HP-35’s x^y Why?

[J-F Garnier]

(11-03-2021 02:38 PM)robve Wrote:  

(11-03-2021 07:47 AM)J-F Garnier Wrote:  Example on Saturn-based HP machines:
125^(1/3) = 4.9999...
but XROOT(125,3)=5 exactly.

Wow. This is even worse,

Rob, I can be interested by comparing math algorithms, but not by systematic denigrating.

Quote:... if true:

I can't imagine you believe that I wrote something without checking, or worse that I may deliberately be giving incorrect information :-(

To go back to a fair discussion, the 125^(1/3) result is right with 12-digit arguments, there is no incorrect rounding.
125 ^ 0.333333333333 = 4.99999999999195...
It is inaccurate if you think you are computing the 3rd root of 125. Thus the interest of the y^(1/x) aka XROOT function.

As for machines that are lying to artificially give nice results (1/3*3 = 1 or 0.999..99 ?, SIN(pi [rad]) = exactly 0 or a small number?), this was discussed many times, especially about the HP and TI differences. Of course, I'm speaking about numeric, not symbolic calculations.

(11-03-2021 03:21 PM)Albert Chan Wrote:  Does HP71B has XROOT (or equivalent ?)
I am curious of how to efficiently implement this ...

No, unfortunately, even in the MATH ROM.

J-F