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 | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 124 | 130 | 86 | 212 | 0 | 104 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.69 | 1.71 | 0.00 | 0.84 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.311 | 10.054 | 2.479 | 0.000 | 0.143 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 78 | 78 | 54 | 158 | 0 | 69 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.69 | 2.03 | 0.00 | 0.88 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.238 | 10.031 | 2.763 | 0.000 | 0.212 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 31 | 31 | 38 | 121 | 0 | 32 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.23 | 3.90 | 0.00 | 1.03 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.194 | 10.027 | 2.770 | 0.000 | 0.081 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 80 | 40 | 183 | 0 | 113 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.50 | 2.29 | 0.00 | 1.41 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.249 | 10.040 | 2.786 | 0.000 | 0.102 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 134 | 40 | 339 | 0 | 188 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.32 | 2.69 | 0.00 | 1.49 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.304 | 10.034 | 4.348 | 0.000 | 0.100 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 172 | 188 | 40 | 457 | 0 | 275 | 0 | 0 | 0 |
| N.S. |
1 | 1.09 | 0.23 | 2.66 | 0.00 | 1.60 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.369 | 10.024 | 5.647 | 0.000 | 0.121 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 157 | 161 | 86 | 245 | 0 | 129 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.55 | 1.56 | 0.00 | 0.82 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.389 | 10.061 | 2.627 | 0.000 | 0.170 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 111 | 109 | 54 | 183 | 0 | 91 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.49 | 1.65 | 0.00 | 0.82 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.296 | 10.033 | 2.616 | 0.000 | 0.122 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 64 | 40 | 118 | 0 | 36 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.63 | 1.87 | 0.00 | 0.57 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.240 | 10.025 | 2.672 | 0.000 | 0.116 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 109 | 38 | 143 | 0 | 93 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.36 | 1.34 | 0.00 | 0.87 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.305 | 10.020 | 2.658 | 0.000 | 0.117 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 159 | 163 | 40 | 282 | 0 | 168 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.25 | 1.77 | 0.00 | 1.06 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.379 | 10.021 | 3.440 | 0.000 | 0.100 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 320 | 424 | 104 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.32 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.531 | 10.079 | 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 | A | F | B | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 44 | 44 | 50 | 44 | 0 | 194 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.14 | 1.00 | 0.00 | 4.41 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.179 | 4.936 | 2.718 | 0.000 | 0.383 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 89 | 74 | 76 | 0 | 409 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.83 | 0.85 | 0.00 | 4.60 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.221 | 4.896 | 2.591 | 0.000 | 0.396 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 133 | 151 | 122 | 139 | 783 | 687 | 0 | 0 | 0 |
