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 | A | F | F(-2) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 282 | 282 | 219 | 240 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.78 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.082 | 10.200 | 0.048 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | A | F | F(-2) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 309 | 309 | 228 | 257 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.74 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.117 | 10.160 | 0.076 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | A | F | F(-2) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 326 | 326 | 234 | 274 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.72 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.145 | 10.172 | 0.065 | 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 | 297 | 297 | 430 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.267 | 10.653 | 0.011 | 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 | 297 | 297 | 386 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.224 | 15.520 | 0.009 | 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 | 295 | 295 | 386 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.228 | 10.476 | 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 | F | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 295 | 295 | 370 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.220 | 10.571 | 0.008 | 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 | 299 | 299 | 567 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.240 | 10.938 | 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 | F | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 299 | 299 | 490 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.242 | 15.782 | 0.009 | 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 | 297 | 297 | 487 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.245 | 10.800 | 0.011 | 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 | 297 | 297 | 447 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.250 | 10.682 | 0.012 | 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 | 297 | 297 | 354 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.225 | 10.404 | 0.007 | 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 | 297 | 297 | 242 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.233 | 15.143 | 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 | F | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 295 | 295 | 241 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.231 | 10.132 | 0.012 | 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 | 295 | 295 | 356 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.233 | 10.422 | 0.011 | 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 | 303 | 303 | 375 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.251 | 10.502 | 0.011 | 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 | 303 | 303 | 397 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.250 | 15.523 | 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 | F | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 301 | 301 | 395 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.248 | 10.472 | 0.019 | 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 | 301 | 301 | 460 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.249 | 10.655 | 0.015 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | A | B | B | B | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 243 | 243 | 191 | 1935 | 438 | 1376 | 11266 | 2816 | 769 |
