A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34 }
B grade: { }
C grade: { }
F grade: { }
A grade: { 2, 3, 7, 16, 19, 20, 32, 33, 34 }
B grade: { 9, 10, 11, 12, 13, 14, 15, 25, 26, 27, 28, 29, 30, 31 }
C grade: { 1, 5, 6, 8, 17, 18, 22, 23, 24 }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 }
A grade: { 32 }
B grade: { 1, 2, 3, 18, 19, 20 }
C grade: { }
F grade: { 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34 }
A grade: { 2, 3, 19, 20, 32, 34 }
C grade: { }
F grade: { 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33 }
A grade: { 32 }
B grade: { }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34 }
A grade: { 32 }
B grade: { }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34 }
A grade: { 34 }
B grade: { 1, 2, 3, 18, 19, 20, 32, 33 }
C grade: { }
F grade: { 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 }
Detailed conclusion table per each integral is given by table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given just an F.
In this table,the column normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\)
Problem 1 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | F | B | B | F(-1) | F | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 384 | 384 | 899 | 0 | 892 | 777 | 0 | 0 | 1110 |
normalized size | 1 | 1.00 | 2.34 | 0.00 | 2.32 | 2.02 | 0.00 | 0.00 | 2.89 |
time (sec) | N/A | 0.932 | 6.981 | 3.656 | 0.882 | 0.558 | 0.000 | 0.000 | 23.158 |
Problem 2 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | F | B | A | F(-1) | F | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 285 | 264 | 0 | 648 | 461 | 0 | 0 | 714 |
normalized size | 1 | 1.00 | 0.93 | 0.00 | 2.27 | 1.62 | 0.00 | 0.00 | 2.51 |
time (sec) | N/A | 0.719 | 3.629 | 3.632 | 0.718 | 0.486 | 0.000 | 0.000 | 20.659 |
Problem 3 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | F | B | A | F | F | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 180 | 160 | 0 | 441 | 261 | 0 | 0 | 185 |
normalized size | 1 | 1.00 | 0.89 | 0.00 | 2.45 | 1.45 | 0.00 | 0.00 | 1.03 |
time (sec) | N/A | 0.570 | 0.807 | 3.585 | 0.828 | 0.474 | 0.000 | 0.000 | 17.164 |
Problem 4 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | F(-1) | F | F | F | F | F | F |
verified | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 123 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.293 | 180.002 | 3.400 | 0.000 | 0.431 | 0.000 | 0.000 | 0.000 |
Problem 5 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | F | F | F | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 202 | 4061 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 20.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.586 | 7.130 | 3.300 | 0.000 | 0.467 | 0.000 | 0.000 | 0.000 |
Problem 6 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | F | F | F | F(-1) | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 207 | 8316 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 40.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.628 | 7.081 | 3.419 | 0.000 | 0.473 | 0.000 | 0.000 | 0.000 |
Problem 7 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F | F | F | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 167 | 190 | 343 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.14 | 2.05 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.651 | 0.622 | 0.826 | 0.000 | 2.005 | 0.000 | 0.000 | 0.000 |
Problem 8 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | F | F | F | F(-1) | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 257 | 4861 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 18.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.665 | 15.324 | 10.347 | 0.000 | 0.479 | 0.000 | 0.000 | 0.000 |
Problem 9 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | F | F | F | F(-1) | F(-1) | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 366 | 365 | 1873 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 5.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.812 | 8.546 | 3.770 | 0.000 | 0.566 | 0.000 | 0.000 | 0.000 |
Problem 10 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | F | F | F | F(-1) | F(-1) | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 392 | 392 | 7530 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 19.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.992 | 59.054 | 20.396 | 0.000 | 0.541 | 0.000 | 0.000 | 0.000 |
Problem 11 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | F | F | F | F(-1) | F(-1) | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 385 | 384 | 4492 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 11.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.974 | 18.158 | 3.643 | 0.000 | 0.559 | 0.000 | 0.000 | 0.000 |
