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V8 slow like a snail

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  • Subject: [mg127688] V8 slow like a snail
  • From: "Dr. Wolfgang Hintze" <weh at snafu.de>
  • Date: Wed, 15 Aug 2012 03:33:25 -0400 (EDT)
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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



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