| N.S. |
1 | 1.14 | 0.92 | 1.05 | 5.89 | 5.17 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.295 | 4.988 | 2.386 | 0.404 | 0.525 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 597 | 569 | 104 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.531 | 10.053 | 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 | C | F | F | F | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 581 | 563 | 104 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.492 | 10.050 | 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 | C | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 591 | 557 | 112 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.452 | 10.065 | 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 | C | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 637 | 640 | 112 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.509 | 4.991 | 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 | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 99 | 141 | 104 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.42 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.257 | 10.044 | 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 | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 99 | 141 | 104 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.42 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.240 | 10.055 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 99 | 141 | 112 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.42 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.247 | 10.076 | 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 | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 141 | 141 | 103 | 626 | 1299 | 691 | 9491 | 1506 | 655 |
| N.S. |
1 | 1.00 | 0.73 | 4.44 | 9.21 | 4.90 | 67.31 | 10.68 | 4.65 |
| time (sec) |
N/A | 0.315 | 0.213 | 2.468 | 0.256 | 0.309 | 2.036 | 0.288 | 10.370 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 77 | 255 | 539 | 307 | 3196 | 651 | 307 |
| N.S. |
1 | 1.00 | 0.75 | 2.48 | 5.23 | 2.98 | 31.03 | 6.32 | 2.98 |
| time (sec) |
N/A | 0.271 | 0.109 | 2.543 | 0.226 | 0.277 | 0.910 | 0.278 | 10.028 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 64 | 76 | 167 | 106 | 707 | 209 | 120 |
| N.S. |
1 | 1.00 | 0.98 | 1.17 | 2.57 | 1.63 | 10.88 | 3.22 | 1.85 |
| time (sec) |
N/A | 0.204 | 0.067 | 2.395 | 0.210 | 0.305 | 0.455 | 0.277 | 9.765 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 67 | 74 | 68 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.10 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.213 | 0.109 | 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 | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 68 | 75 | 69 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.10 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.212 | 0.097 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 70 | 77 | 71 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.10 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.211 | 0.110 | 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 | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 147 | 115 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.79 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.249 | 0.589 | 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 | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 149 | 113 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.52 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.243 | 0.487 | 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 | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 137 | 105 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.40 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.242 | 0.270 | 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 | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 134 | 102 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.40 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.246 | 0.325 | 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 | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 94 | 142 | 110 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.51 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.245 | 0.530 | 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 | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 143 | 111 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.49 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.246 | 1.087 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 143 | 113 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.34 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.230 | 0.522 | 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 | A | B | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 112 | 145 | 233 | 295 | 401 | 0 | 297 | 375 |
| N.S. |
1 | 0.93 | 1.20 | 1.93 | 2.44 | 3.31 | 0.00 | 2.45 | 3.10 |
| time (sec) |
N/A | 0.259 | 0.221 | 2.844 | 0.226 | 0.297 | 0.000 | 0.288 | 9.938 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 128 | 92 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.42 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.222 | 0.165 | 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 | A | A | B | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 68 | 68 | 58 | 74 | 123 | 151 | 877 | 88 | 160 |
| N.S. |
1 | 1.00 | 0.85 | 1.09 | 1.81 | 2.22 | 12.90 | 1.29 | 2.35 |
| time (sec) |
N/A | 0.198 | 0.146 | 3.072 | 0.268 | 0.281 | 108.683 | 0.270 | 9.610 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 128 | 92 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.42 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.218 | 0.124 | 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 | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 21 | 21 | 20 | 22 | 21 | 32 | 112 | 21 | 42 |
| N.S. |
1 | 1.00 | 0.95 | 1.05 | 1.00 | 1.52 | 5.33 | 1.00 | 2.00 |
| time (sec) |
N/A | 0.143 | 0.051 | 2.341 | 0.198 | 0.295 | 30.217 | 0.269 | 9.417 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 97 | 64 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.54 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.212 | 0.125 | 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 | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 88 | 128 | 90 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.45 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.220 | 0.427 | 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 | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 97 | 64 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.54 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.218 | 0.399 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 128 | 92 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.42 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.212 | 0.481 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 97 | 64 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.54 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.222 | 0.425 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 128 | 92 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.42 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.213 | 0.562 | 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 | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 16 | 16 | 16 | 13 | 12 | 12 | 14 | 12 | 11 |
| N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.75 | 0.88 | 0.75 | 0.69 |
| time (sec) |
N/A | 0.138 | 0.013 | 2.555 | 0.197 | 0.262 | 0.074 | 0.278 | 9.644 |
| 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 | 19 | 19 | 19 | 16 | 15 | 15 | 17 | 15 | 15 |
| N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.79 | 0.79 | 0.89 | 0.79 | 0.79 |
| time (sec) |
N/A | 0.146 | 0.022 | 2.674 | 0.189 | 0.300 | 0.112 | 0.272 | 9.688 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 26 | 26 | 23 | 18 | 27 | 24 | 0 | 37 | 26 |
| N.S. |
1 | 1.00 | 0.88 | 0.69 | 1.04 | 0.92 | 0.00 | 1.42 | 1.00 |
| time (sec) |
N/A | 0.157 | 0.010 | 2.302 | 0.189 | 0.301 | 0.000 | 0.276 | 9.888 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 50 | 57 | 54 | 58 | 79 | 63 | 0 | 110 | 51 |
| N.S. |
1 | 1.14 | 1.08 | 1.16 | 1.58 | 1.26 | 0.00 | 2.20 | 1.02 |
| time (sec) |
N/A | 0.187 | 0.015 | 2.808 | 0.315 | 0.279 | 0.000 | 0.276 | 10.187 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 148 | 157 | 156 | 156 | 168 | 170 | 144 |
| N.S. |
1 | 1.00 | 2.28 | 2.42 | 2.40 | 2.40 | 2.58 | 2.62 | 2.22 |
| time (sec) |
N/A | 0.274 | 0.028 | 2.353 | 0.204 | 0.265 | 0.034 | 0.266 | 10.257 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 122 | 121 | 124 | 124 | 133 | 130 | 115 |
| N.S. |
1 | 1.00 | 1.88 | 1.86 | 1.91 | 1.91 | 2.05 | 2.00 | 1.77 |
| time (sec) |
N/A | 0.251 | 0.014 | 2.272 | 0.196 | 0.249 | 0.030 | 0.260 | 10.014 |
| 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 | 65 | 65 | 79 | 84 | 81 | 81 | 87 | 89 | 74 |
| N.S. |
1 | 1.00 | 1.22 | 1.29 | 1.25 | 1.25 | 1.34 | 1.37 | 1.14 |
| time (sec) |
N/A | 0.242 | 0.011 | 2.067 | 0.197 | 0.294 | 0.026 | 0.254 | 0.046 |
| 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 | 38 | 38 | 46 | 48 | 48 | 48 | 49 | 49 | 47 |
| N.S. |
1 | 1.00 | 1.21 | 1.26 | 1.26 | 1.26 | 1.29 | 1.29 | 1.24 |
| time (sec) |
N/A | 0.202 | 0.007 | 0.183 | 0.187 | 0.244 | 0.020 | 0.263 | 0.048 |
| 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 | 22 | 14 | 22 | 13 | 20 | 20 | 19 | 20 | 20 |
| N.S. |
1 | 0.64 | 1.00 | 0.59 | 0.91 | 0.91 | 0.86 | 0.91 | 0.91 |
| time (sec) |
N/A | 0.144 | 0.000 | 0.047 | 0.197 | 0.259 | 0.017 | 0.265 | 0.029 |
| 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 | 50 | 50 | 43 | 56 | 60 | 62 | 44 | 60 | 62 |
| N.S. |
1 | 1.00 | 0.86 | 1.12 | 1.20 | 1.24 | 0.88 | 1.20 | 1.24 |
| time (sec) |
N/A | 0.198 | 0.015 | 2.066 | 0.190 | 0.257 | 0.115 | 0.254 | 10.157 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 51 | 51 | 47 | 63 | 67 | 92 | 60 | 114 | 71 |
| N.S. |
1 | 1.00 | 0.92 | 1.24 | 1.31 | 1.80 | 1.18 | 2.24 | 1.39 |
| time (sec) |
N/A | 0.213 | 0.027 | 2.240 | 0.209 | 0.296 | 0.185 | 0.264 | 0.081 |
| 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 | 59 | 59 | 48 | 66 | 80 | 100 | 80 | 69 | 77 |
| N.S. |
1 | 1.00 | 0.81 | 1.12 | 1.36 | 1.69 | 1.36 | 1.17 | 1.31 |
| time (sec) |
N/A | 0.222 | 0.018 | 2.404 | 0.202 | 0.257 | 0.242 | 0.261 | 10.104 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 28 | 28 | 53 | 60 | 84 | 84 | 88 | 59 | 80 |
| N.S. |
1 | 1.00 | 1.89 | 2.14 | 3.00 | 3.00 | 3.14 | 2.11 | 2.86 |
| time (sec) |
N/A | 0.159 | 0.019 | 2.054 | 0.186 | 0.289 | 0.321 | 0.264 | 0.050 |
| 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 | 65 | 65 | 55 | 62 | 98 | 98 | 104 | 96 | 96 |
| N.S. |
1 | 1.00 | 0.85 | 0.95 | 1.51 | 1.51 | 1.60 | 1.48 | 1.48 |
| time (sec) |
N/A | 0.219 | 0.016 | 2.342 | 0.191 | 0.261 | 0.416 | 0.265 | 0.059 |
| 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 | 65 | 65 | 55 | 62 | 109 | 109 | 116 | 61 | 107 |
| N.S. |
1 | 1.00 | 0.85 | 0.95 | 1.68 | 1.68 | 1.78 | 0.94 | 1.65 |
| time (sec) |
N/A | 0.209 | 0.023 | 2.221 | 0.188 | 0.268 | 0.520 | 0.272 | 9.965 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 55 | 62 | 120 | 120 | 128 | 61 | 118 |
| N.S. |
1 | 1.00 | 0.85 | 0.95 | 1.85 | 1.85 | 1.97 | 0.94 | 1.82 |
| time (sec) |
N/A | 0.219 | 0.015 | 2.377 | 0.195 | 0.259 | 0.613 | 0.270 | 10.088 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 119 | 398 | 417 | 418 | 418 | 462 | 470 | 402 |
| N.S. |
1 | 1.00 | 3.34 | 3.50 | 3.51 | 3.51 | 3.88 | 3.95 | 3.38 |
| time (sec) |
N/A | 0.438 | 0.045 | 5.686 | 0.190 | 0.283 | 0.050 | 0.265 | 9.937 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 119 | 350 | 353 | 360 | 360 | 401 | 396 | 340 |
| N.S. |
1 | 1.00 | 2.94 | 2.97 | 3.03 | 3.03 | 3.37 | 3.33 | 2.86 |
| time (sec) |
N/A | 0.396 | 0.031 | 2.259 | 0.189 | 0.270 | 0.047 | 0.267 | 0.146 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 119 | 273 | 288 | 285 | 285 | 318 | 321 | 271 |
| N.S. |
1 | 1.00 | 2.29 | 2.42 | 2.39 | 2.39 | 2.67 | 2.70 | 2.28 |
| time (sec) |
N/A | 0.371 | 0.026 | 2.259 | 0.198 | 0.296 | 0.043 | 0.275 | 0.093 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 92 | 92 | 217 | 222 | 225 | 225 | 243 | 245 | 208 |
| N.S. |
1 | 1.00 | 2.36 | 2.41 | 2.45 | 2.45 | 2.64 | 2.66 | 2.26 |
| time (sec) |
N/A | 0.326 | 0.021 | 2.269 | 0.199 | 0.281 | 0.038 | 0.261 | 9.589 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 148 | 157 | 156 | 156 | 168 | 170 | 144 |
| N.S. |
1 | 1.00 | 2.28 | 2.42 | 2.40 | 2.40 | 2.58 | 2.62 | 2.22 |
| time (sec) |
N/A | 0.270 | 0.017 | 2.259 | 0.193 | 0.263 | 0.036 | 0.260 | 9.653 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 38 | 38 | 84 | 94 | 96 | 96 | 100 | 97 | 88 |
| N.S. |
1 | 1.00 | 2.21 | 2.47 | 2.53 | 2.53 | 2.63 | 2.55 | 2.32 |
| time (sec) |
N/A | 0.193 | 0.013 | 2.231 | 0.192 | 0.264 | 0.028 | 0.268 | 9.619 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 14 | 14 | 14 | 43 | 53 | 42 | 42 | 42 | 42 |
| N.S. |
1 | 1.00 | 1.00 | 3.07 | 3.79 | 3.00 | 3.00 | 3.00 | 3.00 |
| time (sec) |
N/A | 0.143 | 0.004 | 2.334 | 0.186 | 0.247 | 0.021 | 0.264 | 0.022 |
| 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 | 98 | 98 | 115 | 168 | 177 | 179 | 136 | 184 | 189 |
| N.S. |
1 | 1.00 | 1.17 | 1.71 | 1.81 | 1.83 | 1.39 | 1.88 | 1.93 |
| time (sec) |
N/A | 0.254 | 0.031 | 2.570 | 0.203 | 0.283 | 0.215 | 0.256 | 0.055 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 104 | 104 | 165 | 175 | 183 | 267 | 155 | 245 | 203 |
| N.S. |
1 | 1.00 | 1.59 | 1.68 | 1.76 | 2.57 | 1.49 | 2.36 | 1.95 |
| time (sec) |
N/A | 0.298 | 0.042 | 2.202 | 0.191 | 0.268 | 0.383 | 0.271 | 9.649 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 167 | 172 | 191 | 291 | 185 | 183 | 196 |
| N.S. |
1 | 1.00 | 1.62 | 1.67 | 1.85 | 2.83 | 1.80 | 1.78 | 1.90 |
| time (sec) |
N/A | 0.280 | 0.037 | 2.233 | 0.198 | 0.284 | 0.670 | 0.257 | 0.094 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 163 | 178 | 201 | 292 | 209 | 177 | 204 |
| N.S. |
1 | 1.00 | 1.58 | 1.73 | 1.95 | 2.83 | 2.03 | 1.72 | 1.98 |
| time (sec) |
N/A | 0.287 | 0.053 | 2.227 | 0.197 | 0.287 | 1.029 | 0.254 | 9.676 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 111 | 111 | 119 | 176 | 220 | 268 | 230 | 281 | 213 |
| N.S. |
1 | 1.00 | 1.07 | 1.59 | 1.98 | 2.41 | 2.07 | 2.53 | 1.92 |
| time (sec) |
N/A | 0.289 | 0.040 | 2.229 | 0.195 | 0.269 | 1.625 | 0.260 | 9.766 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 28 | 28 | 140 | 161 | 215 | 215 | 236 | 180 | 203 |
| N.S. |
1 | 1.00 | 5.00 | 5.75 | 7.68 | 7.68 | 8.43 | 6.43 | 7.25 |
| time (sec) |
N/A | 0.165 | 0.035 | 2.227 | 0.209 | 0.292 | 4.607 | 0.261 | 0.087 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 58 | 58 | 144 | 171 | 236 | 236 | 255 | 184 | 226 |
| N.S. |
1 | 1.00 | 2.48 | 2.95 | 4.07 | 4.07 | 4.40 | 3.17 | 3.90 |
| time (sec) |
N/A | 0.187 | 0.031 | 2.246 | 0.199 | 0.287 | 22.764 | 0.264 | 0.100 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 102 | 144 | 171 | 247 | 247 | 267 | 184 | 237 |
| N.S. |
1 | 1.15 | 1.62 | 1.92 | 2.78 | 2.78 | 3.00 | 2.07 | 2.66 |
| time (sec) |
N/A | 0.206 | 0.035 | 2.243 | 0.202 | 0.286 | 114.329 | 0.263 | 9.684 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 117 | 117 | 144 | 171 | 258 | 258 | 0 | 184 | 248 |
| N.S. |
1 | 1.00 | 1.23 | 1.46 | 2.21 | 2.21 | 0.00 | 1.57 | 2.12 |
| time (sec) |
N/A | 0.285 | 0.032 | 2.272 | 0.202 | 0.307 | 0.000 | 0.254 | 9.679 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 119 | 144 | 171 | 269 | 269 | 0 | 184 | 259 |
| N.S. |
1 | 1.00 | 1.21 | 1.44 | 2.26 | 2.26 | 0.00 | 1.55 | 2.18 |
| time (sec) |
N/A | 0.276 | 0.036 | 2.556 | 0.206 | 0.298 | 0.000 | 0.259 | 9.717 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 119 | 144 | 171 | 280 | 280 | 0 | 184 | 270 |
| N.S. |
1 | 1.00 | 1.21 | 1.44 | 2.35 | 2.35 | 0.00 | 1.55 | 2.27 |
| time (sec) |
N/A | 0.278 | 0.033 | 2.475 | 0.208 | 0.324 | 0.000 | 0.266 | 0.231 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 173 | 173 | 771 | 789 | 797 | 797 | 884 | 906 | 768 |
| N.S. |
1 | 1.00 | 4.46 | 4.56 | 4.61 | 4.61 | 5.11 | 5.24 | 4.44 |
| time (sec) |
N/A | 0.670 | 0.072 | 2.278 | 0.201 | 0.252 | 0.075 | 0.267 | 10.246 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 173 | 173 | 684 | 697 | 706 | 706 | 796 | 798 | 683 |
| N.S. |
1 | 1.00 | 3.95 | 4.03 | 4.08 | 4.08 | 4.60 | 4.61 | 3.95 |
| time (sec) |
N/A | 0.588 | 0.060 | 2.257 | 0.220 | 0.303 | 0.068 | 0.258 | 0.292 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 171 | 171 | 573 | 604 | 599 | 599 | 677 | 689 | 579 |
| N.S. |
1 | 1.00 | 3.35 | 3.53 | 3.50 | 3.50 | 3.96 | 4.03 | 3.39 |
| time (sec) |
N/A | 0.550 | 0.052 | 2.286 | 0.204 | 0.305 | 0.060 | 0.270 | 10.287 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 143 | 143 | 501 | 510 | 517 | 517 | 580 | 579 | 492 |
| N.S. |
1 | 1.00 | 3.50 | 3.57 | 3.62 | 3.62 | 4.06 | 4.05 | 3.44 |
| time (sec) |
N/A | 0.489 | 0.046 | 2.250 | 0.197 | 0.299 | 0.056 | 0.261 | 0.213 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 119 | 398 | 417 | 418 | 418 | 462 | 470 | 402 |
| N.S. |
1 | 1.00 | 3.34 | 3.50 | 3.51 | 3.51 | 3.88 | 3.95 | 3.38 |
| time (sec) |
N/A | 0.436 | 0.042 | 2.265 | 0.186 | 0.301 | 0.049 | 0.254 | 10.162 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 92 | 92 | 276 | 325 | 327 | 327 | 364 | 362 | 308 |
| N.S. |
1 | 1.00 | 3.00 | 3.53 | 3.55 | 3.55 | 3.96 | 3.93 | 3.35 |
| time (sec) |
N/A | 0.369 | 0.056 | 2.303 | 0.192 | 0.279 | 0.043 | 0.258 | 10.162 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 199 | 232 | 234 | 234 | 252 | 253 | 214 |
| N.S. |
1 | 1.00 | 3.06 | 3.57 | 3.60 | 3.60 | 3.88 | 3.89 | 3.29 |
| time (sec) |
N/A | 0.302 | 0.043 | 2.266 | 0.188 | 0.305 | 0.040 | 0.258 | 0.092 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 38 | 38 | 122 | 140 | 142 | 142 | 148 | 145 | 126 |
| N.S. |
1 | 1.00 | 3.21 | 3.68 | 3.74 | 3.74 | 3.89 | 3.82 | 3.32 |
| time (sec) |
N/A | 0.195 | 0.025 | 2.523 | 0.192 | 0.279 | 0.033 | 0.257 | 0.063 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 14 | 14 | 14 | 65 | 97 | 64 | 66 | 64 | 64 |
| N.S. |
1 | 1.00 | 1.00 | 4.64 | 6.93 | 4.57 | 4.71 | 4.57 | 4.57 |
| time (sec) |
N/A | 0.143 | 0.004 | 2.335 | 0.198 | 0.275 | 0.025 | 0.260 | 0.029 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 146 | 146 | 230 | 333 | 349 | 351 | 296 | 375 | 385 |
| N.S. |
1 | 1.00 | 1.58 | 2.28 | 2.39 | 2.40 | 2.03 | 2.57 | 2.64 |
| time (sec) |
N/A | 0.304 | 0.070 | 2.276 | 0.191 | 0.274 | 0.356 | 0.257 | 10.171 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 156 | 302 | 345 | 357 | 496 | 311 | 446 | 523 |
| N.S. |
1 | 1.00 | 1.94 | 2.21 | 2.29 | 3.18 | 1.99 | 2.86 | 3.35 |
| time (sec) |
N/A | 0.413 | 0.087 | 2.210 | 0.200 | 0.302 | 0.640 | 0.262 | 0.090 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 158 | 158 | 303 | 343 | 364 | 548 | 340 | 362 | 441 |
| N.S. |
1 | 1.00 | 1.92 | 2.17 | 2.30 | 3.47 | 2.15 | 2.29 | 2.79 |
| time (sec) |
N/A | 0.390 | 0.104 | 2.229 | 0.206 | 0.286 | 1.155 | 0.266 | 10.116 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 156 | 302 | 344 | 374 | 576 | 367 | 356 | 393 |
| N.S. |
1 | 1.00 | 1.94 | 2.21 | 2.40 | 3.69 | 2.35 | 2.28 | 2.52 |
| time (sec) |
N/A | 0.376 | 0.074 | 2.247 | 0.212 | 0.339 | 4.737 | 0.259 | 10.004 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 155 | 155 | 301 | 343 | 387 | 571 | 394 | 516 | 387 |
| N.S. |
1 | 1.00 | 1.94 | 2.21 | 2.50 | 3.68 | 2.54 | 3.33 | 2.50 |
| time (sec) |
N/A | 0.366 | 0.077 | 2.281 | 0.292 | 0.300 | 106.629 | 0.255 | 0.153 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 155 | 155 | 297 | 348 | 397 | 542 | 0 | 351 | 399 |
| N.S. |
1 | 1.00 | 1.92 | 2.25 | 2.56 | 3.50 | 0.00 | 2.26 | 2.57 |
| time (sec) |
N/A | 0.364 | 0.079 | 2.266 | 0.253 | 0.313 | 0.000 | 0.269 | 10.233 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 167 | 233 | 342 | 416 | 492 | 0 | 359 | 353 |
| N.S. |
1 | 1.00 | 1.40 | 2.05 | 2.49 | 2.95 | 0.00 | 2.15 | 2.11 |
| time (sec) |
N/A | 0.358 | 0.082 | 2.392 | 0.238 | 0.302 | 0.000 | 0.255 | 9.815 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 28 | 28 | 271 | 314 | 398 | 398 | 0 | 369 | 378 |
| N.S. |
1 | 1.00 | 9.68 | 11.21 | 14.21 | 14.21 | 0.00 | 13.18 | 13.50 |
| time (sec) |
N/A | 0.166 | 0.064 | 2.622 | 0.242 | 0.318 | 0.000 | 0.249 | 9.707 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 58 | 58 | 277 | 335 | 430 | 430 | 0 | 375 | 410 |
| N.S. |
1 | 1.00 | 4.78 | 5.78 | 7.41 | 7.41 | 0.00 | 6.47 | 7.07 |
| time (sec) |
N/A | 0.184 | 0.063 | 2.253 | 0.262 | 0.273 | 0.000 | 0.252 | 0.134 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 102 | 277 | 335 | 441 | 441 | 0 | 375 | 423 |
| N.S. |
1 | 1.15 | 3.11 | 3.76 | 4.96 | 4.96 | 0.00 | 4.21 | 4.75 |
| time (sec) |
N/A | 0.206 | 0.065 | 2.248 | 0.217 | 0.318 | 0.000 | 0.257 | 9.743 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 120 | 146 | 277 | 335 | 452 | 452 | 0 | 375 | 434 |
| N.S. |
1 | 1.22 | 2.31 | 2.79 | 3.77 | 3.77 | 0.00 | 3.12 | 3.62 |
| time (sec) |
N/A | 0.235 | 0.058 | 2.209 | 0.235 | 0.344 | 0.000 | 0.260 | 9.846 |