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 | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 182 | 156 | 144 | 296 | 882 | 457 | 998 | 487 | 1024 |
N.S. |
1 | 0.86 | 0.79 | 1.63 | 4.85 | 2.51 | 5.48 | 2.68 | 5.63 |
time (sec) |
N/A | 0.302 | 0.064 | 1.289 | 0.241 | 0.297 | 4.024 | 63.426 | 1.686 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 151 | 132 | 122 | 233 | 645 | 343 | 707 | 358 | 567 |
N.S. |
1 | 0.87 | 0.81 | 1.54 | 4.27 | 2.27 | 4.68 | 2.37 | 3.75 |
time (sec) |
N/A | 0.287 | 0.051 | 0.990 | 0.231 | 0.287 | 2.190 | 10.537 | 1.488 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 108 | 98 | 185 | 436 | 245 | 517 | 243 | 296 |
N.S. |
1 | 0.90 | 0.82 | 1.54 | 3.63 | 2.04 | 4.31 | 2.02 | 2.47 |
time (sec) |
N/A | 0.261 | 0.034 | 0.776 | 0.214 | 0.290 | 1.475 | 1.797 | 1.320 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 77 | 72 | 113 | 250 | 149 | 250 | 132 | 120 |
N.S. |
1 | 0.99 | 0.92 | 1.45 | 3.21 | 1.91 | 3.21 | 1.69 | 1.54 |
time (sec) |
N/A | 0.232 | 0.027 | 0.650 | 0.213 | 0.256 | 0.916 | 0.702 | 1.164 |
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 | 83 | 83 | 87 | 162 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.05 | 1.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.477 | 0.028 | 0.743 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 76 | 89 | 93 | 187 | 110 | 253 | 187 | 108 |
N.S. |
1 | 0.75 | 0.87 | 0.91 | 1.83 | 1.08 | 2.48 | 1.83 | 1.06 |
time (sec) |
N/A | 0.208 | 0.033 | 0.836 | 0.218 | 0.265 | 0.696 | 0.417 | 2.908 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 138 | 128 | 162 | 306 | 240 | 418 | 268 | 206 |
N.S. |
1 | 0.99 | 0.92 | 1.17 | 2.20 | 1.73 | 3.01 | 1.93 | 1.48 |
time (sec) |
N/A | 0.302 | 0.062 | 1.173 | 0.209 | 0.273 | 1.137 | 0.392 | 2.541 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 177 | 165 | 140 | 211 | 480 | 432 | 677 | 477 | 341 |
N.S. |
1 | 0.93 | 0.79 | 1.19 | 2.71 | 2.44 | 3.82 | 2.69 | 1.93 |
time (sec) |
N/A | 0.325 | 0.073 | 1.410 | 0.215 | 0.283 | 1.783 | 0.380 | 3.315 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 208 | 188 | 162 | 232 | 699 | 658 | 947 | 424 | 579 |
N.S. |
1 | 0.90 | 0.78 | 1.12 | 3.36 | 3.16 | 4.55 | 2.04 | 2.78 |
time (sec) |
N/A | 0.340 | 0.102 | 2.570 | 0.223 | 0.277 | 2.589 | 0.409 | 4.546 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 515 | 709 | 524 | 0 | 2660 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.38 | 1.02 | 0.00 | 5.17 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.836 | 0.316 | 0.000 | 0.376 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 422 | 523 | 402 | 0 | 1950 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.24 | 0.95 | 0.00 | 4.62 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.303 | 0.210 | 0.000 | 0.349 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 343 | 369 | 298 | 0 | 1333 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.87 | 0.00 | 3.89 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.926 | 0.147 | 0.000 | 0.342 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 211 | 235 | 195 | 0 | 730 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 0.92 | 0.00 | 3.46 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.599 | 0.111 | 0.000 | 0.325 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 132 | 125 | 259 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 1.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.404 | 1.242 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 157 | 116 | 322 | 188 | 573 | 200 | 450 | 388 | 227 |
N.S. |
1 | 0.74 | 2.05 | 1.20 | 3.65 | 1.27 | 2.87 | 2.47 | 1.45 |
time (sec) |
N/A | 0.260 | 0.270 | 0.962 | 0.243 | 0.273 | 1.198 | 0.653 | 3.279 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | B | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 299 | 222 | 452 | 490 | 1001 | 413 | 877 | 0 | 504 |
N.S. |
1 | 0.74 | 1.51 | 1.64 | 3.35 | 1.38 | 2.93 | 0.00 | 1.69 |
time (sec) |
N/A | 0.325 | 0.277 | 1.418 | 0.276 | 0.280 | 2.186 | 0.000 | 3.328 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | B | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 407 | 325 | 595 | 694 | 1576 | 721 | 1561 | 0 | 1069 |
N.S. |
1 | 0.80 | 1.46 | 1.71 | 3.87 | 1.77 | 3.84 | 0.00 | 2.63 |
time (sec) |
N/A | 0.445 | 0.357 | 1.847 | 0.316 | 0.277 | 13.024 | 0.000 | 5.733 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | B | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 501 | 388 | 680 | 886 | 2278 | 1088 | 0 | 883 | 1882 |
N.S. |
1 | 0.77 | 1.36 | 1.77 | 4.55 | 2.17 | 0.00 | 1.76 | 3.76 |
time (sec) |
N/A | 0.468 | 0.515 | 3.063 | 0.398 | 0.291 | 0.000 | 1.095 | 8.911 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 36 | 34 | 36 | 75 | 258 | 36 | 36 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 2.21 | 7.59 | 1.06 | 1.06 |
time (sec) |
N/A | 0.191 | 0.102 | 0.881 | 0.230 | 0.266 | 3.564 | 0.503 | 3.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 34 | 32 | 34 | 57 | 165 | 34 | 34 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 1.78 | 5.16 | 1.06 | 1.06 |
time (sec) |
N/A | 0.180 | 0.079 | 0.734 | 0.226 | 0.253 | 2.774 | 0.515 | 3.536 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 36 | 34 | 36 | 65 | 170 | 36 | 36 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 1.91 | 5.00 | 1.06 | 1.06 |
time (sec) |
N/A | 0.195 | 0.103 | 0.849 | 0.236 | 0.256 | 3.758 | 0.453 | 4.969 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.289 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 151 | 139 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.365 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 36 | 34 | 312 | 125 | 792 | 36 | 36 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 9.18 | 3.68 | 23.29 | 1.06 | 1.06 |
time (sec) |
N/A | 0.196 | 0.309 | 0.783 | 0.246 | 0.294 | 16.082 | 0.644 | 9.728 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 34 | 32 | 234 | 107 | 559 | 34 | 34 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 7.31 | 3.34 | 17.47 | 1.06 | 1.06 |
time (sec) |
N/A | 0.183 | 0.236 | 0.737 | 0.233 | 0.263 | 10.733 | 0.562 | 11.962 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 36 | 34 | 170 | 129 | 158 | 36 | 36 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 5.00 | 3.79 | 4.65 | 1.06 | 1.06 |
time (sec) |
N/A | 0.195 | 0.155 | 0.726 | 0.272 | 0.274 | 2.389 | 0.555 | 13.930 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 147 | 136 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.331 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 206 | 282 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.589 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | A | F(-1) | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 96 | 94 | 0 | 0 | 0 | 62 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.411 | 0.000 | 0.000 | 0.000 | 0.283 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 355 | 343 | 279 | 594 | 593 | 636 | 1436 | 10664 | 1392 |
N.S. |
1 | 0.97 | 0.79 | 1.67 | 1.67 | 1.79 | 4.05 | 30.04 | 3.92 |
time (sec) |
N/A | 0.650 | 0.383 | 1.207 | 0.222 | 0.637 | 55.682 | 1.233 | 1.865 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 227 | 223 | 215 | 412 | 415 | 445 | 998 | 6073 | 741 |
N.S. |
1 | 0.98 | 0.95 | 1.81 | 1.83 | 1.96 | 4.40 | 26.75 | 3.26 |
time (sec) |
N/A | 0.472 | 0.172 | 1.030 | 0.211 | 0.384 | 8.132 | 0.793 | 1.587 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 150 | 155 | 142 | 265 | 262 | 280 | 658 | 3076 | 356 |
N.S. |
1 | 1.03 | 0.95 | 1.77 | 1.75 | 1.87 | 4.39 | 20.51 | 2.37 |
time (sec) |
N/A | 0.347 | 0.088 | 0.931 | 0.205 | 0.308 | 3.120 | 0.607 | 1.289 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 123 | 114 | 122 | 140 | 150 | 318 | 1145 | 144 |
N.S. |
1 | 1.13 | 1.05 | 1.12 | 1.28 | 1.38 | 2.92 | 10.50 | 1.32 |
time (sec) |
N/A | 0.293 | 0.070 | 0.768 | 0.201 | 0.263 | 1.421 | 0.495 | 1.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 52 | 51 | 54 | 56 | 83 | 406 | 47 |
N.S. |
1 | 1.00 | 1.00 | 0.98 | 1.04 | 1.08 | 1.60 | 7.81 | 0.90 |
time (sec) |
N/A | 0.181 | 0.008 | 0.631 | 0.185 | 0.276 | 0.434 | 0.443 | 0.852 |
