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 | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 35 | 25 | 34 | 34 | 35 | 105 | 51 | 36 | 35 |
| N.S. |
1 | 1.00 | 0.71 | 0.97 | 0.97 | 1.00 | 3.00 | 1.46 | 1.03 | 1.00 |
| time (sec) |
N/A | 0.168 | 0.022 | 0.048 | 0.045 | 0.125 | 0.195 | 0.135 | 0.227 | 0.462 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | B | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 76 | 76 | 56 | 0 | 0 | 0 | 201 | 0 | 13 | 0 |
| N.S. |
1 | 1.00 | 0.74 | 0.00 | 0.00 | 0.00 | 2.64 | 0.00 | 0.17 | 0.00 |
| time (sec) |
N/A | 0.194 | 0.069 | 0.000 | 0.000 | 0.000 | 1.647 | 0.000 | 0.229 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 81 | 0 | 0 | 0 | 954 | 0 | 19 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 9.26 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 0.211 | 0.081 | 0.000 | 0.000 | 0.000 | 13.855 | 0.000 | 0.244 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 81 | 0 | 0 | 0 | 3199 | 0 | 30 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 31.06 | 0.00 | 0.29 | 0.00 |
| time (sec) |
N/A | 0.215 | 0.086 | 0.000 | 0.000 | 0.000 | 49.388 | 0.000 | 0.211 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 118 | 111 | 0 | 0 | 0 | 246 | 0 | 65 | 0 |
| N.S. |
1 | 1.02 | 0.96 | 0.00 | 0.00 | 0.00 | 2.12 | 0.00 | 0.56 | 0.00 |
| time (sec) |
N/A | 0.232 | 0.303 | 0.000 | 0.000 | 0.000 | 4.157 | 0.000 | 0.315 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 117 | 110 | 0 | 0 | 0 | 121 | 0 | 40 | 0 |
| N.S. |
1 | 1.02 | 0.96 | 0.00 | 0.00 | 0.00 | 1.05 | 0.00 | 0.35 | 0.00 |
| time (sec) |
N/A | 0.233 | 0.199 | 0.000 | 0.000 | 0.000 | 1.574 | 0.000 | 0.282 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 117 | 110 | 0 | 0 | 0 | 117 | 0 | 44 | 0 |
| N.S. |
1 | 1.02 | 0.96 | 0.00 | 0.00 | 0.00 | 1.02 | 0.00 | 0.38 | 0.00 |
| time (sec) |
N/A | 0.234 | 0.229 | 0.000 | 0.000 | 0.000 | 1.417 | 0.000 | 0.235 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 113 | 124 | 113 | 0 | 0 | 0 | 117 | 0 | 20 | 0 |
| N.S. |
1 | 1.10 | 1.00 | 0.00 | 0.00 | 0.00 | 1.04 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 0.234 | 0.331 | 0.000 | 0.000 | 0.000 | 4.362 | 0.000 | 0.224 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 122 | 132 | 113 | 0 | 0 | 0 | 117 | 0 | 36 | 0 |
| N.S. |
1 | 1.08 | 0.93 | 0.00 | 0.00 | 0.00 | 0.96 | 0.00 | 0.30 | 0.00 |
| time (sec) |
N/A | 0.246 | 0.433 | 0.000 | 0.000 | 0.000 | 60.181 | 0.000 | 0.196 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 116 | 98 | 225 | 182 | 256 | 3432 | 437 | 279 | 231 |
| N.S. |
1 | 0.94 | 0.80 | 1.83 | 1.48 | 2.08 | 27.90 | 3.55 | 2.27 | 1.88 |
| time (sec) |
N/A | 0.264 | 0.133 | 0.477 | 0.062 | 0.098 | 21.906 | 0.143 | 0.227 | 0.613 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 88 | 84 | 84 | 127 | 123 | 161 | 1586 | 204 | 167 | 154 |
| N.S. |
1 | 0.95 | 0.95 | 1.44 | 1.40 | 1.83 | 18.02 | 2.32 | 1.90 | 1.75 |
| time (sec) |
N/A | 0.225 | 0.109 | 0.458 | 0.052 | 0.133 | 10.436 | 0.132 | 0.211 | 0.538 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 56 | 54 | 48 | 55 | 71 | 88 | 564 | 75 | 84 | 96 |
| N.S. |
1 | 0.96 | 0.86 | 0.98 | 1.27 | 1.57 | 10.07 | 1.34 | 1.50 | 1.71 |
| time (sec) |
N/A | 0.194 | 0.086 | 0.516 | 0.040 | 0.108 | 4.412 | 0.124 | 0.197 | 0.493 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 67 | 66 | 52 | 0 | 0 | 0 | 76 | 0 | 128 | 0 |
| N.S. |
