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Re: V8 slow like a snail
*To*: mathgroup at smc.vnet.net
*Subject*: [mg127759] Re: V8 slow like a snail
*From*: David Bailey <dave at removedbailey.co.uk>
*Date*: Mon, 20 Aug 2012 04:13:46 -0400 (EDT)
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On 15/08/2012 08:32, Dr. Wolfgang Hintze wrote:
> Great disappointment on my side with 8.0.4.0 Home edition which I
> installed yesterday!
> My first impression: looks good, many nice features ... but incredibly
> slow in comparision to my good old 5.2.
> I then carried out a modest benchmark test the results of which I'll
> show below and which I like to express in terms of a "snail
> factor" ( = time in v5.2/ time in v8).
>
> Consider this integral for which we can safely expect Mathematica to
> be expert in solving:
>
> f1[n_, m_] :=
> Integrate[n t^m Exp[-n t] (Exp[t] - 1)^(n - 1), {t, 0, \[Infinity]},
> Assumptions -> {{n, m} \[Element] Integers, m>= 0, n> 0}]
>
> I carried out Timing[f1[n, m]] for m=0,1,2,3,10 in both versions. Here
> are the results in the format
>
> {m, V5.2 f1 first call, V5.2 second call, V8 first call, V8 second
> call, snail factor first call, snail factor second call}
>
> {
> { 0, 0.328, 0.078, 2.122, 2.044, 6.46951, 26.2051},
> { 1, 0.109, 0.063, 30.202, 30.483, 277.083, 483.857},
> { 2, 0.421, 0.11, 30.42, 30.17, 72.2565, 274.273},
> { 3, 0.452, 0.156, 31.528, 31.325, 69.7522, 200.801},
> {10, 5.366, 5.382, 42.448, 42.682, 7.91055, 7.93051}
> }
>
> Even if we compare only the first calls the range of the snail factor
> goes up to 277 at m = 1, is 72 for m = 2, and is still close to 8 for
> larger m.
>
> This is my story in other words: I own a very old car, and have
> considered for a long time to change to a newer one - although it
> still can go at 200 km/h on the Autobahn.
> So now I am proud owner of the new brilliant car, and I must learn the
> on important tours (m=1) =EDts maximum speed turns out to be less than 1
> km/h, about 3 km/h (m=2) or at most about 30 km/h. Who laughes? Me
> not! Obviously I'll definitely keep the old car!
>
> Ok, maybe I have chosen the wrong example (though in other test runs a
> similar pictures emerged and this example is just the type I'm using
> Mathematica for). Are there perhaps acknowleged benchmarks for such a
> comparison of versions?
>
> Finally, dear group, as you might have noticed, I'm asking for
> consolation. Please comment and give me useful hints. Many thanks in
> advance.
>
> Best regards,
> Wolfgang
>
It is important to realise two things:
1) The home edition is the same code as the normal version.
2) The speed of Mathematica depends on what calculation you are
interested in - many things have speed-ed up since 5.2. A lot of extra
analysis was added to symbolic integrals (at v6.0) to ensure that the
result was always valid. This slowed down symbolic integration
(particularly definite integrals), but is presumably worth it. There is
an option to Integrate that will stop at least some of this extra CPU
time: GenerateConditions->False
David Bailey
http://www.dbaileyconsultancy.co.uk
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