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 | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 42 | 40 | 0 | 0 | 0 | 110 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 2.62 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.179 | 0.128 | 0.000 | 0.000 | 0.000 | 1.047 | 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 | 72 | 72 | 64 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.197 | 0.099 | 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(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 141 | 121 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.15 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.311 | 0.199 | 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(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 210 | 248 | 210 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.18 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.505 | 0.271 | 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 | 341 | 344 | 217 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.712 | 6.394 | 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 | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 200 | 204 | 2050 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 10.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.445 | 4.826 | 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 | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 117 | 666 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 5.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.281 | 1.828 | 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 | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 72 | 56 | 0 | 0 | 0 | 741 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.00 | 10.29 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.199 | 0.088 | 0.000 | 0.000 | 0.000 | 3.216 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 122 | 142 | 108 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.16 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.314 | 0.221 | 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(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 193 | 224 | 147 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.16 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.456 | 0.286 | 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 | 299 | 343 | 233 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.15 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.691 | 0.411 | 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 | B | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 81 | 81 | 190 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.233 | 0.447 | 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 | C | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 402 | 385 | 168 | 0 | 0 | 0 | 243 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.42 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.821 | 5.309 | 0.000 | 0.000 | 0.000 | 42.878 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 202 | 188 | 140 | 0 | 0 | 0 | 175 | 0 | 0 |
| N.S. |
1 | 0.93 | 0.69 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.451 | 5.198 | 0.000 | 0.000 | 0.000 | 17.299 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 89 | 94 | 0 | 0 | 0 | 107 | 0 | 0 |
| N.S. |
1 | 0.91 | 0.96 | 0.00 | 0.00 | 0.00 | 1.09 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.233 | 0.081 | 0.000 | 0.000 | 0.000 | 2.688 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 46 | 46 | 0 | 0 | 0 | 46 | 0 | 47 |
| N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 1.02 |
| time (sec) |
N/A | 0.171 | 0.004 | 0.000 | 0.000 | 0.000 | 0.944 | 0.000 | 6.462 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 180 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.191 | 0.337 | 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 | B | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 180 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.192 | 0.353 | 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 | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 180 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.191 | 0.467 | 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(-2) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 93 | 94 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.198 | 0.163 | 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 | F | B | B | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 178 | 160 | 218 | 1288 | 0 | 478 | 2822 | 0 | 0 |
