Again Multiple Precision

There is the famous Ramanujan constant exp(pi sqrt(163)) which is very close to the integer 640320^3+744 One has to be careful when doing computations with computers:

Mathematica:

N[Exp[Pi Sqrt[163]]-640320*640320*640320-744]
-480

which is nonsense but

Mathematica:

N[Exp[Pi Sqrt[163]]-640320^3-744,1]
-7.10^-13

works. Again, Wolfram support tells that this is intended as equating N[x] as N[x,16] for example would be a performance hit. It is not a surprise that Python does give a similar nonsense number as Python has no multiple precision built in.

python:

>>> from math import sqrt, exp, pi
>>> exp(pi*sqrt(163))-640320**3-744
-488.0

With mpmath, one gets

python:
from math import sqrt, exp, pi
from mpmath import mp
mp.dps=40
mp.exp(mp.pi*mp.sqrt(163))-640320**3-744
mpf('-0.00000000000074992....')

Also Pari, by default gives

pari: 
>>> exp(pi*sqrt(163))-640320*640320*640320-744
-488.0

Also Sage, by default

exp(pi*sqrt(163))-640320*640320*640320-744
-480.000000

which is the same mysterious -480 as mathematica.