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, 35 }
B grade: { }
C grade: { }
F grade: { }
A grade: { 8, 9, 13, 14, 23, 24 }
B grade: { 6, 7, 10, 11, 12, 15, 21, 22, 25, 31, 32, 33, 34, 35 }
C grade: { 1, 2, 3, 4, 5, 16, 17, 18, 19, 20, 26, 27, 28, 29, 30 }
F grade: { }
A grade: { }
B 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, 35 }
C grade: { }
F grade: { }
A grade: { }
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, 32, 33, 34, 35 }
A grade: { }
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, 32, 33, 34, 35 }
A grade: { }
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, 32, 33, 34, 35 }
A grade: { }
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, 32, 33, 34, 35 }
A grade: { }
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, 32, 33, 34, 35 }
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 | B | F | F | F(-1) | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 700 | 699 | 806 | 8125 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.15 | 11.61 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 2.332 | 11.825 | 0.077 | 0.000 | 0.591 | 0.000 | 0.000 | 0.000 |
Problem 2 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | B | F | F | F(-1) | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 405 | 404 | 450 | 3224 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.11 | 7.96 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.858 | 5.276 | 0.036 | 0.000 | 0.573 | 0.000 | 0.000 | 0.000 |
Problem 3 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | B | F | F | F | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 284 | 284 | 319 | 559 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.12 | 1.97 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.172 | 1.949 | 0.028 | 0.000 | 0.525 | 0.000 | 0.000 | 0.000 |
Problem 4 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | B | F | F(-1) | F(-1) | F(-2) | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 313 | 313 | 245 | 665 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.78 | 2.12 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.747 | 2.097 | 0.041 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Problem 5 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | B | F | F(-1) | F(-1) | F(-1) | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 678 | 678 | 14548 | 13380 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 21.46 | 19.73 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 1.535 | 15.855 | 0.115 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Problem 6 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | B | F | F(-1) | F(-1) | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 981 | 976 | 21611 | 54623 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.99 | 22.03 | 55.68 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 3.412 | 18.156 | 0.156 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Problem 7 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | B | F | F(-1) | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 736 | 735 | 6648 | 20733 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 9.03 | 28.17 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.660 | 15.852 | 0.087 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Problem 8 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F | F(-1) | F | F(-2) | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 442 | 442 | 586 | 2453 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.33 | 5.55 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.461 | 6.376 | 0.092 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Problem 9 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F | F | F(-1) | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 606 | 606 | 333 | 9328 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.55 | 15.39 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.986 | 9.587 | 0.180 | 0.000 | 6.134 | 0.000 | 0.000 | 0.000 |
Problem 10 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | B | F | F | F(-1) | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1081 | 1080 | 10667 | 71656 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 9.87 | 66.29 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 3.372 | 24.057 | 1.783 | 0.000 | 10.478 | 0.000 | 0.000 | 0.000 |
Problem 11 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | B | F | F(-1) | F(-1) | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 898 | 897 | 14893 | 35476 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 16.58 | 39.51 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 2.518 | 16.066 | 0.121 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Problem 12 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | B | F | F(-1) | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 472 | 472 | 6583 | 13177 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 13.95 | 27.92 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.520 | 15.463 | 0.073 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Problem 13 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F | F(-1) | F | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 449 | 449 | 724 | 2454 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.61 | 5.47 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.464 | 7.556 | 0.075 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Problem 14 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F | F | F(-1) | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 625 | 625 | 341 | 12900 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.55 | 20.64 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 1.063 | 9.177 | 0.136 | 0.000 | 7.789 | 0.000 | 0.000 | 0.000 |
Problem 15 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | B | F | F | F(-1) | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1090 | 1090 | 10629 | 65243 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 9.75 | 59.86 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 3.016 | 20.646 | 0.866 | 0.000 | 8.566 | 0.000 | 0.000 | 0.000 |
Problem 16 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | B | F | F | F(-1) | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 721 | 720 | 825 | 8421 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.14 | 11.68 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 1.922 | 12.757 | 0.059 | 0.000 | 1.481 | 0.000 | 0.000 | 0.000 |
Problem 17 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | B | F | F | F | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 410 | 410 | 442 | 2825 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.08 | 6.89 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.586 | 6.618 | 0.040 | 0.000 | 1.232 | 0.000 | 0.000 | 0.000 |
Problem 18 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | B | F | F | F(-1) | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 291 | 291 | 326 | 673 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.12 | 2.31 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.279 | 2.476 | 0.029 | 0.000 | 1.000 | 0.000 | 0.000 | 0.000 |
