The following table gives the largest ratio found in each test file, between each CAS antiderivative and the optimal antiderivative.
For each test input file, the problem with the largest ratio \(\frac {\text {CAS leaf size}}{\text {Optimal leaf size}}\) is recorded with the corresponding problem number.
In each column in the table below, the first number is the maximum leaf size ratio, and the number that follows inside the parentheses is the problem number in that specific file where this maximum ratio was found. This ratio is determined only when CAS solved the the problem and also when an optimal antiderivative is known.
If it happens that a CAS was not able to solve all the integrals in the input test file, or if it was not possible to obtain leaf size for the CAS result for all the problems in the file, then a zero is used for the ratio and -1 is used for the problem number.
This makes it easy to locate the problem. In the future, a direct link will be added as well. To help make the table fit, Mathematica was abbreviated to MMA and IntegrateAlgebraic to I.A.
| file # | Rubi | MMA | Maple | Maxima | FriCAS | Sympy | Giac | Mupad | I.A. |
| 1 | 7.1 (369) | 23.8 (1217) | 30.9 (1217) | 32.9 (1217) | 32.9 (1217) | 136.1 (671) | 34. (1217) | 38.1 (1217) | 10. (1041) |
| 2 | 1.3 (329) | 16.5 (962) | 22.6 (962) | 22.2 (1577) | 21.8 (962) | 76.7 (2548) | 46.7 (802) | 328.9 (2161) | 46.2 (665) |
| 3 | 2.6 (44) | 2.4 (44) | 4.6 (35) | 2.8 (33) | 10.8 (21) | 49.2 (33) | 10. (33) | 23.6 (21) | 2.6 (43) |
| 4 | 1. (1) | 1.5 (17) | 11. (25) | 4. (25) | 9. (25) | 59.8 (27) | 19.9 (25) | 1.7 (3) | 3.2 (9) |
| 5 | 2.6 (35) | 4.9 (45) | 23.3 (53) | 1.7 (35) | 6.4 (7) | 5.3 (35) | 16.5 (52) | 330.8 (32) | 15.4 (51) |
| 6 | 8.2 (583) | 6.9 (582) | 7.9 (196) | 10. (196) | 10. (196) | 55.3 (519) | 8. (425) | 10.1 (196) | 3.6 (425) |
| 7 | 1.2 (134) | 6.4 (94) | 147.4 (69) | 4.4 (73) | 19.9 (130) | 10.2 (24) | 5.9 (69) | 37.7 (26) | 30.6 (88) |
| 8 | 1. (578) | 11.4 (708) | 46.7 (736) | 3.1 (313) | 17.2 (811) | 28.8 (322) | 8.6 (535) | 224.1 (484) | 2.1 (692) |
| 9 | 1. (1) | 2.6 (29) | 15.2 (23) | 1.3 (15) | 8.1 (26) | 3. (21) | 3. (30) | 1.7 (21) | 12.4 (29) |
| 10 | 1. (1) | 1.1 (13) | 10.4 (9) | 2. (9) | 7. (9) | 43. (10) | 13.8 (9) | 2.5 (1) | 1.3 (13) |
| 11 | 1.2 (169) | 1.9 (45) | 2. (158) | 3.6 (157) | 5.2 (26) | 47.9 (55) | 4. (153) | 1.8 (129) | 1.4 (43) |
| 12 | 8.4 (2158) | 13.4 (2357) | 141.8 (2357) | 13.2 (1809) | 23. (2357) | 84.8 (1312) | 28.4 (2260) | 16.4 (2357) | 11.3 (2079) |
| 13 | 4.3 (81) | 4.6 (236) | 17.9 (168) | 4. (35) | 15.1 (168) | 27.8 (141) | 6. (183) | 62.5 (109) | 2.8 (198) |
| 14 | 4.2 (492) | 12.3 (672) | 77.4 (336) | 29.1 (684) | 17.4 (237) | 36.6 (124) | 9.8 (673) | 78.2 (320) | 16.5 (645) |
| 15 | 1. (1) | 0.9 (9) | 51.1 (9) | 2.5 (9) | 28.4 (9) | 78.7 (3) | 49.5 (10) | 7.2 (9) | 0. (-1) |
