Detailed conclusion table per each integral is given by 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 just an F.
In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 251 | 251 | 273 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.288 | 0.297 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 337 | 337 | 227 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.348 | 0.184 | 0.021 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 443 | 443 | 199 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.374 | 0.159 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 383 | 383 | 244 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.379 | 0.566 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | A | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 89 | 101 | 0 | 0 | 134 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.13 | 0.00 | 0.00 | 1.51 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.071 | 0.091 | 0.020 | 0.000 | 0.402 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | A | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 113 | 113 | 116 | 0 | 0 | 167 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.03 | 0.00 | 0.00 | 1.48 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.046 | 0.083 | 0.021 | 0.000 | 0.383 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | A | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 166 | 166 | 144 | 0 | 0 | 200 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 1.20 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.111 | 0.112 | 0.021 | 0.000 | 0.404 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | A | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 230 | 230 | 182 | 0 | 0 | 253 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 1.10 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.173 | 0.137 | 0.021 | 0.000 | 0.433 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | A | A | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 251 | 251 | 163 | 0 | 184 | 122 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.65 | 0.00 | 0.73 | 0.49 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.343 | 0.243 | 0.034 | 0.545 | 0.396 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | A | A | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 148 | 148 | 113 | 0 | 98 | 69 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.76 | 0.00 | 0.66 | 0.47 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.199 | 0.099 | 0.035 | 0.507 | 0.383 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 301 | 301 | 310 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.397 | 1.182 | 0.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 489 | 489 | 255 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.493 | 0.593 | 0.034 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 406 | 406 | 316 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.403 | 1.892 | 0.034 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 248 | 248 | 217 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.145 | 0.353 | 0.035 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | A | A | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 142 | 142 | 70 | 0 | 87 | 77 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.49 | 0.00 | 0.61 | 0.54 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.264 | 0.117 | 0.033 | 0.508 | 0.353 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | A | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 252 | 252 | 116 | 0 | 0 | 131 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.46 | 0.00 | 0.00 | 0.52 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.309 | 0.177 | 0.037 | 0.000 | 0.380 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | A | A | A | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 34 | 34 | 27 | 119 | 27 | 27 | 29 | 28 | -1 |
| N.S. | 1 | 1.00 | 0.79 | 3.50 | 0.79 | 0.79 | 0.85 | 0.82 | -0.03 |
| time (sec) |
N/A | 0.026 | 0.017 | 0.118 | 0.485 | 0.367 | 1.554 | 1.761 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | B | B | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 211 | 235 | 5139 | 286 | 1023 | 6217 | 553 | -1 |
