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 | C | A | C | A | F(-1) | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 407 | 407 | 257 | 477 | 561 | 445 | 0 | 2434 | 0 |
N.S. |
1 | 1.00 | 0.63 | 1.17 | 1.38 | 1.09 | 0.00 | 5.98 | 0.00 |
time (sec) |
N/A | 0.869 | 0.307 | 34.412 | 0.377 | 0.285 | 0.000 | 2.667 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 138 | 104 | 150 | 0 | 244 | 0 | 0 | 0 |
N.S. |
1 | 1.23 | 0.93 | 1.34 | 0.00 | 2.18 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.751 | 0.796 | 3.778 | 0.000 | 0.275 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 102 | 72 | 112 | 0 | 162 | 0 | 0 | 0 |
N.S. |
1 | 1.23 | 0.87 | 1.35 | 0.00 | 1.95 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.616 | 0.138 | 2.604 | 0.000 | 0.259 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 60 | 0 | 45 | 0 | 206 | 56 |
N.S. |
1 | 1.00 | 1.00 | 1.82 | 0.00 | 1.36 | 0.00 | 6.24 | 1.70 |
time (sec) |
N/A | 0.321 | 0.042 | 2.530 | 0.000 | 0.255 | 0.000 | 0.304 | 24.447 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 180 | 0 | 159 | 240 | 3740 | 508 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.88 | 1.33 | 20.78 | 2.82 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.473 | 4.583 | 0.638 | 0.281 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 0 | 111 | 170 | 2842 | 370 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.05 | 1.60 | 26.81 | 3.49 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.418 | 4.300 | 0.500 | 0.296 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 93 | 62 | 109 | 1718 | 203 | 0 | 0 | 0 |
N.S. |
1 | 1.27 | 0.85 | 1.49 | 23.53 | 2.78 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.928 | 0.191 | 4.210 | 0.363 | 0.274 | 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 | 14 | 14 | 16 | 20 | 22 | 22 | 20 | 22 | 24 |
N.S. |
1 | 1.00 | 1.14 | 1.43 | 1.57 | 1.57 | 1.43 | 1.57 | 1.71 |
time (sec) |
N/A | 0.183 | 3.724 | 0.340 | 0.341 | 0.264 | 30.374 | 0.288 | 24.671 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 158 | 195 | 157 | 625 | 803 | 1410 | 0 | 0 | 0 |
N.S. |
1 | 1.23 | 0.99 | 3.96 | 5.08 | 8.92 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.822 | 0.156 | 1.240 | 0.413 | 0.311 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 132 | 155 | 126 | 432 | 497 | 974 | 0 | 0 | 0 |
N.S. |
1 | 1.17 | 0.95 | 3.27 | 3.77 | 7.38 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.637 | 0.151 | 1.215 | 0.382 | 0.295 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 113 | 100 | 266 | 284 | 594 | 0 | 0 | 0 |
N.S. |
1 | 1.18 | 1.04 | 2.77 | 2.96 | 6.19 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.495 | 0.089 | 1.186 | 0.388 | 0.303 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 73 | 70 | 123 | 115 | 310 | 0 | 0 | 148 |
N.S. |
1 | 1.11 | 1.06 | 1.86 | 1.74 | 4.70 | 0.00 | 0.00 | 2.24 |
time (sec) |
N/A | 0.331 | 0.180 | 1.026 | 0.370 | 0.263 | 0.000 | 0.000 | 25.461 |
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 | 14 | 14 | 16 | 20 | 22 | 22 | 19 | 22 | 24 |
N.S. |
1 | 1.00 | 1.14 | 1.43 | 1.57 | 1.57 | 1.36 | 1.57 | 1.71 |
time (sec) |
N/A | 0.184 | 5.281 | 0.536 | 0.428 | 0.246 | 0.594 | 0.295 | 25.425 |
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 | 14 | 14 | 16 | 20 | 22 | 33 | 20 | 22 | 24 |
N.S. |
1 | 1.00 | 1.14 | 1.43 | 1.57 | 2.36 | 1.43 | 1.57 | 1.71 |
time (sec) |
N/A | 0.185 | 3.484 | 0.534 | 0.549 | 0.240 | 0.964 | 2.223 | 26.122 |
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 | 20 | 20 | 22 | 22 | 24 | 27 | 22 | 24 | 26 |
N.S. |
1 | 1.00 | 1.10 | 1.10 | 1.20 | 1.35 | 1.10 | 1.20 | 1.30 |
time (sec) |
N/A | 0.460 | 11.880 | 0.552 | 0.680 | 0.246 | 121.927 | 0.299 | 25.232 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 275 | 299 | 557 | 901 | 934 | 1075 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 2.03 | 3.28 | 3.40 | 3.91 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.236 | 1.573 | 2.507 | 0.517 | 0.306 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 186 | 197 | 315 | 512 | 516 | 656 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.69 | 2.75 | 2.77 | 3.53 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.811 | 0.926 | 2.193 | 0.394 | 0.288 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 213 | 180 | 0 | 331 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.07 | 1.75 | 0.00 | 3.21 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.456 | 0.498 | 1.386 | 0.000 | 0.278 | 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 | 20 | 20 | 22 | 22 | 210 | 27 | 20 | 24 | 26 |
