Re: Advanced expression simplification

Truly, Igor Chudov wrote on 07/11/05 13:03:
> (x^2-1)/(x-1) simplifies to x+1. GOOD
>
> (1^100-1)/(x-1) "simplifies" to x^99+x^98+...+x+1. NOT GOOD.


But watch out, neither case preserves the division-by-zero
condition for x==1. The code around the expression might
actually depend on this behaviour, much like the elimination
of memory stores/loads might omit null-pointer checks that
the surrounding code might depend on.


Also, if you are transforming floating-point expressions,
a seemingly more complicated expresson might be numerically
stable and more robust wrt. rounding errors that the simplified
version. In particular, inside a fixed-point iteration, a longer
expression that is better conditioned might reduce the number
of iterations needed for convergence, so that simplifying it
would be counter-productive.


yours,
Florian
--
=======================================================================
Florian Liekweg | Dot is a very forgiving language; it should
Universität Karlsruhe | be considered some form of religion.
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