Re: Speed improvements in Mathematica 5 ??
- To: mathgroup at smc.vnet.net
- Subject: [mg42430] Re: Speed improvements in Mathematica 5 ??
- From: "Dana DeLouis" <delouis at bellsouth.net>
- Date: Mon, 7 Jul 2003 03:05:56 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
I am new at this, but I was getting a feel for ver 5 by looking at old
Mathematica articles that had the word "bug" in it.
I came across one article where the consensus was that the following
"simple" integral was giving wrong output.
I do not know what the correct solution is, but it is interesting that
ver 5 takes me about 4.5 minutes to solve. Apparently, (I think) it was
much faster earlier.
It generates a very long list of If conditions. I think it is trying to
be more correct, but I am not sure. I have to look carefully to find
the answer in the full-page mess.
On[ShowTime]
Integrate[Log[(x - s)^2 + (y + 1)^2], {s, -1, 0}]
254.225*Second
If[((Im[x]*Im[y] + Re[x] +
Re[x]*Re[y])/
(1 + Re[y]) >= 0 ||
(Im[x]*Im[y] + (1 + Re[x])*
(1 + Re[y]))/
(1 + Re[y]) <= 0 ||
Re[y] == -1 &&
Im[x]*Im[y] + (1 + Re[x])*
(1 + Re[y]) != 0) &&
(Sqrt[-(1 + y)^2] == x ||
Sqrt[-(1 + y)^2] ==
1 + x ||
Im[x] - Im[Sqrt[
-(1 + y)^2]] != 0 ||
..Long list cut..etc
If I make use of the new $Assumptions, I get about half a minute speed
increase.
$Assumptions[{Elements[{x, y},Reals]}]
Integrate[Log[(x - s)^2 + (y + 1)^2], {s, -1, 0}]
227.447*Second
If[((Im[x]*Im[y] + Re[x] +
Re[x]*Re[y])/
(1 + Re[y]) >= 0 ||
(Im[x]*Im[y] + (1 + Re[x])*
(1 + Re[y]))/
(1 + Re[y]) <= 0 ||
Re[y] == -1 &&
Im[x]*Im[y] +
.etc
Can anyone explain the following if you use $Assumption to specify that
x and y are Reals?
Why does Mathematica spend so much time generating output like
Im[x]*Im[y], or Re[x], Re[y], etc when one already told it that x & y
are Reals?
Im[x] should be zero, and Re[x] should just be x. (I think). Do you
think this could be adding to some of the observed slowdown?
Dana DeLouis
Windows XP
Mathematica $VersionNumber -> 5.0 for Microsoft Windows (June 10, 2003)
delouis at bellsouth.net
= = = = = = = = = = = = = = = = =
"Axel Kowald" <kowald at molgen.mpg.de> wrote in message
news:be5u0e$jg1$1 at smc.vnet.net...
> Hello everybody,
>
> I just downloaded the demoversion of Mathematica 5 and tried to find
the
> advertised speed improvements. I got a benchmark notebook from
> http://smc.vnet.net/timings40.html and run it on my old Mathematica
4.1 and the
> new Mathematica 5 on the same machine (1.8GHz, win2k, 768MB RAM).
>
> To my surprise Mathematica 5 was only 1.6% better than the 4.1 version
!!
>
> Any comments ?
>
>
> Axel Kowald
>