1 | 0.99 | 0.78 | 0.00 | 0.00 | 0.00 | 1.13 | 0.00 | 1.91 | 0.00 |
| time (sec) |
N/A | 0.181 | 0.050 | 0.000 | 0.000 | 0.000 | 4.698 | 0.000 | 0.188 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 72 | 63 | 0 | 0 | 0 | 83 | 0 | 100 | 0 |
| N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 1.15 | 0.00 | 1.39 | 0.00 |
| time (sec) |
N/A | 0.186 | 0.053 | 0.000 | 0.000 | 0.000 | 5.322 | 0.000 | 0.226 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 92 | 92 | 78 | 0 | 0 | 0 | 56 | 0 | 894 | 0 |
| N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 | 9.72 | 0.00 |
| time (sec) |
N/A | 0.210 | 0.069 | 0.000 | 0.000 | 0.000 | 7.607 | 0.000 | 0.206 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 85 | 90 | 0 | 0 | 0 | 53 | 0 | 498 | 0 |
| N.S. |
1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.62 | 0.00 | 5.86 | 0.00 |
| time (sec) |
N/A | 0.201 | 0.017 | 0.000 | 0.000 | 0.000 | 4.170 | 0.000 | 0.207 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 80 | 76 | 0 | 0 | 0 | 51 | 0 | 412 | 102 |
| N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 | 5.15 | 1.28 |
| time (sec) |
N/A | 0.192 | 0.086 | 0.000 | 0.000 | 0.000 | 4.589 | 0.000 | 0.202 | 0.779 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 89 | 81 | 0 | 0 | 0 | 60 | 0 | 583 | 0 |
| N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.67 | 0.00 | 6.55 | 0.00 |
| time (sec) |
N/A | 0.202 | 0.083 | 0.000 | 0.000 | 0.000 | 6.739 | 0.000 | 0.234 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 107 | 83 | 0 | 0 | 0 | 90 | 0 | 971 | 0 |
| N.S. |
1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 | 9.07 | 0.00 |
| time (sec) |
N/A | 0.229 | 0.234 | 0.000 | 0.000 | 0.000 | 173.532 | 0.000 | 0.271 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 107 | 83 | 0 | 0 | 0 | 90 | 0 | 526 | 0 |
| N.S. |
1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 | 4.92 | 0.00 |
| time (sec) |
N/A | 0.225 | 0.171 | 0.000 | 0.000 | 0.000 | 35.324 | 0.000 | 0.231 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 105 | 105 | 98 | 0 | 0 | 0 | 90 | 0 | 546 | 0 |
| N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.86 | 0.00 | 5.20 | 0.00 |
| time (sec) |
N/A | 0.221 | 0.198 | 0.000 | 0.000 | 0.000 | 28.625 | 0.000 | 0.223 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 99 | 99 | 97 | 0 | 0 | 0 | 94 | 0 | 597 | 0 |
| N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.95 | 0.00 | 6.03 | 0.00 |
| time (sec) |
N/A | 0.221 | 0.251 | 0.000 | 0.000 | 0.000 | 33.658 | 0.000 | 0.265 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 102 | 102 | 97 | 0 | 0 | 0 | 94 | 0 | 606 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 | 5.94 | 0.00 |
| time (sec) |
N/A | 0.218 | 0.249 | 0.000 | 0.000 | 0.000 | 72.652 | 0.000 | 0.246 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 96 | 0 | 0 | 0 | 0 | 0 | 621 | 0 |
| N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 6.03 | 0.00 |
| time (sec) |
N/A | 0.223 | 0.209 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.270 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 15 | 15 | 82 | 16 | 21 | 21 | 26 | 29 | 20 | 15 |
| N.S. |
1 | 1.00 | 5.47 | 1.07 | 1.40 | 1.40 | 1.73 | 1.93 | 1.33 | 1.00 |
| time (sec) |
N/A | 0.148 | 0.089 | 0.421 | 0.099 | 0.134 | 3.143 | 0.123 | 0.244 | 0.521 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 15 | 15 | 15 | 16 | 116 | 21 | 26 | 66 | 20 | 15 |
| N.S. |
1 | 1.00 | 1.00 | 1.07 | 7.73 | 1.40 | 1.73 | 4.40 | 1.33 | 1.00 |
