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Topic: An independent integration test suite
Replies: 128   Last Post: Dec 8, 2013 3:21 PM

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clicliclic@freenet.de

Posts: 981
Registered: 4/26/08
Re: The A. F. Timofeev symbolic integration test suite
Posted: Oct 5, 2013 7:34 AM
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Albert Rich schrieb:
>
> The 84 integration problems in the Timofeev Chapter 1 test suite and
> their optimal antiderivatives is now available as a pdf file at
>
> http://www.apmaths.uwo.ca/~arich/TimofeevChapter1TestResults.pdf
>
> Also shown in the file are the test scores on each problem earned by
> various integrators. The bottom line totals were as follows:
>
> Rubi 4.2 Mathematica 9 Derive 6.1 Maple 17 Maxima 5.28
> Totals: 168 161 158 161 158
> Percent: 100% 95.8% 94.0% 95.8% 94.0%
>


You have replaced "+-" by "+" in examples #14 and #15 on p. 26. In your
place I would prefer if Timofeev's choice of integrands (inasmuch as
they can be inferred from the printed book at all) were not modified in
any way, lest you open yourself to accusations of having introduced a
selection bias which compromises the strict neutrality of the test suite
- Timofeev couldn't have known about the systems tested, but you do.
Hence I suggest to duplicate these integrands to "+" and "-" versions
and to split the example numbers into 14a/b and 15a/b. In fact, integral
tables and symbolic integrators often distinguish between expressions
like b^2*SIN(x)^2 + a^2 and b^2*SIN(x)^2 - a^2, although the evaluations
in these two cases are not much affected (which fact is worth noting
too).

This being a matter of principle, the choice of model antiderivatives is
often just a matter of taste. In examples #16 and #56 you list the
simpler but discontinuous ATAN evaluations. Are you retracting your
statement of June 18 that "continuity of antiderivatives trumps
compactness"?

<http://mathforum.org/kb/thread.jspa?forumID=228&threadID=2573190&messageID=9138546>

In the evaluation of example #59, -4 + 4*SIN(x)^2 may be simplified to
-4*COS(x)^2, and the evaluation of example #70 can (accidentally?) be
written more compactly as 1/48*SIN(2*x)^3 - 1/64*SIN(4*x) + x/16.

Finally a more detailed explanation why ATANH(1-2*x^2) in your
evaluation of example #42 from Chapter 9 is bad: The vast majority of
people being presented with an integrand like x^2*ASEC(x)/(x^2-1)^(5/2)
do attach meaning to it for real x with |x| > 1 only. Similarly, they
attach meaning to ATANH(1-2*x^2) for real 1-2*x^2 with |1-2*x^2| < 1
only. Your antiderivative is consequently meaningless to them - and this
group is likely to include almost all of Professor Charlwood's students.

Martin.