N.S. |
1 | 1.00 | 1.10 | 1.10 | 10.50 | 1.35 | 1.00 | 1.20 | 1.30 |
time (sec) |
N/A | 0.529 | 3.402 | 0.885 | 0.658 | 0.251 | 1.318 | 0.551 | 24.449 |
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 | 20 | 20 | 22 | 22 | 270 | 38 | 22 | 24 | 26 |
N.S. |
1 | 1.00 | 1.10 | 1.10 | 13.50 | 1.90 | 1.10 | 1.20 | 1.30 |
time (sec) |
N/A | 0.651 | 7.189 | 0.904 | 0.867 | 0.243 | 2.020 | 3.020 | 24.921 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 24 | 33 | 0 | 24 | 26 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.50 | 0.00 | 1.09 | 1.18 |
time (sec) |
N/A | 0.549 | 13.664 | 0.677 | 0.685 | 0.234 | 0.000 | 0.314 | 25.789 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 251 | 282 | 1731 | 650 | 692 | 1134 | 0 | 0 | 0 |
N.S. |
1 | 1.12 | 6.90 | 2.59 | 2.76 | 4.52 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.282 | 6.528 | 3.112 | 0.438 | 0.321 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 184 | 195 | 518 | 388 | 383 | 688 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 2.82 | 2.11 | 2.08 | 3.74 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.912 | 6.579 | 2.634 | 0.428 | 0.287 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 126 | 134 | 179 | 146 | 346 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 1.17 | 1.56 | 1.27 | 3.01 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.595 | 0.713 | 2.572 | 0.336 | 0.280 | 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 | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 182 | 33 | 0 | 24 | 26 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 8.27 | 1.50 | 0.00 | 1.09 | 1.18 |
time (sec) |
N/A | 0.632 | 0.886 | 1.004 | 0.486 | 0.241 | 0.000 | 0.325 | 25.531 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 242 | 44 | 0 | 24 | 26 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 11.00 | 2.00 | 0.00 | 1.09 | 1.18 |
time (sec) |
N/A | 0.726 | 2.961 | 1.030 | 0.772 | 0.245 | 0.000 | 2.803 | 25.569 |
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 | 20 | 20 | 22 | 20 | 22 | 22 | 20 | 22 | 26 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 1.00 | 1.10 | 1.30 |
time (sec) |
N/A | 0.314 | 10.153 | 0.307 | 0.394 | 0.233 | 33.987 | 0.310 | 25.956 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 247 | 301 | 578 | 1242 | 1794 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.22 | 2.34 | 5.03 | 7.26 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.966 | 1.231 | 1.332 | 0.521 | 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 | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 197 | 223 | 350 | 816 | 1078 | 1786 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 1.78 | 4.14 | 5.47 | 9.07 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.708 | 1.079 | 1.303 | 0.506 | 0.379 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 140 | 213 | 469 | 599 | 1098 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 1.68 | 3.69 | 4.72 | 8.65 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.498 | 0.744 | 1.208 | 0.422 | 0.323 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 73 | 141 | 208 | 269 | 554 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.99 | 2.93 | 3.79 | 7.80 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.317 | 0.210 | 1.010 | 0.411 | 0.318 | 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 | 20 | 20 | 22 | 20 | 22 | 22 | 19 | 22 | 26 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.95 | 1.10 | 1.30 |
time (sec) |
N/A | 0.243 | 5.046 | 0.720 | 0.545 | 0.243 | 0.614 | 0.396 | 25.325 |
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 | 20 | 20 | 22 | 20 | 22 | 33 | 20 | 22 | 26 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.65 | 1.00 | 1.10 | 1.30 |
time (sec) |
N/A | 0.241 | 6.558 | 0.727 | 0.985 | 0.243 | 1.003 | 4.083 | 24.844 |
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 | 22 | 22 | 24 | 22 | 24 | 24 | 22 | 24 | 26 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 1.00 | 1.09 | 1.18 |
time (sec) |
