Re: Advanced expression simplification

"Gene" <eugene.ressler@frontiernet.net>
17 Jul 2005 13:46:38 -0400

          From comp.compilers

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From: "Gene" <eugene.ressler@frontiernet.net>
Newsgroups: comp.compilers
Date: 17 Jul 2005 13:46:38 -0400
Organization: http://groups.google.com
References: 05-07-04005-07-053
Keywords: optimize

Also Maxima, which is old but does simplification quite well. The
source is GPL.


Simplification uses the standard heuristic search algorithm: You need
an "evaluator" G(E) that accepts expression E and returns e.g. a
non-negative number s.t. larger is better.


Let S = expression to simplify
Closed = empty // the empty set
Open = { S } // the set consisting of S
Best = S // best simplification seen so far
while (G(Best) < GoodEnough and Timeleft) {
    Let Next be element of greatest G(E) removed from Open
    Add Next to Closed
    Let set S be all possible simplifications of Next NOT in Closed
    for each s in S {
            if G(s) > G(Best) Best = s
            add s to Open
    }
}


The set Closed prevents infinite loops. In real implementations this
is implemented with an efficient hashing scheme because it can become
large.


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