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 | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 229 | 212 | 461 | 779 | 0 | 339 | 0 | 0 | 65 | 0 |
| N.S. |
1 | 0.93 | 2.01 | 3.40 | 0.00 | 1.48 | 0.00 | 0.00 | 0.28 | 0.00 |
| time (sec) |
N/A | 1.032 | 7.047 | 7.451 | 0.000 | 0.100 | 0.000 | 0.000 | 0.161 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 192 | 184 | 372 | 466 | 0 | 308 | 0 | 0 | 65 | 0 |
| N.S. |
1 | 0.96 | 1.94 | 2.43 | 0.00 | 1.60 | 0.00 | 0.00 | 0.34 | 0.00 |
| time (sec) |
N/A | 0.834 | 3.779 | 5.674 | 0.000 | 0.096 | 0.000 | 0.000 | 0.162 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 153 | 154 | 420 | 318 | 0 | 248 | 0 | 0 | 63 | 0 |
| N.S. |
1 | 1.01 | 2.75 | 2.08 | 0.00 | 1.62 | 0.00 | 0.00 | 0.41 | 0.00 |
| time (sec) |
N/A | 0.796 | 4.503 | 2.040 | 0.000 | 0.095 | 0.000 | 0.000 | 0.162 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 128 | 200 | 243 | 0 | 237 | 0 | 0 | 55 | 0 |
| N.S. |
1 | 1.04 | 1.63 | 1.98 | 0.00 | 1.93 | 0.00 | 0.00 | 0.45 | 0.00 |
| time (sec) |
N/A | 0.633 | 2.235 | 1.516 | 0.000 | 0.093 | 0.000 | 0.000 | 0.160 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 128 | 133 | 445 | 244 | 0 | 241 | 0 | 0 | 56 | 0 |
| N.S. |
1 | 1.04 | 3.48 | 1.91 | 0.00 | 1.88 | 0.00 | 0.00 | 0.44 | 0.00 |
| time (sec) |
N/A | 0.683 | 3.279 | 2.773 | 0.000 | 0.095 | 0.000 | 0.000 | 0.157 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 164 | 160 | 232 | 262 | 0 | 260 | 0 | 0 | 65 | 0 |
| N.S. |
1 | 0.98 | 1.41 | 1.60 | 0.00 | 1.59 | 0.00 | 0.00 | 0.40 | 0.00 |
| time (sec) |
N/A | 0.804 | 3.320 | 4.205 | 0.000 | 0.096 | 0.000 | 0.000 | 0.210 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 197 | 188 | 540 | 282 | 0 | 278 | 0 | 0 | 67 | 0 |
| N.S. |
1 | 0.95 | 2.74 | 1.43 | 0.00 | 1.41 | 0.00 | 0.00 | 0.34 | 0.00 |
| time (sec) |
N/A | 0.856 | 4.270 | 5.305 | 0.000 | 0.104 | 0.000 | 0.000 | 0.153 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 230 | 216 | 568 | 300 | 0 | 297 | 0 | 0 | 67 | 0 |
| N.S. |
1 | 0.94 | 2.47 | 1.30 | 0.00 | 1.29 | 0.00 | 0.00 | 0.29 | 0.00 |
| time (sec) |
N/A | 0.994 | 4.476 | 6.925 | 0.000 | 0.107 | 0.000 | 0.000 | 0.155 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 237 | 234 | 480 | 723 | 0 | 426 | 0 | 0 | 85 | 0 |
| N.S. |
1 | 0.99 | 2.03 | 3.05 | 0.00 | 1.80 | 0.00 | 0.00 | 0.36 | 0.00 |
| time (sec) |
N/A | 1.193 | 7.256 | 30.798 | 0.000 | 0.111 | 0.000 | 0.000 | 0.160 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 204 | 206 | 455 | 492 | 0 | 365 | 0 | 0 | 85 | 0 |
| N.S. |
1 | 1.01 | 2.23 | 2.41 | 0.00 | 1.79 | 0.00 | 0.00 | 0.42 | 0.00 |
| time (sec) |
N/A | 1.151 | 6.108 | 29.775 | 0.000 | 0.101 | 0.000 | 0.000 | 0.164 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 161 | 170 | 256 | 350 | 0 | 325 | 0 | 0 | 83 | 0 |
| N.S. |
1 | 1.06 | 1.59 | 2.17 | 0.00 | 2.02 | 0.00 | 0.00 | 0.52 | 0.00 |
| time (sec) |
N/A | 0.960 | 3.348 | 2.623 | 0.000 | 0.103 | 0.000 | 0.000 | 0.161 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 168 | 174 | 256 | 350 | 0 | 324 | 0 | 0 | 75 | 0 |
| N.S. |
1 | 1.04 | 1.52 | 2.08 | 0.00 | 1.93 | 0.00 | 0.00 | 0.45 | 0.00 |
| time (sec) |
N/A | 0.972 | 3.729 | 3.069 | 0.000 | 0.097 | 0.000 | 0.000 | 0.192 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 177 | 184 | 507 | 421 | 0 | 364 | 0 | 0 | 76 | 0 |
| N.S. |
1 | 1.04 | 2.86 | 2.38 | 0.00 | 2.06 | 0.00 | 0.00 | 0.43 | 0.00 |
| time (sec) |
N/A | 1.001 | 6.457 | 4.330 | 0.000 | 0.100 | 0.000 | 0.000 | 0.165 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 213 | 553 | 435 | 0 | 377 | 0 | 0 | 85 | 0 |