| N.S. | 1 | 1.00 | 0.79 | 7.96 | 1.80 | 5.66 | 46.36 | 11.59 | 3.16 |
| time (sec) |
N/A | 0.115 | 0.770 | 0.030 | 0.309 | 0.389 | 1.618 | 5.868 | 1.058 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | A | B | B | B | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 155 | 155 | 117 | 783 | 248 | 578 | 4068 | 1178 | 429 |
| N.S. | 1 | 1.00 | 0.75 | 5.05 | 1.60 | 3.73 | 26.25 | 7.60 | 2.77 |
| time (sec) |
N/A | 0.065 | 0.445 | 0.017 | 0.294 | 0.414 | 0.856 | 3.826 | 0.598 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | B | B | B | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 83 | 83 | 59 | 82 | 113 | 179 | 1015 | 350 | 171 |
| N.S. | 1 | 1.00 | 0.71 | 0.99 | 1.36 | 2.16 | 12.23 | 4.22 | 2.06 |
| time (sec) |
N/A | 0.033 | 0.072 | 0.017 | 0.309 | 0.383 | 0.389 | 3.330 | 0.339 |
| 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 | 194 | 194 | 156 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.212 | 0.330 | 0.016 | 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 | 392 | 358 | 160 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 0.91 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.775 | 0.566 | 0.006 | 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 | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 319 | 319 | 466 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.260 | 1.761 | 0.006 | 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 | 317 | 317 | 267 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.238 | 0.859 | 0.006 | 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 | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 317 | 317 | 267 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.239 | 1.592 | 0.008 | 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 | 323 | 323 | 307 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.261 | 10.262 | 0.004 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 134 | 134 | 134 | 103 | 118 | 273 | 0 | 121 | 181 |
| N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.88 | 2.04 | 0.00 | 0.90 | 1.35 |
| time (sec) |
N/A | 0.116 | 0.042 | 0.176 | 0.498 | 3.269 | 0.000 | 5.690 | 0.873 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 118 | 99 | 92 | 104 | 211 | 0 | 105 | 166 |
| N.S. |
1 | 1.00 | 0.84 | 0.78 | 0.88 | 1.79 | 0.00 | 0.89 | 1.41 |
| time (sec) |
N/A | 0.098 | 0.065 | 0.171 | 0.491 | 1.389 | 0.000 | 4.385 | 0.722 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 105 | 105 | 77 | 80 | 89 | 172 | 0 | 90 | 138 |
| N.S. |
1 | 1.00 | 0.73 | 0.76 | 0.85 | 1.64 | 0.00 | 0.86 | 1.31 |
| time (sec) |
N/A | 0.092 | 0.024 | 0.177 | 0.496 | 0.949 | 0.000 | 3.819 | 0.989 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 96 | 66 | 72 | 81 | 147 | 0 | 86 | 944 |
| N.S. |
1 | 1.00 | 0.69 | 0.75 | 0.84 | 1.53 | 0.00 | 0.90 | 9.83 |
| time (sec) |
N/A | 0.060 | 0.028 | 0.169 | 0.498 | 0.507 | 0.000 | 4.577 | 1.936 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 96 | 67 | 75 | 82 | 150 | 0 | 85 | 328 |
| N.S. |
1 | 1.00 | 0.70 | 0.78 | 0.85 | 1.56 | 0.00 | 0.89 | 3.42 |
| time (sec) |
N/A | 0.042 | 0.026 | 0.191 | 0.532 | 0.601 | 0.000 | 3.105 | 1.020 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 114 | 114 | 134 | 90 | 99 | 199 | 0 | 102 | 527 |
| N.S. |
1 | 1.00 | 1.18 | 0.79 | 0.87 | 1.75 | 0.00 | 0.89 | 4.62 |
| time (sec) |
N/A | 0.084 | 0.042 | 0.187 | 0.500 | 4.720 | 0.000 | 3.581 | 0.961 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 129 | 129 | 169 | 107 | 119 | 275 | 0 | 132 | 820 |
| N.S. |
1 | 1.00 | 1.31 | 0.83 | 0.92 | 2.13 | 0.00 | 1.02 | 6.36 |
