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[MUG] Optimize tryhard

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[MUG] Optimize tryhard
Author: Moore, Brian    Posted: Tue, 26 Nov 2002 11:28:57 -0500
>> From: "Moore, Brian" "Brian.Moore" I'm looking for information on the algorithm used in the optimize with tryhard option in the codegen package. I would also be very interested in other general packages developed for converting a Maple expression in efficient code (similar to the optimize tryhard). Actually, the optimize tryhard seems to generate very efficient code, but it takes a long time to generate the code. Does anyone have some information concerning this topic ? Thanks, Brian Moore Canadian Space Agency 6767 route de l'Aeroport, Saint-Hubert Quebec, Canada J3Y 8Y9 email: "Brian.Moore"

[MUG] Re: Optimize tryhard
Author: Maple User Group    Posted: Fri, 29 Nov 2002 09:10:55 -0500
>> From: Maple User Group "maple_gr" -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- From: Gaston Gonnet "gonnet" Date: Wed, 27 Nov 2002 17:53:49 +0100 (MET) To: "maple-list" Subject: Optimize tryhard Yes, I have some information about tryhard, I have coded it some time ago. I coded it because I was doing molecular dynamics at the time, and that requires hundreds of hours of computation, hence optimization time is not very relevant, but quality of the optimization is. optimize/tryhard is unique to that piece of code, all the rest of codegen or Maple do not utilize it. I never had the time to write a paper about it.... apologies.... Is there anything in particular you would like to know about it? Best wishes, Gaston Gonnet. -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Wed, 27 Nov 2002 18:11:28 -0500 (EST) From: Carl Devore "devore" To: "maple-list" Subject: Optimize tryhard On Tue, 26 Nov 2002, Moore, Brian wrote: > I'm looking for information on the algorithm used in the optimize with > tryhard option in the codegen package. It is all in procedures `codegen/optimize/tryhard/frontend` and its subsidiaries. Just read the procedures with showstat. > Actually, the optimize tryhard seems to generate very efficient code, > but it takes a long time to generate the code. Yeah, it is pretty good. With a tiny bit of tweaking, it can also be used as an expression simplifier. For lengthy algebraic number expressions, it often gives significantly more simplification than the other simplification commands. Here is the tweaking: Tryhard:= proc(expr) local _E; subs( pow= `^` ,codegen[optimize](subs(_E= expr, ()-> _E), tryhard) )() end proc: Show that is does something potentially useful: _EnvExplicit:= true: p:= randpoly([x,y], degree= 4, dense); root1:= solve(p, y)[1]; # Root is 11 screens long on my computer simplify(root1); # Still 11 screens long r:= Tryhard(root1); # 2 1/2 screens long, and it only took twice as long as the simplify. The actual procedure returned by codegen[optimize] in this case is only 1/3 of a screen long. So, looking at that procedure can give a deeper understanding of the internal structure of root1 than can be obtained by looking at the 2 1/2 screens. Test validity: simplify(eval(p, y= r)); 0 So people who collect such things can file that in their Maple trick bag.

[MUG] Re: Optimize tryhard
Author: Maple User Group    Posted: Wed, 4 Dec 2002 10:25:19 -0500 (
>> From: Maple User Group "maple_gr" -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Fri, 29 Nov 2002 12:00:18 -0800 (PST) From: Robert Israel "israel" To: "maple-list" Subject: Optimize tryhard Carl, your Tryhard looks interesting, but it doesn't quite work: I get > Tryhard(root1); Error, (in procmake) unbound lexically scoped identifier in procedure or module I think you have to make _E a global rather than a local. I'm puzzled about this, because the function passed to codegen[optimize] looks the same in both cases. But appearances are deceiving. Consider: > TL:= proc(expr) local _E; subs(_E=expr, () -> _E) end proc; TG:= proc(expr) global _E; subs(_E=expr, () -> _E) end proc; > FL:= TL(x+1); > FG:= TG(x+1); FL := () -> x + 1 FG := () -> x + 1 > codegen[optimize](FL,tryhard); Error, (in procmake) unbound lexically scoped identifier in procedure or module > codegen[optimize](FG,tryhard); proc() local result; global x; result := x + 1 end proc Although FL and FG look the same, FL contains a lexical table while FG does not. > op(7,eval(FL)); _E, x + 1 > op(7,eval(FG)); (nothing returned) Robert Israel "israel" Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 > Date: Wed, 27 Nov 2002 18:11:28 -0500 (EST) > From: Carl Devore "devore" > To: "maple-list" > Subject: Optimize tryhard > > > > On Tue, 26 Nov 2002, Moore, Brian wrote: > > I'm looking for information on the algorithm used in the optimize with > > tryhard option in the codegen package. > > It is all in procedures `codegen/optimize/tryhard/frontend` and its > subsidiaries. Just read the procedures with showstat. > > > Actually, the optimize tryhard seems to generate very efficient code, > > but it takes a long time to generate the code. > > Yeah, it is pretty good. With a tiny bit of tweaking, it can also be used > as an expression simplifier. For lengthy algebraic number expressions, it > often gives significantly more simplification than the other > simplification commands. Here is the tweaking: > > Tryhard:= proc(expr) > local _E; > subs( > pow= `^` > ,codegen[optimize](subs(_E= expr, ()-> _E), tryhard) > )() > end proc: > > Show that is does something potentially useful: > > _EnvExplicit:= true: > p:= randpoly([x,y], degree= 4, dense); > root1:= solve(p, y)[1]; > # Root is 11 screens long on my computer > simplify(root1); > # Still 11 screens long > r:= Tryhard(root1); > # 2 1/2 screens long, and it only took twice as long as the simplify. > > The actual procedure returned by codegen[optimize] in this case is only > 1/3 of a screen long. So, looking at that procedure can give a deeper > understanding of the internal structure of root1 than can be obtained by > looking at the 2 1/2 screens. > > Test validity: > > simplify(eval(p, y= r)); > 0 > > So people who collect such things can file that in their Maple trick bag. -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Fri, 29 Nov 2002 17:08:31 -0500 (EST) From: Carl Devore "devore" To: Robert Israel "israel" Subject: Optimize tryhard On Fri, 29 Nov 2002, Robert Israel wrote: > Carl, your Tryhard looks interesting, but it doesn't quite work: I get > > Tryhard(root1); > > Error, (in procmake) unbound lexically scoped identifier in > procedure or module > > I think you have to make _E a global rather than a local. Professor Israel is correct. I had switched from a global to a local without restesting (foolish not to retest). One can substitute for a string and avoid the dangers of global variables. Here is a correction: Tryhard:= expr-> subs(pow= `^`, codegen[optimize](subs("E"= expr, ()-> "E", tryhard))() ; And all of the benefits of this simplification method that I mentioned before still hold. There might be some functions other than `^` that get their name unfortunately changed by the tryhard. If you find any, they can be back-substituted also, and please let me know. That explains why there are all those substitutions for strings in the newer code in `dsolve/numeric` and its subsidiaries. For example, check out line 168 in the Maple 8 version.

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