| N.S. |
1 | 0.90 | 1.22 | 7.24 | 0.00 | 2.69 | 15.85 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.295 | 0.212 | 5.015 | 0.000 | 0.274 | 29.868 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | B | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 109 | 113 | 588 | 0 | 231 | 1035 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.97 | 5.07 | 0.00 | 1.99 | 8.92 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.234 | 0.140 | 4.506 | 0.000 | 0.248 | 12.920 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | A | B | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 58 | 58 | 82 | 199 | 0 | 85 | 311 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.41 | 3.43 | 0.00 | 1.47 | 5.36 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.181 | 0.167 | 4.212 | 0.000 | 0.252 | 2.214 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 18 | 18 | 18 | 47 | 0 | 31 | 42 | 0 | 75 |
| N.S. |
1 | 1.00 | 1.00 | 2.61 | 0.00 | 1.72 | 2.33 | 0.00 | 4.17 |
| time (sec) |
N/A | 0.142 | 0.055 | 4.077 | 0.000 | 0.248 | 0.678 | 0.000 | 5.883 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 53 | 52 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.172 | 0.067 | 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(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 54 | 54 | 53 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.172 | 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(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 56 | 56 | 55 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.172 | 0.089 | 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 | F | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 193 | 181 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.296 | 0.000 | 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 | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 55 | 334 | 0 | 108 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.96 | 5.86 | 0.00 | 1.89 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.184 | 0.571 | 8.574 | 0.000 | 0.264 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | A | B | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 327 | 231 | 136 | 1059 | 0 | 400 | 2746 | 0 | 0 |
| N.S. |
1 | 0.71 | 0.42 | 3.24 | 0.00 | 1.22 | 8.40 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.382 | 0.442 | 4.525 | 0.000 | 0.267 | 13.315 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | A | B | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 113 | 94 | 434 | 0 | 173 | 959 | 0 | 0 |
| N.S. |
1 | 0.89 | 0.74 | 3.42 | 0.00 | 1.36 | 7.55 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.246 | 0.207 | 4.398 | 0.000 | 0.264 | 2.479 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | A | B | F | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 50 | 50 | 55 | 0 | 0 | 68 | 250 | 0 | 64 |
| N.S. |
1 | 1.00 | 1.10 | 0.00 | 0.00 | 1.36 | 5.00 | 0.00 | 1.28 |
| time (sec) |
N/A | 0.173 | 0.050 | 0.000 | 0.000 | 0.254 | 0.768 | 0.000 | 5.934 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 95 | 153 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.210 | 6.530 | 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 | C | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 127 | 212 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.251 | 8.562 | 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 | C | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 131 | 333 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.250 | 8.796 | 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(-2) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 133 | 133 | 6405 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 48.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.256 | 36.956 | 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 | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 152 | 151 | 97 | 92 | 178 | 114 | 0 | 621 | 152 |
| N.S. |
1 | 0.99 | 0.64 | 0.61 | 1.17 | 0.75 | 0.00 | 4.09 | 1.00 |
| time (sec) |