| N.S. | 1 | 1.00 | 1.11 | 24.36 | 1.36 | 4.85 | 29.46 | 2.62 | -0.00 |
| time (sec) |
N/A | 1.062 | 0.387 | 0.452 | 0.303 | 0.374 | 20.008 | 2.595 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | B | B | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 153 | 153 | 172 | 2790 | 207 | 553 | 2820 | 396 | -1 |
| N.S. | 1 | 1.00 | 1.12 | 18.24 | 1.35 | 3.61 | 18.43 | 2.59 | -0.01 |
| time (sec) |
N/A | 0.133 | 0.203 | 0.280 | 0.289 | 0.345 | 8.694 | 2.541 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | B | B | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 95 | 94 | 1180 | 128 | 225 | 920 | 239 | -1 |
| N.S. | 1 | 1.00 | 0.99 | 12.42 | 1.35 | 2.37 | 9.68 | 2.52 | -0.01 |
| time (sec) |
N/A | 0.061 | 0.096 | 0.103 | 0.300 | 0.361 | 4.251 | 2.054 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | A | B | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 46 | 32 | 371 | 57 | 52 | 141 | 95 | -1 |
| N.S. | 1 | 1.00 | 0.70 | 8.07 | 1.24 | 1.13 | 3.07 | 2.07 | -0.02 |
| time (sec) |
N/A | 0.012 | 0.011 | 0.029 | 0.325 | 0.342 | 4.937 | 1.827 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | A |
| verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 28 | 0 | 108 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 0.00 | 3.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
| time (sec) |
N/A | 0.046 | 0.149 | 0.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | A |
| verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 28 | 0 | 108 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 0.00 | 3.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
| time (sec) |
N/A | 0.043 | 0.074 | 0.035 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1198 | 1198 | 2215 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.058 | 7.210 | 0.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 860 | 860 | 1379 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.577 | 6.074 | 0.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 520 | 520 | 571 | 1388 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.10 | 2.67 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.322 | 1.004 | 0.152 | 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(-1) | A | A |
| verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
| time (sec) |
N/A | 0.022 | 4.045 | 0.040 | 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(-1) | A | A |
| verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
| time (sec) |
N/A | 0.020 | 19.218 | 0.010 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F | F | A | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 185 | 185 | 171 | 867 | 0 | 0 | 316 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.92 | 4.69 | 0.00 | 0.00 | 1.71 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.141 | 0.074 | 0.104 | 0.000 | 0.000 | 115.413 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F | F | A | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 148 | 148 | 142 | 693 | 0 | 0 | 267 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.96 | 4.68 | 0.00 | 0.00 | 1.80 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.121 | 0.051 | 0.057 | 0.000 | 0.000 | 121.400 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F | F | A | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 107 | 105 | 521 | 0 | 0 | 218 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.98 | 4.87 | 0.00 | 0.00 | 2.04 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.085 | 0.036 | 0.053 | 0.000 | 0.000 | 77.888 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F | F | A | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 69 | 66 | 343 | 0 | 0 | 163 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.96 | 4.97 | 0.00 | 0.00 | 2.36 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.057 | 0.025 | 0.075 | 0.000 | 0.000 | 67.872 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 39 | 39 | 37 | 195 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.95 | 5.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
| time (sec) |
N/A | 0.049 | 0.007 | 0.057 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F | F | C | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 44 | 44 | 63 | 336 | 0 | 0 | 173 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.43 | 7.64 | 0.00 | 0.00 | 3.93 | 0.00 | -0.02 |