| time (sec) |
N/A | 0.095 | 0.067 | 0.185 | 0.496 | 22.839 | 0.000 | 3.920 | 1.381 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 156 | 209 | 127 | 143 | 350 | 0 | 168 | 1017 |
| N.S. |
1 | 1.00 | 1.34 | 0.81 | 0.92 | 2.24 | 0.00 | 1.08 | 6.52 |
| time (sec) |
N/A | 0.119 | 0.063 | 0.182 | 0.486 | 54.530 | 0.000 | 5.416 | 1.868 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 359 | 359 | 344 | 279 | 291 | 4154 | 0 | 363 | 2500 |
| N.S. |
1 | 1.00 | 0.96 | 0.78 | 0.81 | 11.57 | 0.00 | 1.01 | 6.96 |
| time (sec) |
N/A | 0.226 | 0.258 | 0.203 | 0.503 | 5.531 | 0.000 | 2.999 | 2.056 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 345 | 345 | 373 | 263 | 287 | 4110 | 0 | 333 | 2500 |
| N.S. |
1 | 1.00 | 1.08 | 0.76 | 0.83 | 11.91 | 0.00 | 0.97 | 7.25 |
| time (sec) |
N/A | 0.194 | 0.165 | 0.183 | 0.506 | 1.134 | 0.000 | 3.642 | 1.827 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 336 | 336 | 233 | 254 | 266 | 3790 | 0 | 327 | 2500 |
| N.S. |
1 | 1.00 | 0.69 | 0.76 | 0.79 | 11.28 | 0.00 | 0.97 | 7.44 |
| time (sec) |
N/A | 0.181 | 0.103 | 0.188 | 0.505 | 0.586 | 0.000 | 3.652 | 2.199 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 337 | 337 | 232 | 246 | 274 | 3651 | 0 | 336 | 2500 |
| N.S. |
1 | 1.00 | 0.69 | 0.73 | 0.81 | 10.83 | 0.00 | 1.00 | 7.42 |
| time (sec) |
N/A | 0.172 | 0.085 | 0.179 | 0.501 | 0.443 | 0.000 | 4.004 | 1.589 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 336 | 336 | 234 | 253 | 266 | 3842 | 0 | 339 | 2500 |
| N.S. |
1 | 1.00 | 0.70 | 0.75 | 0.79 | 11.43 | 0.00 | 1.01 | 7.44 |
| time (sec) |
N/A | 0.170 | 0.097 | 0.155 | 0.493 | 0.903 | 0.000 | 3.608 | 1.672 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 348 | 348 | 389 | 266 | 290 | 4120 | 0 | 348 | 2500 |
| N.S. |
1 | 1.00 | 1.12 | 0.76 | 0.83 | 11.84 | 0.00 | 1.00 | 7.18 |
| time (sec) |
N/A | 0.191 | 0.170 | 0.191 | 0.497 | 1.961 | 0.000 | 3.261 | 1.999 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 360 | 360 | 367 | 284 | 296 | 4228 | 0 | 364 | 2500 |
| N.S. |
1 | 1.00 | 1.02 | 0.79 | 0.82 | 11.74 | 0.00 | 1.01 | 6.94 |
| time (sec) |
N/A | 0.195 | 0.286 | 0.181 | 0.513 | 5.607 | 0.000 | 4.137 | 2.257 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 169 | 169 | 135 | 160 | 214 | 548 | 0 | 251 | 305 |
| N.S. |
1 | 1.00 | 0.80 | 0.95 | 1.27 | 3.24 | 0.00 | 1.49 | 1.80 |
| time (sec) |
N/A | 0.238 | 0.143 | 0.227 | 0.498 | 9.525 | 0.000 | 3.619 | 1.302 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 150 | 142 | 146 | 191 | 460 | 0 | 223 | 647 |
| N.S. |
1 | 1.00 | 0.95 | 0.97 | 1.27 | 3.07 | 0.00 | 1.49 | 4.31 |
| time (sec) |
N/A | 0.163 | 0.075 | 0.186 | 0.489 | 4.635 | 0.000 | 4.382 | 1.487 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 155 | 153 | 120 | 136 | 187 | 484 | 0 | 220 | 528 |
| N.S. |
1 | 0.99 | 0.77 | 0.88 | 1.21 | 3.12 | 0.00 | 1.42 | 3.41 |
| time (sec) |
N/A | 0.160 | 0.106 | 0.178 | 0.504 | 1.997 | 0.000 | 3.220 | 1.520 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 149 | 148 | 114 | 132 | 178 | 475 | 0 | 188 | 527 |
| N.S. |
1 | 0.99 | 0.77 | 0.89 | 1.19 | 3.19 | 0.00 | 1.26 | 3.54 |
| time (sec) |
N/A | 0.119 | 0.099 | 0.200 | 0.511 | 1.929 | 0.000 | 3.150 | 1.411 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 151 | 151 | 117 | 146 | 187 | 433 | 0 | 199 | 649 |
| N.S. |
1 | 1.00 | 0.77 | 0.97 | 1.24 | 2.87 | 0.00 | 1.32 | 4.30 |
| time (sec) |
N/A | 0.118 | 0.093 | 0.201 | 0.511 | 4.452 | 0.000 | 3.770 | 1.493 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 209 | 209 | 241 | 171 | 220 | 671 | 0 | 279 | 1082 |
| N.S. |