Problem 12 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | F | F | F | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 375 | 374 | 1874 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 5.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.863 | 7.769 | 3.568 | 0.000 | 0.525 | 0.000 | 0.000 | 0.000 |
Problem 13 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | F | F | F | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 365 | 365 | 9629 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 26.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.870 | 31.235 | 1.959 | 0.000 | 0.478 | 0.000 | 0.000 | 0.000 |
Problem 14 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | F | F | F | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 413 | 413 | 19634 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 47.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.958 | 32.111 | 1.933 | 0.000 | 0.491 | 0.000 | 0.000 | 0.000 |
Problem 15 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | F | F | F | F(-1) | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 424 | 424 | 25065 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 59.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 1.035 | 32.456 | 1.940 | 0.000 | 0.556 | 0.000 | 0.000 | 0.000 |
Problem 16 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F | F | F | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 174 | 196 | 476 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.13 | 2.74 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.686 | 0.733 | 0.942 | 0.000 | 4.627 | 0.000 | 0.000 | 0.000 |
Problem 17 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | F | F | F | F(-1) | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 269 | 269 | 6226 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 23.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.745 | 16.504 | 13.733 | 0.000 | 0.471 | 0.000 | 0.000 | 0.000 |
Problem 18 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | F | B | B | F(-1) | F | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 435 | 435 | 1029 | 0 | 1324 | 937 | 0 | 0 | 1253 |
normalized size | 1 | 1.00 | 2.37 | 0.00 | 3.04 | 2.15 | 0.00 | 0.00 | 2.88 |
time (sec) | N/A | 0.892 | 7.235 | 6.268 | 0.723 | 0.544 | 0.000 | 0.000 | 22.847 |
Problem 19 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | F | B | A | F(-1) | F | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 322 | 322 | 306 | 0 | 950 | 563 | 0 | 0 | 790 |
normalized size | 1 | 1.00 | 0.95 | 0.00 | 2.95 | 1.75 | 0.00 | 0.00 | 2.45 |
time (sec) | N/A | 0.711 | 5.112 | 6.067 | 0.587 | 0.542 | 0.000 | 0.000 | 23.159 |
Problem 20 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | F | B | A | F | F | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 197 | 177 | 0 | 644 | 310 | 0 | 0 | 510 |
normalized size | 1 | 1.00 | 0.90 | 0.00 | 3.27 | 1.57 | 0.00 | 0.00 | 2.59 |
time (sec) | N/A | 0.629 | 1.063 | 5.906 | 0.687 | 0.483 | 0.000 | 0.000 | 19.422 |
Problem 21 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | F(-1) | F | F | F | F | F | F |
verified | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 170 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.468 | 180.004 | 4.334 | 0.000 | 0.472 | 0.000 | 0.000 | 0.000 |
Problem 22 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | F | F | F | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 216 | 4066 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 18.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.678 | 7.171 | 4.128 | 0.000 | 0.460 | 0.000 | 0.000 | 0.000 |
Problem 23 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | F | F | F | F(-1) | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 230 | 230 | 8321 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 36.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.697 | 7.316 | 4.200 | 0.000 | 0.479 | 0.000 | 0.000 | 0.000 |
Problem 24 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | F | F | F | F(-1) | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 232 | 1087 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 4.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.720 | 17.383 | 20.079 | 0.000 | 0.457 | 0.000 | 0.000 | 0.000 |
Problem 25 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | F | F | F | F(-1) | F(-1) | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 383 | 381 | 2572 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.99 | 6.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.904 | 8.767 | 4.481 | 0.000 | 0.552 | 0.000 | 0.000 | 0.000 |