| time (sec) |
N/A | 0.151 | 0.054 | 0.516 | 0.042 | 0.179 | 2.016 | 0.128 | 0.215 | 0.481 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 13 | 13 | 13 | 14 | 19 | 19 | 24 | 27 | 18 | 13 |
| N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.46 | 1.46 | 1.85 | 2.08 | 1.38 | 1.00 |
| time (sec) |
N/A | 0.141 | 0.064 | 0.503 | 0.102 | 0.161 | 1.474 | 0.128 | 0.205 | 0.478 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 11 | 11 | 27 | 12 | 11 | 17 | 94 | 11 | 17 | 11 |
| N.S. |
1 | 1.00 | 2.45 | 1.09 | 1.00 | 1.55 | 8.55 | 1.00 | 1.55 | 1.00 |
| time (sec) |
N/A | 0.143 | 0.003 | 0.491 | 0.029 | 0.135 | 0.264 | 0.124 | 0.209 | 0.526 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 15 | 15 | 15 | 16 | 20 | 20 | 22 | 0 | 20 | 15 |
| N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.33 | 1.33 | 1.47 | 0.00 | 1.33 | 1.00 |
| time (sec) |
N/A | 0.144 | 0.079 | 0.427 | 0.092 | 0.142 | 2.207 | 0.000 | 0.223 | 0.493 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 15 | 15 | 15 | 16 | 20 | 20 | 22 | 0 | 20 | 15 |
| N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.33 | 1.33 | 1.47 | 0.00 | 1.33 | 1.00 |
| time (sec) |
N/A | 0.154 | 0.048 | 0.427 | 0.091 | 0.236 | 2.267 | 0.000 | 0.222 | 0.516 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 15 | 15 | 15 | 16 | 20 | 20 | 24 | 0 | 20 | 15 |
| N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.33 | 1.33 | 1.60 | 0.00 | 1.33 | 1.00 |
| time (sec) |
N/A | 0.145 | 0.079 | 0.437 | 0.102 | 0.155 | 3.579 | 0.000 | 0.199 | 0.505 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 121 | 108 | 0 | 0 | 0 | 114 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.91 | 0.00 | 0.00 | 0.00 | 0.96 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.245 | 0.070 | 0.000 | 0.000 | 0.000 | 54.415 | 0.000 | 0.206 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 89 | 81 | 0 | 0 | 0 | 78 | 0 | 119 | 0 |
| N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 | 1.34 | 0.00 |
| time (sec) |
N/A | 0.208 | 0.095 | 0.000 | 0.000 | 0.000 | 28.282 | 0.000 | 0.232 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 22 | 22 | 106 | 19 | 32 | 24 | 34 | 37 | 24 | 18 |
| N.S. |
1 | 1.00 | 4.82 | 0.86 | 1.45 | 1.09 | 1.55 | 1.68 | 1.09 | 0.82 |
| time (sec) |
N/A | 0.153 | 0.092 | 1.076 | 0.102 | 0.203 | 17.065 | 0.132 | 0.214 | 0.550 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 55 | 55 | 55 | 52 | 51 | 51 | 56 | 53 | 55 | 51 |
| N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.93 | 0.93 | 1.02 | 0.96 | 1.00 | 0.93 |
| time (sec) |
N/A | 0.194 | 0.006 | 0.382 | 0.036 | 0.161 | 0.020 | 0.117 | 0.212 | 0.461 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 55 | 59 | 55 | 52 | 51 | 51 | 53 | 53 | 55 | 51 |
| N.S. |
1 | 1.07 | 1.00 | 0.95 | 0.93 | 0.93 | 0.96 | 0.96 | 1.00 | 0.93 |
| time (sec) |
N/A | 0.208 | 0.006 | 0.365 | 0.041 | 0.104 | 0.021 | 0.123 | 0.220 | 0.046 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 55 | 55 | 55 | 52 | 51 | 51 | 56 | 53 | 55 | 51 |
| N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.93 | 0.93 | 1.02 | 0.96 | 1.00 | 0.93 |
| time (sec) |
N/A | 0.190 | 0.006 | 0.376 | 0.036 | 0.162 | 0.020 | 0.127 | 0.241 | 0.050 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 46 | 51 | 52 | 51 | 51 | 53 | 53 | 55 | 51 |
| N.S. |
1 | 1.10 | 1.21 | 1.24 | 1.21 | 1.21 | 1.26 | 1.26 | 1.31 | 1.21 |
| time (sec) |