N/A | 0.274 | 0.300 | 4.043 | 0.315 | 0.301 | 0.000 | 0.449 | 5.921 |
| 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 | 109 | 110 | 75 | 68 | 124 | 90 | 0 | 495 | 118 |
| N.S. |
1 | 1.01 | 0.69 | 0.62 | 1.14 | 0.83 | 0.00 | 4.54 | 1.08 |
| time (sec) |
N/A | 0.241 | 0.215 | 4.186 | 0.306 | 0.267 | 0.000 | 0.377 | 5.791 |
| 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 | 67 | 72 | 49 | 44 | 70 | 66 | 0 | 361 | 83 |
| N.S. |
1 | 1.07 | 0.73 | 0.66 | 1.04 | 0.99 | 0.00 | 5.39 | 1.24 |
| time (sec) |
N/A | 0.196 | 0.163 | 4.146 | 0.290 | 0.355 | 0.000 | 0.353 | 5.754 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 81 | 75 | 174 | 52 | 80 | 0 | 78 | 248 |
| N.S. |
1 | 1.01 | 0.94 | 2.18 | 0.65 | 1.00 | 0.00 | 0.98 | 3.10 |
| time (sec) |
N/A | 0.234 | 0.223 | 4.021 | 0.340 | 0.260 | 0.000 | 0.328 | 7.769 |
| 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 | 96 | 99 | 74 | 138 | 98 | 85 | 0 | 157 | 584 |
| N.S. |
1 | 1.03 | 0.77 | 1.44 | 1.02 | 0.89 | 0.00 | 1.64 | 6.08 |
| time (sec) |
N/A | 0.252 | 0.287 | 4.064 | 0.389 | 0.258 | 0.000 | 0.349 | 11.295 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 142 | 99 | 150 | 162 | 100 | 0 | 324 | 1004 |
| N.S. |
1 | 1.17 | 0.82 | 1.24 | 1.34 | 0.83 | 0.00 | 2.68 | 8.30 |
| time (sec) |
N/A | 0.266 | 0.281 | 4.201 | 0.372 | 0.270 | 0.000 | 0.362 | 22.149 |
| 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 | 208 | 185 | 142 | 184 | 246 | 138 | 0 | 558 | 2314 |
| N.S. |
1 | 0.89 | 0.68 | 0.88 | 1.18 | 0.66 | 0.00 | 2.68 | 11.12 |
| time (sec) |
N/A | 0.297 | 0.456 | 4.186 | 0.257 | 0.292 | 0.000 | 0.405 | 49.014 |
| 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 | 159 | 143 | 116 | 159 | 192 | 112 | 0 | 432 | 1681 |
| N.S. |
1 | 0.90 | 0.73 | 1.00 | 1.21 | 0.70 | 0.00 | 2.72 | 10.57 |
| time (sec) |
N/A | 0.269 | 0.363 | 4.196 | 0.278 | 0.268 | 0.000 | 0.378 | 55.455 |
| 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 | 114 | 105 | 92 | 135 | 137 | 88 | 0 | 288 | 734 |
| N.S. |
1 | 0.92 | 0.81 | 1.18 | 1.20 | 0.77 | 0.00 | 2.53 | 6.44 |
| time (sec) |
N/A | 0.205 | 0.263 | 4.202 | 0.294 | 0.254 | 0.000 | 0.335 | 23.405 |
| 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 | 104 | 97 | 74 | 117 | 105 | 83 | 0 | 110 | 243 |
| N.S. |
1 | 0.93 | 0.71 | 1.12 | 1.01 | 0.80 | 0.00 | 1.06 | 2.34 |
| time (sec) |
N/A | 0.239 | 0.296 | 4.199 | 0.344 | 0.259 | 0.000 | 0.346 | 7.592 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-2) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 85 | 81 | 124 | 75 | 100 | 0 | 171 | 236 |
| N.S. |
1 | 1.01 | 0.96 | 1.48 | 0.89 | 1.19 | 0.00 | 2.04 | 2.81 |
| time (sec) |
N/A | 0.231 | 0.269 | 4.204 | 0.340 | 0.273 | 0.000 | 0.336 | 7.534 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 125 | 118 | 96 | 129 | 153 | 96 | 0 | 172 | 1154 |
| N.S. |
1 | 0.94 | 0.77 | 1.03 | 1.22 | 0.77 | 0.00 | 1.38 | 9.23 |
| time (sec) |
N/A | 0.248 | 0.314 | 4.223 | 0.270 | 0.292 | 0.000 | 0.299 | 45.444 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | C | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 98 | 61 | 57 | 95 | 55 | 216 | 108 | 108 |
| N.S. |
1 | 0.95 | 0.59 | 0.55 | 0.92 | 0.53 | 2.10 | 1.05 | 1.05 |
| time (sec) |
N/A | 0.230 | 0.151 | 4.317 | 0.272 | 0.261 | 5.567 | 0.288 | 6.643 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 82 | 77 | 111 | 113 | 77 | 0 | 121 | 720 |
| N.S. |
1 | 0.94 | 0.89 | 1.28 | 1.30 | 0.89 | 0.00 | 1.39 | 8.28 |
| time (sec) |
N/A | 0.214 | 0.253 | 4.283 | 0.280 | 0.259 | 0.000 | 0.284 | 29.408 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | C | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 43 | 38 | 54 | 37 | 202 | 59 | 66 |
| N.S. |
1 | 1.00 | 0.66 | 0.58 | 0.83 | 0.57 | 3.11 | 0.91 | 1.02 |
| time (sec) |
N/A | 0.193 | 0.119 | 4.070 | 0.283 | 0.249 | 4.077 | 0.276 | 6.574 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | A | F(-1) | A | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 47 | 47 | 58 | 91 | 74 | 55 | 0 | 69 | 293 |
| N.S. |
1 | 1.00 | 1.23 | 1.94 | 1.57 | 1.17 | 0.00 | 1.47 | 6.23 |
| time (sec) |
N/A | 0.168 | 0.166 | 4.029 | 0.282 | 0.304 | 0.000 | 0.282 | 17.424 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | C | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 46 | 45 | 62 | 29 | 48 | 162 | 45 | 77 |
| N.S. |