1 | 1.00 | 1.15 | 0.82 | 1.05 | 3.21 | 0.00 | 1.33 | 5.18 |
| time (sec) |
N/A | 0.159 | 0.120 | 0.201 | 0.496 | 72.445 | 0.000 | 5.193 | 2.577 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 236 | 236 | 248 | 181 | 269 | 863 | 0 | 344 | 1337 |
| N.S. |
1 | 1.00 | 1.05 | 0.77 | 1.14 | 3.66 | 0.00 | 1.46 | 5.67 |
| time (sec) |
N/A | 0.177 | 0.287 | 0.204 | 0.505 | 210.296 | 0.000 | 3.097 | 2.942 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | F(-1) | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 265 | 265 | 278 | 209 | 320 | 0 | 0 | 350 | 1545 |
| N.S. |
1 | 1.00 | 1.05 | 0.79 | 1.21 | 0.00 | 0.00 | 1.32 | 5.83 |
| time (sec) |
N/A | 0.217 | 0.269 | 0.206 | 0.516 | 0.000 | 0.000 | 4.049 | 3.477 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 712 | 712 | 431 | 334 | 487 | 9273 | 0 | 581 | 2500 |
| N.S. |
1 | 1.00 | 0.61 | 0.47 | 0.68 | 13.02 | 0.00 | 0.82 | 3.51 |
| time (sec) |
N/A | 0.438 | 0.202 | 0.200 | 0.525 | 10.104 | 0.000 | 3.893 | 2.864 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 687 | 687 | 428 | 339 | 462 | 9239 | 0 | 595 | 2500 |
| N.S. |
1 | 1.00 | 0.62 | 0.49 | 0.67 | 13.45 | 0.00 | 0.87 | 3.64 |
| time (sec) |
N/A | 0.383 | 0.248 | 0.208 | 0.506 | 7.143 | 0.000 | 3.571 | 2.825 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 685 | 685 | 423 | 327 | 470 | 9091 | 0 | 586 | 2500 |
| N.S. |
1 | 1.00 | 0.62 | 0.48 | 0.69 | 13.27 | 0.00 | 0.86 | 3.65 |
| time (sec) |
N/A | 0.389 | 0.180 | 0.208 | 0.506 | 6.223 | 0.000 | 4.419 | 4.873 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 685 | 685 | 428 | 339 | 458 | 9185 | 0 | 603 | 2500 |
| N.S. |
1 | 1.00 | 0.62 | 0.49 | 0.67 | 13.41 | 0.00 | 0.88 | 3.65 |
| time (sec) |
N/A | 0.364 | 0.186 | 0.234 | 0.533 | 6.787 | 0.000 | 3.887 | 2.867 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 689 | 689 | 429 | 334 | 489 | 9294 | 0 | 603 | 2500 |
| N.S. |
1 | 1.00 | 0.62 | 0.48 | 0.71 | 13.49 | 0.00 | 0.88 | 3.63 |
| time (sec) |
N/A | 0.377 | 0.174 | 0.166 | 0.520 | 12.504 | 0.000 | 4.462 | 2.732 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 745 | 745 | 499 | 355 | 506 | 9600 | 0 | 639 | 2500 |
| N.S. |
1 | 1.00 | 0.67 | 0.48 | 0.68 | 12.89 | 0.00 | 0.86 | 3.36 |
| time (sec) |
N/A | 0.497 | 0.247 | 0.198 | 0.521 | 28.269 | 0.000 | 4.201 | 5.161 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 751 | 751 | 513 | 355 | 527 | 9816 | 0 | 628 | 2500 |
| N.S. |
1 | 1.00 | 0.68 | 0.47 | 0.70 | 13.07 | 0.00 | 0.84 | 3.33 |
| time (sec) |
N/A | 0.436 | 0.260 | 0.232 | 0.538 | 63.536 | 0.000 | 5.360 | 5.219 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | C | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 70 | 70 | 40 | 110 | 0 | 31 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.57 | 1.57 | 0.00 | 0.44 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.037 | 10.088 | 0.202 | 0.000 | 0.129 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | C | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 70 | 70 | 36 | 112 | 0 | 55 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.51 | 1.60 | 0.00 | 0.79 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.041 | 10.091 | 0.198 | 0.000 | 0.124 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | F | F(-2) | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 99 | 99 | 46 | 96 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.46 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.035 | 10.100 | 0.145 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | F | F(-2) | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 61 | 37 | 143 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.61 | 2.34 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
| time (sec) |
N/A | 0.026 | 10.074 | 0.155 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | F | A | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 113 | 113 | 54 | 99 | 0 | 17 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.48 | 0.88 | 0.00 | 0.15 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.042 | 10.068 | 0.161 | 0.000 | 0.096 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | F | A | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 35 | 134 | 0 | 17 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.61 | 2.35 | 0.00 | 0.30 | 0.00 | 0.00 | -0.02 |
| time (sec) |
N/A | 0.035 | 10.073 | 0.154 | 0.000 | 0.081 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | C | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 74 | 60 | 168 | 0 | 74 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.81 | 2.27 | 0.00 | 1.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.040 | 10.082 | 0.192 | 0.000 | 0.100 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | C | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 74 | 56 | 115 | 0 | 73 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.76 | 1.55 | 0.00 | 0.99 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.041 | 10.080 | 0.198 | 0.000 | 0.107 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | F | A | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 243 | 243 | 120 | 159 | 124 | 206 | 0 | 156 | -1 |
| N.S. | 1 | 1.00 | 0.49 | 0.65 | 0.51 | 0.85 | 0.00 | 0.64 | -0.00 |
| time (sec) |
N/A | 0.086 | 0.124 | 0.124 | 0.295 | 0.379 | 0.000 | 4.421 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | F | A | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 108 | 108 | 56 | 51 | 50 | 50 | 0 | 68 | -1 |
| N.S. | 1 | 1.00 | 0.52 | 0.47 | 0.46 | 0.46 | 0.00 | 0.63 | -0.01 |
| time (sec) |
N/A | 0.074 | 0.027 | 0.117 | 0.267 | 0.341 | 0.000 | 3.980 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | F | A | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 178 | 178 | 96 | 119 | 81 | 155 | 0 | 109 | -1 |
| N.S. | 1 | 1.00 | 0.54 | 0.67 | 0.46 | 0.87 | 0.00 | 0.61 | -0.01 |
| time (sec) |
N/A | 0.050 | 0.092 | 0.131 | 0.270 | 0.376 | 0.000 | 2.784 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | F | A | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 152 | 152 | 83 | 80 | 45 | 123 | 0 | 84 | -1 |
| N.S. | 1 | 1.00 | 0.55 | 0.53 | 0.30 | 0.81 | 0.00 | 0.55 | -0.01 |
| time (sec) |
N/A | 0.063 | 0.061 | 0.125 | 0.284 | 0.383 | 0.000 | 3.477 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | F | A | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 177 | 177 | 93 | 130 | 59 | 134 | 0 | 116 | -1 |
| N.S. | 1 | 1.00 | 0.53 | 0.73 | 0.33 | 0.76 | 0.00 | 0.66 | -0.01 |
| time (sec) |
N/A | 0.063 | 0.106 | 0.125 | 0.273 | 0.366 | 0.000 | 3.624 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | F | A | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 177 | 177 | 90 | 133 | 83 | 141 | 0 | 100 | -1 |
| N.S. | 1 | 1.00 | 0.51 | 0.75 | 0.47 | 0.80 | 0.00 | 0.56 | -0.01 |
| time (sec) |
N/A | 0.082 | 0.100 | 0.137 | 0.278 | 0.371 | 0.000 | 4.547 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 78 | 78 | 72 | 73 | 72 | 77 | 76 | 79 | 73 |
| N.S. | 1 | 1.00 | 0.92 | 0.94 | 0.92 | 0.99 | 0.97 | 1.01 | 0.94 |
| time (sec) |
N/A | 0.091 | 0.017 | 0.171 | 0.275 | 0.342 | 0.012 | 3.846 | 0.038 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 78 | 78 | 78 | 73 | 72 | 77 | 82 | 79 | 73 |
| N.S. | 1 | 1.00 | 1.00 | 0.94 | 0.92 | 0.99 | 1.05 | 1.01 | 0.94 |
| time (sec) |
N/A | 0.043 | 0.011 | 0.145 | 0.286 | 0.350 | 0.012 | 3.518 | 0.028 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 75 | 72 | 73 | 72 | 77 | 76 | 79 | 73 |
| N.S. | 1 | 1.00 | 0.96 | 0.97 | 0.96 | 1.03 | 1.01 | 1.05 | 0.97 |
| time (sec) |
N/A | 0.093 | 0.016 | 0.141 | 0.293 | 0.334 | 0.012 | 3.028 | 0.029 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 73 | 73 | 73 | 70 | 69 | 74 | 78 | 76 | 70 |
| N.S. | 1 | 1.00 | 1.00 | 0.96 | 0.95 | 1.01 | 1.07 | 1.04 | 0.96 |
| time (sec) |
N/A | 0.032 | 0.011 | 0.107 | 0.302 | 0.374 | 0.013 | 2.906 | 0.029 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 74 | 74 | 77 | 73 | 75 | 73 | 79 | 70 |
| N.S. | 1 | 1.00 | 1.00 | 1.04 | 0.99 | 1.01 | 0.99 | 1.07 | 0.95 |
| time (sec) |
N/A | 0.065 | 0.014 | 0.108 | 0.279 | 0.333 | 0.061 | 3.113 | 0.034 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 71 | 75 | 69 | 78 | 73 | 74 | 70 |
| N.S. | 1 | 1.00 | 1.00 | 1.06 | 0.97 | 1.10 | 1.03 | 1.04 | 0.99 |
| time (sec) |
N/A | 0.033 | 0.022 | 0.118 | 0.299 | 0.346 | 0.059 | 5.144 | 0.033 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 74 | 71 | 74 | 73 | 83 | 71 | 97 | 70 |
| N.S. | 1 | 1.00 | 0.96 | 1.00 | 0.99 | 1.12 | 0.96 | 1.31 | 0.95 |
| time (sec) |
N/A | 0.064 | 0.029 | 0.115 | 0.286 | 0.368 | 0.115 | 6.219 | 0.038 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 168 | 168 | 165 | 159 | 154 | 415 | 320 | 160 | 251 |
| N.S. | 1 | 1.00 | 0.98 | 0.95 | 0.92 | 2.47 | 1.90 | 0.95 | 1.49 |
| time (sec) |
N/A | 0.158 | 0.090 | 0.132 | 0.521 | 0.367 | 0.672 | 4.389 | 0.325 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 135 | 133 | 122 | 122 | 341 | 189 | 125 | 179 |
| N.S. | 1 | 1.00 | 0.99 | 0.90 | 0.90 | 2.53 | 1.40 | 0.93 | 1.33 |
| time (sec) |
N/A | 0.105 | 0.053 | 0.137 | 0.504 | 0.387 | 0.709 | 4.156 | 0.322 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 106 | 106 | 102 | 90 | 90 | 300 | 162 | 91 | 95 |
| N.S. | 1 | 1.00 | 0.96 | 0.85 | 0.85 | 2.83 | 1.53 | 0.86 | 0.90 |
| time (sec) |
N/A | 0.072 | 0.043 | 0.131 | 0.524 | 0.353 | 0.606 | 5.892 | 0.342 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 83 | 87 | 88 | 79 | 74 | 266 | 153 | 75 | 77 |
| N.S. | 1 | 1.05 | 1.06 | 0.95 | 0.89 | 3.20 | 1.84 | 0.90 | 0.93 |
| time (sec) |
N/A | 0.059 | 0.038 | 0.126 | 0.499 | 0.345 | 0.430 | 4.109 | 0.357 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 86 | 89 | 85 | 81 | 274 | 155 | 83 | 81 |
| N.S. | 1 | 0.97 | 1.00 | 0.96 | 0.91 | 3.08 | 1.74 | 0.93 | 0.91 |
| time (sec) |
N/A | 0.075 | 0.040 | 0.144 | 0.479 | 0.378 | 0.608 | 4.408 | 0.367 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 106 | 106 | 105 | 94 | 101 | 340 | 167 | 94 | 98 |
| N.S. | 1 | 1.00 | 0.99 | 0.89 | 0.95 | 3.21 | 1.58 | 0.89 | 0.92 |
| time (sec) |
N/A | 0.092 | 0.044 | 0.134 | 0.493 | 0.346 | 0.808 | 3.663 | 0.357 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 136 | 136 | 135 | 122 | 135 | 389 | 284 | 131 | 128 |
| N.S. | 1 | 1.00 | 0.99 | 0.90 | 0.99 | 2.86 | 2.09 | 0.96 | 0.94 |
| time (sec) |
N/A | 0.166 | 0.061 | 0.133 | 0.493 | 0.374 | 1.094 | 3.513 | 0.383 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 167 | 166 | 149 | 165 | 458 | 328 | 164 | 156 |
| N.S. | 1 | 1.00 | 0.99 | 0.89 | 0.99 | 2.74 | 1.96 | 0.98 | 0.93 |
| time (sec) |
N/A | 0.213 | 0.064 | 0.132 | 0.516 | 0.373 | 1.347 | 4.411 | 0.403 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 173 | 173 | 170 | 151 | 165 | 488 | 235 | 160 | 223 |
| N.S. | 1 | 1.00 | 0.98 | 0.87 | 0.95 | 2.82 | 1.36 | 0.92 | 1.29 |
| time (sec) |
N/A | 0.213 | 0.074 | 0.138 | 0.511 | 0.372 | 2.022 | 4.469 | 0.354 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 143 | 143 | 141 | 120 | 132 | 450 | 212 | 125 | 137 |
| N.S. | 1 | 1.00 | 0.99 | 0.84 | 0.92 | 3.15 | 1.48 | 0.87 | 0.96 |
| time (sec) |
N/A | 0.139 | 0.059 | 0.144 | 0.491 | 0.369 | 1.873 | 4.675 | 0.344 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 124 | 124 | 122 | 106 | 114 | 415 | 201 | 107 | 118 |
| N.S. | 1 | 1.00 | 0.98 | 0.85 | 0.92 | 3.35 | 1.62 | 0.86 | 0.95 |
| time (sec) |
N/A | 0.091 | 0.069 | 0.162 | 0.515 | 0.362 | 1.374 | 4.893 | 0.386 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 119 | 110 | 107 | 110 | 389 | 196 | 101 | 112 |
| N.S. | 1 | 1.03 | 0.96 | 0.93 | 0.96 | 3.38 | 1.70 | 0.88 | 0.97 |
| time (sec) |
N/A | 0.077 | 0.065 | 0.134 | 0.509 | 0.359 | 0.785 | 3.228 | 0.379 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 127 | 124 | 124 | 111 | 121 | 428 | 202 | 110 | 118 |
| N.S. | 1 | 0.98 | 0.98 | 0.87 | 0.95 | 3.37 | 1.59 | 0.87 | 0.93 |
| time (sec) |
N/A | 0.131 | 0.093 | 0.159 | 0.517 | 0.384 | 1.099 | 3.299 | 0.390 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 142 | 142 | 141 | 124 | 143 | 491 | 214 | 128 | 138 |
| N.S. | 1 | 1.00 | 0.99 | 0.87 | 1.01 | 3.46 | 1.51 | 0.90 | 0.97 |
| time (sec) |
N/A | 0.139 | 0.057 | 0.135 | 0.503 | 0.372 | 1.422 | 4.456 | 0.398 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 171 | 171 | 173 | 151 | 175 | 534 | 330 | 164 | 168 |
| N.S. | 1 | 1.00 | 1.01 | 0.88 | 1.02 | 3.12 | 1.93 | 0.96 | 0.98 |
| time (sec) |
N/A | 0.239 | 0.077 | 0.136 | 0.507 | 0.364 | 1.949 | 4.014 | 0.412 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | F(-2) | F(-1) | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 230 | 230 | 228 | 216 | 0 | 0 | 0 | 236 | 2500 |
| N.S. |
1 | 1.00 | 0.99 | 0.94 | 0.00 | 0.00 | 0.00 | 1.03 | 10.87 |
| time (sec) |
N/A | 0.333 | 0.162 | 0.256 | 0.000 | 0.000 | 0.000 | 4.166 | 69.941 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | F(-2) | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 189 | 189 | 186 | 172 | 0 | 609 | 0 | 194 | 2304 |
| N.S. |
1 | 1.00 | 0.98 | 0.91 | 0.00 | 3.22 | 0.00 | 1.03 | 12.19 |
| time (sec) |
N/A | 0.217 | 0.122 | 0.180 | 0.000 | 117.401 | 0.000 | 5.482 | 15.207 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | F(-2) | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 158 | 158 | 139 | 137 | 0 | 421 | 0 | 157 | 1853 |
| N.S. |
1 | 1.00 | 0.88 | 0.87 | 0.00 | 2.66 | 0.00 | 0.99 | 11.73 |
| time (sec) |
N/A | 0.170 | 0.070 | 0.227 | 0.000 | 33.105 | 0.000 | 4.524 | 11.051 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | F(-2) | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 132 | 132 | 114 | 112 | 0 | 325 | 0 | 133 | 2500 |
| N.S. |
1 | 1.00 | 0.86 | 0.85 | 0.00 | 2.46 | 0.00 | 1.01 | 18.94 |
| time (sec) |
N/A | 0.105 | 0.046 | 0.161 | 0.000 | 11.051 | 0.000 | 5.531 | 9.751 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | F(-2) | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 133 | 133 | 112 | 113 | 0 | 329 | 0 | 134 | 2434 |
| N.S. |
1 | 1.00 | 0.84 | 0.85 | 0.00 | 2.47 | 0.00 | 1.01 | 18.30 |
| time (sec) |
N/A | 0.084 | 0.046 | 0.197 | 0.000 | 7.889 | 0.000 | 6.404 | 8.707 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | F(-2) | F(-1) | F(-1) | A | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 167 | 242 | 166 | 0 | 0 | 0 | 172 | 2500 |
| N.S. |
1 | 1.00 | 1.45 | 0.99 | 0.00 | 0.00 | 0.00 | 1.03 | 14.97 |
| time (sec) |
N/A | 0.202 | 0.204 | 0.217 | 0.000 | 0.000 | 0.000 | 7.255 | 17.199 |