N/A | 0.195 | 0.009 | 0.358 | 0.043 | 0.087 | 0.023 | 0.117 | 0.242 | 0.048 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 50 | 50 | 50 | 49 | 48 | 48 | 53 | 50 | 53 | 48 |
| N.S. |
1 | 1.00 | 1.00 | 0.98 | 0.96 | 0.96 | 1.06 | 1.00 | 1.06 | 0.96 |
| time (sec) |
N/A | 0.183 | 0.005 | 0.429 | 0.035 | 0.109 | 0.022 | 0.131 | 0.206 | 0.046 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 43 | 50 | 51 | 49 | 52 | 49 | 49 | 53 | 50 | 48 |
| N.S. |
1 | 1.16 | 1.19 | 1.14 | 1.21 | 1.14 | 1.14 | 1.23 | 1.16 | 1.12 |
| time (sec) |
N/A | 0.178 | 0.010 | 0.325 | 0.029 | 0.121 | 0.057 | 0.117 | 0.197 | 0.043 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 48 | 48 | 48 | 49 | 48 | 53 | 48 | 48 | 55 | 48 |
| N.S. |
1 | 1.00 | 1.00 | 1.02 | 1.00 | 1.10 | 1.00 | 1.00 | 1.15 | 1.00 |
| time (sec) |
N/A | 0.185 | 0.012 | 0.336 | 0.029 | 0.129 | 0.057 | 0.120 | 0.230 | 0.055 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 51 | 52 | 49 | 48 | 52 | 54 | 48 | 70 | 58 | 48 |
| N.S. |
1 | 1.02 | 0.96 | 0.94 | 1.02 | 1.06 | 0.94 | 1.37 | 1.14 | 0.94 |
| time (sec) |
N/A | 0.191 | 0.017 | 0.403 | 0.040 | 0.144 | 0.109 | 0.123 | 0.235 | 0.047 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 48 | 48 | 50 | 46 | 50 | 52 | 51 | 50 | 54 | 50 |
| N.S. |
1 | 1.00 | 1.04 | 0.96 | 1.04 | 1.08 | 1.06 | 1.04 | 1.12 | 1.04 |
| time (sec) |
N/A | 0.183 | 0.015 | 0.323 | 0.031 | 0.107 | 0.120 | 0.119 | 0.209 | 0.053 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 87 | 87 | 89 | 85 | 85 | 100 | 94 | 96 | 78 |
| N.S. |
1 | 1.00 | 1.00 | 1.02 | 0.98 | 0.98 | 1.15 | 1.08 | 1.10 | 0.90 |
| time (sec) |
N/A | 0.235 | 0.011 | 0.417 | 0.038 | 0.175 | 0.022 | 0.117 | 0.212 | 0.055 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 91 | 81 | 89 | 85 | 85 | 92 | 94 | 96 | 78 |
| N.S. |
1 | 1.05 | 0.93 | 1.02 | 0.98 | 0.98 | 1.06 | 1.08 | 1.10 | 0.90 |
| time (sec) |
N/A | 0.243 | 0.018 | 0.394 | 0.043 | 0.155 | 0.023 | 0.123 | 0.233 | 0.035 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 87 | 87 | 89 | 85 | 85 | 100 | 94 | 96 | 78 |
| N.S. |
1 | 1.00 | 1.00 | 1.02 | 0.98 | 0.98 | 1.15 | 1.08 | 1.10 | 0.90 |
| time (sec) |
N/A | 0.229 | 0.013 | 0.414 | 0.034 | 0.089 | 0.022 | 0.116 | 0.214 | 0.031 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 75 | 81 | 89 | 85 | 85 | 94 | 94 | 96 | 78 |
| N.S. |
1 | 1.06 | 1.14 | 1.25 | 1.20 | 1.20 | 1.32 | 1.32 | 1.35 | 1.10 |
| time (sec) |
N/A | 0.224 | 0.015 | 0.392 | 0.028 | 0.087 | 0.025 | 0.122 | 0.194 | 0.031 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 82 | 82 | 86 | 82 | 82 | 97 | 91 | 94 | 75 |
| N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.00 | 1.00 | 1.18 | 1.11 | 1.15 | 0.91 |
| time (sec) |
N/A | 0.214 | 0.011 | 0.338 | 0.045 | 0.092 | 0.022 | 0.122 | 0.213 | 0.030 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 87 | 80 | 84 | 85 | 82 | 85 | 92 | 89 | 74 |
| N.S. |
1 | 1.09 | 1.00 | 1.05 | 1.06 | 1.02 | 1.06 | 1.15 | 1.11 | 0.92 |
| time (sec) |
N/A | 0.220 | 0.017 | 0.506 | 0.036 | 0.071 | 0.074 | 0.128 | 0.244 | 0.036 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 81 | 81 | 81 | 90 | 83 | 87 | 92 | 90 | 96 | 76 |
| N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.02 | 1.07 | 1.14 | 1.11 | 1.19 | 0.94 |
| time (sec) |
N/A | 0.215 | 0.026 | 0.453 | 0.038 | 0.091 | 0.075 | 0.117 | 0.245 | 0.033 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 82 | 83 | 88 | 85 | 88 | 87 | 114 | 99 | 82 |