| time (sec) |
N/A | 0.042 | 0.027 | 0.055 | 0.000 | 0.000 | 7.474 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F | F | A | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 95 | 88 | 504 | 0 | 0 | 216 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.93 | 5.31 | 0.00 | 0.00 | 2.27 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.106 | 0.062 | 0.057 | 0.000 | 0.000 | 59.408 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F | F | A | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 135 | 124 | 689 | 0 | 0 | 265 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.92 | 5.10 | 0.00 | 0.00 | 1.96 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.120 | 0.141 | 0.061 | 0.000 | 0.000 | 63.205 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | F | A | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 170 | 170 | 156 | 258 | 184 | 0 | 299 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.92 | 1.52 | 1.08 | 0.00 | 1.76 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.126 | 0.057 | 0.131 | 0.318 | 0.000 | 110.948 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | F | A | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 136 | 136 | 125 | 211 | 146 | 0 | 253 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.92 | 1.55 | 1.07 | 0.00 | 1.86 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.109 | 0.047 | 0.071 | 0.327 | 0.000 | 126.326 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | F | A | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 98 | 99 | 160 | 102 | 0 | 207 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.01 | 1.63 | 1.04 | 0.00 | 2.11 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.081 | 0.031 | 0.066 | 0.319 | 0.000 | 87.499 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | F | A | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 63 | 64 | 101 | 68 | 0 | 156 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.02 | 1.60 | 1.08 | 0.00 | 2.48 | 0.00 | -0.02 |
| time (sec) |
N/A | 0.050 | 0.022 | 0.061 | 0.318 | 0.000 | 74.396 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 36 | 36 | 34 | 62 | 42 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.94 | 1.72 | 1.17 | 0.00 | 0.00 | 0.00 | -0.03 |
| time (sec) |
N/A | 0.048 | 0.006 | 0.058 | 0.313 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | A | F | C | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 41 | 41 | 54 | 103 | 62 | 0 | 170 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.32 | 2.51 | 1.51 | 0.00 | 4.15 | 0.00 | -0.02 |
| time (sec) |
N/A | 0.042 | 0.020 | 0.067 | 0.372 | 0.000 | 8.232 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | F | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 84 | 77 | 148 | 92 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.92 | 1.76 | 1.10 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.095 | 0.063 | 0.071 | 0.306 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | F | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 121 | 110 | 200 | 141 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.91 | 1.65 | 1.17 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.111 | 0.103 | 0.080 | 0.313 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | B | B | F(-2) | F | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 17 | 17 | 17 | 14 | 54 | 38 | 0 | 0 | 13 |
| N.S. |
1 | 1.00 | 1.00 | 0.82 | 3.18 | 2.24 | 0.00 | 0.00 | 0.76 |
| time (sec) |
N/A | 0.045 | 0.010 | 0.213 | 0.441 | 0.349 | 0.000 | 0.000 | 3.526 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | B | B | F(-2) | F | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 16 | 16 | 17 | 13 | 45 | 50 | 0 | 0 | 12 |
| N.S. |
1 | 1.00 | 1.06 | 0.81 | 2.81 | 3.12 | 0.00 | 0.00 | 0.75 |
| time (sec) |
N/A | 0.043 | 0.009 | 0.142 | 0.380 | 0.369 | 0.000 | 0.000 | 3.478 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | B | B | F(-2) | F | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 20 | 20 | 21 | 19 | 66 | 58 | 0 | 0 | 18 |
| N.S. |
1 | 1.00 | 1.05 | 0.95 | 3.30 | 2.90 | 0.00 | 0.00 | 0.90 |
