Are Floating Point Numbers still a Can of Worms?

[Pieter van Oostrum]

Mostowski Collapse <bursejan at gmail.com> writes:

> I also get:
>
> Python 3.11.0rc1 (main, Aug 8 2022, 11:30:54)
>>>> 2.718281828459045**0.8618974796837966
> 2.367649
>
> Nice try, but isn't this one the more correct?
>
> ?- X is 2.718281828459045**0.8618974796837966.
> X = 2.3676489999999997.
>

That's probably the accuracy of the underlying C implementation of the exp function.

In [25]: exp(0.8618974796837966)
Out[25]: 2.367649

But even your answer can be improved:

Maxima:

(%i1) fpprec:30$

(%i2) bfloat(2.718281828459045b0)^bfloat(.8618974796837966b0);
(%o2)                  2.36764899999999983187397393143b0

but:

(%i7) bfloat(%e)^bfloat(.8618974796837966b0);
(%o7)                  2.3676490000000000085638369695b0
surprisingly closer to Python's answer.

but 2.718281828459045 isn't e. Close but no cigar.

(%i10) bfloat(2.718281828459045b0) - bfloat(%e);
(%o10)               - 2.35360287471352802147785151603b-16

Fricas:

(1) -> 2.718281828459045^0.8618974796837966 

   (1)  2.3676489999_999998319

(2) -> exp(0.8618974796837966)

   (2)  2.3676490000_000000086

-- 
Pieter van Oostrum <pieter at vanoostrum.org>
www: http://pieter.vanoostrum.org/
PGP key: [8DAE142BE17999C4]