compile / optimize

*To*: mathgroup at smc.vnet.net*Subject*: [mg53745] compile / optimize*From*: Frank Brand <frank.brand at t-online.de>*Date*: Wed, 26 Jan 2005 04:36:22 -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>*Sender*: owner-wri-mathgroup at wolfram.com

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 > >