N/A | 0.326 | 23.115 | 0.287 | 0.538 | 0.243 | 118.630 | 0.331 | 25.445 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 350 | 387 | 739 | 1158 | 3257 | 1753 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 2.11 | 3.31 | 9.31 | 5.01 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.950 | 6.389 | 1.922 | 0.992 | 0.359 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 226 | 260 | 593 | 556 | 1638 | 1067 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 2.62 | 2.46 | 7.25 | 4.72 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.705 | 6.277 | 1.608 | 0.502 | 0.318 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 128 | 517 | 235 | 0 | 434 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 3.95 | 1.79 | 0.00 | 3.31 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.319 | 3.826 | 1.200 | 0.000 | 0.294 | 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 | 22 | 22 | 24 | 22 | 677 | 24 | 20 | 24 | 26 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 30.77 | 1.09 | 0.91 | 1.09 | 1.18 |
time (sec) |
N/A | 0.306 | 22.399 | 0.609 | 0.797 | 0.257 | 1.114 | 5.153 | 24.817 |
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 | 22 | 22 | 24 | 22 | 1008 | 35 | 22 | 3 | 26 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 45.82 | 1.59 | 1.00 | 0.14 | 1.18 |
time (sec) |
N/A | 0.310 | 21.434 | 0.634 | 1.570 | 0.245 | 2.029 | 4.246 | 25.028 |
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 | 22 | 22 | 24 | 22 | 24 | 24 | 0 | 24 | 26 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.00 | 1.09 | 1.18 |
time (sec) |
N/A | 0.368 | 26.593 | 0.316 | 0.535 | 0.241 | 0.000 | 0.327 | 24.774 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 325 | 350 | 1526 | 1223 | 5165 | 3475 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 4.70 | 3.76 | 15.89 | 10.69 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.043 | 6.997 | 1.829 | 1.623 | 0.420 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 201 | 228 | 880 | 632 | 2528 | 1995 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 4.38 | 3.14 | 12.58 | 9.93 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.730 | 6.925 | 1.500 | 0.608 | 0.363 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 138 | 224 | 270 | 1028 | 942 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 1.59 | 1.91 | 7.29 | 6.68 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.326 | 1.715 | 1.065 | 0.460 | 0.311 | 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 | 22 | 22 | 24 | 22 | 2040 | 24 | 20 | 24 | 26 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 92.73 | 1.09 | 0.91 | 1.09 | 1.18 |
time (sec) |
N/A | 0.301 | 19.660 | 0.626 | 2.698 | 0.290 | 2.586 | 0.757 | 24.859 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 2702 | 35 | 22 | 0 | 26 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 122.82 | 1.59 | 1.00 | 0.00 | 1.18 |
time (sec) |
N/A | 0.316 | 18.156 | 0.642 | 9.087 | 0.370 | 4.941 | 0.000 | 24.831 |
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 | 20 | 20 | 22 | 20 | 22 | 22 | 20 | 22 | 24 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 1.00 | 1.10 | 1.20 |
time (sec) |
N/A | 0.291 | 3.089 | 0.293 | 0.639 | 0.247 | 3.972 | 0.342 | 23.762 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 227 | 247 | 428 | 767 | 2944 | 1190 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.89 | 3.38 | 12.97 | 5.24 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.811 | 1.153 | 4.669 | 0.588 | 0.309 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 169 | 256 | 463 | 1770 | 783 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.61 | 2.91 | 11.13 | 4.92 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.557 | 0.796 | 2.236 | 0.439 | 0.288 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 99 | 174 | 227 | 0 | 446 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.79 | 2.34 | 0.00 | 4.60 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.363 | 1.842 | 1.230 | 0.000 | 0.291 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 93 | 67 | 259 | 60 | 0 | 1267 | 78 |
N.S. |
1 | 1.00 | 3.21 | 2.31 | 8.93 | 2.07 | 0.00 | 43.69 | 2.69 |
time (sec) |
N/A | 0.229 | 0.132 | 0.615 | 0.330 | 0.253 | 0.000 | 0.610 | 27.600 |
