Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 263 | 277 | 184 | 267 | 0 | 965 | 0 | 338 | 6743 |
| N.S. |
1 | 1.05 | 0.70 | 1.02 | 0.00 | 3.67 | 0.00 | 1.29 | 25.64 |
| time (sec) |
N/A | 1.438 | 2.284 | 1.368 | 0.000 | 0.376 | 0.000 | 0.327 | 11.106 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 155 | 185 | 147 | 205 | 0 | 788 | 0 | 1116 | 3276 |
| N.S. |
1 | 1.19 | 0.95 | 1.32 | 0.00 | 5.08 | 0.00 | 7.20 | 21.14 |
| time (sec) |
N/A | 0.957 | 1.736 | 1.133 | 0.000 | 0.330 | 0.000 | 0.429 | 6.947 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 122 | 149 | 119 | 160 | 0 | 552 | 0 | 199 | 3775 |
| N.S. |
1 | 1.22 | 0.98 | 1.31 | 0.00 | 4.52 | 0.00 | 1.63 | 30.94 |
| time (sec) |
N/A | 0.544 | 1.136 | 0.698 | 0.000 | 0.285 | 0.000 | 0.328 | 9.554 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 100 | 111 | 97 | 127 | 0 | 379 | 0 | 157 | 113 |
| N.S. |
1 | 1.11 | 0.97 | 1.27 | 0.00 | 3.79 | 0.00 | 1.57 | 1.13 |
| time (sec) |
N/A | 0.488 | 0.566 | 0.833 | 0.000 | 0.293 | 0.000 | 0.322 | 2.101 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 133 | 158 | 191 | 182 | 0 | 684 | 0 | 225 | 3763 |
| N.S. |
1 | 1.19 | 1.44 | 1.37 | 0.00 | 5.14 | 0.00 | 1.69 | 28.29 |
| time (sec) |
N/A | 0.855 | 1.169 | 1.305 | 0.000 | 2.959 | 0.000 | 0.352 | 9.668 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 189 | 208 | 240 | 241 | 0 | 1088 | 0 | 404 | 5464 |
| N.S. |
1 | 1.10 | 1.27 | 1.28 | 0.00 | 5.76 | 0.00 | 2.14 | 28.91 |
| time (sec) |
N/A | 1.322 | 2.633 | 1.784 | 0.000 | 7.230 | 0.000 | 0.373 | 10.573 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 398 | 424 | 734 | 402 | 0 | 1812 | 0 | 2712 | 10598 |
| N.S. |
1 | 1.07 | 1.84 | 1.01 | 0.00 | 4.55 | 0.00 | 6.81 | 26.63 |
| time (sec) |
N/A | 2.253 | 5.306 | 2.110 | 0.000 | 0.478 | 0.000 | 0.628 | 14.150 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 280 | 317 | 232 | 341 | 0 | 1561 | 0 | 543 | 5542 |
| N.S. |
1 | 1.13 | 0.83 | 1.22 | 0.00 | 5.58 | 0.00 | 1.94 | 19.79 |
| time (sec) |
N/A | 1.545 | 3.420 | 1.701 | 0.000 | 0.412 | 0.000 | 0.376 | 9.476 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 247 | 204 | 282 | 0 | 1152 | 0 | 455 | 6923 |
| N.S. |
1 | 1.17 | 0.97 | 1.34 | 0.00 | 5.46 | 0.00 | 2.16 | 32.81 |
| time (sec) |
N/A | 1.081 | 2.355 | 1.271 | 0.000 | 0.354 | 0.000 | 0.376 | 11.654 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 180 | 206 | 172 | 234 | 0 | 740 | 0 | 391 | 248 |
| N.S. |
1 | 1.14 | 0.96 | 1.30 | 0.00 | 4.11 | 0.00 | 2.17 | 1.38 |
| time (sec) |
N/A | 0.615 | 1.519 | 1.092 | 0.000 | 0.340 | 0.000 | 0.356 | 5.418 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 164 | 190 | 157 | 232 | 0 | 742 | 0 | 390 | 248 |
| N.S. |
1 | 1.16 | 0.96 | 1.41 | 0.00 | 4.52 | 0.00 | 2.38 | 1.51 |
| time (sec) |
N/A | 0.698 | 0.899 | 1.465 | 0.000 | 0.342 | 0.000 | 0.367 | 5.163 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 214 | 258 | 269 | 302 | 0 | 1400 | 0 | 481 | 6911 |
| N.S. |
1 | 1.21 | 1.26 | 1.41 | 0.00 | 6.54 | 0.00 | 2.25 | 32.29 |
| time (sec) |
N/A | 1.345 | 1.982 | 2.156 | 0.000 | 12.834 | 0.000 | 0.378 | 11.663 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 299 | 335 | 352 | 376 | 0 | 2100 | 0 | 574 | 9312 |
| N.S. |
1 | 1.12 | 1.18 | 1.26 | 0.00 | 7.02 | 0.00 | 1.92 | 31.14 |
| time (sec) |
N/A | 2.139 | 6.982 | 2.460 | 0.000 | 27.639 | 0.000 | 0.410 | 14.733 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 303 | 317 | 232 | 1305 | 0 | 561 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.77 | 4.31 | 0.00 | 1.85 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.773 | 1.569 | 21.276 | 0.000 | 0.154 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 231 | 237 | 179 | 993 | 0 | 492 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.77 | 4.30 | 0.00 | 2.13 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.117 | 3.105 | 10.592 | 0.000 | 0.133 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 171 | 172 | 146 | 600 | 0 | 435 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.85 | 3.51 | 0.00 | 2.54 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.948 | 0.811 | 11.020 | 0.000 | 0.109 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 178 | 179 | 107 | 247 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.60 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.363 | 12.694 | 8.390 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 213 | 227 | 372 | 746 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 1.75 | 3.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.991 | 17.748 | 13.402 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 292 | 298 | 420 | 1290 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 1.44 | 4.