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 | 140 | 149 | 115 | 372 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.82 | 2.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.452 | 0.042 | 3.980 | 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 | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 137 | 105 | 242 | 138 | 255 | 0 | 511 | 166 |
N.S. |
1 | 1.57 | 1.21 | 2.78 | 1.59 | 2.93 | 0.00 | 5.87 | 1.91 |
time (sec) |
N/A | 0.277 | 0.076 | 1.188 | 0.196 | 3.546 | 0.000 | 0.498 | 1.781 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 183 | 186 | 169 | 694 | 351 | 1017 | 0 | 2969 | 417 |
N.S. |
1 | 1.02 | 0.92 | 3.79 | 1.92 | 5.56 | 0.00 | 16.22 | 2.28 |
time (sec) |
N/A | 0.405 | 0.291 | 1.894 | 0.208 | 45.301 | 0.000 | 0.523 | 3.689 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | F(-1) | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 275 | 270 | 260 | 1504 | 848 | 0 | 0 | 9339 | 1154 |
N.S. |
1 | 0.98 | 0.95 | 5.47 | 3.08 | 0.00 | 0.00 | 33.96 | 4.20 |
time (sec) |
N/A | 0.551 | 0.393 | 3.046 | 0.258 | 0.000 | 0.000 | 0.784 | 7.324 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | F(-1) | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 379 | 367 | 355 | 2850 | 1757 | 0 | 0 | 20791 | 2518 |
N.S. |
1 | 0.97 | 0.94 | 7.52 | 4.64 | 0.00 | 0.00 | 54.86 | 6.64 |
time (sec) |
N/A | 0.776 | 0.529 | 6.654 | 0.329 | 0.000 | 0.000 | 0.991 | 12.462 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 874 | 1069 | 733 | 0 | 2140 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.22 | 0.84 | 0.00 | 2.45 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.537 | 0.628 | 0.000 | 0.321 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 532 | 682 | 486 | 0 | 1300 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.28 | 0.91 | 0.00 | 2.44 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.161 | 0.334 | 0.000 | 0.301 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 270 | 392 | 346 | 0 | 673 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.45 | 1.28 | 0.00 | 2.49 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.789 | 0.194 | 0.000 | 0.274 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 125 | 120 | 214 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 1.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.597 | 0.108 | 0.000 | 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 | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 277 | 347 | 1348 | 818 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.25 | 4.87 | 2.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.695 | 0.370 | 4.263 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 196 | 212 | 402 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 2.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.458 | 0.290 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 369 | 499 | 595 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.35 | 1.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.985 | 0.767 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 714 | 885 | 894 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.24 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.525 | 1.571 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1159 | 1398 | 1301 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.21 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.135 | 3.650 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 61 | 30 | 29 | 32 | 29 | 20 | 103 | 28 |
N.S. |
1 | 1.74 | 0.86 | 0.83 | 0.91 | 0.83 | 0.57 | 2.94 | 0.80 |
time (sec) |
N/A | 0.203 | 0.006 | 0.279 | 0.196 | 0.285 | 0.073 | 0.347 | 0.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 31 | 42 | 31 | 31 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 1.45 | 1.07 | 1.07 | 1.07 |
time (sec) |
N/A | 0.192 | 0.170 | 1.440 | 0.226 | 0.255 | 8.776 | 13.778 | 1.754 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 27 | 29 | 31 | 29 | 29 | 29 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 1.15 | 1.07 | 1.07 | 1.07 |
time (sec) |