Problem 26 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | F | F | F | F(-1) | F(-1) | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 410 | 410 | 5175 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 12.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 1.060 | 40.078 | 24.343 | 0.000 | 0.537 | 0.000 | 0.000 | 0.000 |
Problem 27 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | F | F | F | F(-1) | F(-1) | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 406 | 403 | 6591 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.99 | 16.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 1.034 | 9.628 | 4.473 | 0.000 | 0.563 | 0.000 | 0.000 | 0.000 |
Problem 28 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | F | F | F | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 396 | 393 | 2574 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.99 | 6.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.923 | 8.518 | 4.240 | 0.000 | 0.560 | 0.000 | 0.000 | 0.000 |
Problem 29 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | F | F | F | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 389 | 386 | 9760 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.99 | 25.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.928 | 32.508 | 4.052 | 0.000 | 0.478 | 0.000 | 0.000 | 0.000 |
Problem 30 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | F | F | F | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 433 | 433 | 31369 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 72.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 1.090 | 33.051 | 3.959 | 0.000 | 0.492 | 0.000 | 0.000 | 0.000 |
Problem 31 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | F | F | F | F(-1) | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 451 | 451 | 20654 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 45.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 1.163 | 33.476 | 3.999 | 0.000 | 0.565 | 0.000 | 0.000 | 0.000 |
Problem 32 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | A | A | A | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 113 | 92 | 104 | 102 | 71 | 189 | 76 | 93 |
normalized size | 1 | 1.40 | 1.14 | 1.28 | 1.26 | 0.88 | 2.33 | 0.94 | 1.15 |
time (sec) | N/A | 0.102 | 0.214 | 0.326 | 0.333 | 0.447 | 0.794 | 0.134 | 13.758 |
Problem 33 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F | F | F(-1) | F | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 97 | 516 | 0 | 0 | 0 | 0 | 169 |
normalized size | 1 | 1.00 | 0.83 | 4.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.44 |
time (sec) | N/A | 0.219 | 0.875 | 1.455 | 0.000 | 0.466 | 0.000 | 0.000 | 14.847 |
Problem 34 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | F(-1) | A | F(-2) | F(-1) | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) | N/A | 0.118 | 46.523 | 4.256 | 0.000 | 2.380 | 0.000 | 0.000 | 0.000 |
The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [10] had the largest ratio of [.1707]
# | grade |
|
|
|
|
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\) | |||||||||||
1 | A | 5 | 4 | 1.00 | 40 | 0.100 | |||||||||||
2 | A | 4 | 4 | 1.00 | 40 | 0.100 | |||||||||||
3 | A | 4 | 3 | 1.00 | 40 | 0.075 | |||||||||||
4 | A | 4 | 4 | 1.00 | 40 | 0.100 | |||||||||||
5 | A | 5 | 5 | 1.00 | 40 | 0.125 | |||||||||||
6 | A | 5 | 5 | 1.00 | 40 | 0.125 | |||||||||||
7 | A | 8 | 5 | 1.00 | 42 | 0.119 | |||||||||||
8 | A | 6 | 6 | 1.00 | 38 | 0.158 | |||||||||||
9 | A | 10 | 6 | 1.00 | 37 | 0.162 | |||||||||||
10 | A | 8 | 7 | 1.00 | 41 | 0.171 | |||||||||||
11 | A | 10 | 6 | 1.00 | 39 | 0.154 | |||||||||||
12 | A | 10 | 6 | 1.00 | 39 | 0.154 | |||||||||||
13 | A | 10 | 6 | 1.00 | 39 | 0.154 | |||||||||||
14 | A | 10 | 6 | 1.00 | 39 | 0.154 | |||||||||||
15 | A | 10 | 6 | 1.00 | 39 | 0.154 | |||||||||||
16 | A | 8 | 5 | 1.00 | 50 | 0.100 | |||||||||||
17 | A | 6 | 6 | 1.00 | 46 | 0.130 | |||||||||||
18 | A | 5 | 4 | 1.00 | 48 | 0.083 | |||||||||||
19 | A | 4 | 4 | 1.00 | 48 | 0.083 | |||||||||||
20 | A | 4 | 3 | 1.00 | 48 | 0.062 | |||||||||||
21 | A | 5 | 5 | 1.00 | 48 | 0.104 | |||||||||||
22 | A | 5 | 5 | 1.00 | 48 | 0.104 | |||||||||||
23 | A | 5 | 5 | 1.00 | 48 | 0.104 | |||||||||||
24 | A | 6 | 6 | 1.00 | 50 | 0.120 | |||||||||||
25 | A | 10 | 6 | 0.99 | 45 | 0.133 | |||||||||||
26 | A | 8 | 7 | 1.00 | 49 | 0.143 | |||||||||||
27 | A | 10 | 6 | 0.99 | 47 | 0.128 | |||||||||||
28 | A | 10 | 6 | 0.99 | 47 | 0.128 | |||||||||||
29 | A | 10 | 6 | 0.99 | 47 | 0.128 | |||||||||||
30 | A | 10 | 6 | 1.00 | 47 | 0.128 | |||||||||||
31 | A | 10 | 6 | 1.00 | 47 | 0.128 | |||||||||||
32 | A | 2 | 2 | 1.40 | 31 | 0.065 | |||||||||||
33 | A | 5 | 5 | 1.00 | 41 | 0.122 | |||||||||||
34 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||