| N.S. |
1 | 1.01 | 2.62 | 2.06 | 0.00 | 1.79 | 0.00 | 0.00 | 0.40 | 0.00 |
| time (sec) |
N/A | 1.173 | 8.178 | 4.944 | 0.000 | 0.107 | 0.000 | 0.000 | 0.158 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 244 | 240 | 946 | 465 | 0 | 395 | 0 | 0 | 87 | 0 |
| N.S. |
1 | 0.98 | 3.88 | 1.91 | 0.00 | 1.62 | 0.00 | 0.00 | 0.36 | 0.00 |
| time (sec) |
N/A | 1.230 | 8.716 | 6.004 | 0.000 | 0.105 | 0.000 | 0.000 | 0.159 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 292 | 293 | 499 | 876 | 0 | 536 | 0 | 0 | 105 | 0 |
| N.S. |
1 | 1.00 | 1.71 | 3.00 | 0.00 | 1.84 | 0.00 | 0.00 | 0.36 | 0.00 |
| time (sec) |
N/A | 1.669 | 7.698 | 93.771 | 0.000 | 0.111 | 0.000 | 0.000 | 0.160 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 261 | 267 | 924 | 685 | 0 | 481 | 0 | 0 | 105 | 0 |
| N.S. |
1 | 1.02 | 3.54 | 2.62 | 0.00 | 1.84 | 0.00 | 0.00 | 0.40 | 0.00 |
| time (sec) |
N/A | 1.550 | 8.366 | 92.572 | 0.000 | 0.100 | 0.000 | 0.000 | 0.163 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 220 | 235 | 919 | 451 | 0 | 474 | 0 | 0 | 105 | 0 |
| N.S. |
1 | 1.07 | 4.18 | 2.05 | 0.00 | 2.15 | 0.00 | 0.00 | 0.48 | 0.00 |
| time (sec) |
N/A | 1.345 | 8.337 | 92.969 | 0.000 | 0.101 | 0.000 | 0.000 | 0.203 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 216 | 231 | 918 | 451 | 0 | 472 | 0 | 0 | 103 | 0 |
| N.S. |
1 | 1.07 | 4.25 | 2.09 | 0.00 | 2.19 | 0.00 | 0.00 | 0.48 | 0.00 |
| time (sec) |
N/A | 1.330 | 8.222 | 4.717 | 0.000 | 0.098 | 0.000 | 0.000 | 0.164 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 222 | 237 | 919 | 451 | 0 | 474 | 0 | 0 | 95 | 0 |
| N.S. |
1 | 1.07 | 4.14 | 2.03 | 0.00 | 2.14 | 0.00 | 0.00 | 0.43 | 0.00 |
| time (sec) |
N/A | 1.350 | 8.494 | 5.020 | 0.000 | 0.103 | 0.000 | 0.000 | 0.160 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 228 | 243 | 364 | 451 | 0 | 478 | 0 | 0 | 96 | 0 |
| N.S. |
1 | 1.07 | 1.60 | 1.98 | 0.00 | 2.10 | 0.00 | 0.00 | 0.42 | 0.00 |
| time (sec) |
N/A | 1.417 | 6.670 | 5.429 | 0.000 | 0.106 | 0.000 | 0.000 | 0.169 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F(-2) | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 261 | 271 | 377 | 465 | 0 | 489 | 0 | 0 | 105 | 0 |
| N.S. |
1 | 1.04 | 1.44 | 1.78 | 0.00 | 1.87 | 0.00 | 0.00 | 0.40 | 0.00 |
| time (sec) |
N/A | 1.553 | 7.348 | 6.023 | 0.000 | 0.112 | 0.000 | 0.000 | 0.164 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F(-1) | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 294 | 299 | 1032 | 493 | 0 | 506 | 0 | 0 | 107 | 0 |
| N.S. |
1 | 1.02 | 3.51 | 1.68 | 0.00 | 1.72 | 0.00 | 0.00 | 0.36 | 0.00 |
| time (sec) |
N/A | 1.687 | 10.296 | 6.955 | 0.000 | 0.125 | 0.000 | 0.000 | 0.193 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 176 | 166 | 156 | 313 | 3342 | 445 | 0 | 783 | 62 | 0 |
| N.S. |
1 | 0.94 | 0.89 | 1.78 | 18.99 | 2.53 | 0.00 | 4.45 | 0.35 | 0.00 |
| time (sec) |
N/A | 0.826 | 0.566 | 1.977 | 0.411 | 0.144 | 0.000 | 2.040 | 0.198 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 123 | 121 | 294 | 1927 | 399 | 0 | 557 | 60 | 0 |
| N.S. |
1 | 0.94 | 0.92 | 2.24 | 14.71 | 3.05 | 0.00 | 4.25 | 0.46 | 0.00 |
| time (sec) |
N/A | 0.582 | 0.470 | 1.929 | 0.353 | 0.159 | 0.000 | 1.566 | 0.201 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | F | B | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 78 | 78 | 93 | 244 | 905 | 319 | 0 | 305 | 52 | 0 |
| N.S. |
1 | 1.00 | 1.19 | 3.13 | 11.60 | 4.09 | 0.00 | 3.91 | 0.67 | 0.00 |