N/A | 0.178 | 0.116 | 2.559 | 0.228 | 0.256 | 4.695 | 10.803 | 1.884 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 21 | 23 | 25 | 19 | 23 | 23 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.19 | 0.90 | 1.10 | 1.10 |
time (sec) |
N/A | 0.154 | 0.013 | 1.006 | 0.211 | 0.280 | 0.848 | 11.526 | 0.986 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 31 | 38 | 31 | 31 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 1.31 | 1.07 | 1.07 | 1.07 |
time (sec) |
N/A | 0.180 | 0.644 | 1.079 | 0.237 | 0.260 | 2.742 | 17.436 | 1.889 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 31 | 62 | 32 | 31 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 2.14 | 1.10 | 1.07 | 1.07 |
time (sec) |
N/A | 0.178 | 1.377 | 0.934 | 0.233 | 0.274 | 166.168 | 27.733 | 5.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 31 | 86 | 0 | 31 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 2.97 | 0.00 | 1.07 | 1.07 |
time (sec) |
N/A | 0.177 | 21.204 | 1.453 | 0.226 | 0.270 | 0.000 | 38.331 | 7.908 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 318 | 69 | 0 | 31 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 10.97 | 2.38 | 0.00 | 1.07 | 1.07 |
time (sec) |
N/A | 0.176 | 0.648 | 1.088 | 0.234 | 0.268 | 0.000 | 0.748 | 4.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 27 | 225 | 58 | 337 | 29 | 29 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 8.33 | 2.15 | 12.48 | 1.07 | 1.07 |
time (sec) |
N/A | 0.167 | 0.410 | 0.799 | 0.246 | 0.260 | 22.021 | 1.202 | 4.513 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 21 | 171 | 52 | 158 | 23 | 23 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 8.14 | 2.48 | 7.52 | 1.10 | 1.10 |
time (sec) |
N/A | 0.155 | 0.223 | 0.766 | 0.220 | 0.260 | 8.146 | 0.959 | 1.963 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 452 | 77 | 0 | 31 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 15.59 | 2.66 | 0.00 | 1.07 | 1.07 |
time (sec) |
N/A | 0.179 | 1.435 | 0.609 | 0.247 | 0.266 | 0.000 | 0.936 | 5.479 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 688 | 118 | 0 | 31 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 23.72 | 4.07 | 0.00 | 1.07 | 1.07 |
time (sec) |
N/A | 0.178 | 1.550 | 0.780 | 0.238 | 0.264 | 0.000 | 1.068 | 22.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 921 | 159 | 0 | 31 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 31.76 | 5.48 | 0.00 | 1.07 | 1.07 |
time (sec) |
N/A | 0.178 | 48.734 | 2.677 | 0.256 | 0.284 | 0.000 | 1.733 | 31.878 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 357 | 345 | 282 | 599 | 855 | 660 | 1477 | 0 | 1403 |
N.S. |
1 | 0.97 | 0.79 | 1.68 | 2.39 | 1.85 | 4.14 | 0.00 | 3.93 |
time (sec) |
N/A | 0.656 | 0.371 | 0.663 | 0.230 | 0.674 | 57.415 | 0.000 | 1.932 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 229 | 225 | 217 | 416 | 623 | 468 | 998 | 410 | 743 |
N.S. |
1 | 0.98 | 0.95 | 1.82 | 2.72 | 2.04 | 4.36 | 1.79 | 3.24 |
time (sec) |
N/A | 0.460 | 0.166 | 0.573 | 0.231 | 0.388 | 8.165 | 75.813 | 1.628 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 152 | 157 | 142 | 270 | 419 | 301 | 692 | 257 | 362 |
N.S. |
1 | 1.03 | 0.93 | 1.78 | 2.76 | 1.98 | 4.55 | 1.69 | 2.38 |
time (sec) |
N/A | 0.334 | 0.087 | 0.517 | 0.209 | 0.334 | 3.270 | 5.199 | 1.378 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 123 | 118 | 123 | 246 | 174 | 314 | 139 | 133 |
N.S. |
1 | 1.18 | 1.13 | 1.18 | 2.37 | 1.67 | 3.02 | 1.34 | 1.28 |
time (sec) |
N/A | 0.283 | 0.070 | 0.391 | 0.204 | 0.285 | 1.408 | 0.702 | 1.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 54 | 54 | 57 | 80 | 104 | 82 | 50 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.06 | 1.48 | 1.93 | 1.52 | 0.93 |
time (sec) |
N/A | 0.178 | 0.018 | 0.303 | 0.191 | 0.266 | 0.479 | 0.320 | 0.931 |
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 | 144 | 152 | 119 | 396 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.83 | 2.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.442 | 0.041 | 3.368 | 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 | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 140 | 108 | 245 | 192 | 279 | 0 | 454 | 191 |
N.S. |
1 | 1.56 | 1.20 | 2.72 | 2.13 | 3.10 | 0.00 | 5.04 | 2.12 |
time (sec) |
N/A | 0.271 | 0.075 | 0.670 | 0.215 | 3.499 | 0.000 | 0.521 | 1.904 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 175 | 185 | 172 | 629 | 405 | 1036 | 0 | 486 | 412 |
N.S. |
1 | 1.06 | 0.98 | 3.59 | 2.31 | 5.92 | 0.00 | 2.78 | 2.35 |
time (sec) |
N/A | 0.390 | 0.279 | 1.221 | 0.230 | 47.453 | 0.000 | 0.502 | 3.969 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | F(-1) | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 277 | 272 | 263 | 1293 | 900 | 0 | 0 | 1359 | 1147 |
N.S. |
1 | 0.98 | 0.95 | 4.67 | 3.25 | 0.00 | 0.00 | 4.91 | 4.14 |
time (sec) |
N/A | 0.539 | 0.381 | 2.043 | 0.251 | 0.000 | 0.000 | 0.844 | 7.905 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | F(-1) | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 381 | 369 | 358 | 2299 | 1809 | 0 | 0 | 2159 | 2520 |
N.S. |
1 | 0.97 | 0.94 | 6.03 | 4.75 | 0.00 | 0.00 | 5.67 | 6.61 |
time (sec) |
N/A | 0.751 | 0.514 | 5.498 | 0.323 | 0.000 | 0.000 | 3.176 | 13.522 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 869 | 1074 | 746 | 0 | 2351 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.24 | 0.86 | 0.00 | 2.71 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.536 | 0.615 | 0.000 | 0.349 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 542 | 686 | 497 | 0 | 1458 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.27 | 0.92 | 0.00 | 2.69 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.117 | 0.335 | 0.000 | 0.328 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 281 | 401 | 351 | 0 | 786 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.43 | 1.25 | 0.00 | 2.80 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.806 | 0.181 | 0.000 | 0.305 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 129 | 124 | 220 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 1.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.584 | 0.105 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 285 | 355 | 1370 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.25 | 4.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.685 | 0.417 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 200 | 216 | 409 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 2.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.451 | 0.285 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 381 | 510 | 603 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.34 | 1.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.976 | 0.729 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 724 | 889 | 909 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.23 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.485 | 1.538 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1154 | 1400 | 1317 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.21 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.150 | 3.698 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 31 | 33 | 65 | 85 | 33 | 33 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 2.10 | 2.74 | 1.06 | 1.06 |
time (sec) |
N/A | 0.184 | 0.111 | 0.747 | 0.237 | 0.333 | 21.419 | 0.565 | 2.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 31 | 54 | 83 | 31 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 1.86 | 2.86 | 1.07 | 1.07 |
time (sec) |
N/A | 0.174 | 0.080 | 0.635 | 0.223 | 0.328 | 6.770 | 0.561 | 2.350 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 48 | 22 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 2.09 | 0.96 | 1.09 | 1.09 |
time (sec) |
N/A | 0.158 | 0.023 | 0.533 | 0.220 | 0.323 | 1.636 | 0.476 | 1.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 31 | 33 | 61 | 0 | 33 | 33 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 1.97 | 0.00 | 1.06 | 1.06 |
time (sec) |
N/A | 0.188 | 0.062 | 0.611 | 0.233 | 0.314 | 0.000 | 0.513 | 2.406 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 31 | 33 | 85 | 0 | 33 | 33 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 2.74 | 0.00 | 1.06 | 1.06 |
time (sec) |
N/A | 0.184 | 0.062 | 0.650 | 0.237 | 0.311 | 0.000 | 1.197 | 7.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 31 | 33 | 109 | 0 | 33 | 33 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 3.52 | 0.00 | 1.06 | 1.06 |
time (sec) |
N/A | 0.185 | 0.067 | 0.702 | 0.249 | 0.283 | 0.000 | 0.511 | 12.412 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 31 | 321 | 115 | 0 | 33 | 33 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 10.35 | 3.71 | 0.00 | 1.06 | 1.06 |
time (sec) |
N/A | 0.183 | 0.466 | 0.683 | 0.226 | 0.326 | 0.000 | 0.585 | 5.851 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 228 | 104 | 729 | 31 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 7.86 | 3.59 | 25.14 | 1.07 | 1.07 |
time (sec) |
N/A | 0.174 | 0.245 | 0.579 | 0.227 | 0.329 | 26.300 | 0.578 | 6.344 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 174 | 98 | 333 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 7.57 | 4.26 | 14.48 | 1.09 | 1.09 |
time (sec) |
N/A | 0.157 | 0.143 | 0.529 | 0.218 | 0.292 | 8.939 | 0.477 | 2.493 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 31 | 455 | 123 | 0 | 33 | 33 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 14.68 | 3.97 | 0.00 | 1.06 | 1.06 |
time (sec) |
N/A | 0.184 | 0.283 | 0.540 | 0.235 | 0.313 | 0.000 | 0.761 | 8.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 31 | 690 | 164 | 0 | 33 | 33 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 22.26 | 5.29 | 0.00 | 1.06 | 1.06 |
time (sec) |
N/A | 0.184 | 0.348 | 0.573 | 0.253 | 0.348 | 0.000 | 1.455 | 32.232 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 31 | 924 | 205 | 0 | 33 | 33 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 29.81 | 6.61 | 0.00 | 1.06 | 1.06 |
time (sec) |
N/A | 0.185 | 0.356 | 0.757 | 0.262 | 0.333 | 0.000 | 1.091 | 48.710 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F(-2) | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 365 | 348 | 463 | 1170 | 671 | 805 | 0 | 0 | 1434 |
N.S. |
1 | 0.95 | 1.27 | 3.21 | 1.84 | 2.21 | 0.00 | 0.00 | 3.93 |
time (sec) |
N/A | 0.643 | 0.637 | 85.504 | 0.218 | 0.339 | 0.000 | 0.000 | 1.800 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F(-2) | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 236 | 228 | 314 | 984 | 467 | 571 | 0 | 0 | 767 |
N.S. |
1 | 0.97 | 1.33 | 4.17 | 1.98 | 2.42 | 0.00 | 0.00 | 3.25 |
time (sec) |
N/A | 0.464 | 0.386 | 33.088 | 0.217 | 0.318 | 0.000 | 0.000 | 1.491 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 158 | 160 | 204 | 623 | 294 | 365 | 0 | 304 | 372 |
N.S. |
1 | 1.01 | 1.29 | 3.94 | 1.86 | 2.31 | 0.00 | 1.92 | 2.35 |
time (sec) |
N/A | 0.342 | 0.239 | 11.353 | 0.204 | 0.324 | 0.000 | 46.925 | 1.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 128 | 124 | 371 | 154 | 192 | 0 | 153 | 154 |
N.S. |
1 | 1.10 | 1.07 | 3.20 | 1.33 | 1.66 | 0.00 | 1.32 | 1.33 |
time (sec) |
N/A | 0.287 | 0.108 | 3.158 | 0.198 | 0.323 | 0.000 | 2.533 | 1.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 57 | 83 | 59 | 59 | 0 | 58 | 53 |
N.S. |
1 | 1.00 | 1.00 | 1.46 | 1.04 | 1.04 | 0.00 | 1.02 | 0.93 |
time (sec) |
N/A | 0.177 | 0.009 | 0.476 | 0.196 | 0.322 | 0.000 | 0.387 | 0.823 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 148 | 155 | 150 | 521 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.01 | 3.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.443 | 0.068 | 2.521 | 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 | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 136 | 117 | 368 | 151 | 250 | 0 | 169 | 141 |
N.S. |
1 | 1.13 | 0.98 | 3.07 | 1.26 | 2.08 | 0.00 | 1.41 | 1.18 |
time (sec) |
N/A | 0.313 | 0.114 | 8.523 | 0.203 | 3.578 | 0.000 | 0.368 | 1.462 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 191 | 191 | 178 | 1385 | 382 | 1127 | 0 | 531 | 431 |
N.S. |
1 | 1.00 | 0.93 | 7.25 | 2.00 | 5.90 | 0.00 | 2.78 | 2.26 |
time (sec) |
N/A | 0.390 | 0.348 | 28.812 | 0.218 | 52.004 | 0.000 | 0.520 | 3.177 |