| time (sec) |
N/A | 0.048 | 0.009 | 0.163 | 0.410 | 0.341 | 0.000 | 0.000 | 3.526 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | B | A | C | F | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 14 | 14 | 16 | 11 | 72 | 13 | 82 | 0 | 10 |
| N.S. | 1 | 1.00 | 1.14 | 0.79 | 5.14 | 0.93 | 5.86 | 0.00 | 0.71 |
| time (sec) |
N/A | 0.053 | 0.005 | 0.109 | 0.277 | 0.357 | 5.568 | 0.000 | 3.463 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | B | A | C | F | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 17 | 17 | 21 | 12 | 81 | 14 | 92 | 0 | 11 |
| N.S. | 1 | 1.00 | 1.24 | 0.71 | 4.76 | 0.82 | 5.41 | 0.00 | 0.65 |
| time (sec) |
N/A | 0.059 | 0.006 | 0.102 | 0.321 | 0.366 | 6.543 | 0.000 | 3.501 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 26 | 26 | 23 | 0 | 0 | 89 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.88 | 0.00 | 0.00 | 3.42 | 0.00 | 0.00 | -0.04 |
| time (sec) |
N/A | 0.067 | 0.009 | 0.066 | 0.000 | 0.440 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | A | F(-2) | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 171 | 171 | 140 | 806 | 259 | 189 | 0 | 335 | -1 |
| N.S. |
1 | 1.00 | 0.82 | 4.71 | 1.51 | 1.11 | 0.00 | 1.96 | -0.01 |
| time (sec) |
N/A | 0.147 | 0.111 | 0.198 | 0.303 | 0.357 | 0.000 | 3.948 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | A | B | A | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 142 | 142 | 101 | 616 | 186 | 135 | 1593 | 241 | -1 |
| N.S. | 1 | 1.00 | 0.71 | 4.34 | 1.31 | 0.95 | 11.22 | 1.70 | -0.01 |
| time (sec) |
N/A | 0.138 | 0.083 | 0.180 | 0.297 | 0.386 | 40.510 | 4.427 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | A | B | A | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 113 | 61 | 425 | 115 | 80 | 445 | 150 | -1 |
| N.S. | 1 | 1.26 | 0.68 | 4.72 | 1.28 | 0.89 | 4.94 | 1.67 | -0.01 |
| time (sec) |
N/A | 0.084 | 0.049 | 0.097 | 0.298 | 0.359 | 16.533 | 4.085 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | A | B | A | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 38 | 38 | 29 | 281 | 48 | 42 | 119 | 64 | -1 |
| N.S. | 1 | 1.00 | 0.76 | 7.39 | 1.26 | 1.11 | 3.13 | 1.68 | -0.03 |
| time (sec) |
N/A | 0.013 | 0.008 | 0.052 | 0.285 | 0.355 | 6.495 | 4.770 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | A | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 77 | 77 | 141 | 0 | 0 | 79 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.83 | 0.00 | 0.00 | 1.03 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.132 | 0.089 | 0.054 | 0.000 | 0.359 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | A | A | F | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 69 | 89 | 0 | 108 | 92 | 0 | 206 | -1 |
| N.S. | 1 | 1.00 | 1.29 | 0.00 | 1.57 | 1.33 | 0.00 | 2.99 | -0.01 |
| time (sec) |
N/A | 0.070 | 0.075 | 0.058 | 0.361 | 0.379 | 0.000 | 7.405 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | A | A | F(-1) | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 150 | 137 | 0 | 165 | 168 | 0 | 628 | -1 |
| N.S. |
1 | 1.00 | 0.91 | 0.00 | 1.10 | 1.12 | 0.00 | 4.19 | -0.01 |
| time (sec) |
N/A | 0.150 | 0.090 | 0.058 | 0.307 | 0.351 | 0.000 | 5.049 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | A | A | F(-1) | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 188 | 188 | 178 | 0 | 228 | 239 | 0 | 1080 | -1 |
| N.S. |
1 | 1.00 | 0.95 | 0.00 | 1.21 | 1.27 | 0.00 | 5.74 | -0.01 |
| time (sec) |
N/A | 0.161 | 0.095 | 0.056 | 0.302 | 0.360 | 0.000 | 7.816 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | A | F(-2) | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 372 | 372 | 285 | 4156 | 585 | 570 | 0 | 985 | -1 |
| N.S. |
1 | 1.00 | 0.77 | 11.17 | 1.57 | 1.53 | 0.00 | 2.65 | -0.00 |
| time (sec) |
N/A | 0.341 | 0.172 | 0.438 | 0.313 | 0.386 | 0.000 | 7.283 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | A | F(-2) | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 298 | 298 | 207 | 3038 | 425 | 411 | 0 | 715 | -1 |
| N.S. |
1 | 1.00 | 0.69 | 10.19 | 1.43 | 1.38 | 0.00 | 2.40 | -0.00 |
| time (sec) |
N/A | 0.301 | 0.135 | 0.325 | 0.295 | 0.391 | 0.000 | 7.723 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | A | B | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 226 | 226 | 125 | 1919 | 266 | 250 | 1535 | 445 | -1 |