1 | 1.00 | 0.98 | 1.35 | 0.63 | 1.04 | 3.52 | 0.98 | 1.67 |
| time (sec) |
N/A | 0.204 | 0.124 | 4.012 | 0.359 | 0.261 | 15.947 | 0.280 | 7.661 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | A | C | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 33 | 33 | 48 | 77 | 44 | 56 | 148 | 58 | 61 |
| N.S. |
1 | 1.00 | 1.45 | 2.33 | 1.33 | 1.70 | 4.48 | 1.76 | 1.85 |
| time (sec) |
N/A | 0.183 | 0.137 | 4.030 | 0.352 | 0.272 | 15.319 | 0.276 | 6.848 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 60 | 60 | 55 | 71 | 45 | 57 | 0 | 114 | 297 |
| N.S. |
1 | 1.00 | 0.92 | 1.18 | 0.75 | 0.95 | 0.00 | 1.90 | 4.95 |
| time (sec) |
N/A | 0.202 | 0.157 | 4.192 | 0.404 | 0.248 | 0.000 | 0.274 | 13.843 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | C | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 62 | 42 | 37 | 54 | 52 | 146 | 116 | 53 |
| N.S. |
1 | 1.00 | 0.68 | 0.60 | 0.87 | 0.84 | 2.35 | 1.87 | 0.85 |
| time (sec) |
N/A | 0.196 | 0.141 | 4.018 | 0.363 | 0.251 | 10.918 | 0.285 | 6.725 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 99 | 94 | 78 | 94 | 85 | 78 | 0 | 268 | 650 |
| N.S. |
1 | 0.95 | 0.79 | 0.95 | 0.86 | 0.79 | 0.00 | 2.71 | 6.57 |
| time (sec) |
N/A | 0.232 | 0.290 | 4.050 | 0.366 | 0.269 | 0.000 | 0.288 | 31.048 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 164 | 148 | 119 | 160 | 196 | 115 | 0 | 203 | 1682 |
| N.S. |
1 | 0.90 | 0.73 | 0.98 | 1.20 | 0.70 | 0.00 | 1.24 | 10.26 |
| time (sec) |
N/A | 0.278 | 0.377 | 4.076 | 0.274 | 0.271 | 0.000 | 0.308 | 58.965 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | C | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 110 | 74 | 68 | 124 | 66 | 240 | 124 | 130 |
| N.S. |
1 | 0.93 | 0.63 | 0.58 | 1.05 | 0.56 | 2.03 | 1.05 | 1.10 |
| time (sec) |
N/A | 0.239 | 0.191 | 4.191 | 0.296 | 0.267 | 6.166 | 0.283 | 7.120 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 107 | 92 | 136 | 142 | 90 | 0 | 140 | 1048 |
| N.S. |
1 | 0.91 | 0.78 | 1.15 | 1.20 | 0.76 | 0.00 | 1.19 | 8.88 |
| time (sec) |
N/A | 0.249 | 0.286 | 4.210 | 0.242 | 0.273 | 0.000 | 0.291 | 33.909 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | C | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 72 | 48 | 43 | 69 | 42 | 223 | 65 | 76 |
| N.S. |
1 | 1.00 | 0.67 | 0.60 | 0.96 | 0.58 | 3.10 | 0.90 | 1.06 |
| time (sec) |
N/A | 0.201 | 0.142 | 4.194 | 0.249 | 0.263 | 4.396 | 0.281 | 7.142 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 68 | 68 | 68 | 111 | 89 | 63 | 0 | 79 | 417 |
| N.S. |
1 | 1.00 | 1.00 | 1.63 | 1.31 | 0.93 | 0.00 | 1.16 | 6.13 |
| time (sec) |
N/A | 0.189 | 0.178 | 4.167 | 0.251 | 0.251 | 0.000 | 0.282 | 15.566 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | A | C | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 56 | 56 | 54 | 108 | 37 | 61 | 178 | 55 | 108 |
| N.S. |
1 | 1.00 | 0.96 | 1.93 | 0.66 | 1.09 | 3.18 | 0.98 | 1.93 |
| time (sec) |
N/A | 0.215 | 0.147 | 4.272 | 0.345 | 0.261 | 16.137 | 0.289 | 8.310 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | A | C | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 57 | 97 | 55 | 68 | 165 | 66 | 77 |
| N.S. |
1 | 1.00 | 1.00 | 1.70 | 0.96 | 1.19 | 2.89 | 1.16 | 1.35 |
| time (sec) |
N/A | 0.209 | 0.166 | 4.217 | 0.345 | 0.265 | 15.379 | 0.280 | 7.168 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 76 | 76 | 70 | 123 | 60 | 73 | 0 | 141 | 457 |
| N.S. |
1 | 1.00 | 0.92 | 1.62 | 0.79 | 0.96 | 0.00 | 1.86 | 6.01 |
| time (sec) |
N/A | 0.223 | 0.192 | 4.226 | 0.352 | 0.267 | 0.000 | 0.307 | 12.131 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | C | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 75 | 54 | 49 | 75 | 67 | 170 | 137 | 79 |
| N.S. |
1 | 1.00 | 0.72 | 0.65 | 1.00 | 0.89 | 2.27 | 1.83 | 1.05 |
| time (sec) |
N/A | 0.221 | 0.168 | 4.205 | 0.355 | 0.253 | 15.094 | 0.290 | 7.002 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 115 | 101 | 151 | 114 | 100 | 0 | 325 | 1005 |
| N.S. |
1 | 0.93 | 0.82 | 1.23 | 0.93 | 0.81 | 0.00 | 2.64 | 8.17 |
| time (sec) |
N/A | 0.253 | 0.287 | 4.068 | 0.348 | 0.257 | 0.000 | 0.302 | 27.648 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 161 | 141 | 137 | 275 | 196 | 190 | 0 | 214 | 0 |
| N.S. |
1 | 0.88 | 0.85 | 1.71 | 1.22 | 1.18 | 0.00 | 1.33 | 0.00 |
| time (sec) |
