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Re: Optimize evaluation of symbolic expressions

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  • Subject: [mg102017] Re: Optimize evaluation of symbolic expressions
  • From: Stonewall Ballard <stoneyb at>
  • Date: Sun, 26 Jul 2009 03:57:35 -0400 (EDT)
  • References: <h4ef4m$t1b$>

On Jul 25, 4:18 am, Harrie Kraai <hakr... at> wrote:

> ...
> If I would program this myself, I would, of course, evaluate the
> subexpression (1 + x^2 + y^2) first and use this result 4 times in the
> subsequent calculations.
> It looks to me like Mathematica is not able to or at least does not make
> this optimization. (Find out using 'Trace').  Perhaps this is difficult
> to do in a general sense because any subexpression may have
> side-effects. However, in this case it should be possible to instruct
> Mathematica to collect common subexpressions first. It would surely make
> calculations much faster.
> The symbolic calculations have led to an expression that is
> "Simplify"-ed  in terms of reading (perhaps) but not in terms of
> evaluation. Is there, or should there be a function that translates
> expressions to a form that is optimized for evaluation?

I have read that internally, Mathematica recognizes common
subexpressions and evaluates them only once. That doesn't help me when
I use Mathematica to create C code, so I wrote an explicit common
subexpression hoister that rewrites an expression into one with
variables holding multiply-used parts. It's not perfect, but it works
for me.

Maybe this would be useful to you too.

 - Stoney

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