FYI With the help of the SQL database I am using now for CAS integration tests, I was able to generate some more interesting observations. Added new statistic section called "Performance based on Rubi rules"
<https://12000.org/my_notes/CAS_integration_tests/reports/summer_2022/indexchapter1.htm#x2-50001.3> <https://12000.org/my_notes/CAS_integration_tests/reports/summer_2022/indexchapter1.htm#x2-50001.3> This section basically looks at how percentage solved by each CAS correlate to how many rules and how many steps Rubi itself used to solve the same integral. I also added histograms showing distribution of leaf size of anti-derivatives for each CAS. Hope this is something that is useful to see. --Nasser On Saturday, September 24, 2022 at 9:09:24 AM UTC-5 Waldek Hebisch wrote: > On Thu, Sep 22, 2022 at 04:37:21AM -0700, 'Nasser M. Abbasi' via FriCAS - > computer algebra system wrote: > > Fyi, > > > > CAS integrations tests SQL database is now fully build. > > > > Thanks for the database. I looked at result in terms of Rubi > steps and FriCAS performace is decreasing with number of Rubi > steps (first is number of steps, second is fraction solved > by FriCAS): > > [1.0, 0.8345051379_1238507301] > [2.0, 0.8338310374 <(833)%20831-0374>_7230517291] > [3.0, 0.8501565276_2501057619] > [4.0, 0.8362068965_5172413793 <(517)%20241-3793>] > [5.0, 0.8186005976 <(818)%20600-5976>_0956175299] > [6.0, 0.8175120430 <(817)%20512-0430>_7169169736 <(716)%20916-9736>] > [7.0, 0.7909229984_7016828149 <(701)%20682-8149>] > [8.0, 0.7562585343_6504324078 <(650)%20432-4078>] > [9.0, 0.7237969676_994067238] > [10.0, 0.6470033034_4502123643 <(450)%20212-3643>] > [11.0, 0.6482444733_4200260078] > [12.0, 0.6384388807_0692194404] > [13.0, 0.6023007395 <(602)%20300-7395>_2341824158] > [14.0, 0.6090225563_9097744361 <(909)%20774-4361>] > [15.0, 0.5511288180_6108897742 <(610)%20889-7742>] > [16.0, 0.6092307692 <(609)%20230-7692>_3076923077] > [17.0, 0.5546719681_9085487078 <(908)%20548-7078>] > [18.0, 0.5558510638_2978723404] > [19.0, 0.5223880597 <(522)%20388-0597>_0149253731] > [20.0, 0.5607843137_2549019608 <(254)%20901-9608>] > > > BTW: I am not sure how you maintain "has_known_anti". The following > 9 have has_known_anti = 0, but belong to well-known class having > elementary integrals: > > integrate(cos(d*x+c)^4/(a+b*sin(d*x+c)^3)^2,x, algorithm="fricas") > integrate(cos(d*x+c)^2/(a+b*sin(d*x+c)^3)^2,x, algorithm="fricas") > integrate(1/(a+b*sin(d*x+c)^3)^2,x, algorithm="fricas") > integrate(sec(d*x+c)^2/(a+b*sin(d*x+c)^3)^2,x, algorithm="fricas") > integrate(sec(d*x+c)^4/(a+b*sin(d*x+c)^3)^2,x, algorithm="fricas") > integrate(sinh(d*x+c)^3/(a+b*tanh(d*x+c)^3),x, algorithm="fricas") > integrate(sinh(d*x+c)/(a+b*tanh(d*x+c)^3),x, algorithm="fricas") > integrate(csch(d*x+c)/(a+b*tanh(d*x+c)^3),x, algorithm="fricas") > integrate(csch(d*x+c)^3/(a+b*tanh(d*x+c)^3),x, algorithm="fricas") > > FriCAS, Maple and almost surely MMa can do them. I suspect that > Maple or MMa answer is nicer, so you can use it as optimal one. > There is buch of others, one would have to check if they are correct. > But the above are easy ones. > > -- > Waldek Hebisch > -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/05cbe489-5fe3-4342-9bcc-002b65a70329n%40googlegroups.com.