N/A | 0.279 | 0.389 | 4.240 | 0.270 | 0.258 | 0.000 | 0.325 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 103 | 72 | 68 | 123 | 80 | 0 | 200 | 90 |
| N.S. |
1 | 0.90 | 0.63 | 0.59 | 1.07 | 0.70 | 0.00 | 1.74 | 0.78 |
| time (sec) |
N/A | 0.246 | 0.200 | 4.074 | 0.251 | 0.260 | 0.000 | 0.305 | 7.252 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 152 | 133 | 108 | 251 | 138 | 159 | 0 | 147 | 0 |
| N.S. |
1 | 0.88 | 0.71 | 1.65 | 0.91 | 1.05 | 0.00 | 0.97 | 0.00 |
| time (sec) |
N/A | 0.271 | 0.288 | 4.256 | 0.271 | 0.266 | 0.000 | 0.322 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 76 | 73 | 45 | 43 | 69 | 56 | 0 | 152 | 67 |
| N.S. |
1 | 0.96 | 0.59 | 0.57 | 0.91 | 0.74 | 0.00 | 2.00 | 0.88 |
| time (sec) |
N/A | 0.213 | 0.166 | 4.245 | 0.282 | 0.257 | 0.000 | 0.315 | 6.930 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 63 | 71 | 166 | 76 | 129 | 0 | 113 | 0 |
| N.S. |
1 | 1.00 | 1.13 | 2.63 | 1.21 | 2.05 | 0.00 | 1.79 | 0.00 |
| time (sec) |
N/A | 0.189 | 0.286 | 4.067 | 0.273 | 0.258 | 0.000 | 0.298 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | A | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 70 | 194 | 58 | 101 | 0 | 115 | 0 |
| N.S. |
1 | 1.00 | 1.08 | 2.98 | 0.89 | 1.55 | 0.00 | 1.77 | 0.00 |
| time (sec) |
N/A | 0.220 | 0.238 | 4.206 | 0.390 | 0.247 | 0.000 | 0.336 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 67 | 66 | 51 | 48 | 71 | 103 | 0 | 219 | 73 |
| N.S. |
1 | 0.99 | 0.76 | 0.72 | 1.06 | 1.54 | 0.00 | 3.27 | 1.09 |
| time (sec) |
N/A | 0.216 | 0.175 | 4.244 | 0.363 | 0.263 | 0.000 | 0.344 | 7.109 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | A | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 117 | 105 | 93 | 239 | 104 | 138 | 0 | 211 | 0 |
| N.S. |
1 | 0.90 | 0.79 | 2.04 | 0.89 | 1.18 | 0.00 | 1.80 | 0.00 |
| time (sec) |
N/A | 0.257 | 0.329 | 4.253 | 0.298 | 0.258 | 0.000 | 0.355 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 106 | 77 | 73 | 125 | 132 | 0 | 242 | 104 |
| N.S. |
1 | 0.89 | 0.65 | 0.61 | 1.05 | 1.11 | 0.00 | 2.03 | 0.87 |
| time (sec) |
N/A | 0.248 | 0.222 | 4.596 | 0.283 | 0.265 | 0.000 | 0.396 | 7.366 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 166 | 146 | 122 | 267 | 162 | 165 | 0 | 402 | 0 |
| N.S. |
1 | 0.88 | 0.73 | 1.61 | 0.98 | 0.99 | 0.00 | 2.42 | 0.00 |
| time (sec) |
N/A | 0.294 | 0.443 | 4.263 | 0.275 | 0.367 | 0.000 | 0.410 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | C | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 40 | 40 | 40 | 53 | 23 | 39 | 148 | 40 | 72 |
| N.S. |
1 | 1.00 | 1.00 | 1.32 | 0.58 | 0.98 | 3.70 | 1.00 | 1.80 |
| time (sec) |
N/A | 0.197 | 0.108 | 4.025 | 0.303 | 0.241 | 15.828 | 0.271 | 8.068 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | A | A | C | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 53 | 244 | 66 | 79 | 65 | 1867 | 0 | 96 |
| N.S. |
1 | 1.00 | 4.60 | 1.25 | 1.49 | 1.23 | 35.23 | 0.00 | 1.81 |
| time (sec) |
N/A | 0.225 | 10.294 | 4.058 | 0.297 | 0.278 | 36.677 | 0.000 | 7.451 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 36 | 36 | 44 | 0 | 0 | 69 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.22 | 0.00 | 0.00 | 1.92 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.198 | 9.814 | 0.000 | 0.000 | 0.247 | 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 | 75 | 75 | 75 | 0 | 0 | 50 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.67 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.268 | 10.038 | 0.000 | 0.000 | 0.262 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 113 | 113 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.329 | 0.000 | 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 | 87 | 87 | 87 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.294 | 0.115 | 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 | B | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 76 | 76 | 258 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.280 | 0.478 | 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 | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 103 | 103 | 0 | 0 | 180 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 1.07 | 0.00 | 0.00 | 1.88 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.413 | 1.417 | 0.000 | 0.000 | 0.299 | 0.000 | 0.000 | 0.000 |