| time (sec) |
N/A | 0.432 | 0.271 | 1.766 | 0.296 | 0.143 | 0.000 | 1.727 | 0.174 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | B | F | B | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 76 | 76 | 83 | 151 | 262 | 304 | 0 | 163 | 54 | 0 |
| N.S. |
1 | 1.00 | 1.09 | 1.99 | 3.45 | 4.00 | 0.00 | 2.14 | 0.71 | 0.00 |
| time (sec) |
N/A | 0.429 | 0.288 | 1.701 | 0.257 | 0.107 | 0.000 | 1.051 | 0.160 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 82 | 56 | 59 | 134 | 74 | 0 | 108 | 62 | 81 |
| N.S. |
1 | 1.00 | 0.68 | 0.72 | 1.63 | 0.90 | 0.00 | 1.32 | 0.76 | 0.99 |
| time (sec) |
N/A | 0.422 | 0.172 | 1.152 | 0.251 | 0.082 | 0.000 | 0.828 | 0.154 | 11.610 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 130 | 128 | 71 | 78 | 317 | 92 | 0 | 154 | 62 | 106 |
| N.S. |
1 | 0.98 | 0.55 | 0.60 | 2.44 | 0.71 | 0.00 | 1.18 | 0.48 | 0.82 |
| time (sec) |
N/A | 0.617 | 0.232 | 1.208 | 0.278 | 0.080 | 0.000 | 0.708 | 0.182 | 12.141 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 175 | 171 | 91 | 97 | 498 | 110 | 0 | 199 | 62 | 130 |
| N.S. |
1 | 0.98 | 0.52 | 0.55 | 2.85 | 0.63 | 0.00 | 1.14 | 0.35 | 0.74 |
| time (sec) |
N/A | 0.772 | 0.239 | 1.230 | 0.273 | 0.078 | 0.000 | 0.870 | 0.155 | 13.172 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 227 | 219 | 191 | 328 | 5879 | 491 | 0 | 942 | 121 | 0 |
| N.S. |
1 | 0.96 | 0.84 | 1.44 | 25.90 | 2.16 | 0.00 | 4.15 | 0.53 | 0.00 |
| time (sec) |
N/A | 1.145 | 1.107 | 4.521 | 0.611 | 0.201 | 0.000 | 3.943 | 0.259 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F(-1) | A | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 180 | 176 | 0 | 308 | 4606 | 455 | 0 | 783 | 119 | 0 |
| N.S. |
1 | 0.98 | 0.00 | 1.71 | 25.59 | 2.53 | 0.00 | 4.35 | 0.66 | 0.00 |
| time (sec) |
N/A | 0.923 | 0.000 | 4.287 | 0.463 | 0.147 | 0.000 | 2.435 | 0.255 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 133 | 132 | 150 | 282 | 3389 | 407 | 0 | 557 | 109 | 0 |
| N.S. |
1 | 0.99 | 1.13 | 2.12 | 25.48 | 3.06 | 0.00 | 4.19 | 0.82 | 0.00 |
| time (sec) |
N/A | 0.727 | 0.639 | 4.344 | 0.352 | 0.150 | 0.000 | 2.920 | 0.270 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F | B | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 124 | 131 | 107 | 300 | 1417 | 361 | 0 | 349 | 103 | 0 |
| N.S. |
1 | 1.06 | 0.86 | 2.42 | 11.43 | 2.91 | 0.00 | 2.81 | 0.83 | 0.00 |
| time (sec) |
N/A | 0.718 | 0.992 | 4.247 | 0.327 | 0.148 | 0.000 | 2.573 | 0.201 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F | B | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 125 | 128 | 109 | 190 | 314 | 365 | 0 | 231 | 113 | 0 |
| N.S. |
1 | 1.02 | 0.87 | 1.52 | 2.51 | 2.92 | 0.00 | 1.85 | 0.90 | 0.00 |
| time (sec) |
N/A | 0.695 | 0.376 | 4.274 | 0.250 | 0.120 | 0.000 | 1.580 | 0.168 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 129 | 73 | 79 | 250 | 94 | 0 | 150 | 121 | 107 |
| N.S. |
1 | 0.98 | 0.56 | 0.60 | 1.91 | 0.72 | 0.00 | 1.15 | 0.92 | 0.82 |
| time (sec) |
N/A | 0.617 | 0.315 | 2.255 | 0.235 | 0.086 | 0.000 | 1.450 | 0.185 | 12.851 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 181 | 181 | 92 | 98 | 514 | 113 | 0 | 195 | 121 | 131 |
| N.S. |
1 | 1.00 | 0.51 | 0.54 | 2.84 | 0.62 | 0.00 | 1.08 | 0.67 | 0.72 |
| time (sec) |
N/A | 0.931 | 0.302 | 1.863 | 0.255 | 0.084 | 0.000 | 1.344 | 0.171 | 13.643 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 228 | 224 | 113 | 118 | 700 | 132 | 0 | 238 | 121 | 155 |
| N.S. |
1 | 0.98 | 0.50 | 0.52 | 3.07 | 0.58 | 0.00 | 1.04 | 0.53 | 0.68 |