| 16 | 1. (1) | 3.8 (45) | 10.4 (43) | 10. (43) | 47.2 (62) | 14.9 (417) | 8.1 (424) | 34.3 (124) | 3. (6) |
| 17 | 1. (1) | 10. (231) | 51.5 (207) | 11.2 (251) | 10.2 (251) | 10. (231) | 10.6 (234) | 12.5 (251) | 8. (251) |
| 18 | 1. (1) | 6.4 (228) | 4.9 (220) | 3.2 (114) | 4. (220) | 21.6 (220) | 6.3 (220) | 3.4 (190) | 1.9 (28) |
| 19 | 2.8 (64) | 3.9 (25) | 5.8 (55) | 2.2 (64) | 7.2 (108) | 16.4 (44) | 3.1 (55) | 3.5 (25) | 8.1 (25) |
| 20 | 2. (2088) | 23.9 (1971) | 70.8 (2020) | 28.7 (477) | 36.4 (1962) | 67.3 (1143) | 39.4 (1707) | 209.3 (1969) | 228.8 (1646) |
| 21 | 1.3 (1297) | 7.2 (2335) | 82.2 (1035) | 50.9 (1940) | 46.2 (1278) | 64.1 (936) | 28.9 (1401) | 179.2 (1977) | 148. (1990) |
| 22 | 2.1 (576) | 58.6 (328) | 116.1 (552) | 5.9 (381) | 34. (418) | 71.6 (629) | 20. (631) | 201.9 (561) | 228.8 (316) |
| 23 | 1. (1) | 10.3 (6) | 425.1 (75) | 2.7 (92) | 30.2 (109) | 1.2 (16) | 13.3 (5) | 3. (97) | 70.4 (110) |
| 24 | 1. (129) | 9.7 (37) | 14197.2 (12) | 6.6 (27) | 30.2 (117) | 8.6 (14) | 5.8 (37) | 110.2 (16) | 5.6 (24) |
| 25 | 1.8 (76) | 42.8 (200) | 421. (258) | 89. (258) | 123.4 (258) | 114.1 (258) | 119.2 (258) | 101.3 (258) | 40.9 (196) |
| 26 | 1.7 (464) | 4.3 (295) | 9.5 (688) | 5.4 (343) | 25.4 (844) | 28.5 (856) | 13.7 (688) | 91.3 (855) | 26.2 (752) |
| 27 | 1.7 (154) | 13.9 (210) | 50.7 (162) | 6.5 (76) | 33.5 (97) | 15.8 (206) | 110.2 (158) | 360. (197) | 2.5 (164) |
| 28 | 1.7 (274) | 32.6 (281) | 26. (114) | 5.6 (50) | 55.6 (227) | 47.5 (156) | 35.3 (231) | 123.2 (231) | 28.8 (238) |
| 29 | 1. (59) | 1.5 (25) | 15.8 (54) | 1.4 (106) | 2.6 (46) | 43. (11) | 21.7 (25) | 107.5 (41) | 1. (103) |
| 30 | 1.6 (133) | 2.4 (134) | 13.8 (37) | 1.6 (129) | 48.1 (58) | 27.3 (39) | 20.4 (58) | 94.8 (128) | 3. (132) |
| 31 | 1. (1) | 3. (2) | 2.8 (1) | 0. (-1) | 4.2 (2) | 0. (-1) | 2.5 (9) | 3.8 (1) | 1.1 (2) |
| 32 | 2.1 (141) | 5.8 (496) | 54.7 (496) | 6.3 (496) | 46.7 (524) | 21.4 (493) | 46.6 (492) | 99.1 (261) | 17.5 (114) |
| 33 | 1. (1) | 1.9 (26) | 2.7 (37) | 1.8 (44) | 12.2 (37) | 42.2 (44) | 15.3 (37) | 116. (41) | 0. (-1) |
| 34 | 1. (59) | 12.9 (72) | 2909.3 (71) | 88.7 (74) | 90.4 (71) | 82.9 (71) | 73.6 (74) | 165.9 (43) | 64.6 (74) |
| 35 | 1. (1) | 1. (4) | 1.7 (3) | 2.1 (8) | 2.2 (8) | 3.2 (3) | 3.3 (8) | 215.3 (1) | 1.1 (2) |
| 36 | 1. (1) | 1.7 (99) | 4. (72) | 1.1 (72) | 9.5 (102) | 18.1 (72) | 12.1 (79) | 41.4 (99) | 1.4 (112) |
| 37 | 6.2 (420) | 11.6 (158) | 1223.1 (188) | 42.3 (59) | 93.1 (188) | 84.3 (188) | 27.1 (198) | 166.7 (20) | 2.8 (98) |
| 38 | 4.1 (689) | 172.1 (699) | 3059.3 (699) | 5.1 (357) | 40.5 (574) | 58.4 (55) | 16.9 (191) | 54.2 (187) | 51.8 (192) |
| 39 | 135.9 (517) | 2947.4 (1435) | 2183.5 (589) | 6.9 (940) | 90.4 (889) | 99.5 (780) | 4.5 (2303) | 323.4 (2346) | 2.4 (2379) |