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 N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F | F(-1) | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 547 | 547 | 416 | 9581948 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.76 | 17517.27 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.777 | 19.501 | 0.955 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F | F(-1) | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 384 | 384 | 352 | 9581713 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.92 | 24952.38 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.507 | 14.549 | 0.699 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F(-2) | F(-1) | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 294 | 294 | 253 | 9338543 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.86 | 31763.75 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.209 | 8.629 | 0.514 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 349 | 349 | 64621 | 49800 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 185.16 | 142.69 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.501 | 34.953 | 12.684 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 501 | 501 | 134907 | 1840144 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 269.28 | 3672.94 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.582 | 33.255 | 40.177 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 976 | 976 | 4224 | 17768513 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 4.33 | 18205.44 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 23.558 | 43.031 | 0.766 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F | F(-1) | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 747 | 747 | 411 | 17768080 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.55 | 23785.92 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 23.177 | 31.220 | 0.533 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F | F(-1) | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 602 | 602 | 350 | 17767874 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.58 | 29514.74 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 22.853 | 30.393 | 0.534 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F(-2) | F(-1) | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 570 | 570 | 278 | 103617 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.49 | 181.78 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 23.144 | 17.203 | 14.948 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 691 | 691 | 465721 | 2710966 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 673.98 | 3923.25 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 23.236 | 44.805 | 51.355 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1189 | 1189 | 5618 | 13067599 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 4.72 | 10990.41 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 4.473 | 45.158 | 0.507 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F(-1) | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 865 | 865 | 737 | 13066867 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.85 | 15106.20 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 3.567 | 32.723 | 0.621 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F(-2) | F(-1) | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 686 | 686 | 382 | 13067316 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.56 | 19048.57 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 3.292 | 30.761 | 0.572 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F(-2) | F(-1) | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 635 | 635 | 375 | 13066366 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.59 | 20576.95 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 2.789 | 30.175 | 0.316 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F(-1) | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 749 | 749 | 558961 | 21338039 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 746.28 | 28488.70 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 3.398 | 39.437 | 61.682 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F(-1) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1008 | 1008 | 930953 | 29682798 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 923.56 | 29447.22 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 3.642 | 44.736 | 252.392 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | A | F(-1) | B | F | F(-1) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 182 | 182 | 179905 | 232 | 0 | 2180 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 988.49 | 1.27 | 0.00 | 11.98 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.265 | 34.238 | 0.402 | 0.000 | 5.214 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | A | F | B | F | F(-1) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 141 | 141 | 64578 | 153 | 0 | 1759 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 458.00 | 1.09 | 0.00 | 12.48 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.138 | 125.399 | 0.240 | 0.000 | 4.550 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | A | F | B | F | F(-1) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 79 | 79 | 24736 | 102 | 0 | 447 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 313.11 | 1.29 | 0.00 | 5.66 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.078 | 74.785 | 0.358 | 0.000 | 3.559 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | B | F | F(-1) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 142 | 142 | 44361 | 0 | 0 | 1197 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 312.40 | 0.00 | 0.00 | 8.43 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.165 | 28.787 | 0.901 | 0.000 | 4.789 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F(-1) | A | F | F(-1) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 249 | 249 | 37459 | 0 | 0 | 1516 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 150.44 | 0.00 | 0.00 | 6.09 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.221 | 32.128 | 0.843 | 0.000 | 5.217 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 270 | 270 | 539292 | 627 | 0 | 3147 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1997.38 | 2.32 | 0.00 | 11.66 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.377 | 38.347 | 0.295 | 0.000 | 8.558 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F | B | F | F(-1) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 209 | 209 | 412434 | 425 | 0 | 2452 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1973.37 | 2.03 | 0.00 | 11.73 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.236 | 36.396 | 0.228 | 0.000 | 7.160 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | A | F | B | F | F(-1) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 179 | 179 | 286262 | 281 | 0 | 2012 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1599.23 | 1.57 | 0.00 | 11.24 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.155 | 34.929 | 0.243 | 0.000 | 6.431 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | A | F | F(-1) | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 203 | 203 | 253 | 0 | 0 | 2670 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.25 | 0.00 | 0.00 | 13.15 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.188 | 12.544 | 0.713 | 0.000 | 4.714 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | A | F | F(-1) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 435 | 435 | 215131 | 0 | 0 | 1354 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 494.55 | 0.00 | 0.00 | 3.11 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.359 | 34.555 | 0.793 | 0.000 | 6.502 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F(-2) | B | F | F(-1) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 236 | 236 | 243520 | 721 | 0 | 6139 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1031.86 | 3.06 | 0.00 | 26.01 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.373 | 36.141 | 2.029 | 0.000 | 8.570 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F | B | F | F(-1) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 160 | 160 | 25130 | 507 | 0 | 1785 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 157.06 | 3.17 | 0.00 | 11.16 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.266 | 31.630 | 0.285 | 0.000 | 3.775 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F | B | F | F(-1) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 153 | 153 | 25123 | 457 | 0 | 1759 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 164.20 | 2.99 | 0.00 | 11.50 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.191 | 31.733 | 0.241 | 0.000 | 3.877 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F | B | F | F(-1) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 156 | 25149 | 406 | 0 | 1813 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 161.21 | 2.60 | 0.00 | 11.62 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.162 | 7.671 | 0.266 | 0.000 | 4.177 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F(-2) | B | F | F(-1) | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 280 | 280 | 181078 | 0 | 0 | 4269 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 646.71 | 0.00 | 0.00 | 15.25 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.271 | 35.454 | 0.729 | 0.000 | 8.026 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F(-1) | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 478 | 478 | 293889 | 0 | 0 | 5394 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 614.83 | 0.00 | 0.00 | 11.28 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.383 | 37.665 | 0.750 | 0.000 | 9.045 | 0.000 | 0.000 | 0.000 |