| N.S. | 1 | 1.00 | 0.55 | 8.49 | 1.18 | 1.11 | 6.79 | 1.97 | -0.00 |
| time (sec) |
N/A | 0.202 | 0.092 | 0.192 | 0.300 | 0.402 | 47.983 | 8.654 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | A | B | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 69 | 67 | 1008 | 117 | 124 | 311 | 198 | -1 |
| N.S. | 1 | 1.00 | 0.97 | 14.61 | 1.70 | 1.80 | 4.51 | 2.87 | -0.01 |
| time (sec) |
N/A | 0.034 | 0.018 | 0.090 | 0.301 | 0.353 | 16.339 | 4.793 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | A | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 129 | 129 | 502 | 0 | 0 | 181 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 3.89 | 0.00 | 0.00 | 1.40 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.204 | 0.148 | 0.057 | 0.000 | 0.430 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F(-1) | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 138 | 138 | 157 | 0 | 0 | 276 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.14 | 0.00 | 0.00 | 2.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.224 | 0.280 | 0.054 | 0.000 | 0.366 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F(-1) | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 214 | 214 | 207 | 0 | 0 | 539 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 2.52 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.341 | 0.216 | 0.056 | 0.000 | 0.371 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F(-1) | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 346 | 346 | 240 | 0 | 0 | 802 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.69 | 0.00 | 0.00 | 2.32 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.465 | 0.332 | 0.056 | 0.000 | 0.375 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | B | B | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 73 | 613 | 76 | 158 | 398 | 137 | -1 |
| N.S. | 1 | 1.00 | 1.24 | 10.39 | 1.29 | 2.68 | 6.75 | 2.32 | -0.02 |
| time (sec) |
N/A | 0.056 | 0.080 | 0.081 | 0.288 | 0.350 | 12.554 | 4.280 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | B | B | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 73 | 613 | 76 | 158 | 398 | 137 | -1 |
| N.S. | 1 | 1.00 | 1.24 | 10.39 | 1.29 | 2.68 | 6.75 | 2.32 | -0.02 |
| time (sec) |
N/A | 0.056 | 0.073 | 0.079 | 0.283 | 0.347 | 3.841 | 3.321 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | B | B | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 73 | 613 | 76 | 158 | 398 | 137 | -1 |
| N.S. | 1 | 1.00 | 1.24 | 10.39 | 1.29 | 2.68 | 6.75 | 2.32 | -0.02 |
| time (sec) |
N/A | 0.045 | 0.072 | 0.084 | 0.284 | 0.369 | 0.982 | 1.777 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | A | B | A | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 53 | 51 | 278 | 56 | 69 | 131 | 69 | -1 |
| N.S. | 1 | 1.00 | 0.96 | 5.25 | 1.06 | 1.30 | 2.47 | 1.30 | -0.02 |
| time (sec) |
N/A | 0.060 | 0.050 | 0.100 | 0.287 | 0.419 | 5.235 | 2.724 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F(-2) | B | B | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 72 | 613 | 0 | 140 | 495 | 396 | -1 |
| N.S. |
1 | 1.00 | 1.01 | 8.63 | 0.00 | 1.97 | 6.97 | 5.58 | -0.01 |
| time (sec) |
N/A | 0.051 | 0.082 | 0.101 | 0.000 | 0.365 | 3.449 | 4.316 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F(-2) | B | B | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 72 | 613 | 0 | 140 | 495 | 397 | -1 |
| N.S. |
1 | 1.00 | 1.01 | 8.63 | 0.00 | 1.97 | 6.97 | 5.59 | -0.01 |
| time (sec) |
N/A | 0.051 | 0.085 | 0.101 | 0.000 | 0.362 | 5.564 | 3.443 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | B | B | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 73 | 614 | 76 | 158 | 398 | 137 | -1 |
| N.S. | 1 | 1.00 | 1.24 | 10.41 | 1.29 | 2.68 | 6.75 | 2.32 | -0.02 |
| time (sec) |
N/A | 0.056 | 0.073 | 0.081 | 0.286 | 0.363 | 7.077 | 2.690 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | B | B | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 73 | 614 | 76 | 158 | 398 | 137 | -1 |
| N.S. | 1 | 1.00 | 1.24 | 10.41 | 1.29 | 2.68 | 6.75 | 2.32 | -0.02 |
| time (sec) |