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 | 20 | 20 | 22 | 20 | 349 | 22 | 19 | 22 | 24 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 17.45 | 1.10 | 0.95 | 1.10 | 1.20 |
time (sec) |
N/A | 0.258 | 12.683 | 0.494 | 0.573 | 0.259 | 0.408 | 0.818 | 25.357 |
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 | 20 | 20 | 22 | 20 | 494 | 33 | 20 | 22 | 24 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 24.70 | 1.65 | 1.00 | 1.10 | 1.20 |
time (sec) |
N/A | 0.267 | 19.628 | 0.538 | 0.851 | 0.252 | 0.630 | 9.173 | 25.429 |
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 | 16 | 16 | 18 | 16 | 18 | 18 | 15 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.94 | 1.12 | 1.12 |
time (sec) |
N/A | 0.203 | 3.147 | 0.297 | 0.539 | 0.233 | 0.980 | 0.567 | 24.711 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 151 | 424 | 356 | 1363 | 373 | 0 | 0 | 0 |
N.S. |
1 | 1.18 | 3.31 | 2.78 | 10.65 | 2.91 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.669 | 6.537 | 1.700 | 0.396 | 0.255 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 111 | 276 | 199 | 418 | 210 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 2.88 | 2.07 | 4.35 | 2.19 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.473 | 6.397 | 1.582 | 0.386 | 0.242 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 42 | 76 | 52 | 237 | 53 | 65 | 203 | 52 |
N.S. |
1 | 1.05 | 1.90 | 1.30 | 5.92 | 1.32 | 1.62 | 5.08 | 1.30 |
time (sec) |
N/A | 0.251 | 0.415 | 1.182 | 0.307 | 0.241 | 0.156 | 0.454 | 25.918 |
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 | 16 | 16 | 18 | 16 | 388 | 18 | 14 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 24.25 | 1.12 | 0.88 | 1.12 | 1.12 |
time (sec) |
N/A | 0.200 | 5.082 | 0.672 | 0.483 | 0.233 | 0.360 | 0.580 | 25.445 |
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 | 16 | 16 | 18 | 16 | 523 | 29 | 15 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 32.69 | 1.81 | 0.94 | 1.12 | 1.12 |
time (sec) |
N/A | 0.200 | 6.351 | 0.674 | 0.905 | 0.227 | 0.535 | 7.916 | 25.268 |
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 | 22 | 22 | 24 | 22 | 24 | 24 | 22 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 1.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.570 | 29.048 | 0.294 | 1.057 | 0.239 | 32.349 | 0.608 | 26.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 228 | 244 | 532 | 677 | 11010 | 896 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 2.33 | 2.97 | 48.29 | 3.93 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.192 | 1.676 | 3.573 | 1.315 | 0.314 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 145 | 149 | 362 | 345 | 0 | 511 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 2.50 | 2.38 | 0.00 | 3.52 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.772 | 3.482 | 2.273 | 0.000 | 0.280 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 107 | 123 | 2123 | 93 | 0 | 2330 | 151 |
N.S. |
1 | 1.00 | 1.91 | 2.20 | 37.91 | 1.66 | 0.00 | 41.61 | 2.70 |
time (sec) |
N/A | 0.446 | 0.864 | 1.583 | 0.323 | 0.256 | 0.000 | 1.110 | 1.535 |
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 | 22 | 22 | 24 | 22 | 1268 | 24 | 20 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 57.64 | 1.09 | 0.91 | 1.09 | 1.09 |
time (sec) |
N/A | 0.658 | 4.213 | 0.421 | 0.744 | 0.253 | 0.634 | 1.565 | 27.958 |
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 | 22 | 22 | 24 | 22 | 1412 | 35 | 22 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 64.18 | 1.59 | 1.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.809 | 4.485 | 0.455 | 1.298 | 0.256 | 1.095 | 18.138 | 28.434 |
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 | 22 | 22 | 24 | 22 | 24 | 24 | 22 | 24 | 26 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 1.00 | 1.09 | 1.18 |
time (sec) |