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.639 | 4.748 | 17.717 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 378 | 394 | 291 | 1635 | 0 | 639 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.77 | 4.33 | 0.00 | 1.69 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.165 | 2.782 | 18.175 | 0.000 | 0.168 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 297 | 305 | 233 | 1305 | 0 | 562 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.78 | 4.39 | 0.00 | 1.89 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.491 | 4.389 | 11.774 | 0.000 | 0.145 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 225 | 231 | 203 | 993 | 0 | 493 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.90 | 4.41 | 0.00 | 2.19 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.294 | 1.473 | 12.594 | 0.000 | 0.129 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 236 | 244 | 406 | 701 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 1.72 | 2.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.128 | 3.305 | 11.746 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 232 | 246 | 398 | 991 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 1.72 | 4.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.170 | 3.169 | 12.388 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 295 | 309 | 422 | 1403 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 1.43 | 4.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.786 | 5.731 | 17.346 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 375 | 390 | 634 | 2327 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.69 | 6.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.497 | 6.933 | 22.914 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 462 | 480 | 357 | 1983 | 0 | 726 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.77 | 4.29 | 0.00 | 1.57 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.717 | 3.517 | 29.409 | 0.000 | 0.166 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 372 | 382 | 291 | 1635 | 0 | 639 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.78 | 4.40 | 0.00 | 1.72 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.923 | 5.432 | 16.268 | 0.000 | 0.146 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 288 | 299 | 254 | 1305 | 0 | 562 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.88 | 4.53 | 0.00 | 1.95 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.647 | 2.181 | 15.622 | 0.000 | 0.130 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 292 | 305 | 453 | 1067 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.55 | 3.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.718 | 4.033 | 13.790 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 296 | 310 | 442 | 1490 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 1.49 | 5.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.756 | 4.412 | 25.416 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 315 | 323 | 451 | 1742 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 1.43 | 5.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.789 | 6.382 | 64.691 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 376 | 395 | 486 | 2438 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 1.29 | 6.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.490 | 6.679 | 181.697 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 465 | 485 | 729 | 3548 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.57 | 7.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 4.283 | 7.266 | 455.475 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 246 | 258 | 180 | 993 | 0 | 493 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.73 | 4.04 | 0.00 | 2.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.365 | 1.692 | 13.873 | 0.000 | 0.135 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 183 | 187 | 154 | 671 | 0 | 435 | 0 | 0 | 199 |
| N.S. |
1 | 1.02 | 0.84 | 3.67 | 0.00 | 2.38 | 0.00 | 0.00 | 1.09 |
| time (sec) |
N/A | 0.852 | 1.991 | 8.308 | 0.000 | 0.120 | 0.000 | 0.000 | 2.827 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 130 | 130 | 93 | 249 | 0 | 371 | 0 | 0 | 135 |
| N.S. |
1 | 1.00 | 0.72 | 1.92 | 0.00 | 2.85 | 0.00 | 0.00 | 1.04 |
| time (sec) |