N/A | 0.056 | 0.073 | 0.086 | 0.288 | 0.359 | 2.025 | 2.350 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | B | B | A | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 61 | 606 | 68 | 136 | 323 | 115 | -1 |
| N.S. | 1 | 1.00 | 1.07 | 10.63 | 1.19 | 2.39 | 5.67 | 2.02 | -0.02 |
| time (sec) |
N/A | 0.024 | 0.060 | 0.082 | 0.288 | 0.395 | 0.476 | 2.446 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F(-2) | B | B | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 67 | 67 | 67 | 614 | 0 | 130 | 348 | 193 | -1 |
| N.S. |
1 | 1.00 | 1.00 | 9.16 | 0.00 | 1.94 | 5.19 | 2.88 | -0.01 |
| time (sec) |
N/A | 0.054 | 0.079 | 0.102 | 0.000 | 0.385 | 3.203 | 2.396 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F(-2) | B | B | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 72 | 614 | 0 | 140 | 495 | 397 | -1 |
| N.S. |
1 | 1.00 | 1.01 | 8.65 | 0.00 | 1.97 | 6.97 | 5.59 | -0.01 |
| time (sec) |
N/A | 0.051 | 0.087 | 0.109 | 0.000 | 0.368 | 4.136 | 2.386 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F(-2) | B | B | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 72 | 614 | 0 | 140 | 495 | 397 | -1 |
| N.S. |
1 | 1.00 | 1.01 | 8.65 | 0.00 | 1.97 | 6.97 | 5.59 | -0.01 |
| time (sec) |
N/A | 0.050 | 0.072 | 0.101 | 0.000 | 0.353 | 7.998 | 3.349 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | B | B | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 115 | 1924 | 148 | 441 | 1634 | 744 | -1 |
| N.S. | 1 | 1.00 | 1.12 | 18.68 | 1.44 | 4.28 | 15.86 | 7.22 | -0.01 |
| time (sec) |
N/A | 0.111 | 0.181 | 0.202 | 0.291 | 0.391 | 38.435 | 2.601 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | B | B | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 115 | 1924 | 148 | 440 | 1625 | 744 | -1 |
| N.S. | 1 | 1.00 | 1.12 | 18.68 | 1.44 | 4.27 | 15.78 | 7.22 | -0.01 |
| time (sec) |
N/A | 0.109 | 0.166 | 0.203 | 0.283 | 0.383 | 10.101 | 2.503 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | B | B | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 102 | 102 | 114 | 1922 | 148 | 440 | 1622 | 744 | -1 |
| N.S. | 1 | 1.00 | 1.12 | 18.84 | 1.45 | 4.31 | 15.90 | 7.29 | -0.01 |
| time (sec) |
N/A | 0.092 | 0.161 | 0.194 | 0.287 | 0.386 | 2.400 | 2.632 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | A | B | A | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 104 | 104 | 87 | 487 | 114 | 116 | 216 | 140 | -1 |
| N.S. | 1 | 1.00 | 0.84 | 4.68 | 1.10 | 1.12 | 2.08 | 1.35 | -0.01 |
| time (sec) |
N/A | 0.094 | 0.139 | 0.147 | 0.322 | 0.481 | 5.338 | 3.442 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F(-2) | B | B | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 135 | 114 | 1923 | 0 | 413 | 2118 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.84 | 14.24 | 0.00 | 3.06 | 15.69 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.114 | 0.170 | 0.211 | 0.000 | 0.353 | 4.672 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F(-2) | B | B | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 135 | 115 | 1924 | 0 | 413 | 2127 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.85 | 14.25 | 0.00 | 3.06 | 15.76 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.113 | 0.166 | 0.216 | 0.000 | 0.380 | 8.586 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | B | F(-1) | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 105 | 105 | 119 | 1930 | 152 | 449 | 0 | 746 | -1 |
| N.S. |
1 | 1.00 | 1.13 | 18.38 | 1.45 | 4.28 | 0.00 | 7.10 | -0.01 |
| time (sec) |
N/A | 0.114 | 0.168 | 0.187 | 0.286 | 0.374 | 0.000 | 3.086 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | B | F(-2) | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 105 | 105 | 119 | 1930 | 152 | 449 | 0 | 746 | -1 |
| N.S. |
1 | 1.00 | 1.13 | 18.38 | 1.45 | 4.28 | 0.00 | 7.10 | -0.01 |
| time (sec) |
N/A | 0.114 | 0.169 | 0.185 | 0.295 | 0.528 | 0.000 | 1.607 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | B | A | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 113 | 113 | 106 | 1921 | 144 | 416 | 211 | 244 | -1 |
| N.S. | 1 | 1.00 | 0.94 | 17.00 | 1.27 | 3.68 | 1.87 | 2.16 | -0.01 |
| time (sec) |
