Re: compile / optimize

*To*: mathgroup at smc.vnet.net*Subject*: [mg53770] Re: compile / optimize*From*: "Drago Ganic" <drago.ganic at in2.hr>*Date*: Thu, 27 Jan 2005 05:41:03 -0500 (EST)*References*: <comgvp$9hg$1@smc.vnet.net> <copavk$ps8$1@smc.vnet.net> <csl1pm$6ve$1@smc.vnet.net> <csnstt$4cr$1@smc.vnet.net> <ct4hka$b1g$1@smc.vnet.net> <ct7p0c$f5$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi, I thought that OptimizeExpression is used automatically by Compile in this particular case. Therefore we could just use Compile[vars, Evaluate[expr] ] instead of Compile[vars, Evaluate[Experimental`OptimizeExpression[expr]] ] Here is an example: f[n_] := Module[{x = 0}, Do[x += Sin[t^2]/(1 + x), {n}]; x] e = f[2] Sin[t^2] + Sin[t^2]/(1 + Sin[t^2]) eo := Experimental`OptimizeExpression[e]; eo Experimental`OptimizedExpression[Block[{$$16, $$17}, $$16 = t^2; $$17 = Sin[$$16]; $$17 + $$17/(1 + $$17)]] fc := Compile[t, Evaluate[e]]; fc CompiledFunction[{t}, Block[{$$23, $$24}, $$23 = t^2 ; $$24 = Sin[$$23]; $$24 + $$24/(1 + $$24)], -CompiledCode-] fco := Compile[t, Evaluate[eo]]; fco CompiledFunction[{t}, Block[{$$29, $$30}, $$29 = t^2 ; $$30 = Sin[$$29]; $$30 + $$30/(1 + $$30)], -CompiledCode-] The code looks the same. But, see the timings for n = 12: e = f[12]; Timing[e /. t -> 0.5] {0.09 Second, 1.68267} Timing[eo[[1]] /. t -> 0.5] {0.091 Second, 1.68267} Timing[fc[0.5]] {0.08 Second, 1.68267} Timing[fco[0.5]] {0.02 Second, 1.68267} ?!?!? I use $Version 5.0. Greetings from Croatia, Drago Ganic "Frank Brand" <frank.brand at t-online.de> wrote in message news:ct7p0c$f5$1 at smc.vnet.net... > Thanks Paul, > > but the special point I´m interesting in is if there is a possibility to > generally optimize and perhaps compile the following function (maximal > iteration number 12 substituted by n) > > f[n_]=Module[{x = 0}, Do[x += Sin[t^2]/(1 + x), {n}]; x]] > > ? > > Greetings > Frank > > > Paul Abbott wrote: >> In article <csnstt$4cr$1 at smc.vnet.net>, >> "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de> wrote: >> >> >>>ff = Experimental`OptimizeExpression[ >>>Module[{x = 0}, Do[x += Sin[t^2]/(1 + x), {12}]; x]] >>> >>> >>>myfun=Compile[{{t, _Real}}, Evaluate[ff]] >> >> >> However, using OptimizeExpression with Compile does not give any speed >> up for the given problem. Compare the following timings: >> >> g = Nest[Function[t, (t + x/t)/2], x, 15]; >> >> f1 = Compile[{{x, _Real}}, Evaluate[g]]; >> >> First[Timing[vals1 = f1 /@ Range[0.1, 20., 0.001]; ]] >> 0.11 Second >> >> f2 = Compile[{{x, _Real}}, >> Evaluate[Experimental`OptimizeExpression[Evaluate[g]]]]; >> >> First[Timing[vals2 = f2 /@ Range[0.1, 20., 0.001]; ]] >> 0.1 Second >> >> vals1 == vals2 >> True >> >> Cheers, >> Paul >> >> >>>"Frank Brand" <frank.brand at t-online.de> schrieb im Newsbeitrag >>>news:csl1pm$6ve$1 at smc.vnet.net... >>> >>>>Dear mathgroup members, >>>> >>>>can anybody give me an advice how to generally >>>> >>>>1.optimize (using the optimization package "optimize.m") and after that >>>>2. compile pieces of code like >>>> >>>>Module[{t}, t = x; Do[t = (t + x/t)/2, {n}]; t] >> >> >> Note that this code is much clearer as >> >> Nest[Function[t, (t + x/t)/2], x, n] >> >> And, of course, NewtonIteration is built-in (FindRoot). >> >> >>>>Applying the two-step approach to the code above with a given n (=15) >>>>there is a speed up ratio of 8500 compared with the original exprssion. >>>> >>>>Is it possible to apply this procedure to general expressions? >>>> >>>>Thanks in advance >>>>Frank >> >> >

**Follow-Ups**:**Re: Re: compile / optimize***From:*DrBob <drbob@bigfoot.com>