Riccardo Guida wrote:
> I write the question here because I think that Nasser Abbasi is in the list
> and maybe he could comment on this topic that in my view is quite important
> for FriCAS.
>
> I was eager to know the results of Nasser's test [1] with Rubi' integration
> suite, which includes Maple, Mathematica and (beginning 2018) also FriCAS.
> Having a good rating in comparison with M&M would obviously be a very good
> advertisement for FriCAS ...but apparently FriCAS is not included in the
> final result with 7 10^4 integrals, only in the small benchmark. Why? Is
> this a problem that can be fixed?
I can not answer for Nasser, but I run parts of Rubi testsuite at
various times and have some observations. On earlier version
of Rubi testsuite which had about 10000 integrals FriCAS was
close to 100% effective on elementary functions. More precisely,
there more than 7000 integrals with elementary answers and
FriCAS failed on about 40 and did all other. OTOH failure
rate on integrals expressible in terms of special functions
was quite high. Running time had "heavy tail", that is most
integrals were done in less than 10ms, but many integrals
required several seconds and some required hours. In effect
average time was much higher than median time and time for
running testsuite was high.
What changed? FriCAS is now much better at finding integrals
with nonelementary answer. There are some speed improvements
but most integrals that were slow still is slow. Rubi testsuite
is now highly unbalanced. About 80% of it consists of families
forming regular pattern, mostly combinations of roots.
Such integrals may require quite long time to do. Some fail
due to capacity limitations, some hit unimplemented cases
in Trager algorithm.
Part that Nasser run consists of integrals collected from
various sources and IMO is more balanced than whole testsuite.
It contains several tricky examples integrable in terms of
elementary functions and gives FriCAS opportunity to show
its strength. I expect that if sombody runs the whole testsuite
results will be worse. Namely, the large familes that I mention
above contains many integrals integrable in terms of elliptic
functions or hypergeometric functions -- but not in terms of
elementary functions. FriCAS currently can not do integrals
integrable in terms of such functions. So significant part
of Rubi testuite (of order of 20%) will fail in FriCAS, but
will take a lot of time (FriCAS will try to find elementary
answer and hit unimplemented part or finally declare integral
as nonelementary).
As I wrote several integrals in Rubi testsuite take extremally
long time. It it possible that some go into infinite loop,
but since there are similar examples that simply need long
time it is hard finnd out which one simply require bigger
and faster computer and which one will never terminate.
I suspect that long runtime is main reason that Nasser did
not gave full results.
Of course running the whole testsuite is of some interest, it
is likely to uncover some bugs. But the main info will be
about exact composition of testsuite: if integral is expressible
in terms of functions which FriCAS handles there is high
probability that FriCAS will do it. If integral needs
functions that FriCAS can not genererate, than of course
integral will fail. I have run parts of testsuite, but
ATM for me information gain from running more of it does
not justify effort.
--
Waldek Hebisch
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