Some (alarming?) information, for some integrals, if you run them
in a fresh session, there's no problem, but when run as part of
the test set, FriCAS gives wrong answer.
Example integrals are:
x*(tan(x**2 - 4)**2 + 1)*(tan(1/(2*(tan(x**2 - 4) + 1)))**2 +
1)/(2*(tan(x**2 - 4) + 1)**2*sqrt(tan(1/(2*(tan(x**2 - 4) + 1))))) + 0
(6*x**2 + 1)*sin(2*x**3 + x + log(3)**5)/cosh(cos(2*x**3 + x +
log(3)**5))**2 + 0
On 11/26/20 5:51 PM, Qian Yun wrote:
6. The DL system is slow. To solve the FWD test set, the DL system
may use around 100 hours of CPU time.
You mean 10000 examples? That would be average 36 seconds
per example... IIUC you run on CPU, they probably got
much shorter runtime on GPU.
Solve one example takes around 2 seconds with over 10 threads.
7. For the BWD test set, (which is generate random expression first,
then take derivatives as integrand), FriCAS can roughly solve 95%.
Compared with DL's claimed 99.5%. The paper says Mathematica can
solve 84.0%, I'll a little skeptical about that.
I posted here generator that attemped to match parameters
to the DL paper and got 78% success rate. That discoverd
few bugs and percentage should be higher now, but much
lower than 95%. So apparently they used easier examples
(several details in the paper were rather unclear and
I had to use my guesses). I wonder how well DL would
do on examples from my generator? In particular, the
paper does not mention simplification of examples.
Unsimplified derivatives tend to contain visible traces
of primitive, after simplification problem gets harder.
The "95%" number was based on the first 1000 integrals or so.
So I did a full run and I'm attaching my test run log.
I took the first 7707 integrals from the tests (minus integrals
containing 'sign(x)' and treating 'Abs(x)' as 'x').
I use a timeout of 10 seconds for FriCAS to run this test.
The total run time of FriCAS is 40 minutes.
There are 191 timeout, 530 integration error, and 61
integrals that FriCAS falsely claim it's unintegrable.
So success rate is 89.8%.
(I didn't 'diff' them back and use 'normalize' to check equality,
there are extra complexity involving constant that are complex number.)
(There are regressions between 1.3.4 and 1.3.5, I'm looking at some.)
- Qian
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