Detailed conclusion table per each integral is given by the 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 as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 376 | 376 | 241 | 457 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.64 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.494 | 0.672 | 0.866 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | F(-1) | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 466 | 466 | 453 | 1064 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.97 | 2.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.861 | 1.149 | 0.827 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | B | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 341 | 341 | 410 | 960 | 0 | 17339 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.20 | 2.82 | 0.00 | 50.85 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.631 | 0.743 | 0.871 | 0.000 | 22.372 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | B | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 297 | 297 | 371 | 946 | 0 | 17285 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.25 | 3.19 | 0.00 | 58.20 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.289 | 0.684 | 0.770 | 0.000 | 13.619 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | B | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 299 | 299 | 407 | 899 | 0 | 17258 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.36 | 3.01 | 0.00 | 57.72 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.238 | 0.722 | 0.684 | 0.000 | 15.820 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | B | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 310 | 310 | 464 | 903 | 0 | 17397 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.50 | 2.91 | 0.00 | 56.12 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.270 | 0.758 | 0.769 | 0.000 | 14.101 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 394 | 394 | 486 | 990 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.23 | 2.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.703 | 1.233 | 0.747 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 454 | 454 | 620 | 1065 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.37 | 2.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.790 | 2.103 | 0.948 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 761 | 761 | 864 | 1148 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.14 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.017 | 1.142 | 0.915 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 549 | 549 | 642 | 1022 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.17 | 1.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.314 | 0.678 | 0.907 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 431 | 431 | 539 | 1547 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.25 | 3.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.450 | 0.035 | 0.935 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 523 | 521 | 467 | 1691 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.89 | 3.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.286 | 0.502 | 1.048 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 736 | 736 | 582 | 976 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.465 | 0.690 | 0.952 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 545 | 545 | 423 | 914 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.78 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.373 | 0.712 | 1.073 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | F(-1) | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 463 | 463 | 318 | 844 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.69 | 1.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.178 | 0.436 | 0.878 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 402 | 402 | 204 | 794 | 0 | 11311 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.51 | 1.98 | 0.00 | 28.14 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.621 | 0.364 | 0.898 | 0.000 | 3.566 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 374 | 374 | 218 | 761 | 0 | 11287 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.58 | 2.03 | 0.00 | 30.18 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.182 | 0.014 | 0.826 | 0.000 | 4.272 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 451 | 451 | 319 | 859 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.71 | 1.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.705 | 0.455 | 0.888 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 543 | 543 | 423 | 927 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.78 | 1.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.112 | 0.676 | 1.216 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 679 | 679 | 547 | 991 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.81 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 8.697 | 1.224 | 1.151 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | F(-1) | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 779 | 779 | 690 | 2083 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.89 | 2.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 8.628 | 1.129 | 0.996 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | F(-1) | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 609 | 609 | 534 | 1992 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.88 | 3.