-2014 03:09 PM)Dieter Wrote:  If (!) the user was able to provide a 39-digit representation of 355/226 (for instance with a dedicated TAN_Y/X function) the 34s might get 31 digits right. Otherwise just 26 correct digits can be expected here. That's why I wonder why the 34s returns 31-32 correct digits. ;-)

With a 39-digit 255/226 you get:

Tan[1.570796460176991150442477876106194690265486725663716814159`39] = -7.4972581853255871129050718318912*10^6

a 32-digit result, and as you point out and I've been hopelessly trying to convey to readers indoctrinated with the fallacy that x significant digits in the input grant x significant digits in the output, no matter what, there's nothing you can do about it in order to get 39... because that would mean that you can work with 46 (in this particular case).

Why, oh why should all the functions be isometries?