| time (sec) |
N/A | 1.170 | 6.578 | 2.306 | 0.288 | 0.086 | 0.000 | 1.904 | 0.197 | 14.653 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 274 | 273 | 567 | 356 | 9242 | 555 | 0 | 1191 | 183 | 0 |
| N.S. |
1 | 1.00 | 2.07 | 1.30 | 33.73 | 2.03 | 0.00 | 4.35 | 0.67 | 0.00 |
| time (sec) |
N/A | 1.531 | 6.583 | 0.921 | 1.107 | 0.207 | 0.000 | 5.164 | 0.324 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 227 | 230 | 190 | 336 | 7331 | 515 | 0 | 942 | 181 | 0 |
| N.S. |
1 | 1.01 | 0.84 | 1.48 | 32.30 | 2.27 | 0.00 | 4.15 | 0.80 | 0.00 |
| time (sec) |
N/A | 1.262 | 0.945 | 4.485 | 0.674 | 0.206 | 0.000 | 3.878 | 0.320 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 180 | 185 | 204 | 309 | 6297 | 475 | 0 | 783 | 171 | 0 |
| N.S. |
1 | 1.03 | 1.13 | 1.72 | 34.98 | 2.64 | 0.00 | 4.35 | 0.95 | 0.00 |
| time (sec) |
N/A | 1.033 | 0.596 | 4.320 | 3.200 | 0.147 | 0.000 | 3.981 | 0.289 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 180 | 183 | 137 | 328 | 14322 | 451 | 0 | 599 | 163 | 0 |
| N.S. |
1 | 1.02 | 0.76 | 1.82 | 79.57 | 2.51 | 0.00 | 3.33 | 0.91 | 0.00 |
| time (sec) |
N/A | 1.020 | 1.226 | 4.366 | 3.051 | 0.151 | 0.000 | 3.708 | 0.296 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 177 | 184 | 133 | 332 | 12088 | 421 | 0 | 414 | 165 | 0 |
| N.S. |
1 | 1.04 | 0.75 | 1.88 | 68.29 | 2.38 | 0.00 | 2.34 | 0.93 | 0.00 |
| time (sec) |
N/A | 1.065 | 0.568 | 4.401 | 0.391 | 0.147 | 0.000 | 2.097 | 0.211 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 172 | 180 | 127 | 210 | 655 | 421 | 0 | 276 | 175 | 0 |
| N.S. |
1 | 1.05 | 0.74 | 1.22 | 3.81 | 2.45 | 0.00 | 1.60 | 1.02 | 0.00 |
| time (sec) |
N/A | 1.032 | 1.292 | 4.296 | 0.267 | 0.120 | 0.000 | 1.866 | 0.192 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 178 | 173 | 91 | 100 | 385 | 120 | 0 | 196 | 183 | 133 |
| N.S. |
1 | 0.97 | 0.51 | 0.56 | 2.16 | 0.67 | 0.00 | 1.10 | 1.03 | 0.75 |
| time (sec) |
N/A | 0.810 | 0.576 | 2.375 | 0.241 | 0.083 | 0.000 | 2.512 | 0.188 | 13.330 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 228 | 235 | 108 | 120 | 746 | 141 | 0 | 241 | 183 | 157 |
| N.S. |
1 | 1.03 | 0.47 | 0.53 | 3.27 | 0.62 | 0.00 | 1.06 | 0.80 | 0.69 |
| time (sec) |
N/A | 1.354 | 0.694 | 2.315 | 0.271 | 0.083 | 0.000 | 1.963 | 0.228 | 14.968 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 275 | 278 | 127 | 140 | 945 | 162 | 0 | 286 | 183 | 392 |
| N.S. |
1 | 1.01 | 0.46 | 0.51 | 3.44 | 0.59 | 0.00 | 1.04 | 0.67 | 1.43 |
| time (sec) |
N/A | 1.584 | 2.851 | 2.391 | 0.277 | 0.087 | 0.000 | 2.212 | 0.195 | 18.107 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 190 | 203 | 234 | 401 | 2524 | 614 | 0 | 532 | 85 | 0 |
| N.S. |
1 | 1.07 | 1.23 | 2.11 | 13.28 | 3.23 | 0.00 | 2.80 | 0.45 | 0.00 |
| time (sec) |
N/A | 1.219 | 0.460 | 2.200 | 0.340 | 0.175 | 0.000 | 2.397 | 0.165 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 141 | 150 | 173 | 357 | 1353 | 528 | 0 | 320 | 83 | 0 |
| N.S. |
1 | 1.06 | 1.23 | 2.53 | 9.60 | 3.74 | 0.00 | 2.27 | 0.59 | 0.00 |
| time (sec) |
N/A | 0.832 | 0.256 | 2.005 | 0.327 | 0.166 | 0.000 | 1.529 | 0.159 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 100 | 100 | 95 | 211 | 567 | 363 | 0 | 177 | 75 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 2.11 | 5.67 | 3.63 | 0.00 | 1.77 | 0.75 | 0.00 |
| time (sec) |
N/A | 0.567 | 0.124 | 1.825 | 0.274 | 0.116 | 0.000 | 1.131 | 0.169 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F | A | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 99 | 99 | 114 | 151 | 195 | 306 | 0 | 96 | 76 | 0 |