| N.S. |
1 | 0.98 | 0.99 | 1.05 | 1.01 | 1.05 | 1.04 | 1.36 | 1.18 | 0.98 |
| time (sec) |
N/A | 0.242 | 0.028 | 0.354 | 0.033 | 0.106 | 0.127 | 0.125 | 0.210 | 0.039 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 80 | 80 | 81 | 84 | 87 | 92 | 88 | 96 | 82 |
| N.S. |
1 | 1.00 | 1.00 | 1.01 | 1.05 | 1.09 | 1.15 | 1.10 | 1.20 | 1.02 |
| time (sec) |
N/A | 0.227 | 0.027 | 0.366 | 0.029 | 0.090 | 0.140 | 0.116 | 0.203 | 0.058 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 127 | 127 | 126 | 127 | 127 | 143 | 135 | 137 | 119 |
| N.S. |
1 | 1.00 | 1.00 | 0.99 | 1.00 | 1.00 | 1.13 | 1.06 | 1.08 | 0.94 |
| time (sec) |
N/A | 0.275 | 0.017 | 0.521 | 0.036 | 0.189 | 0.026 | 0.126 | 0.216 | 0.057 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 106 | 110 | 119 | 126 | 127 | 127 | 138 | 135 | 137 | 119 |
| N.S. |
1 | 1.04 | 1.12 | 1.19 | 1.20 | 1.20 | 1.30 | 1.27 | 1.29 | 1.12 |
| time (sec) |
N/A | 0.274 | 0.021 | 0.405 | 0.028 | 0.170 | 0.028 | 0.123 | 0.223 | 0.043 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 127 | 127 | 126 | 127 | 127 | 143 | 135 | 137 | 119 |
| N.S. |
1 | 1.00 | 1.00 | 0.99 | 1.00 | 1.00 | 1.13 | 1.06 | 1.08 | 0.94 |
| time (sec) |
N/A | 0.258 | 0.015 | 0.408 | 0.035 | 0.102 | 0.026 | 0.121 | 0.210 | 0.044 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 75 | 119 | 125 | 127 | 127 | 136 | 134 | 137 | 118 |
| N.S. |
1 | 1.06 | 1.68 | 1.76 | 1.79 | 1.79 | 1.92 | 1.89 | 1.93 | 1.66 |
| time (sec) |
N/A | 0.237 | 0.020 | 0.391 | 0.028 | 0.129 | 0.027 | 0.123 | 0.214 | 0.043 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 122 | 122 | 122 | 122 | 124 | 124 | 136 | 131 | 135 | 116 |
| N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.02 | 1.02 | 1.11 | 1.07 | 1.11 | 0.95 |
| time (sec) |
N/A | 0.252 | 0.013 | 0.435 | 0.039 | 0.092 | 0.025 | 0.124 | 0.227 | 0.042 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 126 | 123 | 122 | 128 | 125 | 133 | 134 | 131 | 116 |
| N.S. |
1 | 1.02 | 1.00 | 0.99 | 1.04 | 1.02 | 1.08 | 1.09 | 1.07 | 0.94 |
| time (sec) |
N/A | 0.260 | 0.020 | 0.362 | 0.029 | 0.101 | 0.093 | 0.120 | 0.225 | 0.046 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 120 | 120 | 120 | 126 | 124 | 129 | 131 | 130 | 137 | 115 |
| N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.03 | 1.08 | 1.09 | 1.08 | 1.14 | 0.96 |
| time (sec) |
N/A | 0.258 | 0.026 | 0.366 | 0.040 | 0.083 | 0.094 | 0.129 | 0.207 | 0.045 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 124 | 120 | 127 | 128 | 131 | 133 | 160 | 141 | 121 |
| N.S. |
1 | 1.01 | 0.98 | 1.03 | 1.04 | 1.07 | 1.08 | 1.30 | 1.15 | 0.98 |
| time (sec) |
N/A | 0.261 | 0.032 | 0.458 | 0.037 | 0.084 | 0.150 | 0.125 | 0.196 | 0.439 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 120 | 120 | 120 | 124 | 126 | 129 | 131 | 129 | 137 | 121 |
| N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.05 | 1.08 | 1.09 | 1.08 | 1.14 | 1.01 |
| time (sec) |
N/A | 0.247 | 0.029 | 0.348 | 0.039 | 0.105 | 0.162 | 0.125 | 0.237 | 0.043 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 104 | 104 | 104 | 143 | 139 | 302 | 246 | 153 | 179 | 169 |
| N.S. |
1 | 1.00 | 1.00 | 1.38 | 1.34 | 2.90 | 2.37 | 1.47 | 1.72 | 1.62 |
| time (sec) |
N/A | 0.256 | 0.061 | 0.523 | 0.111 | 0.162 | 0.261 | 0.119 | 0.205 | 0.476 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 79 | 78 | 82 | 95 | 100 | 101 | 83 | 107 | 122 | 106 |
| N.S. |