Date Subject Author
2/24/13
Read An independent integration test suite
clicliclic@freenet.de
3/19/13
Read where the air gets thin for Axiom & Co.
clicliclic@freenet.de
3/21/13
Read Re: where the air gets thin for Axiom & Co.
Waldek Hebisch
3/22/13
Read Re: where the air gets thin for Axiom & Co.
clicliclic@freenet.de
3/26/13
Read Re: where the air gets thin for Axiom & Co.
Waldek Hebisch
3/26/13
Read Re: where the air gets thin for Axiom & Co.
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Nasser Abbasi
4/20/13
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Rouben Rostamian
4/20/13
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clicliclic@freenet.de
4/20/13
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Rouben Rostamian
4/20/13
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Axel Vogt
4/20/13
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clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Axel Vogt
4/21/13
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Axel Vogt
4/21/13
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clicliclic@freenet.de
4/21/13
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Waldek Hebisch
4/22/13
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clicliclic@freenet.de
4/22/13
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Axel Vogt
4/22/13
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clicliclic@freenet.de
4/23/13
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Waldek Hebisch
4/24/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/25/13
Read Re: An independent integration test suite
Waldek Hebisch
4/26/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/27/13
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Waldek Hebisch
4/24/13
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Richard Fateman
4/24/13
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clicliclic@freenet.de
4/25/13
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Richard Fateman
4/26/13
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clicliclic@freenet.de
4/26/13
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Axel Vogt
4/27/13
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clicliclic@freenet.de
4/25/13
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Waldek Hebisch
4/25/13
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Peter Pein
4/25/13
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Nasser Abbasi
4/26/13
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Peter Pein
4/26/13
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clicliclic@freenet.de
4/26/13
Read Re: An independent integration test suite
Peter Pein
4/26/13
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clicliclic@freenet.de
4/26/13
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Richard Fateman
4/27/13
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clicliclic@freenet.de
4/27/13
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Richard Fateman
6/30/13
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clicliclic@freenet.de
6/30/13
Read Re: An independent integration test suite / Chap 3
Axel Vogt
7/1/13
Read Re: An independent integration test suite / Chap 3
clicliclic@freenet.de
7/1/13
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Axel Vogt
7/1/13
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Waldek Hebisch
7/2/13
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clicliclic@freenet.de
7/2/13
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clicliclic@freenet.de
7/2/13
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clicliclic@freenet.de
7/2/13
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Nasser Abbasi
7/2/13
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Nasser Abbasi
7/4/13
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clicliclic@freenet.de
7/4/13
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Nasser Abbasi
7/4/13
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Nasser Abbasi
7/5/13
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clicliclic@freenet.de
7/5/13
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Nasser Abbasi
7/9/13
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7/10/13
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Nasser Abbasi
7/10/13
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Richard Fateman
7/10/13
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Nasser Abbasi
7/10/13
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clicliclic@freenet.de
8/6/13
Read Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/15/13
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Albert D. Rich
9/15/13
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clicliclic@freenet.de
9/15/13
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clicliclic@freenet.de
9/21/13
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Albert D. Rich
9/21/13
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clicliclic@freenet.de
9/22/13
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daly@axiom-developer.org
9/24/13
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9/30/13
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9/22/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/25/13
Read The Timofeev symbolic integration test suite
Albert D. Rich
9/25/13
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Albert D. Rich
9/25/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/25/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/26/13
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Albert D. Rich
9/26/13
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clicliclic@freenet.de
9/26/13
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Albert D. Rich
9/29/13
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clicliclic@freenet.de
10/1/13
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10/1/13
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clicliclic@freenet.de
10/1/13
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Albert D. Rich
10/5/13
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clicliclic@freenet.de
10/5/13
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Albert D. Rich
10/6/13
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clicliclic@freenet.de
10/10/13
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Albert D. Rich
10/10/13
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Nasser Abbasi
10/11/13
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clicliclic@freenet.de
11/6/13
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Albert D. Rich
11/6/13
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11/7/13
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did
11/7/13
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11/7/13
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11/12/13
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11/12/13
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Albert D. Rich
11/13/13
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11/13/13
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Albert D. Rich
11/14/13
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clicliclic@freenet.de
11/14/13
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Albert D. Rich
11/15/13
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clicliclic@freenet.de
11/15/13
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Albert D. Rich
11/16/13
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clicliclic@freenet.de
11/16/13
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11/21/13
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Albert D. Rich
11/21/13
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clicliclic@freenet.de
11/21/13
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Nasser Abbasi
11/21/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/21/13
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Albert D. Rich
11/22/13
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clicliclic@freenet.de
11/14/13
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Albert D. Rich
11/15/13
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clicliclic@freenet.de
11/15/13
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Nasser Abbasi
11/16/13
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clicliclic@freenet.de
11/16/13
Read Re: The A. F. Timofeev symbolic integration test suite
Nasser Abbasi
11/7/13
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did
11/7/13
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clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Richard Fateman
4/21/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Axel Vogt
4/20/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Waldek Hebisch
4/21/13
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G. A. Edgar
12/8/13
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clicliclic@freenet.de
10/5/13
Read Re: An independent integration test suite
Albert D. Rich
10/6/13
Read Re: An independent integration test suite
clicliclic@freenet.de

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