N/A | 0.357 | 24.666 | 0.299 | 0.656 | 0.240 | 118.021 | 0.308 | 26.275 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 469 | 507 | 694 | 1866 | 5709 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 1.48 | 3.98 | 12.17 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.114 | 3.668 | 2.047 | 1.766 | 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 | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 343 | 381 | 473 | 1152 | 3202 | 1705 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 1.38 | 3.36 | 9.34 | 4.97 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.897 | 1.429 | 1.861 | 0.853 | 0.365 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 219 | 254 | 317 | 568 | 1590 | 1035 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 1.45 | 2.59 | 7.26 | 4.73 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.706 | 2.806 | 1.651 | 0.467 | 0.319 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 121 | 212 | 160 | 800 | 366 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 1.88 | 1.42 | 7.08 | 3.24 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.321 | 1.124 | 1.162 | 0.435 | 0.273 | 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 | 22 | 22 | 24 | 22 | 603 | 24 | 20 | 24 | 26 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 27.41 | 1.09 | 0.91 | 1.09 | 1.18 |
time (sec) |
N/A | 0.292 | 19.488 | 0.617 | 0.747 | 0.254 | 1.189 | 4.947 | 25.476 |
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 | 22 | 22 | 24 | 22 | 931 | 35 | 22 | 3 | 26 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 42.32 | 1.59 | 1.00 | 0.14 | 1.18 |
time (sec) |
N/A | 0.291 | 19.832 | 0.594 | 1.353 | 0.262 | 1.971 | 4.099 | 26.026 |
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 | 24 | 24 | 26 | 24 | 26 | 26 | 0 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.00 | 1.08 | 1.08 |
time (sec) |
N/A | 0.345 | 3.211 | 0.289 | 0.481 | 0.243 | 0.000 | 0.338 | 25.709 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 161 | 285 | 687 | 2360 | 1635 | 0 | 0 | 0 |
N.S. |
1 | 1.36 | 2.42 | 5.82 | 20.00 | 13.86 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.751 | 2.291 | 1.994 | 0.506 | 0.350 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 113 | 277 | 351 | 772 | 950 | 0 | 0 | 0 |
N.S. |
1 | 1.28 | 3.15 | 3.99 | 8.77 | 10.80 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.565 | 1.876 | 1.898 | 0.410 | 0.317 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 44 | 32 | 72 | 308 | 75 | 0 | 10271 | 55 |
N.S. |
1 | 1.26 | 0.91 | 2.06 | 8.80 | 2.14 | 0.00 | 293.46 | 1.57 |
time (sec) |
N/A | 0.312 | 0.536 | 1.524 | 0.319 | 0.257 | 0.000 | 2.843 | 27.600 |
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 | 24 | 24 | 26 | 24 | 687 | 26 | 22 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 28.62 | 1.08 | 0.92 | 1.08 | 1.08 |
time (sec) |
N/A | 0.282 | 9.216 | 0.591 | 0.781 | 0.243 | 2.587 | 0.308 | 26.544 |
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 | 24 | 24 | 26 | 24 | 1024 | 37 | 24 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 42.67 | 1.54 | 1.00 | 1.08 | 1.08 |
time (sec) |
N/A | 0.277 | 9.968 | 0.635 | 1.731 | 0.251 | 4.804 | 1.527 | 26.685 |
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 | 24 | 24 | 26 | 24 | 26 | 26 | 0 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.00 | 1.08 | 1.08 |
time (sec) |
N/A | 0.360 | 27.554 | 0.282 | 0.951 | 0.248 | 0.000 | 0.344 | 26.971 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 601 | 623 | 907 | 1613 | 8032 | 3173 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.51 | 2.68 | 13.36 | 5.28 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.280 | 8.188 | 2.444 | 3.615 | 0.430 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 305 | 335 | 889 | 802 | 3814 | 1801 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 2.91 | 2.63 | 12.50 | 5.90 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.136 | 7.929 | 2.014 | 0.987 | 0.342 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 154 | 171 | 520 | 267 | 1481 | 621 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 3.38 | 1.73 | 9.62 | 4.03 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.376 | 6.158 | 1.428 | 0.579 | 0.284 | 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 | 24 | 24 | 26 | 24 | 3697 | 26 | 22 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 154.04 | 1.08 | 0.92 | 1.08 | 1.08 |
time (sec) |
N/A | 0.342 | 23.773 | 0.647 | 3.320 | 0.293 | 7.687 | 119.208 | 26.186 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 4757 | 37 | 24 | 0 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 198.21 | 1.54 | 1.00 | 0.00 | 1.08 |
time (sec) |
N/A | 0.351 | 29.139 | 0.596 | 11.085 | 0.334 | 14.706 | 0.000 | 26.580 |
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 | 20 | 20 | 22 | 20 | 22 | 22 | 0 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.00 | 1.10 | 1.10 |
time (sec) |
N/A | 0.843 | 46.748 | 0.183 | 0.815 | 0.249 | 0.000 | 0.338 | 26.526 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 387 | 417 | 672 | 0 | 3940 | 1747 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 1.74 | 0.00 | 10.18 | 4.51 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.218 | 7.307 | 0.000 | 0.768 | 0.364 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 235 | 235 | 613 | 429 | 2205 | 1237 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.61 | 1.83 | 9.38 | 5.26 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.677 | 6.898 | 1.461 | 0.526 | 0.333 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 282 | 519 | 1173 | 531 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.24 | 4.12 | 9.31 | 4.21 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.345 | 3.693 | 0.698 | 0.493 | 0.262 | 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 | 20 | 20 | 22 | 20 | 1872 | 22 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 93.60 | 1.10 | 0.95 | 1.10 | 1.10 |
time (sec) |
N/A | 0.544 | 54.244 | 0.316 | 1.001 | 0.256 | 8.697 | 1.199 | 26.042 |
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 | 20 | 20 | 22 | 20 | 1884 | 22 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 94.20 | 1.10 | 1.00 | 1.10 | 1.10 |
time (sec) |
N/A | 0.575 | 23.742 | 0.309 | 1.089 | 0.246 | 11.405 | 1.821 | 26.392 |
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 | 22 | 22 | 24 | 22 | 24 | 24 | 22 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 1.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.326 | 6.619 | 0.168 | 0.634 | 0.242 | 9.714 | 0.365 | 25.501 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 166 | 418 | 489 | 3446 | 892 | 0 | 0 | 0 |
N.S. |
1 | 1.19 | 3.01 | 3.52 | 24.79 | 6.42 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.778 | 6.600 | 4.888 | 0.489 | 0.313 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 128 | 286 | 301 | 668 | 540 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 2.49 | 2.62 | 5.81 | 4.70 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.575 | 6.401 | 3.176 | 0.443 | 0.294 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 57 | 66 | 149 | 988 | 86 | 0 | 4331 | 150 |
N.S. |
1 | 1.04 | 1.20 | 2.71 | 17.96 | 1.56 | 0.00 | 78.75 | 2.73 |
time (sec) |
N/A | 0.341 | 0.651 | 1.529 | 0.307 | 0.259 | 0.000 | 1.104 | 27.525 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 48 | 61 | 283 | 36 | 0 | 571 | 53 |
N.S. |
1 | 1.00 | 1.37 | 1.74 | 8.09 | 1.03 | 0.00 | 16.31 | 1.51 |
time (sec) |
N/A | 0.243 | 0.641 | 0.878 | 0.209 | 0.254 | 0.000 | 0.384 | 26.279 |
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 | 22 | 22 | 24 | 22 | 1090 | 24 | 20 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 49.55 | 1.09 | 0.91 | 1.09 | 1.09 |
time (sec) |
N/A | 0.266 | 8.444 | 0.389 | 0.769 | 0.254 | 0.460 | 0.439 | 24.834 |
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 | 22 | 22 | 24 | 22 | 1396 | 35 | 22 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 63.45 | 1.59 | 1.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.290 | 12.786 | 0.349 | 1.705 | 0.244 | 0.712 | 6.735 | 26.933 |
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 | 22 | 22 | 24 | 22 | 24 | 24 | 22 | 24 | 26 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 1.00 | 1.09 | 1.18 |
time (sec) |
N/A | 0.294 | 51.865 | 0.175 | 1.079 | 0.257 | 9.301 | 0.604 | 28.195 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 337 | 580 | 530 | 1127 | 3831 | 1315 | 0 | 0 | 0 |
N.S. |
1 | 1.72 | 1.57 | 3.34 | 11.37 | 3.90 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.068 | 3.749 | 2.008 | 1.370 | 0.330 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 193 | 351 | 526 | 584 | 1891 | 795 | 0 | 0 | 0 |
N.S. |
1 | 1.82 | 2.73 | 3.03 | 9.80 | 4.12 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.375 | 7.704 | 1.252 | 0.567 | 0.300 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 117 | 192 | 555 | 267 | 0 | 435 | 0 | 0 | 0 |
N.S. |
1 | 1.64 | 4.74 | 2.28 | 0.00 | 3.72 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.693 | 7.029 | 0.704 | 0.000 | 0.300 | 0.000 | 0.000 | 0.000 |