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Beware of Simplify[] bottlenecks in v 3.0
*To*: mathgroup at smc.vnet.net
*Subject*: [mg8925] Beware of Simplify[] bottlenecks in v 3.0
*From*: carlos at mars.Colorado.EDU (Carlos A. Felippa)
*Date*: Sat, 4 Oct 1997 22:08:04 -0400
*Organization*: University of Colorado, Boulder
*Sender*: owner-wri-mathgroup at wolfram.com
After installing v 3.0 on my Max 8500/120 I have done some side
by side timing tests with old Notebooks comparing the speed of
Mma 2.2 vs 3.0. Generally v. 3.0 is 10% to 60% slower in most cases,
but ocassionally I found it to be an order of magnitude slower.
I traced the difference to the frequent use of the Simplify function.
This used to be a bottleneck in 2.2, and can be even more so in 3.0.
The following code fragment, extracted from an old Notebook,
illustrates the dramatic speed difference:
fp=(a*(2*a + a*Cos[phiQ])*(2*a*Cos[phiQ]*(1 - Cos[theta]) +
a*(1 - Cos[phiQ]*Cos[Pi/8]*Cos[theta] - Sin[phiQ]*Sin[Pi/8])))/
(2*2^(1/2)*(5*a^2 - (2*a + a*Cos[phiQ])*(2*a + a*Cos[Pi/8])*Cos[theta] +
a*(2*a*(Cos[phiQ] + Cos[Pi/8]) - a*Sin[phiQ]*Sin[Pi/8]))^(3/2));
Print[Timing[fp=Simplify[fp]]];
Mma 2.2: 15.75 Seconds
Mma 3.0: 140.517 Seconds - same result
I tried to limit the operation to 15 seconds to see if 3.0 can return the
same answer quicker:
Print[Timing[fp=Simplify[fp,TimeConstraint->15]]];
but the option is ignored:
Mma 3.0: 142.417 Seconds
The purpose of this post is to warn users converting to 3.0 about
such bottlenecks, and that they are uncontrollable until the
TimeConstraint option works.
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