N/A | 0.744 | 4.755 | 8.378 | 0.000 | 0.105 | 0.000 | 0.000 | 2.250 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 118 | 81 | 194 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.69 | 1.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.962 | 0.609 | 7.112 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 216 | 227 | 320 | 639 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 1.48 | 2.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.965 | 14.347 | 10.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 299 | 305 | 420 | 1182 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 1.40 | 3.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.668 | 6.405 | 15.161 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 387 | 391 | 304 | 1312 | 0 | 910 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.79 | 3.39 | 0.00 | 2.35 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.194 | 2.771 | 20.671 | 0.000 | 0.178 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 262 | 280 | 189 | 1275 | 0 | 789 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 0.72 | 4.87 | 0.00 | 3.01 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.611 | 2.291 | 14.570 | 0.000 | 0.161 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 204 | 219 | 170 | 519 | 0 | 683 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 0.83 | 2.54 | 0.00 | 3.35 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.000 | 1.406 | 10.271 | 0.000 | 0.136 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 185 | 196 | 151 | 432 | 0 | 610 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.82 | 2.34 | 0.00 | 3.30 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.043 | 0.739 | 10.671 | 0.000 | 0.121 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 190 | 198 | 460 | 433 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 2.42 | 2.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.414 | 4.309 | 12.244 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 303 | 335 | 482 | 912 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.11 | 1.59 | 3.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.838 | 6.079 | 17.325 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 413 | 421 | 334 | 1412 | 0 | 1348 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.81 | 3.42 | 0.00 | 3.26 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.367 | 3.969 | 43.796 | 0.000 | 0.224 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 331 | 338 | 274 | 954 | 0 | 1193 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.83 | 2.88 | 0.00 | 3.60 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.761 | 3.152 | 24.271 | 0.000 | 0.183 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 307 | 317 | 224 | 864 | 0 | 1076 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.73 | 2.81 | 0.00 | 3.50 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.477 | 2.590 | 21.922 | 0.000 | 0.157 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 275 | 285 | 193 | 754 | 0 | 956 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.70 | 2.74 | 0.00 | 3.48 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.469 | 1.812 | 27.274 | 0.000 | 0.158 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 349 | 375 | 743 | 858 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 2.13 | 2.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.136 | 7.042 | 31.113 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 437 | 471 | 750 | 1345 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 1.72 | 3.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.874 | 7.341 | 45.296 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 170 | 162 | 125 | 451 | 0 | 211 | 0 | 0 | 177 |
| N.S. |
1 | 0.95 | 0.74 | 2.65 | 0.00 | 1.24 | 0.00 | 0.00 | 1.04 |
| time (sec) |
N/A | 0.889 | 2.662 | 16.560 | 0.000 | 0.146 | 0.000 | 0.000 | 1.102 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 134 | 103 | 413 | 0 | 192 | 0 | 0 | 166 |
| N.S. |
1 | 0.96 | 0.74 | 2.95 | 0.00 | 1.37 | 0.00 | 0.00 | 1.19 |
| time (sec) |
N/A | 0.779 | 2.102 | 8.788 | 0.000 | 0.114 | 0.000 | 0.000 | 3.239 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 108 | 107 | 86 | 371 | 0 | 175 | 0 | 0 | 128 |
| N.S. |
1 | 0.99 | 0.80 | 3.44 | 0.00 | 1.62 | 0.00 | 0.00 | 1.19 |
| time (sec) |
N/A | 0.727 | 1.622 | 7.021 | 0.000 | 0.108 | 0.000 | 0.000 | 2.561 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 78 | 67 | 326 | 0 | 156 | 0 | 0 | 85 |
| N.S. |
1 | 1.04 | 0.89 | 4.35 | 0.00 | 2.08 | 0.00 | 0.00 | 1.13 |
| time (sec) |
N/A | 0.634 | 1.073 | 5.465 | 0.000 | 0.102 | 0.000 | 0.000 | 0.700 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 71 | 64 | 246 | 0 | 185 | 0 | 0 | 96 |
| N.S. |
1 | 1.00 | 0.90 | 3.46 | 0.00 | 2.61 | 0.00 | 0.00 | 1.35 |
| time (sec) |
N/A | 0.626 | 0.640 | 8.769 | 0.000 | 0.102 | 0.000 | 0.000 | 2.852 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 102 | 107 | 401 | 0 | 213 | 0 | 0 | 150 |
| N.S. |
1 | 0.99 | 1.04 | 3.89 | 0.00 | 2.07 | 0.00 | 0.00 | 1.46 |
| time (sec) |
N/A | 0.743 | 0.831 | 10.223 | 0.000 | 0.110 | 0.000 | 0.000 | 3.652 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 130 | 134 | 636 | 0 | 235 | 0 | 0 | 177 |
| N.S. |
1 | 0.93 | 0.96 | 4.54 | 0.00 | 1.68 | 0.00 | 0.00 | 1.26 |
| time (sec) |
N/A | 0.775 | 1.173 | 14.968 | 0.000 | 0.106 | 0.000 | 0.000 | 4.647 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 264 | 231 | 196 | 666 | 0 | 299 | 0 | 0 | 275 |