1 | 0.99 | 1.04 | 1.20 | 1.27 | 1.28 | 1.05 | 1.35 | 1.54 | 1.34 |
| time (sec) |
N/A | 0.238 | 0.027 | 0.424 | 0.038 | 0.115 | 0.206 | 0.121 | 0.221 | 0.066 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 83 | 83 | 83 | 102 | 104 | 228 | 194 | 113 | 137 | 128 |
| N.S. |
1 | 1.00 | 1.00 | 1.23 | 1.25 | 2.75 | 2.34 | 1.36 | 1.65 | 1.54 |
| time (sec) |
N/A | 0.234 | 0.047 | 0.447 | 0.115 | 0.184 | 0.239 | 0.118 | 0.201 | 0.463 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 58 | 60 | 49 | 64 | 65 | 66 | 49 | 67 | 82 | 68 |
| N.S. |
1 | 1.03 | 0.84 | 1.10 | 1.12 | 1.14 | 0.84 | 1.16 | 1.41 | 1.17 |
| time (sec) |
N/A | 0.201 | 0.016 | 0.500 | 0.031 | 0.142 | 0.181 | 0.122 | 0.229 | 0.079 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 63 | 59 | 64 | 68 | 179 | 172 | 72 | 109 | 90 |
| N.S. |
1 | 1.00 | 0.94 | 1.02 | 1.08 | 2.84 | 2.73 | 1.14 | 1.73 | 1.43 |
| time (sec) |
N/A | 0.210 | 0.032 | 0.431 | 0.111 | 0.124 | 0.204 | 0.117 | 0.212 | 0.087 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 51 | 52 | 50 | 59 | 61 | 59 | 41 | 62 | 74 | 58 |
| N.S. |
1 | 1.02 | 0.98 | 1.16 | 1.20 | 1.16 | 0.80 | 1.22 | 1.45 | 1.14 |
| time (sec) |
N/A | 0.206 | 0.017 | 0.430 | 0.056 | 0.102 | 0.643 | 0.114 | 0.226 | 0.527 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 55 | 55 | 55 | 65 | 63 | 164 | 165 | 63 | 104 | 80 |
| N.S. |
1 | 1.00 | 1.00 | 1.18 | 1.15 | 2.98 | 3.00 | 1.15 | 1.89 | 1.45 |
| time (sec) |
N/A | 0.205 | 0.033 | 0.449 | 0.110 | 0.231 | 0.263 | 0.122 | 0.214 | 0.484 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 58 | 59 | 60 | 66 | 70 | 74 | 49 | 91 | 96 | 67 |
| N.S. |
1 | 1.02 | 1.03 | 1.14 | 1.21 | 1.28 | 0.84 | 1.57 | 1.66 | 1.16 |
| time (sec) |
N/A | 0.221 | 0.020 | 0.428 | 0.040 | 0.154 | 0.732 | 0.124 | 0.236 | 0.142 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 66 | 66 | 64 | 68 | 71 | 192 | 172 | 71 | 123 | 90 |
| N.S. |
1 | 1.00 | 0.97 | 1.03 | 1.08 | 2.91 | 2.61 | 1.08 | 1.86 | 1.36 |
| time (sec) |
N/A | 0.212 | 0.038 | 0.446 | 0.108 | 0.113 | 0.331 | 0.122 | 0.190 | 0.471 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 77 | 72 | 91 | 96 | 98 | 66 | 139 | 129 | 93 |
| N.S. |
1 | 1.03 | 0.96 | 1.21 | 1.28 | 1.31 | 0.88 | 1.85 | 1.72 | 1.24 |
| time (sec) |
N/A | 0.236 | 0.029 | 0.419 | 0.043 | 0.123 | 0.679 | 0.126 | 0.196 | 0.569 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 87 | 86 | 100 | 107 | 236 | 207 | 112 | 152 | 129 |
| N.S. |
1 | 1.00 | 0.99 | 1.15 | 1.23 | 2.71 | 2.38 | 1.29 | 1.75 | 1.48 |
| time (sec) |
N/A | 0.234 | 0.048 | 0.466 | 0.122 | 0.192 | 0.377 | 0.128 | 0.195 | 0.491 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 99 | 108 | 123 | 134 | 136 | 105 | 184 | 171 | 129 |
| N.S. |
1 | 1.01 | 1.10 | 1.26 | 1.37 | 1.39 | 1.07 | 1.88 | 1.74 | 1.32 |
| time (sec) |
N/A | 0.254 | 0.040 | 0.442 | 0.039 | 0.135 | 0.755 | 0.123 | 0.225 | 0.532 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 116 | 138 | 141 | 149 | 400 | 286 | 156 | 270 | 200 |
| N.S. |
1 | 0.91 | 1.09 | 1.11 | 1.17 | 3.15 | 2.25 | 1.23 | 2.13 | 1.57 |
| time (sec) |
N/A | 0.271 | 0.064 | 0.557 | 0.113 | 0.136 | 0.483 | 0.123 | 0.222 | 0.485 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 88 | 87 | 80 | 107 | 161 | 99 | 163 | 188 | 112 |
| N.S. |
1 | 0.98 | 0.97 | 0.89 | 1.19 | 1.79 | 1.10 | 1.81 | 2.09 | 1.24 |
| time (sec) |
