Python fails on math

[Mel]

christian schulze wrote:

> #1:
>>>> 2.0 * e * sqrt(3.0) - 2.0 * e
> 3.9798408154464964
> 
> #2:
>>>> 2.0 * e * (sqrt(3.0) -1.0)
> 3.979840815446496
> 
> I was wondering what exactly is failing here. The math module? Python,
> or the IEEE specifications?

Limited-precision calculation, computer floating-point for example, will do 
this.  Intermediate results get rounded off in different ways on different 
paths through the "same" calculation.  The whole truth for this will be 
revealed in a Numerical Analysis textbook, e.g. James B. Scarbourough, 
_Numerical Mathematical Analysis_,

	Mel.