| N.S. |
1 | 1.00 | 1.15 | 1.53 | 1.97 | 3.09 | 0.00 | 0.97 | 0.77 | 0.00 |
| time (sec) |
N/A | 0.449 | 0.175 | 1.220 | 0.250 | 0.092 | 0.000 | 0.902 | 0.161 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F | A | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 142 | 150 | 132 | 190 | 387 | 354 | 0 | 122 | 85 | 0 |
| N.S. |
1 | 1.06 | 0.93 | 1.34 | 2.73 | 2.49 | 0.00 | 0.86 | 0.60 | 0.00 |
| time (sec) |
N/A | 0.714 | 0.264 | 1.255 | 0.279 | 0.097 | 0.000 | 1.117 | 0.208 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 187 | 205 | 133 | 208 | 640 | 388 | 0 | 166 | 87 | 0 |
| N.S. |
1 | 1.10 | 0.71 | 1.11 | 3.42 | 2.07 | 0.00 | 0.89 | 0.47 | 0.00 |
| time (sec) |
N/A | 1.053 | 0.767 | 1.372 | 0.291 | 0.095 | 0.000 | 1.321 | 0.171 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 230 | 260 | 152 | 228 | 805 | 422 | 0 | 191 | 87 | 0 |
| N.S. |
1 | 1.13 | 0.66 | 0.99 | 3.50 | 1.83 | 0.00 | 0.83 | 0.38 | 0.00 |
| time (sec) |
N/A | 1.402 | 1.028 | 1.516 | 0.314 | 0.100 | 0.000 | 1.420 | 0.172 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | B | A | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 247 | 259 | 497 | 506 | 13364 | 758 | 0 | 0 | 105 | 0 |
| N.S. |
1 | 1.05 | 2.01 | 2.05 | 54.11 | 3.07 | 0.00 | 0.00 | 0.43 | 0.00 |
| time (sec) |
N/A | 1.641 | 2.933 | 4.550 | 1.150 | 0.204 | 0.000 | 0.000 | 0.177 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | B | A | F(-1) | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 197 | 205 | 429 | 472 | 7057 | 666 | 0 | 370 | 105 | 0 |
| N.S. |
1 | 1.04 | 2.18 | 2.40 | 35.82 | 3.38 | 0.00 | 1.88 | 0.53 | 0.00 |
| time (sec) |
N/A | 1.213 | 1.267 | 4.431 | 0.573 | 0.207 | 0.000 | 2.945 | 0.186 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | B | B | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 145 | 150 | 394 | 314 | 17843 | 598 | 0 | 0 | 103 | 0 |
| N.S. |
1 | 1.03 | 2.72 | 2.17 | 123.06 | 4.12 | 0.00 | 0.00 | 0.71 | 0.00 |
| time (sec) |
N/A | 0.854 | 1.181 | 4.210 | 1.205 | 0.134 | 0.000 | 0.000 | 0.223 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | B | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 107 | 354 | 200 | 16752 | 376 | 0 | 109 | 95 | 0 |
| N.S. |
1 | 1.00 | 3.31 | 1.87 | 156.56 | 3.51 | 0.00 | 1.02 | 0.89 | 0.00 |
| time (sec) |
N/A | 0.481 | 0.606 | 2.250 | 0.978 | 0.094 | 0.000 | 1.322 | 0.180 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F | A | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 158 | 174 | 214 | 8208 | 430 | 0 | 141 | 96 | 0 |
| N.S. |
1 | 1.01 | 1.12 | 1.37 | 52.62 | 2.76 | 0.00 | 0.90 | 0.62 | 0.00 |
| time (sec) |
N/A | 0.786 | 0.980 | 1.826 | 0.359 | 0.105 | 0.000 | 1.606 | 0.189 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F | A | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 203 | 213 | 173 | 235 | 41138 | 464 | 0 | 177 | 105 | 0 |
| N.S. |
1 | 1.05 | 0.85 | 1.16 | 202.65 | 2.29 | 0.00 | 0.87 | 0.52 | 0.00 |
| time (sec) |
N/A | 1.096 | 1.186 | 2.342 | 0.708 | 0.101 | 0.000 | 2.168 | 0.187 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 250 | 268 | 171 | 258 | 0 | 500 | 0 | 0 | 107 | 0 |
| N.S. |
1 | 1.07 | 0.68 | 1.03 | 0.00 | 2.00 | 0.00 | 0.00 | 0.43 | 0.00 |
| time (sec) |
N/A | 1.448 | 0.957 | 2.372 | 0.000 | 0.101 | 0.000 | 0.000 | 0.186 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 246 | 262 | 164 | 562 | 14037 | 800 | 0 | 406 | 125 | 0 |
| N.S. |
1 | 1.07 | 0.67 | 2.28 | 57.06 | 3.25 | 0.00 | 1.65 | 0.51 | 0.00 |
| time (sec) |
N/A | 1.650 | 2.915 | 4.523 | 2.643 | 0.232 | 0.000 | 4.005 | 0.187 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | B | B | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 194 | 205 | 570 | 382 | 89320 | 746 | 0 | 259 | 125 | 0 |
| N.S. |
1 | 1.06 | 2.94 | 1.97 | 460.41 | 3.85 | 0.00 | 1.34 | 0.64 | 0.00 |
| time (sec) |
N/A | 1.202 | 3.814 | 4.487 | 14.441 | 0.148 | 0.000 | 3.299 | 0.230 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | B | A | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 154 | 570 | 263 | 87207 | 498 | 0 | 0 | 123 | 0 |
| N.S. |
1 | 0.99 | 3.65 | 1.69 | 559.02 | 3.19 | 0.00 | 0.00 | 0.79 | 0.00 |
| time (sec) |
N/A | 0.663 | 3.744 | 2.325 | 14.309 | 0.099 | 0.000 | 0.000 | 0.190 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | B | A | F | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 213 | 443 | 261 | 5924 | 502 | 0 | 144 | 115 | 0 |
| N.S. |
1 | 1.37 | 2.84 | 1.67 | 37.97 | 3.22 | 0.00 | 0.92 | 0.74 | 0.00 |
| time (sec) |
N/A | 1.082 | 6.094 | 2.316 | 0.706 | 0.102 | 0.000 | 1.996 | 0.190 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 203 | 213 | 206 | 261 | 261506 | 524 | 0 | 190 | 116 | 0 |
| N.S. |
1 | 1.05 | 1.01 | 1.29 | 1288.21 | 2.58 | 0.00 | 0.94 | 0.57 | 0.00 |
| time (sec) |
N/A | 1.091 | 1.590 | 2.261 | 2.995 | 0.115 | 0.000 | 2.403 | 0.193 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 250 | 268 | 193 | 284 | 407281 | 564 | 0 | 213 | 125 | 0 |
| N.S. |
1 | 1.07 | 0.77 | 1.14 | 1629.12 | 2.26 | 0.00 | 0.85 | 0.50 | 0.00 |
| time (sec) |
N/A | 1.495 | 1.168 | 2.405 | 5.110 | 0.104 | 0.000 | 3.332 | 0.191 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 297 | 323 | 196 | 316 | 387118 | 592 | 0 | 0 | 127 | 0 |
| N.S. |
1 | 1.09 | 0.66 | 1.06 | 1303.43 | 1.99 | 0.00 | 0.00 | 0.43 | 0.00 |
| time (sec) |
N/A | 1.846 | 1.467 | 2.467 | 6.539 | 0.109 | 0.000 | 0.000 | 0.246 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 406 | 431 | 4445 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
| N.S. |
1 | 1.06 | 10.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 0.946 | 16.998 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 354 | 354 | 2709 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
| N.S. |
1 | 1.00 | 7.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
| time (sec) |
N/A | 0.836 | 16.173 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 415 | 457 | 2901 | 0 | 0 | 0 | 0 | 0 | 80 | 0 |
| N.S. |
1 | 1.10 | 6.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
| time (sec) |
N/A | 0.898 | 16.129 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.187 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 787 | 797 | 4110 | 0 | 0 | 0 | 0 | 0 | 84 | 0 |
| N.S. |
1 | 1.01 | 5.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
| time (sec) |
N/A | 1.178 | 18.162 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.222 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 739 | 752 | 5094 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
| N.S. |
1 | 1.02 | 6.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
| time (sec) |
N/A | 1.056 | 17.473 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 764 | 793 | 4066 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
| N.S. |
1 | 1.04 | 5.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
| time (sec) |
N/A | 1.127 | 18.053 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 233 | 197 | 4897 | 0 | 0 | 0 | 0 | 0 | 61 | 0 |
| N.S. |
1 | 0.85 | 21.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
| time (sec) |
N/A | 0.711 | 20.375 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.207 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 141 | 164 | 111 | 0 | 0 | 0 | 0 | 0 | 63 | 0 |
| N.S. |
1 | 1.16 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
| time (sec) |
N/A | 0.639 | 0.776 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 114 | 106 | 85 | 119 | 163 | 136 | 0 | 304 | 378 | 194 |
| N.S. |
1 | 0.93 | 0.75 | 1.04 | 1.43 | 1.19 | 0.00 | 2.67 | 3.32 | 1.70 |
| time (sec) |
N/A | 0.618 | 0.440 | 1.079 | 0.039 | 0.095 | 0.000 | 0.154 | 0.171 | 14.880 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 91 | 67 | 81 | 127 | 115 | 0 | 210 | 194 | 145 |
| N.S. |
1 | 0.98 | 0.72 | 0.87 | 1.37 | 1.24 | 0.00 | 2.26 | 2.09 | 1.56 |
| time (sec) |
N/A | 0.577 | 0.210 | 0.923 | 0.040 | 0.084 | 0.000 | 0.145 | 0.156 | 14.233 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 64 | 75 | 75 | 88 | 96 | 0 | 153 | 211 | 104 |
| N.S. |
1 | 1.05 | 1.23 | 1.23 | 1.44 | 1.57 | 0.00 | 2.51 | 3.46 | 1.70 |
| time (sec) |
N/A | 0.441 | 0.023 | 0.620 | 0.038 | 0.081 | 0.000 | 0.140 | 0.187 | 13.181 |
| 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 | 35 | 35 | 43 | 43 | 56 | 85 | 71 | 84 | 79 | 114 |
| N.S. |
1 | 1.00 | 1.23 | 1.23 | 1.60 | 2.43 | 2.03 | 2.40 | 2.26 | 3.26 |
| time (sec) |
N/A | 0.304 | 0.011 | 0.396 | 0.031 | 0.085 | 3.956 | 0.134 | 0.158 | 11.805 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 35 | 46 | 48 | 58 | 54 | 0 | 79 | 59 | 100 |
| N.S. |
1 | 1.00 | 1.31 | 1.37 | 1.66 | 1.54 | 0.00 | 2.26 | 1.69 | 2.86 |
| time (sec) |
N/A | 0.255 | 0.035 | 0.212 | 0.037 | 0.093 | 0.000 | 0.140 | 0.156 | 11.381 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 52 | 55 | 51 | 47 | 55 | 42 | 0 | 121 | 45 | 50 |
| N.S. |
1 | 1.06 | 0.98 | 0.90 | 1.06 | 0.81 | 0.00 | 2.33 | 0.87 | 0.96 |
| time (sec) |
N/A | 0.410 | 0.132 | 0.237 | 0.035 | 0.080 | 0.000 | 0.115 | 0.154 | 11.849 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 82 | 75 | 65 | 79 | 60 | 0 | 180 | 63 | 84 |
| N.S. |
1 | 0.98 | 0.89 | 0.77 | 0.94 | 0.71 | 0.00 | 2.14 | 0.75 | 1.00 |
| time (sec) |
N/A | 0.477 | 0.191 | 0.512 | 0.035 | 0.082 | 0.000 | 0.125 | 0.156 | 11.656 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 105 | 97 | 91 | 86 | 101 | 81 | 0 | 272 | 95 | 117 |
| N.S. |
1 | 0.92 | 0.87 | 0.82 | 0.96 | 0.77 | 0.00 | 2.59 | 0.90 | 1.11 |
| time (sec) |
N/A | 0.514 | 0.224 | 0.771 | 0.036 | 0.078 | 0.000 | 0.149 | 0.159 | 11.382 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 198 | 170 | 150 | 171 | 276 | 208 | 0 | 528 | 533 | 359 |
| N.S. |
1 | 0.86 | 0.76 | 0.86 | 1.39 | 1.05 | 0.00 | 2.67 | 2.69 | 1.81 |
| time (sec) |
N/A | 0.970 | 0.947 | 1.566 | 0.040 | 0.092 | 0.000 | 0.178 | 0.162 | 14.826 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 179 | 189 | 120 | 148 | 228 | 180 | 0 | 478 | 426 | 317 |
| N.S. |
1 | 1.06 | 0.67 | 0.83 | 1.27 | 1.01 | 0.00 | 2.67 | 2.38 | 1.77 |
| time (sec) |
N/A | 1.036 | 0.502 | 1.366 | 0.041 | 0.099 | 0.000 | 0.162 | 0.209 | 15.109 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 122 | 97 | 118 | 165 | 150 | 0 | 294 | 314 | 227 |
| N.S. |
1 | 1.05 | 0.84 | 1.02 | 1.42 | 1.29 | 0.00 | 2.53 | 2.71 | 1.96 |
| time (sec) |
N/A | 0.710 | 0.438 | 1.045 | 0.037 | 0.100 | 0.000 | 0.159 | 0.155 | 15.043 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 86 | 86 | 97 | 126 | 136 | 0 | 192 | 239 | 176 |
| N.S. |
1 | 1.00 | 1.00 | 1.13 | 1.47 | 1.58 | 0.00 | 2.23 | 2.78 | 2.05 |
| time (sec) |
N/A | 0.293 | 0.164 | 0.729 | 0.037 | 0.105 | 0.000 | 0.151 | 0.157 | 11.750 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 60 | 60 | 71 | 86 | 103 | 117 | 0 | 154 | 114 | 163 |
| N.S. |
1 | 1.00 | 1.18 | 1.43 | 1.72 | 1.95 | 0.00 | 2.57 | 1.90 | 2.72 |
| time (sec) |
N/A | 0.311 | 0.494 | 0.549 | 0.037 | 0.098 | 0.000 | 0.165 | 0.156 | 11.763 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 84 | 120 | 94 | 99 | 87 | 0 | 178 | 94 | 169 |
| N.S. |
1 | 1.05 | 1.50 | 1.18 | 1.24 | 1.09 | 0.00 | 2.22 | 1.18 | 2.11 |
| time (sec) |
N/A | 0.626 | 0.883 | 0.361 | 0.039 | 0.093 | 0.000 | 0.154 | 0.158 | 11.691 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 109 | 90 | 88 | 108 | 85 | 0 | 254 | 75 | 115 |
| N.S. |
1 | 1.02 | 0.84 | 0.82 | 1.01 | 0.79 | 0.00 | 2.37 | 0.70 | 1.07 |
| time (sec) |
N/A | 0.638 | 0.591 | 0.538 | 0.035 | 0.078 | 0.000 | 0.142 | 0.161 | 11.150 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 136 | 126 | 118 | 118 | 142 | 114 | 0 | 437 | 112 | 169 |
| N.S. |
1 | 0.93 | 0.87 | 0.87 | 1.04 | 0.84 | 0.00 | 3.21 | 0.82 | 1.24 |
| time (sec) |
N/A | 0.781 | 1.602 | 0.864 | 0.039 | 0.084 | 0.000 | 0.165 | 0.201 | 11.281 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 180 | 152 | 146 | 147 | 176 | 142 | 0 | 487 | 139 | 307 |
| N.S. |
1 | 0.84 | 0.81 | 0.82 | 0.98 | 0.79 | 0.00 | 2.71 | 0.77 | 1.71 |
| time (sec) |
N/A | 0.795 | 1.065 | 1.207 | 0.040 | 0.097 | 0.000 | 0.175 | 0.156 | 15.399 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 252 | 264 | 181 | 200 | 341 | 249 | 0 | 722 | 584 | 470 |
| N.S. |
1 | 1.05 | 0.72 | 0.79 | 1.35 | 0.99 | 0.00 | 2.87 | 2.32 | 1.87 |
| time (sec) |
N/A | 1.425 | 2.479 | 1.855 | 0.044 | 0.108 | 0.000 | 0.205 | 0.164 | 14.311 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 180 | 191 | 144 | 185 | 266 | 211 | 0 | 586 | 578 | 395 |
| N.S. |
1 | 1.06 | 0.80 | 1.03 | 1.48 | 1.17 | 0.00 | 3.26 | 3.21 | 2.19 |
| time (sec) |
N/A | 1.058 | 0.781 | 1.466 | 0.042 | 0.097 | 0.000 | 0.177 | 0.166 | 15.026 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 137 | 144 | 145 | 139 | 202 | 189 | 0 | 336 | 356 | 526 |
| N.S. |
1 | 1.05 | 1.06 | 1.01 | 1.47 | 1.38 | 0.00 | 2.45 | 2.60 | 3.84 |
| time (sec) |
N/A | 0.497 | 0.383 | 1.121 | 0.044 | 0.099 | 0.000 | 0.198 | 0.163 | 12.856 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 134 | 105 | 141 | 169 | 167 | 0 | 241 | 295 | 249 |
| N.S. |
1 | 1.13 | 0.88 | 1.18 | 1.42 | 1.40 | 0.00 | 2.03 | 2.48 | 2.09 |
| time (sec) |
N/A | 0.535 | 0.789 | 0.961 | 0.042 | 0.096 | 0.000 | 0.175 | 0.160 | 12.085 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 124 | 126 | 217 | 132 | 144 | 152 | 0 | 234 | 168 | 236 |
| N.S. |
1 | 1.02 | 1.75 | 1.06 | 1.16 | 1.23 | 0.00 | 1.89 | 1.35 | 1.90 |
| time (sec) |
N/A | 0.940 | 1.943 | 0.770 | 0.045 | 0.093 | 0.000 | 0.201 | 0.188 | 12.132 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 145 | 152 | 159 | 137 | 152 | 131 | 0 | 314 | 126 | 1924 |
| N.S. |
1 | 1.05 | 1.10 | 0.94 | 1.05 | 0.90 | 0.00 | 2.17 | 0.87 | 13.27 |
| time (sec) |
N/A | 0.997 | 1.484 | 0.707 | 0.039 | 0.093 | 0.000 | 0.192 | 0.154 | 12.712 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 179 | 187 | 140 | 139 | 171 | 136 | 0 | 536 | 124 | 202 |
| N.S. |
1 | 1.04 | 0.78 | 0.78 | 0.96 | 0.76 | 0.00 | 2.99 | 0.69 | 1.13 |
| time (sec) |
N/A | 1.079 | 1.348 | 0.858 | 0.041 | 0.082 | 0.000 | 0.183 | 0.156 | 11.070 |