N/A | 0.251 | 0.040 | 0.470 | 0.029 | 0.132 | 0.459 | 0.126 | 0.227 | 0.114 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 100 | 104 | 105 | 101 | 109 | 342 | 246 | 114 | 241 | 146 |
| N.S. |
1 | 1.04 | 1.05 | 1.01 | 1.09 | 3.42 | 2.46 | 1.14 | 2.41 | 1.46 |
| time (sec) |
N/A | 0.242 | 0.049 | 0.453 | 0.136 | 0.204 | 0.409 | 0.119 | 0.223 | 0.086 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 61 | 56 | 63 | 74 | 101 | 68 | 110 | 133 | 77 |
| N.S. |
1 | 0.98 | 0.90 | 1.02 | 1.19 | 1.63 | 1.10 | 1.77 | 2.15 | 1.24 |
| time (sec) |
N/A | 0.212 | 0.030 | 0.602 | 0.035 | 0.075 | 0.376 | 0.123 | 0.208 | 0.088 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 82 | 89 | 92 | 96 | 302 | 236 | 95 | 215 | 124 |
| N.S. |
1 | 1.00 | 1.09 | 1.12 | 1.17 | 3.68 | 2.88 | 1.16 | 2.62 | 1.51 |
| time (sec) |
N/A | 0.248 | 0.039 | 0.411 | 0.147 | 0.157 | 0.349 | 0.119 | 0.188 | 0.505 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 67 | 68 | 70 | 67 | 86 | 116 | 80 | 99 | 146 | 80 |
| N.S. |
1 | 1.01 | 1.04 | 1.00 | 1.28 | 1.73 | 1.19 | 1.48 | 2.18 | 1.19 |
| time (sec) |
N/A | 0.225 | 0.029 | 0.417 | 0.048 | 0.093 | 0.634 | 0.132 | 0.214 | 0.566 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 106 | 91 | 97 | 100 | 305 | 238 | 102 | 225 | 128 |
| N.S. |
1 | 1.25 | 1.07 | 1.14 | 1.18 | 3.59 | 2.80 | 1.20 | 2.65 | 1.51 |
| time (sec) |
N/A | 0.234 | 0.041 | 0.443 | 0.135 | 0.150 | 0.429 | 0.119 | 0.237 | 0.535 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 81 | 83 | 72 | 77 | 100 | 159 | 92 | 109 | 176 | 100 |
| N.S. |
1 | 1.02 | 0.89 | 0.95 | 1.23 | 1.96 | 1.14 | 1.35 | 2.17 | 1.23 |
| time (sec) |
N/A | 0.244 | 0.059 | 0.435 | 0.030 | 0.091 | 0.676 | 0.124 | 0.246 | 0.100 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 101 | 131 | 107 | 107 | 118 | 356 | 248 | 111 | 256 | 147 |
| N.S. |
1 | 1.30 | 1.06 | 1.06 | 1.17 | 3.52 | 2.46 | 1.10 | 2.53 | 1.46 |
| time (sec) |
N/A | 0.308 | 0.043 | 0.478 | 0.119 | 0.127 | 0.491 | 0.113 | 0.209 | 0.565 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 142 | 174 | 148 | 137 | 159 | 522 | 240 | 154 | 382 | 159 |
| N.S. |
1 | 1.23 | 1.04 | 0.96 | 1.12 | 3.68 | 1.69 | 1.08 | 2.69 | 1.12 |
| time (sec) |
N/A | 0.384 | 0.058 | 0.535 | 0.148 | 0.101 | 0.875 | 0.121 | 0.222 | 0.507 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 99 | 96 | 114 | 105 | 120 | 178 | 122 | 107 | 206 | 123 |
| N.S. |
1 | 0.97 | 1.15 | 1.06 | 1.21 | 1.80 | 1.23 | 1.08 | 2.08 | 1.24 |
| time (sec) |
N/A | 0.255 | 0.034 | 0.435 | 0.054 | 0.097 | 1.058 | 0.122 | 0.207 | 0.109 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 139 | 130 | 123 | 143 | 475 | 223 | 133 | 356 | 135 |
| N.S. |
1 | 1.13 | 1.06 | 1.00 | 1.16 | 3.86 | 1.81 | 1.08 | 2.89 | 1.10 |
| time (sec) |
N/A | 0.299 | 0.069 | 0.454 | 0.118 | 0.104 | 0.737 | 0.120 | 0.212 | 0.522 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 67 | 69 | 54 | 73 | 87 | 108 | 87 | 76 | 123 | 83 |
| N.S. |
1 | 1.03 | 0.81 | 1.09 | 1.30 | 1.61 | 1.30 | 1.13 | 1.84 | 1.24 |
| time (sec) |
N/A | 0.221 | 0.019 | 0.425 | 0.034 | 0.089 | 0.629 | 0.124 | 0.213 | 0.460 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 129 | 106 | 124 | 138 | 449 | 223 | 126 | 345 | 130 |
| N.S. |
1 | 1.09 | 0.90 | 1.05 | 1.17 | 3.81 | 1.89 | 1.07 | 2.92 | 1.10 |
| time (sec) |
N/A | 0.243 | 0.058 | 0.520 | 0.127 | 0.210 | 0.481 | 0.132 | 0.224 | 0.576 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 87 | 75 | 88 | 109 | 163 | 107 | 110 | 161 | 106 |
| N.S. |