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.779 | 0.896 | 0.859 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | F(-1) | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 609 | 609 | 570 | 1939 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.94 | 3.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.397 | 0.849 | 0.857 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | F(-1) | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 666 | 666 | 806 | 1906 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.21 | 2.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.090 | 0.070 | 1.086 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 816 | 814 | 1025 | 2059 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.26 | 2.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 14.984 | 6.728 | 1.156 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 140 | 99 | 155 | 0 | 178 | 0 | 188 | 0 |
| N.S. |
1 | 1.00 | 0.71 | 1.11 | 0.00 | 1.27 | 0.00 | 1.34 | 0.00 |
| time (sec) |
N/A | 0.340 | 0.225 | 0.976 | 0.000 | 0.280 | 0.000 | 0.295 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 115 | 94 | 144 | 0 | 175 | 0 | 185 | 0 |
| N.S. |
1 | 1.00 | 0.82 | 1.25 | 0.00 | 1.52 | 0.00 | 1.61 | 0.00 |
| time (sec) |
N/A | 0.253 | 0.179 | 0.819 | 0.000 | 0.331 | 0.000 | 0.297 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 98 | 77 | 130 | 0 | 161 | 0 | 171 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 1.33 | 0.00 | 1.64 | 0.00 | 1.74 | 0.00 |
| time (sec) |
N/A | 0.107 | 0.156 | 0.727 | 0.000 | 0.287 | 0.000 | 0.293 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 68 | 69 | 33 | 81 | 0 | 50 | 0 | 68 | 0 |
| N.S. |
1 | 1.01 | 0.49 | 1.19 | 0.00 | 0.74 | 0.00 | 1.00 | 0.00 |
| time (sec) |
N/A | 0.036 | 0.112 | 0.688 | 0.000 | 0.313 | 0.000 | 0.288 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 95 | 54 | 121 | 0 | 132 | 0 | 165 | 0 |
| N.S. |
1 | 1.00 | 0.57 | 1.27 | 0.00 | 1.39 | 0.00 | 1.74 | 0.00 |
| time (sec) |
N/A | 0.062 | 0.153 | 0.684 | 0.000 | 0.304 | 0.000 | 0.287 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 130 | 130 | 90 | 152 | 0 | 170 | 0 | 199 | 0 |
| N.S. |
1 | 1.00 | 0.69 | 1.17 | 0.00 | 1.31 | 0.00 | 1.53 | 0.00 |
| time (sec) |
N/A | 0.258 | 0.174 | 0.768 | 0.000 | 0.295 | 0.000 | 0.292 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 151 | 151 | 113 | 169 | 0 | 194 | 0 | 269 | 0 |
| N.S. |
1 | 1.00 | 0.75 | 1.12 | 0.00 | 1.28 | 0.00 | 1.78 | 0.00 |
| time (sec) |
N/A | 0.288 | 0.219 | 0.831 | 0.000 | 0.299 | 0.000 | 0.306 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 149 | 149 | 89 | 80 | 155 | 88 | 95 | 85 | 187 |
| N.S. |
1 | 1.00 | 0.60 | 0.54 | 1.04 | 0.59 | 0.64 | 0.57 | 1.26 |
| time (sec) |
N/A | 0.061 | 0.501 | 0.658 | 0.267 | 0.275 | 0.531 | 0.304 | 13.916 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 74 | 65 | 104 | 73 | 76 | 70 | 136 |
| N.S. |
1 | 1.00 | 0.72 | 0.63 | 1.01 | 0.71 | 0.74 | 0.68 | 1.32 |
| time (sec) |
N/A | 0.027 | 0.272 | 0.529 | 0.263 | 0.288 | 0.519 | 0.312 | 13.332 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 28 | 28 | 30 | 32 | 0 | 53 | 0 | 63 | 0 |
| N.S. |
1 | 1.00 | 1.07 | 1.14 | 0.00 | 1.89 | 0.00 | 2.25 | 0.00 |
| time (sec) |
N/A | 0.029 | 0.139 | 0.636 | 0.000 | 0.317 | 0.000 | 0.312 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 84 | 80 | 57 | 0 | 126 | 0 | 159 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 0.68 | 0.00 | 1.50 | 0.00 | 1.89 | 0.00 |
| time (sec) |
N/A | 0.046 | 0.263 | 0.770 | 0.000 | 0.269 | 0.000 | 0.323 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 139 | 139 | 95 | 72 | 0 | 186 | 0 | 232 | 0 |
| N.S. |
1 | 1.00 | 0.68 | 0.52 | 0.00 | 1.34 | 0.00 | 1.67 | 0.00 |
| time (sec) |
N/A | 0.075 | 0.357 | 0.808 | 0.000 | 0.269 | 0.000 | 0.318 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 15 | 15 | 13 | 12 | 11 | 11 | 31 | 11 | 15 |
| N.S. |
1 | 1.00 | 0.87 | 0.80 | 0.73 | 0.73 | 2.07 | 0.73 | 1.00 |
| time (sec) |
N/A | 0.003 | 9.279 | 0.552 | 0.180 | 0.281 | 0.084 | 0.278 | 12.694 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 16 | 16 | 13 | 10 | 9 | 11 | 10 | 11 | 13 |
| N.S. |
1 | 1.00 | 0.81 | 0.62 | 0.56 | 0.69 | 0.62 | 0.69 | 0.81 |
| time (sec) |
N/A | 0.004 | 0.001 | 0.520 | 0.185 | 0.275 | 2.276 | 0.277 | 12.354 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 15 | 15 | 13 | 14 | 0 | 11 | 0 | 11 | 15 |
| N.S. |
1 | 1.00 | 0.87 | 0.93 | 0.00 | 0.73 | 0.00 | 0.73 | 1.00 |
| time (sec) |
N/A | 0.017 | 0.004 | 0.512 | 0.000 | 0.270 | 0.000 | 0.303 | 12.442 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 15 | 15 | 13 | 14 | 0 | 11 | 0 | 11 | 13 |
| N.S. |
1 | 1.00 | 0.87 | 0.93 | 0.00 | 0.73 | 0.00 | 0.73 | 0.87 |
| time (sec) |
N/A | 0.031 | 0.003 | 0.451 | 0.000 | 0.262 | 0.000 | 0.270 | 12.488 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 242 | 242 | 381 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.056 | 1.088 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 488 | 488 | 593 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.229 | 2.284 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |