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 | A | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 131 | 122 | 0 | 0 | 96 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.73 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.313 | 0.052 | 0.000 | 0.000 | 0.102 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 14 | 14 | 16 | 14 | 16 | 16 | 14 | 16 | 18 |
| N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.14 | 1.00 | 1.14 | 1.29 |
| time (sec) |
N/A | 0.193 | 9.537 | 0.372 | 0.479 | 0.286 | 2.123 | 0.434 | 14.366 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 16 | 16 | 18 | 16 | 18 | 18 | 15 | 18 | 18 |
| N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.94 | 1.12 | 1.12 |
| time (sec) |
N/A | 0.212 | 0.858 | 0.326 | 0.532 | 0.259 | 5.245 | 0.365 | 13.861 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 75 | 75 | 455 | 0 | 54 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 6.07 | 0.00 | 0.72 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.270 | 0.022 | 0.516 | 0.000 | 0.091 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 79 | 79 | 79 | 354 | 0 | 54 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 4.48 | 0.00 | 0.68 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.279 | 0.020 | 0.500 | 0.000 | 0.088 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 75 | 75 | 291 | 0 | 54 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 3.88 | 0.00 | 0.72 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.268 | 0.018 | 0.423 | 0.000 | 0.101 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 79 | 79 | 79 | 379 | 0 | 50 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 4.80 | 0.00 | 0.63 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.271 | 0.017 | 0.472 | 0.000 | 0.118 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 62 | 427 | 0 | 50 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 6.57 | 0.00 | 0.77 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.265 | 0.029 | 0.438 | 0.000 | 0.092 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 75 | 75 | 530 | 0 | 54 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 7.07 | 0.00 | 0.72 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.271 | 0.019 | 0.509 | 0.000 | 0.094 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 75 | 75 | 600 | 0 | 54 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 8.00 | 0.00 | 0.72 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.270 | 0.018 | 0.460 | 0.000 | 0.094 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 99 | 99 | 92 | 0 | 0 | 77 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.78 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.350 | 0.115 | 0.000 | 0.000 | 0.094 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 96 | 0 | 0 | 77 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.75 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.335 | 0.114 | 0.000 | 0.000 | 0.110 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 97 | 97 | 90 | 0 | 0 | 77 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.79 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.333 | 0.105 | 0.000 | 0.000 | 0.100 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 90 | 0 | 0 | 69 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.67 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.322 | 0.125 | 0.000 | 0.000 | 0.089 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 85 | 77 | 0 | 0 | 64 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.75 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.309 | 0.065 | 0.000 | 0.000 | 0.093 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 101 | 101 | 91 | 0 | 0 | 77 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.76 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.325 | 0.118 | 0.000 | 0.000 | 0.094 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 95 | 95 | 0 | 0 | 77 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.81 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.331 | 0.095 | 0.000 | 0.000 | 0.089 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 89 | 122 | 104 | 456 | 168 | 264 | 154 | 189 |
| N.S. |
1 | 1.00 | 1.37 | 1.17 | 5.12 | 1.89 | 2.97 | 1.73 | 2.12 |
| time (sec) |
N/A | 0.325 | 0.564 | 1.105 | 0.308 | 0.270 | 0.296 | 0.282 | 14.166 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 67 | 67 | 80 | 77 | 235 | 102 | 151 | 92 | 112 |
| N.S. |
1 | 1.00 | 1.19 | 1.15 | 3.51 | 1.52 | 2.25 | 1.37 | 1.67 |
| time (sec) |
N/A | 0.296 | 0.383 | 1.009 | 0.265 | 0.269 | 0.237 | 0.290 | 14.410 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 44 | 44 | 52 | 40 | 91 | 51 | 68 | 44 | 52 |
| N.S. |
1 | 1.00 | 1.18 | 0.91 | 2.07 | 1.16 | 1.55 | 1.00 | 1.18 |
| time (sec) |
N/A | 0.234 | 0.704 | 0.817 | 0.294 | 0.288 | 0.177 | 0.278 | 0.104 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | C | A | F | C | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 55 | 86 | 172 | 71 | 0 | 673 | 0 |
| N.S. |
1 | 1.00 | 0.85 | 1.32 | 2.65 | 1.09 | 0.00 | 10.35 | 0.00 |
| time (sec) |
N/A | 0.345 | 0.216 | 0.928 | 0.333 | 0.271 | 0.000 | 0.301 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | C | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 89 | 78 | 124 | 196 | 105 | 0 | 535 | 0 |
| N.S. |
1 | 1.00 | 0.88 | 1.39 | 2.20 | 1.18 | 0.00 | 6.01 | 0.00 |
| time (sec) |
N/A | 0.383 | 0.482 | 1.073 | 0.322 | 0.264 | 0.000 | 0.306 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 237 | 224 | 217 | 180 | 949 | 369 | 779 | 335 | 452 |
| N.S. |
1 | 0.95 | 0.92 | 0.76 | 4.00 | 1.56 | 3.29 | 1.41 | 1.91 |
| time (sec) |
N/A | 0.500 | 1.659 | 1.568 | 0.403 | 0.289 | 0.444 | 0.310 | 15.277 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 168 | 168 | 193 | 122 | 494 | 212 | 456 | 203 | 255 |
| N.S. |
1 | 1.00 | 1.15 | 0.73 | 2.94 | 1.26 | 2.71 | 1.21 | 1.52 |
| time (sec) |
N/A | 0.406 | 0.781 | 1.299 | 0.317 | 0.299 | 0.333 | 0.280 | 15.196 |
| 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 | 118 | 98 | 80 | 92 | 197 | 98 | 219 | 103 | 117 |
| N.S. |
1 | 0.83 | 0.68 | 0.78 | 1.67 | 0.83 | 1.86 | 0.87 | 0.99 |
| time (sec) |
N/A | 0.312 | 0.932 | 0.977 | 0.272 | 0.287 | 0.229 | 0.297 | 14.941 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | C | A | F | C | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 145 | 139 | 114 | 197 | 339 | 145 | 0 | 6693 | 0 |
| N.S. |
1 | 0.96 | 0.79 | 1.36 | 2.34 | 1.00 | 0.00 | 46.16 | 0.00 |
| time (sec) |
N/A | 0.563 | 0.777 | 1.057 | 0.446 | 0.304 | 0.000 | 0.428 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | C | A | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 159 | 160 | 206 | 276 | 372 | 219 | 0 | 1049 | 0 |
| N.S. |
1 | 1.01 | 1.30 | 1.74 | 2.34 | 1.38 | 0.00 | 6.60 | 0.00 |
| time (sec) |
N/A | 0.538 | 0.854 | 1.159 | 0.465 | 0.307 | 0.000 | 0.448 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 134 | 146 | 151 | 364 | 935 | 422 | 0 | 0 | 0 |
| N.S. |
1 | 1.09 | 1.13 | 2.72 | 6.98 | 3.15 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.786 | 0.342 | 1.615 | 0.450 | 0.305 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 101 | 108 | 125 | 197 | 284 | 226 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 1.24 | 1.95 | 2.81 | 2.24 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.582 | 0.359 | 1.259 | 0.368 | 0.279 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 49 | 51 | 70 | 40 | 160 | 58 | 70 | 194 | 65 |
| N.S. |
1 | 1.04 | 1.43 | 0.82 | 3.27 | 1.18 | 1.43 | 3.96 | 1.33 |
| time (sec) |
N/A | 0.339 | 0.088 | 0.978 | 0.343 | 0.276 | 0.328 | 0.333 | 15.456 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 20 | 20 | 22 | 20 | 285 | 27 | 27 | 22 | 22 |
| N.S. |
1 | 1.00 | 1.10 | 1.00 | 14.25 | 1.35 | 1.35 | 1.10 | 1.10 |
| time (sec) |
N/A | 0.230 | 3.932 | 0.416 | 0.659 | 0.280 | 1.046 | 0.291 | 14.949 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 20 | 20 | 22 | 20 | 442 | 51 | 58 | 22 | 22 |
| N.S. |
1 | 1.00 | 1.10 | 1.00 | 22.10 | 2.55 | 2.90 | 1.10 | 1.10 |
| time (sec) |
N/A | 0.226 | 2.508 | 0.382 | 0.974 | 0.260 | 1.882 | 0.506 | 14.914 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 271 | 273 | 250 | 678 | 3275 | 771 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.92 | 2.50 | 12.08 | 2.85 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.213 | 1.094 | 2.918 | 0.997 | 0.308 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 212 | 206 | 212 | 358 | 776 | 390 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 1.00 | 1.69 | 3.66 | 1.84 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.919 | 1.175 | 2.546 | 0.607 | 0.274 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 119 | 113 | 74 | 763 | 118 | 146 | 661 | 175 |
| N.S. |
1 | 0.97 | 0.92 | 0.60 | 6.20 | 0.96 | 1.19 | 5.37 | 1.42 |
| time (sec) |
N/A | 0.486 | 1.128 | 1.677 | 0.354 | 0.281 | 0.451 | 0.494 | 18.838 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 20 | 20 | 22 | 20 | 2913 | 57 | 54 | 22 | 22 |
| N.S. |
1 | 1.00 | 1.10 | 1.00 | 145.65 | 2.85 | 2.70 | 1.10 | 1.10 |
| time (sec) |
N/A | 0.219 | 11.283 | 0.699 | 10.732 | 0.280 | 1.772 | 0.306 | 14.722 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 20 | 20 | 22 | 20 | 3521 | 99 | 105 | 22 | 22 |
| N.S. |
1 | 1.00 | 1.10 | 1.00 | 176.05 | 4.95 | 5.25 | 1.10 | 1.10 |
| time (sec) |
N/A | 0.217 | 12.478 | 0.709 | 19.786 | 0.283 | 4.511 | 0.878 | 14.159 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 133 | 149 | 164 | 468 | 967 | 467 | 0 | 0 | 0 |
| N.S. |
1 | 1.12 | 1.23 | 3.52 | 7.27 | 3.51 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.776 | 1.590 | 1.335 | 0.448 | 0.295 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 102 | 110 | 292 | 247 | 310 | 283 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 2.86 | 2.42 | 3.04 | 2.77 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.582 | 6.458 | 1.237 | 0.392 | 0.275 | 0.000 | 0.000 | 0.000 |
| 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 | 50 | 53 | 57 | 54 | 160 | 59 | 90 | 189 | 65 |
| N.S. |
1 | 1.06 | 1.14 | 1.08 | 3.20 | 1.18 | 1.80 | 3.78 | 1.30 |
| time (sec) |
N/A | 0.341 | 0.866 | 1.194 | 0.264 | 0.302 | 0.353 | 0.330 | 13.633 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 21 | 21 | 23 | 21 | 285 | 28 | 29 | 25 | 23 |
| N.S. |
1 | 1.00 | 1.10 | 1.00 | 13.57 | 1.33 | 1.38 | 1.19 | 1.10 |
| time (sec) |
N/A | 0.231 | 3.628 | 0.366 | 0.686 | 0.293 | 1.581 | 0.269 | 13.474 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 21 | 21 | 23 | 21 | 442 | 52 | 60 | 25 | 23 |
| N.S. |
1 | 1.00 | 1.10 | 1.00 | 21.05 | 2.48 | 2.86 | 1.19 | 1.10 |
| time (sec) |
N/A | 0.230 | 2.516 | 0.375 | 0.954 | 0.266 | 3.184 | 0.480 | 13.597 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | B | F(-2) | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 110 | 120 | 53 | 132 | 206 | 0 | 0 | 98 | 83 |
| N.S. |
1 | 1.09 | 0.48 | 1.20 | 1.87 | 0.00 | 0.00 | 0.89 | 0.75 |
| time (sec) |
N/A | 0.607 | 0.334 | 0.525 | 0.502 | 0.000 | 0.000 | 0.296 | 13.774 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | F(-2) | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 88 | 93 | 44 | 105 | 122 | 0 | 0 | 77 | 63 |
| N.S. |
1 | 1.06 | 0.50 | 1.19 | 1.39 | 0.00 | 0.00 | 0.88 | 0.72 |
| time (sec) |
N/A | 0.470 | 0.247 | 0.385 | 0.465 | 0.000 | 0.000 | 0.286 | 13.779 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | F(-2) | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 66 | 34 | 80 | 61 | 0 | 0 | 57 | 46 |
| N.S. |
1 | 1.25 | 0.64 | 1.51 | 1.15 | 0.00 | 0.00 | 1.08 | 0.87 |
| time (sec) |
N/A | 0.340 | 0.385 | 0.388 | 0.424 | 0.000 | 0.000 | 0.286 | 0.230 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 26 | 26 | 29 | 43 | 20 | 32 | 0 | 30 | 33 |
| N.S. |
1 | 1.00 | 1.12 | 1.65 | 0.77 | 1.23 | 0.00 | 1.15 | 1.27 |
| time (sec) |
N/A | 0.187 | 0.079 | 0.679 | 0.390 | 0.310 | 0.000 | 0.273 | 13.148 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | C | F(-2) | F | C | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 58 | 55 | 0 | 61 | 0 | 0 | 166 | 0 |
| N.S. |
1 | 0.69 | 0.65 | 0.00 | 0.73 | 0.00 | 0.00 | 1.98 | 0.00 |
| time (sec) |
N/A | 0.449 | 0.315 | 0.000 | 0.409 | 0.000 | 0.000 | 0.308 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | C | F(-2) | F | C | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 110 | 81 | 75 | 0 | 193 | 0 | 0 | 560 | 0 |
| N.S. |
1 | 0.74 | 0.68 | 0.00 | 1.75 | 0.00 | 0.00 | 5.09 | 0.00 |
| time (sec) |
N/A | 0.531 | 0.246 | 0.000 | 0.446 | 0.000 | 0.000 | 0.327 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | C | F(-2) | F | C | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 151 | 108 | 98 | 0 | 227 | 0 | 0 | 662 | 0 |
| N.S. |
1 | 0.72 | 0.65 | 0.00 | 1.50 | 0.00 | 0.00 | 4.38 | 0.00 |
| time (sec) |
N/A | 0.639 | 0.352 | 0.000 | 0.538 | 0.000 | 0.000 | 0.314 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | F(-2) | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 68 | 63 | 33 | 87 | 48 | 0 | 0 | 55 | 91 |
| N.S. |
1 | 0.93 | 0.49 | 1.28 | 0.71 | 0.00 | 0.00 | 0.81 | 1.34 |
| time (sec) |
N/A | 0.485 | 0.134 | 0.542 | 0.354 | 0.000 | 0.000 | 0.285 | 14.227 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | F(-2) | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 49 | 29 | 70 | 36 | 0 | 0 | 43 | 70 |
| N.S. |
1 | 0.92 | 0.55 | 1.32 | 0.68 | 0.00 | 0.00 | 0.81 | 1.32 |
| time (sec) |
N/A | 0.405 | 0.101 | 0.487 | 0.396 | 0.000 | 0.000 | 0.279 | 13.609 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | F(-2) | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 32 | 35 | 22 | 55 | 24 | 0 | 0 | 31 | 50 |
| N.S. |
1 | 1.09 | 0.69 | 1.72 | 0.75 | 0.00 | 0.00 | 0.97 | 1.56 |
| time (sec) |
N/A | 0.307 | 0.074 | 0.469 | 0.360 | 0.000 | 0.000 | 0.299 | 14.284 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 15 | 15 | 18 | 25 | 12 | 18 | 0 | 17 | 34 |
| N.S. |
1 | 1.00 | 1.20 | 1.67 | 0.80 | 1.20 | 0.00 | 1.13 | 2.27 |
| time (sec) |
N/A | 0.171 | 0.045 | 0.881 | 0.478 | 0.270 | 0.000 | 0.282 | 0.131 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | C | F(-2) | F | A | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 23 | 23 | 23 | 0 | 17 | 0 | 0 | 16 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.74 | 0.00 | 0.00 | 0.70 | 0.00 |
| time (sec) |
N/A | 0.281 | 0.009 | 0.000 | 0.489 | 0.000 | 0.000 | 0.296 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | C | F(-2) | F | A | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 39 | 33 | 0 | 23 | 0 | 0 | 34 | 0 |
| N.S. |
1 | 0.93 | 0.79 | 0.00 | 0.55 | 0.00 | 0.00 | 0.81 | 0.00 |
| time (sec) |
N/A | 0.352 | 0.117 | 0.000 | 0.501 | 0.000 | 0.000 | 0.286 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | C | F(-2) | F | A | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 67 | 56 | 44 | 0 | 19 | 0 | 0 | 48 | 0 |
| N.S. |
1 | 0.84 | 0.66 | 0.00 | 0.28 | 0.00 | 0.00 | 0.72 | 0.00 |
| time (sec) |
N/A | 0.427 | 0.131 | 0.000 | 0.475 | 0.000 | 0.000 | 0.280 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | B | F(-2) | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 64 | 34 | 86 | 129 | 0 | 0 | 55 | 92 |
| N.S. |
1 | 0.89 | 0.47 | 1.19 | 1.79 | 0.00 | 0.00 | 0.76 | 1.28 |
| time (sec) |
N/A | 0.507 | 0.161 | 0.627 | 0.383 | 0.000 | 0.000 | 0.282 | 14.844 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | B | F(-2) | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 56 | 50 | 30 | 69 | 100 | 0 | 0 | 51 | 71 |
| N.S. |
1 | 0.89 | 0.54 | 1.23 | 1.79 | 0.00 | 0.00 | 0.91 | 1.27 |
| time (sec) |
N/A | 0.410 | 0.126 | 0.583 | 0.353 | 0.000 | 0.000 | 0.289 | 14.619 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | B | F(-2) | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 34 | 36 | 23 | 54 | 72 | 0 | 0 | 31 | 48 |
| N.S. |
1 | 1.06 | 0.68 | 1.59 | 2.12 | 0.00 | 0.00 | 0.91 | 1.41 |
| time (sec) |
N/A | 0.309 | 0.092 | 0.523 | 0.336 | 0.000 | 0.000 | 0.279 | 14.621 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 16 | 16 | 19 | 25 | 23 | 19 | 0 | 26 | 34 |
| N.S. |
1 | 1.00 | 1.19 | 1.56 | 1.44 | 1.19 | 0.00 | 1.62 | 2.12 |
| time (sec) |
N/A | 0.173 | 0.059 | 0.941 | 0.423 | 0.274 | 0.000 | 0.289 | 14.520 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | F | A | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 24 | 24 | 24 | 0 | 0 | 0 | 0 | 16 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.67 | 0.00 |
| time (sec) |
N/A | 0.292 | 0.086 | 0.000 | 0.000 | 0.000 | 0.000 | 0.290 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | F | A | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 44 | 40 | 34 | 0 | 0 | 0 | 0 | 34 | 0 |
| N.S. |
1 | 0.91 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 |
| time (sec) |
N/A | 0.368 | 0.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.471 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | F | A | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 70 | 58 | 45 | 0 | 0 | 0 | 0 | 48 | 0 |
| N.S. |
1 | 0.83 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
| time (sec) |
N/A | 0.437 | 0.149 | 0.000 | 0.000 | 0.000 | 0.000 | 0.362 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | A | F(-2) | F | A | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 185 | 164 | 67 | 0 | 98 | 0 | 0 | 113 | 0 |
| N.S. |
1 | 0.89 | 0.36 | 0.00 | 0.53 | 0.00 | 0.00 | 0.61 | 0.00 |
| time (sec) |
N/A | 0.991 | 0.383 | 0.000 | 0.365 | 0.000 | 0.000 | 0.346 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | A | F(-2) | F | A | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 145 | 115 | 54 | 0 | 72 | 0 | 0 | 85 | 0 |
| N.S. |
1 | 0.79 | 0.37 | 0.00 | 0.50 | 0.00 | 0.00 | 0.59 | 0.00 |
| time (sec) |
N/A | 0.654 | 0.296 | 0.000 | 0.344 | 0.000 | 0.000 | 0.363 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | A | F(-2) | F | A | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 73 | 45 | 0 | 48 | 0 | 0 | 59 | 0 |
| N.S. |
1 | 0.82 | 0.51 | 0.00 | 0.54 | 0.00 | 0.00 | 0.66 | 0.00 |
| time (sec) |
N/A | 0.408 | 0.117 | 0.000 | 0.522 | 0.000 | 0.000 | 0.359 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | C | F(-2) | F | A | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 55 | 40 | 36 | 0 | 29 | 0 | 0 | 32 | 0 |
| N.S. |
1 | 0.73 | 0.65 | 0.00 | 0.53 | 0.00 | 0.00 | 0.58 | 0.00 |
| time (sec) |
N/A | 0.348 | 0.024 | 0.000 | 0.393 | 0.000 | 0.000 | 0.285 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | C | F(-2) | F | A | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 79 | 58 | 53 | 0 | 37 | 0 | 0 | 62 | 0 |
| N.S. |
1 | 0.73 | 0.67 | 0.00 | 0.47 | 0.00 | 0.00 | 0.78 | 0.00 |
| time (sec) |
N/A | 0.353 | 0.139 | 0.000 | 0.405 | 0.000 | 0.000 | 0.341 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | C | F(-2) | F | A | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 109 | 91 | 66 | 0 | 33 | 0 | 0 | 92 | 0 |
| N.S. |
1 | 0.83 | 0.61 | 0.00 | 0.30 | 0.00 | 0.00 | 0.84 | 0.00 |
| time (sec) |
N/A | 0.510 | 0.065 | 0.000 | 0.386 | 0.000 | 0.000 | 0.366 | 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 | 374 | 241 | 199 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.64 | 0.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.843 | 0.137 | 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 | 262 | 167 | 146 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.64 | 0.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.605 | 0.083 | 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 | 156 | 103 | 89 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.66 | 0.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.397 | 0.054 | 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 | C | B | A | F | B | B |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 46 | 40 | 56 | 90 | 126 | 0 | 93 | 45 |
| N.S. |
1 | 1.00 | 0.87 | 1.22 | 1.96 | 2.74 | 0.00 | 2.02 | 0.98 |
| time (sec) |
N/A | 0.205 | 0.018 | 0.491 | 0.386 | 0.283 | 0.000 | 0.349 | 14.153 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 18 | 18 | 20 | 16 | 18 | 30 | 17 | 18 | 18 |
| N.S. |
1 | 1.00 | 1.11 | 0.89 | 1.00 | 1.67 | 0.94 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.239 | 1.091 | 0.172 | 0.578 | 0.255 | 1.864 | 0.563 | 14.357 |
| 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 | 235 | 150 | 170 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.64 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.675 | 0.202 | 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 | 163 | 102 | 117 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.63 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.514 | 0.130 | 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 | 97 | 64 | 83 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.66 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.352 | 0.100 | 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 | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 37 | 37 | 36 | 25 | 81 | 87 | 0 | 20 | 0 |
| N.S. |
1 | 1.00 | 0.97 | 0.68 | 2.19 | 2.35 | 0.00 | 0.54 | 0.00 |
| time (sec) |
N/A | 0.193 | 0.073 | 0.911 | 0.488 | 0.264 | 0.000 | 0.416 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 15 | 15 | 17 | 13 | 15 | 25 | 15 | 15 | 15 |
| N.S. |
1 | 1.00 | 1.13 | 0.87 | 1.00 | 1.67 | 1.00 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.236 | 4.668 | 0.313 | 0.519 | 0.253 | 1.832 | 0.783 | 13.977 |
| 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 | 423 | 263 | 257 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.62 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.061 | 0.458 | 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 | 257 | 160 | 185 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.62 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.712 | 0.136 | 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 | 150 | 104 | 165 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.69 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.453 | 0.232 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 14 | 14 | 16 | 12 | 14 | 36 | 14 | 14 | 14 |
| N.S. |
1 | 1.00 | 1.14 | 0.86 | 1.00 | 2.57 | 1.00 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.238 | 11.208 | 0.400 | 0.531 | 0.252 | 9.327 | 1.071 | 14.491 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 18 | 18 | 20 | 16 | 18 | 0 | 15 | 18 | 18 |
| N.S. |
1 | 1.00 | 1.11 | 0.89 | 1.00 | 0.00 | 0.83 | 1.00 | 1.00 |
| time (sec) |
N/A | 0.229 | 2.246 | 0.137 | 0.557 | 0.000 | 1.657 | 0.633 | 14.846 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F(-2) | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 383 | 351 | 290 | 0 | 0 | 1030 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 0.76 | 0.00 | 0.00 | 2.69 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.353 | 1.718 | 0.000 | 0.000 | 0.359 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F(-2) | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 329 | 319 | 255 | 0 | 0 | 1263 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.78 | 0.00 | 0.00 | 3.84 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.236 | 0.607 | 0.000 | 0.000 | 0.426 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F(-2) | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 214 | 215 | 756 | 414 | 0 | 915 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.53 | 1.93 | 0.00 | 4.28 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.797 | 0.942 | 0.845 | 0.000 | 0.419 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
| verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 12 | 12 | 14 | 12 | 14 | 13 | 10 | 14 | 14 |
| N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.08 | 0.83 | 1.17 | 1.17 |
| time (sec) |
N/A | 0.206 | 1.453 | 0.201 | 0.358 | 0.313 | 2.084 | 0.277 | 14.017 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F(-2) | B | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 296 | 306 | 933 | 674 | 0 | 1482 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 3.15 | 2.28 | 0.00 | 5.01 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.179 | 10.621 | 3.345 | 0.000 | 0.458 | 0.000 | 0.000 | 0.000 |