1 | 1.01 | 0.87 | 1.02 | 1.27 | 1.90 | 1.24 | 1.28 | 1.87 | 1.23 |
| time (sec) |
N/A | 0.244 | 0.052 | 0.421 | 0.043 | 0.161 | 0.578 | 0.124 | 0.227 | 0.080 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 136 | 133 | 128 | 146 | 475 | 224 | 135 | 365 | 135 |
| N.S. |
1 | 1.07 | 1.05 | 1.01 | 1.15 | 3.74 | 1.76 | 1.06 | 2.87 | 1.06 |
| time (sec) |
N/A | 0.248 | 0.057 | 0.472 | 0.147 | 0.187 | 0.588 | 0.122 | 0.214 | 0.553 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 106 | 109 | 99 | 114 | 142 | 256 | 139 | 177 | 303 | 132 |
| N.S. |
1 | 1.03 | 0.93 | 1.08 | 1.34 | 2.42 | 1.31 | 1.67 | 2.86 | 1.25 |
| time (sec) |
N/A | 0.275 | 0.055 | 0.686 | 0.039 | 0.105 | 0.924 | 0.123 | 0.195 | 0.573 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 143 | 174 | 148 | 142 | 167 | 536 | 240 | 151 | 397 | 156 |
| N.S. |
1 | 1.22 | 1.03 | 0.99 | 1.17 | 3.75 | 1.68 | 1.06 | 2.78 | 1.09 |
| time (sec) |
N/A | 0.369 | 0.048 | 0.506 | 0.142 | 0.242 | 0.655 | 0.123 | 0.204 | 0.563 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 74 | 71 | 68 | 74 | 75 | 70 | 77 | 83 | 76 |
| N.S. |
1 | 0.99 | 0.95 | 0.91 | 0.99 | 1.00 | 0.93 | 1.03 | 1.11 | 1.01 |
| time (sec) |
N/A | 0.242 | 0.021 | 0.611 | 0.029 | 0.193 | 0.163 | 0.124 | 0.237 | 0.492 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 77 | 66 | 77 | 75 | 77 | 178 | 153 | 84 | 93 | 96 |
| N.S. |
1 | 0.86 | 1.00 | 0.97 | 1.00 | 2.31 | 1.99 | 1.09 | 1.21 | 1.25 |
| time (sec) |
N/A | 0.208 | 0.036 | 0.417 | 0.116 | 0.198 | 0.182 | 0.116 | 0.226 | 0.473 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 54 | 53 | 47 | 49 | 50 | 51 | 46 | 52 | 58 | 52 |
| N.S. |
1 | 0.98 | 0.87 | 0.91 | 0.93 | 0.94 | 0.85 | 0.96 | 1.07 | 0.96 |
| time (sec) |
N/A | 0.204 | 0.015 | 0.473 | 0.037 | 0.187 | 0.152 | 0.120 | 0.215 | 0.073 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 58 | 55 | 57 | 51 | 54 | 129 | 90 | 58 | 67 | 70 |
| N.S. |
1 | 0.95 | 0.98 | 0.88 | 0.93 | 2.22 | 1.55 | 1.00 | 1.16 | 1.21 |
| time (sec) |
N/A | 0.177 | 0.026 | 0.418 | 0.117 | 0.204 | 0.162 | 0.121 | 0.203 | 0.082 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 33 | 31 | 32 | 31 | 29 | 27 | 32 | 35 | 31 |
| N.S. |
1 | 0.94 | 0.89 | 0.91 | 0.89 | 0.83 | 0.77 | 0.91 | 1.00 | 0.89 |
| time (sec) |
N/A | 0.183 | 0.008 | 0.404 | 0.036 | 0.152 | 0.121 | 0.120 | 0.244 | 0.465 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 39 | 39 | 40 | 34 | 33 | 98 | 82 | 33 | 52 | 32 |
| N.S. |
1 | 1.00 | 1.03 | 0.87 | 0.85 | 2.51 | 2.10 | 0.85 | 1.33 | 0.82 |
| time (sec) |
N/A | 0.157 | 0.017 | 0.386 | 0.124 | 0.156 | 0.138 | 0.123 | 0.199 | 0.056 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 34 | 38 | 34 | 33 | 35 | 33 | 26 | 36 | 38 | 32 |
| N.S. |
1 | 1.12 | 1.00 | 0.97 | 1.03 | 0.97 | 0.76 | 1.06 | 1.12 | 0.94 |
| time (sec) |
N/A | 0.186 | 0.010 | 0.410 | 0.028 | 0.080 | 0.363 | 0.128 | 0.216 | 0.486 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 43 | 43 | 42 | 37 | 37 | 105 | 82 | 37 | 57 | 34 |
| N.S. |
1 | 1.00 | 0.98 | 0.86 | 0.86 | 2.44 | 1.91 | 0.86 | 1.33 | 0.79 |
| time (sec) |
N/A | 0.161 | 0.019 | 0.628 | 0.129 | 0.092 | 0.163 | 0.118 | 0.191 | 0.499 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 50 | 51 | 49 | 46 | 48 | 48 | 41 | 72 | 60 | 45 |
| N.S. |
1 | 1.02 | 0.98 | 0.92 | 0.96 | 0.96 | 0.82 | 1.44 | 1.20 | 0.90 |
| time (sec) |
N/A | 0.197 | 0.016 | 0.414 | 0.029 | 0.076 | 0.366 | 0.115 | 0.229 | 0.502 |