| N.S. |
1 | 0.88 | 0.74 | 2.52 | 0.00 | 1.13 | 0.00 | 0.00 | 1.04 |
| time (sec) |
N/A | 1.210 | 3.115 | 10.316 | 0.000 | 0.138 | 0.000 | 0.000 | 2.935 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 223 | 203 | 167 | 610 | 0 | 271 | 0 | 0 | 264 |
| N.S. |
1 | 0.91 | 0.75 | 2.74 | 0.00 | 1.22 | 0.00 | 0.00 | 1.18 |
| time (sec) |
N/A | 1.064 | 2.721 | 6.252 | 0.000 | 0.130 | 0.000 | 0.000 | 3.056 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 182 | 175 | 139 | 548 | 0 | 243 | 0 | 0 | 229 |
| N.S. |
1 | 0.96 | 0.76 | 3.01 | 0.00 | 1.34 | 0.00 | 0.00 | 1.26 |
| time (sec) |
N/A | 1.006 | 2.311 | 6.363 | 0.000 | 0.120 | 0.000 | 0.000 | 2.921 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 146 | 106 | 487 | 0 | 216 | 0 | 0 | 177 |
| N.S. |
1 | 1.04 | 0.76 | 3.48 | 0.00 | 1.54 | 0.00 | 0.00 | 1.26 |
| time (sec) |
N/A | 0.903 | 1.808 | 6.289 | 0.000 | 0.107 | 0.000 | 0.000 | 3.271 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 124 | 102 | 405 | 0 | 240 | 0 | 0 | 158 |
| N.S. |
1 | 1.02 | 0.84 | 3.35 | 0.00 | 1.98 | 0.00 | 0.00 | 1.31 |
| time (sec) |
N/A | 0.838 | 1.468 | 6.041 | 0.000 | 0.110 | 0.000 | 0.000 | 3.306 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 129 | 105 | 574 | 0 | 255 | 0 | 0 | 194 |
| N.S. |
1 | 1.02 | 0.83 | 4.56 | 0.00 | 2.02 | 0.00 | 0.00 | 1.54 |
| time (sec) |
N/A | 0.873 | 1.946 | 8.735 | 0.000 | 0.121 | 0.000 | 0.000 | 3.908 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 172 | 161 | 175 | 723 | 0 | 286 | 0 | 0 | 227 |
| N.S. |
1 | 0.94 | 1.02 | 4.20 | 0.00 | 1.66 | 0.00 | 0.00 | 1.32 |
| time (sec) |
N/A | 0.992 | 2.109 | 11.866 | 0.000 | 0.109 | 0.000 | 0.000 | 4.810 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 214 | 190 | 191 | 832 | 0 | 314 | 0 | 0 | 233 |
| N.S. |
1 | 0.89 | 0.89 | 3.89 | 0.00 | 1.47 | 0.00 | 0.00 | 1.09 |
| time (sec) |
N/A | 1.054 | 6.165 | 18.607 | 0.000 | 0.117 | 0.000 | 0.000 | 4.852 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 305 | 272 | 235 | 825 | 0 | 358 | 0 | 0 | 364 |
| N.S. |
1 | 0.89 | 0.77 | 2.70 | 0.00 | 1.17 | 0.00 | 0.00 | 1.19 |
| time (sec) |
N/A | 1.462 | 3.426 | 7.152 | 0.000 | 0.154 | 0.000 | 0.000 | 3.203 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 255 | 244 | 197 | 745 | 0 | 321 | 0 | 0 | 328 |
| N.S. |
1 | 0.96 | 0.77 | 2.92 | 0.00 | 1.26 | 0.00 | 0.00 | 1.29 |
| time (sec) |
N/A | 1.448 | 2.525 | 6.570 | 0.000 | 0.144 | 0.000 | 0.000 | 3.612 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 205 | 216 | 158 | 664 | 0 | 284 | 0 | 0 | 275 |
| N.S. |
1 | 1.05 | 0.77 | 3.24 | 0.00 | 1.39 | 0.00 | 0.00 | 1.34 |
| time (sec) |
N/A | 1.260 | 3.096 | 6.765 | 0.000 | 0.131 | 0.000 | 0.000 | 3.197 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 202 | 208 | 150 | 641 | 0 | 302 | 0 | 0 | 248 |
| N.S. |
1 | 1.03 | 0.74 | 3.17 | 0.00 | 1.50 | 0.00 | 0.00 | 1.23 |
| time (sec) |
N/A | 1.261 | 2.786 | 6.391 | 0.000 | 0.134 | 0.000 | 0.000 | 2.865 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 192 | 191 | 165 | 771 | 0 | 306 | 0 | 0 | 255 |
| N.S. |
1 | 0.99 | 0.86 | 4.02 | 0.00 | 1.59 | 0.00 | 0.00 | 1.33 |
| time (sec) |
N/A | 1.243 | 2.727 | 9.308 | 0.000 | 0.119 | 0.000 | 0.000 | 4.891 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 204 | 208 | 176 | 950 | 0 | 326 | 0 | 0 | 291 |
| N.S. |
1 | 1.02 | 0.86 | 4.66 | 0.00 | 1.60 | 0.00 | 0.00 | 1.43 |
| time (sec) |
N/A | 1.283 | 4.301 | 10.306 | 0.000 | 0.140 | 0.000 | 0.000 | 5.573 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 255 | 240 | 221 | 917 | 0 | 364 | 0 | 0 | 311 |
| N.S. |
1 | 0.94 | 0.87 | 3.60 | 0.00 | 1.43 | 0.00 | 0.00 | 1.22 |
| time (sec) |
N/A | 1.426 | 5.806 | 13.203 | 0.000 | 0.132 | 0.000 | 0.000 | 5.980 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 305 | 268 | 266 | 1166 | 0 | 401 | 0 | 0 | 304 |
| N.S. |
1 | 0.88 | 0.87 | 3.82 | 0.00 | 1.31 | 0.00 | 0.00 | 1.00 |
| time (sec) |
N/A | 1.456 | 7.398 | 24.981 | 0.000 | 0.146 | 0.000 | 0.000 | 7.255 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 246 | 272 | 305 | 1375 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.11 | 1.24 | 5.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.215 | 2.986 | 16.987 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 182 | 200 | 260 | 1074 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.10 | 1.43 | 5.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.606 | 2.747 | 5.701 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 137 | 148 | 207 | 822 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 1.51 | 6.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.171 | 2.530 | 6.722 | 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 | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 86 | 128 | 295 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 1.44 | 3.