Problem 19 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | B | F | F(-1) | F(-1) | F(-2) | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 309 | 309 | 249 | 663 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.81 | 2.15 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.821 | 1.652 | 0.043 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Problem 20 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | B | F | F(-1) | F(-1) | F(-1) | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 680 | 680 | 16859 | 13405 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 24.79 | 19.71 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 1.815 | 16.316 | 0.092 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Problem 21 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | B | F | F(-1) | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 980 | 976 | 21611 | 55327 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 22.05 | 56.46 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 2.787 | 18.120 | 0.155 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Problem 22 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | B | F | F(-1) | F(-1) | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 734 | 732 | 6667 | 20235 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 9.08 | 27.57 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.712 | 15.845 | 0.086 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Problem 23 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F | F(-1) | F(-1) | F(-2) | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 436 | 436 | 583 | 3003 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.34 | 6.89 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.512 | 6.839 | 0.097 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Problem 24 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F | F | F(-1) | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 616 | 616 | 340 | 9443 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.55 | 15.33 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 1.170 | 10.479 | 0.202 | 0.000 | 7.575 | 0.000 | 0.000 | 0.000 |
Problem 25 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | B | F | F | F(-1) | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1128 | 1119 | 10675 | 75992 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.99 | 9.46 | 67.37 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 4.299 | 25.175 | 1.881 | 0.000 | 16.305 | 0.000 | 0.000 | 0.000 |
Problem 26 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | B | F | F | F(-1) | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1097 | 1083 | 18383 | 12279 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.99 | 16.76 | 11.19 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 3.301 | 18.134 | 0.092 | 0.000 | 1.385 | 0.000 | 0.000 | 0.000 |
Problem 27 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | B | F | F | F(-1) | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 611 | 608 | 686 | 5679 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.12 | 9.29 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 1.357 | 9.385 | 0.045 | 0.000 | 1.230 | 0.000 | 0.000 | 0.000 |
Problem 28 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | B | F | F | F | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 368 | 367 | 390 | 1804 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.06 | 4.90 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.490 | 4.649 | 0.031 | 0.000 | 0.964 | 0.000 | 0.000 | 0.000 |
Problem 29 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | B | F | F(-1) | F(-1) | F(-2) | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 465 | 465 | 1036 | 1368 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.23 | 2.94 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.806 | 8.110 | 0.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Problem 30 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | B | F | F(-1) | F(-1) | F(-1) | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 738 | 738 | 637 | 17460 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.86 | 23.66 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 1.907 | 15.202 | 0.115 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Problem 31 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | B | F | F(-1) | F(-1) | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1395 | 1376 | 38402 | 89496 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.99 | 27.53 | 64.15 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 5.742 | 23.826 | 0.260 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Problem 32 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | B | F | F(-1) | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 937 | 936 | 16699 | 42545 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 17.82 | 45.41 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 2.283 | 17.321 | 0.128 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Problem 33 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | B | F | F(-1) | F(-1) | F(-2) | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 757 | 757 | 6223 | 15875 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 8.22 | 20.97 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 1.026 | 14.740 | 0.108 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Problem 34 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | B | F | F(-1) | F(-1) | F(-2) | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 867 | 867 | 2107 | 20597 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 2.43 | 23.76 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 1.813 | 15.662 | 0.199 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Problem 35 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | B | F | F | F(-1) | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1070 | 1070 | 11188 | 72702 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 10.46 | 67.95 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 3.454 | 25.245 | 1.548 | 0.000 | 8.210 | 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 [5] had the largest ratio of [.2500]
# | grade |
|
|
|
|
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\) | |||||||||||
1 | A | 9 | 8 | 1.00 | 40 | 0.200 | |||||||||||
2 | A | 8 | 7 | 1.00 | 38 | 0.184 | |||||||||||
3 | A | 6 | 5 | 1.00 | 33 | 0.152 | |||||||||||
4 | A | 9 | 7 | 1.00 | 40 | 0.175 | |||||||||||
5 | A | 12 | 10 | 1.00 | 40 | 0.250 | |||||||||||
6 | A | 10 | 10 | 0.99 | 42 | 0.238 | |||||||||||
7 | A | 7 | 7 | 1.00 | 42 | 0.167 | |||||||||||
8 | A | 5 | 5 | 1.00 | 42 | 0.119 | |||||||||||
9 | A | 7 | 7 | 1.00 | 42 | 0.167 | |||||||||||
10 | A | 8 | 7 | 1.00 | 42 | 0.167 | |||||||||||
11 | A | 10 | 10 | 1.00 | 49 | 0.204 | |||||||||||
12 | A | 5 | 5 | 1.00 | 49 | 0.102 | |||||||||||
13 | A | 5 | 5 | 1.00 | 49 | 0.102 | |||||||||||
14 | A | 7 | 7 | 1.00 | 49 | 0.143 | |||||||||||
15 | A | 8 | 7 | 1.00 | 49 | 0.143 | |||||||||||
16 | A | 8 | 7 | 1.00 | 58 | 0.121 | |||||||||||
17 | A | 7 | 6 | 1.00 | 53 | 0.113 | |||||||||||
18 | A | 7 | 6 | 1.00 | 60 | 0.100 | |||||||||||
19 | A | 10 | 8 | 1.00 | 60 | 0.133 | |||||||||||
20 | A | 13 | 11 | 1.00 | 60 | 0.183 | |||||||||||
21 | A | 9 | 9 | 1.00 | 62 | 0.145 | |||||||||||
22 | A | 8 | 8 | 1.00 | 62 | 0.129 | |||||||||||
23 | A | 6 | 6 | 1.00 | 62 | 0.097 | |||||||||||
24 | A | 8 | 8 | 1.00 | 62 | 0.129 | |||||||||||
25 | A | 9 | 8 | 0.99 | 62 | 0.129 | |||||||||||
26 | A | 9 | 8 | 0.99 | 42 | 0.190 | |||||||||||
27 | A | 8 | 7 | 1.00 | 40 | 0.175 | |||||||||||
28 | A | 7 | 6 | 1.00 | 35 | 0.171 | |||||||||||
29 | A | 11 | 9 | 1.00 | 42 | 0.214 | |||||||||||
30 | A | 12 | 10 | 1.00 | 42 | 0.238 | |||||||||||
31 | A | 10 | 10 | 0.99 | 44 | 0.227 | |||||||||||
32 | A | 9 | 9 | 1.00 | 44 | 0.204 | |||||||||||
33 | A | 8 | 8 | 1.00 | 44 | 0.182 | |||||||||||
34 | A | 9 | 9 | 1.00 | 44 | 0.204 | |||||||||||
35 | A | 8 | 8 | 1.00 | 44 | 0.182 | |||||||||||