N/A | 0.051 | 0.151 | 0.182 | 0.290 | 0.368 | 5.183 | 2.465 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F(-2) | B | A | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 123 | 112 | 1927 | 0 | 411 | 197 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.91 | 15.67 | 0.00 | 3.34 | 1.60 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.111 | 0.173 | 0.220 | 0.000 | 0.370 | 10.131 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F(-2) | B | A | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 127 | 119 | 1930 | 0 | 422 | 228 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.94 | 15.20 | 0.00 | 3.32 | 1.80 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.115 | 0.168 | 0.246 | 0.000 | 0.383 | 36.086 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F(-2) | B | F(-2) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 127 | 119 | 1930 | 0 | 422 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.94 | 15.20 | 0.00 | 3.32 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.119 | 0.172 | 0.226 | 0.000 | 0.356 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F(-2) | B | F(-2) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 127 | 119 | 1930 | 0 | 422 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.94 | 15.20 | 0.00 | 3.32 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.123 | 0.168 | 0.223 | 0.000 | 0.351 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | B | F(-2) | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 147 | 147 | 156 | 4021 | 218 | 868 | 0 | 1586 | -1 |
| N.S. |
1 | 1.00 | 1.06 | 27.35 | 1.48 | 5.90 | 0.00 | 10.79 | -0.01 |
| time (sec) |
N/A | 0.252 | 0.169 | 0.268 | 0.294 | 0.379 | 0.000 | 1.701 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | B | F(-1) | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 149 | 149 | 160 | 4027 | 222 | 879 | 0 | 1588 | -1 |
| N.S. |
1 | 1.00 | 1.07 | 27.03 | 1.49 | 5.90 | 0.00 | 10.66 | -0.01 |
| time (sec) |
N/A | 0.261 | 0.164 | 0.271 | 0.291 | 0.356 | 0.000 | 2.484 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | B | F(-2) | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 149 | 149 | 160 | 4027 | 222 | 881 | 0 | 1588 | -1 |
| N.S. |
1 | 1.00 | 1.07 | 27.03 | 1.49 | 5.91 | 0.00 | 10.66 | -0.01 |
| time (sec) |
N/A | 0.240 | 0.158 | 0.262 | 0.290 | 0.379 | 0.000 | 1.955 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | A | A | A | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 152 | 152 | 129 | 693 | 172 | 166 | 299 | 210 | -1 |
| N.S. | 1 | 1.00 | 0.85 | 4.56 | 1.13 | 1.09 | 1.97 | 1.38 | -0.01 |
| time (sec) |
N/A | 0.119 | 0.188 | 0.162 | 0.290 | 0.350 | 7.273 | 2.321 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F(-2) | B | A | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 191 | 191 | 160 | 4027 | 0 | 844 | 338 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.84 | 21.08 | 0.00 | 4.42 | 1.77 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.264 | 0.158 | 0.322 | 0.000 | 0.347 | 75.877 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F(-2) | B | F(-2) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 191 | 191 | 160 | 4027 | 0 | 843 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.84 | 21.08 | 0.00 | 4.41 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.267 | 0.159 | 0.321 | 0.000 | 0.379 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | B | F(-1) | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 151 | 151 | 164 | 4031 | 228 | 880 | 0 | 1588 | -1 |
| N.S. |
1 | 1.00 | 1.09 | 26.70 | 1.51 | 5.83 | 0.00 | 10.52 | -0.01 |
| time (sec) |
N/A | 0.263 | 0.159 | 0.287 | 0.289 | 0.372 | 0.000 | 1.880 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | B | F(-2) | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 148 | 148 | 159 | 4027 | 224 | 879 | 0 | 1588 | -1 |
| N.S. |
1 | 1.00 | 1.07 | 27.21 | 1.51 | 5.94 | 0.00 | 10.73 | -0.01 |
| time (sec) |
N/A | 0.259 | 0.159 | 0.275 | 0.284 | 0.371 | 0.000 | 3.264 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | A | B | A | B | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 169 | 169 | 149 | 4023 | 220 | 838 | 325 | 374 | -1 |
| N.S. | 1 | 1.00 | 0.88 | 23.80 | 1.30 | 4.96 | 1.92 | 2.21 | -0.01 |
| time (sec) |
N/A | 0.069 | 0.140 | 0.266 | 0.286 | 0.345 | 9.525 | 3.313 | 0.000 |