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.702 | 1.161 | 4.611 | 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 | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 61 | 58 | 217 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 3.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.541 | 0.516 | 4.003 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 86 | 206 | 300 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.40 | 3.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.795 | 2.675 | 5.490 | 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 | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 162 | 260 | 441 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 1.73 | 2.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.573 | 2.442 | 8.845 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 217 | 232 | 309 | 760 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 1.42 | 3.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.089 | 4.383 | 12.800 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 389 | 375 | 369 | 1348 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.95 | 3.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.593 | 5.027 | 21.901 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 303 | 295 | 318 | 1066 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 1.05 | 3.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.985 | 3.663 | 11.465 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 224 | 220 | 280 | 849 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 1.25 | 3.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.486 | 3.159 | 9.281 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 198 | 192 | 260 | 808 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 1.31 | 4.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.320 | 2.806 | 7.251 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 200 | 185 | 274 | 721 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 1.37 | 3.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.456 | 3.016 | 7.842 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 256 | 242 | 316 | 856 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 1.23 | 3.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.017 | 4.783 | 8.493 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 345 | 327 | 363 | 1004 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 1.05 | 2.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.695 | 7.227 | 15.558 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 461 | 463 | 462 | 2195 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 4.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.030 | 5.682 | 89.442 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 367 | 372 | 390 | 1977 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 1.06 | 5.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.249 | 5.694 | 16.574 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 344 | 349 | 360 | 1937 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 1.05 | 5.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.188 | 4.101 | 14.389 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 337 | 334 | 365 | 1850 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 1.08 | 5.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.169 | 4.991 | 13.710 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 345 | 336 | 383 | 1744 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 1.11 | 5.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.393 | 5.381 | 13.614 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 420 | 412 | 458 | 1975 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 1.09 | 4.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 3.218 | 5.924 | 18.112 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 560 | 563 | 1224 | 4000 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 2.19 | 7.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.866 | 6.881 | 21.006 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 473 | 471 | 1175 | 2775 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.48 | 5.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.169 | 18.948 | 2.345 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 385 | 391 | 408 | 1268 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 1.06 | 3.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.641 | 12.124 | 5.074 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 351 | 351 | 273 | 953 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.78 | 2.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.364 | 13.208 | 4.761 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |