Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 24 | 42 | 0 | 24 | 39 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.75 | 0.00 | 1.00 | 1.62 | 1.00 |
time (sec) |
N/A | 0.380 | 0.272 | 0.096 | 0.185 | 0.138 | 0.000 | 1.754 | 0.260 | 25.257 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 22 | 40 | 0 | 22 | 37 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.82 | 0.00 | 1.00 | 1.68 | 1.00 |
time (sec) |
N/A | 0.368 | 0.315 | 0.096 | 0.172 | 0.097 | 0.000 | 1.785 | 0.169 | 25.361 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 18 | 20 | 38 | 0 | 20 | 35 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.90 | 0.00 | 1.00 | 1.75 | 1.00 |
time (sec) |
N/A | 0.348 | 0.060 | 0.096 | 0.172 | 0.169 | 0.000 | 0.959 | 0.169 | 25.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 24 | 42 | 0 | 24 | 39 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.75 | 0.00 | 1.00 | 1.62 | 1.00 |
time (sec) |
N/A | 0.380 | 0.249 | 0.100 | 0.182 | 0.108 | 0.000 | 1.746 | 0.179 | 25.941 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 24 | 42 | 0 | 24 | 164 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.75 | 0.00 | 1.00 | 6.83 | 1.00 |
time (sec) |
N/A | 0.389 | 0.222 | 0.095 | 0.181 | 0.092 | 0.000 | 1.729 | 0.223 | 25.863 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | B | F(-2) | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 474 | 609 | 373 | 0 | 754 | 1196 | 0 | 556 | 360 | 0 |
N.S. |
1 | 1.28 | 0.79 | 0.00 | 1.59 | 2.52 | 0.00 | 1.17 | 0.76 | 0.00 |
time (sec) |
N/A | 1.566 | 0.394 | 0.000 | 0.131 | 0.121 | 0.000 | 0.154 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | B | F(-2) | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 449 | 581 | 332 | 0 | 731 | 1162 | 0 | 448 | 368 | 0 |
N.S. |
1 | 1.29 | 0.74 | 0.00 | 1.63 | 2.59 | 0.00 | 1.00 | 0.82 | 0.00 |
time (sec) |
N/A | 1.466 | 0.504 | 0.000 | 0.131 | 0.117 | 0.000 | 0.170 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | B | F(-2) | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 431 | 575 | 271 | 0 | 707 | 1236 | 0 | 455 | 365 | 0 |
N.S. |
1 | 1.33 | 0.63 | 0.00 | 1.64 | 2.87 | 0.00 | 1.06 | 0.85 | 0.00 |
time (sec) |
N/A | 1.413 | 0.454 | 0.000 | 0.133 | 0.130 | 0.000 | 0.168 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | B | B | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 460 | 608 | 235 | 0 | 723 | 1348 | 0 | 494 | 400 | 0 |
N.S. |
1 | 1.32 | 0.51 | 0.00 | 1.57 | 2.93 | 0.00 | 1.07 | 0.87 | 0.00 |
time (sec) |
N/A | 1.463 | 0.257 | 0.000 | 0.137 | 0.160 | 0.000 | 0.177 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | B | B | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 481 | 629 | 100 | 0 | 739 | 1369 | 0 | 507 | 410 | 0 |
N.S. |
1 | 1.31 | 0.21 | 0.00 | 1.54 | 2.85 | 0.00 | 1.05 | 0.85 | 0.00 |
time (sec) |
N/A | 1.560 | 0.078 | 0.000 | 0.140 | 0.149 | 0.000 | 0.168 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | B | F(-2) | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 760 | 976 | 628 | 0 | 1165 | 2178 | 0 | 900 | 606 | 0 |
N.S. |
1 | 1.28 | 0.83 | 0.00 | 1.53 | 2.87 | 0.00 | 1.18 | 0.80 | 0.00 |
time (sec) |
N/A | 2.118 | 0.911 | 0.000 | 0.139 | 0.139 | 0.000 | 0.179 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | B | F(-2) | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 709 | 922 | 478 | 0 | 1119 | 2118 | 0 | 577 | 590 | 0 |
N.S. |
1 | 1.30 | 0.67 | 0.00 | 1.58 | 2.99 | 0.00 | 0.81 | 0.83 | 0.00 |
time (sec) |
N/A | 2.068 | 0.922 | 0.000 | 0.141 | 0.167 | 0.000 | 0.210 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | B | F(-2) | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 692 | 904 | 527 | 0 | 1102 | 2112 | 0 | 631 | 595 | 0 |
N.S. |
1 | 1.31 | 0.76 | 0.00 | 1.59 | 3.05 | 0.00 | 0.91 | 0.86 | 0.00 |
time (sec) |
N/A | 2.095 | 1.206 | 0.000 | 0.138 | 0.192 | 0.000 | 0.201 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | B | B | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 693 | 913 | 340 | 0 | 1088 | 2205 | 0 | 675 | 623 | 0 |
N.S. |
1 | 1.32 | 0.49 | 0.00 | 1.57 | 3.18 | 0.00 | 0.97 | 0.90 | 0.00 |
time (sec) |
N/A | 2.033 | 1.077 | 0.000 | 0.137 | 0.257 | 0.000 | 0.203 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | B | B | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 723 | 947 | 294 | 0 | 1110 | 2283 | 0 | 688 | 634 | 0 |
N.S. |
1 | 1.31 | 0.41 | 0.00 | 1.54 | 3.16 | 0.00 | 0.95 | 0.88 | 0.00 |
time (sec) |
N/A | 2.177 | 0.287 | 0.000 | 0.137 | 0.216 | 0.000 | 0.197 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1601 | 1677 | 1506 | 0 | 0 | 0 | 0 | 0 | 354 | 0 |
N.S. |
1 | 1.05 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 4.754 | 1.515 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.340 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1361 | 1261 | 1297 | 0 | 0 | 0 | 0 | 0 | 64 | 0 |
N.S. |
1 | 0.93 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 3.127 | 0.450 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1580 | 1658 | 1336 | 0 | 0 | 0 | 0 | 0 | 421 | 0 |
N.S. |
1 | 1.05 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 4.180 | 1.733 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.478 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 148 | 0 | 35 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 1.00 | 4.48 | 0.00 | 1.06 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.401 | 0.016 | 5.630 | 0.000 | 0.108 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 220 | 496 | 0 | 105 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 2.93 | 6.61 | 0.00 | 1.40 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.665 | 0.285 | 2.611 | 0.000 | 0.083 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 179 | 659 | 0 | 0 | 417 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.11 | 4.09 | 0.00 | 0.00 | 2.59 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 1.165 | 0.335 | 0.000 | 0.000 | 0.142 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 149 | 456 | 0 | 0 | 281 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.13 | 3.45 | 0.00 | 0.00 | 2.13 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.959 | 0.280 | 0.000 | 0.000 | 0.128 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 118 | 265 | 0 | 0 | 161 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.16 | 2.60 | 0.00 | 0.00 | 1.58 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.858 | 0.250 | 0.000 | 0.000 | 0.090 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 47 | 49 | 180 | 0 | 69 | 0 | 0 | 65 | 0 |
N.S. |
1 | 0.96 | 1.00 | 3.67 | 0.00 | 1.41 | 0.00 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.428 | 0.016 | 4.779 | 0.000 | 0.097 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 28 | 28 | 30 | 28 | 44 | 30 | 24 | 30 | 43 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.57 | 1.07 | 0.86 | 1.07 | 1.54 | 1.07 |
time (sec) |
N/A | 0.713 | 0.658 | 0.128 | 0.194 | 0.090 | 46.857 | 0.125 | 0.154 | 25.944 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 28 | 91 | 30 | 0 | 30 | 89 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 3.25 | 1.07 | 0.00 | 1.07 | 3.18 | 1.07 |
time (sec) |
N/A | 0.523 | 3.402 | 0.128 | 0.140 | 0.117 | 0.000 | 0.123 | 0.221 | 26.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 28 | 238 | 30 | 0 | 30 | 79 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 8.50 | 1.07 | 0.00 | 1.07 | 2.82 | 1.07 |
time (sec) |
N/A | 0.507 | 13.935 | 0.129 | 0.151 | 0.094 | 0.000 | 0.132 | 0.228 | 26.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 0 | 113 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 0.00 | 1.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.000 | 0.263 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 0 | 135 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 0.00 | 1.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.000 | 0.236 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 0 | 192 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 0.00 | 1.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.000 | 0.522 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 0 | 118 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 0.00 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.000 | 0.235 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 0 | 136 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 0.00 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.000 | 0.205 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 0 | 113 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 0.00 | 1.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.000 | 0.195 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 0 | 120 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.00 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.000 | 0.329 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 0 | 62 | 76 | 118 | 55 | 70 | 128 | 76 | 0 |
N.S. |
1 | 0.00 | 0.42 | 0.52 | 0.81 | 0.38 | 0.48 | 0.88 | 0.52 | 0.00 |
time (sec) |
N/A | 0.000 | 0.062 | 1.031 | 0.114 | 0.084 | 130.483 | 0.120 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 0 | 49 | 66 | 90 | 45 | 56 | 92 | 58 | 0 |
N.S. |
1 | 0.00 | 0.44 | 0.59 | 0.81 | 0.41 | 0.50 | 0.83 | 0.52 | 0.00 |
time (sec) |
N/A | 0.000 | 0.047 | 1.012 | 0.108 | 0.101 | 37.370 | 0.123 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 0 | 38 | 52 | 61 | 33 | 42 | 54 | 40 | 0 |
N.S. |
1 | 0.00 | 0.52 | 0.71 | 0.84 | 0.45 | 0.58 | 0.74 | 0.55 | 0.00 |
time (sec) |
N/A | 0.000 | 0.035 | 1.037 | 0.108 | 0.092 | 9.243 | 0.124 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 23 | 32 | 31 | 21 | 24 | 31 | 21 | 21 |
N.S. |
1 | 0.00 | 0.66 | 0.91 | 0.89 | 0.60 | 0.69 | 0.89 | 0.60 | 0.60 |
time (sec) |
N/A | 0.000 | 0.011 | 1.876 | 0.026 | 0.083 | 2.478 | 0.112 | 0.166 | 25.250 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 0 | 85 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.00 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.000 | 0.036 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 0 | 144 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.00 | 1.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.000 | 0.098 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 0 | 185 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.00 | 1.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.000 | 0.146 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 374 | 0 | 193 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.00 | 0.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.000 | 0.412 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 0 | 192 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 0.00 | 1.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.000 | 0.137 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | F | A | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 0 | 27 | 43 | 0 | 47 | 60 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 0.93 | 1.48 | 0.00 | 1.62 | 2.07 | 0.00 |
time (sec) |
N/A | 0.000 | 0.035 | 0.000 | 0.108 | 0.111 | 0.000 | 0.131 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | F | A | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 0 | 47 | 0 | 57 | 60 | 0 | 119 | 129 | 0 |
N.S. |
1 | 0.00 | 0.61 | 0.00 | 0.74 | 0.78 | 0.00 | 1.55 | 1.68 | 0.00 |
time (sec) |
N/A | 0.000 | 0.057 | 0.000 | 0.106 | 0.089 | 0.000 | 0.131 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | F | A | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 0 | 58 | 0 | 86 | 70 | 0 | 195 | 195 | 0 |
N.S. |
1 | 0.00 | 0.48 | 0.00 | 0.71 | 0.58 | 0.00 | 1.61 | 1.61 | 0.00 |
time (sec) |
N/A | 0.000 | 0.064 | 0.000 | 0.106 | 0.080 | 0.000 | 0.134 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 0 | 67 | 0 | 114 | 80 | 0 | 267 | 261 | 0 |
N.S. |
1 | 0.00 | 0.41 | 0.00 | 0.69 | 0.48 | 0.00 | 1.62 | 1.58 | 0.00 |
time (sec) |
N/A | 0.000 | 0.076 | 0.000 | 0.111 | 0.114 | 0.000 | 0.137 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 0 | 60 | 62 | 99 | 53 | 139 | 84 | 74 | 0 |
N.S. |
1 | 0.00 | 0.47 | 0.48 | 0.77 | 0.41 | 1.08 | 0.65 | 0.57 | 0.00 |
time (sec) |
N/A | 0.000 | 0.053 | 1.016 | 0.137 | 0.075 | 8.350 | 0.124 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 0 | 50 | 52 | 75 | 43 | 102 | 66 | 56 | 0 |
N.S. |
1 | 0.00 | 0.51 | 0.53 | 0.77 | 0.44 | 1.04 | 0.67 | 0.57 | 0.00 |
time (sec) |
N/A | 0.000 | 0.039 | 1.023 | 0.129 | 0.070 | 2.806 | 0.120 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 0 | 36 | 38 | 50 | 31 | 65 | 46 | 38 | 0 |
N.S. |
1 | 0.00 | 0.56 | 0.59 | 0.78 | 0.48 | 1.02 | 0.72 | 0.59 | 0.00 |
time (sec) |
N/A | 0.000 | 0.030 | 1.008 | 0.112 | 0.076 | 0.902 | 0.113 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 20 | 27 | 26 | 18 | 24 | 26 | 17 | 18 |
N.S. |
1 | 0.00 | 0.67 | 0.90 | 0.87 | 0.60 | 0.80 | 0.87 | 0.57 | 0.60 |
time (sec) |
N/A | 0.000 | 0.009 | 0.940 | 0.106 | 0.104 | 0.297 | 0.119 | 0.166 | 25.662 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 0 | 105 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.00 | 1.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.000 | 0.034 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 0 | 159 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.00 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.000 | 0.101 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 0 | 195 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.00 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.000 | 0.168 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 0 | 238 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.000 | 0.623 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 0 | 189 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.000 | 0.427 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 0 | 136 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 0.00 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.000 | 0.050 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 36 | 0 | 34 | 36 | 37 | 57 | 56 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 0.94 | 1.00 | 1.03 | 1.58 | 1.56 | 0.00 |
time (sec) |
N/A | 0.000 | 0.038 | 0.000 | 0.103 | 0.077 | 3.993 | 0.134 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | F | A | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 0 | 64 | 0 | 66 | 60 | 0 | 94 | 100 | 0 |
N.S. |
1 | 0.00 | 0.79 | 0.00 | 0.81 | 0.74 | 0.00 | 1.16 | 1.23 | 0.00 |
time (sec) |
N/A | 0.000 | 0.045 | 0.000 | 0.112 | 0.077 | 0.000 | 0.138 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | F | A | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 0 | 78 | 0 | 101 | 70 | 0 | 141 | 130 | 0 |
N.S. |
1 | 0.00 | 0.64 | 0.00 | 0.83 | 0.58 | 0.00 | 1.17 | 1.07 | 0.00 |
time (sec) |
N/A | 0.000 | 0.063 | 0.000 | 0.113 | 0.078 | 0.000 | 0.138 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | F | A | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 0 | 87 | 0 | 140 | 80 | 0 | 186 | 160 | 0 |
N.S. |
1 | 0.00 | 0.54 | 0.00 | 0.87 | 0.50 | 0.00 | 1.16 | 0.99 | 0.00 |
time (sec) |
N/A | 0.000 | 0.069 | 0.000 | 0.113 | 0.080 | 0.000 | 0.145 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 0 | 115 | 0 | 206 | 154 | 333 | 225 | 318 | 0 |
N.S. |
1 | 0.00 | 0.52 | 0.00 | 0.92 | 0.69 | 1.49 | 1.01 | 1.43 | 0.00 |
time (sec) |
N/A | 0.000 | 0.133 | 0.000 | 0.043 | 0.103 | 15.285 | 0.123 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 0 | 91 | 0 | 161 | 116 | 250 | 175 | 236 | 0 |
N.S. |
1 | 0.00 | 0.54 | 0.00 | 0.96 | 0.69 | 1.49 | 1.04 | 1.40 | 0.00 |
time (sec) |
N/A | 0.000 | 0.093 | 0.000 | 0.047 | 0.090 | 4.995 | 0.124 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 0 | 64 | 0 | 112 | 75 | 167 | 125 | 154 | 0 |
N.S. |
1 | 0.00 | 0.58 | 0.00 | 1.01 | 0.68 | 1.50 | 1.13 | 1.39 | 0.00 |
time (sec) |
N/A | 0.000 | 0.075 | 0.000 | 0.038 | 0.094 | 1.599 | 0.125 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 0 | 37 | 0 | 60 | 37 | 78 | 76 | 74 | 0 |
N.S. |
1 | 0.00 | 0.70 | 0.00 | 1.13 | 0.70 | 1.47 | 1.43 | 1.40 | 0.00 |
time (sec) |
N/A | 0.000 | 0.019 | 0.000 | 0.034 | 0.087 | 0.571 | 0.120 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 0 | 99 | 0 | 0 | 0 | 0 | 0 | 76 | 0 |
N.S. |
1 | 0.00 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.000 | 0.092 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 0 | 260 | 0 | 0 | 0 | 0 | 0 | 103 | 0 |
N.S. |
1 | 0.00 | 1.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.000 | 0.162 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 0 | 347 | 0 | 0 | 0 | 0 | 0 | 123 | 0 |
N.S. |
1 | 0.00 | 1.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.000 | 0.236 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 383 | 0 | 548 | 0 | 0 | 0 | 0 | 0 | 77 | 0 |
N.S. |
1 | 0.00 | 1.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.000 | 2.746 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 0 | 373 | 0 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.00 | 2.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.000 | 0.564 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 0 | 59 | 0 | 0 | 142 | 0 | 0 | 185 | 0 |
N.S. |
1 | 0.00 | 0.98 | 0.00 | 0.00 | 2.37 | 0.00 | 0.00 | 3.08 | 0.00 |
time (sec) |
N/A | 0.000 | 0.139 | 0.000 | 0.000 | 0.098 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 0 | 81 | 0 | 0 | 219 | 0 | 0 | 307 | 0 |
N.S. |
1 | 0.00 | 0.68 | 0.00 | 0.00 | 1.84 | 0.00 | 0.00 | 2.58 | 0.00 |
time (sec) |
N/A | 0.000 | 0.188 | 0.000 | 0.000 | 0.102 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 0 | 107 | 0 | 0 | 297 | 0 | 0 | 426 | 0 |
N.S. |
1 | 0.00 | 0.59 | 0.00 | 0.00 | 1.63 | 0.00 | 0.00 | 2.34 | 0.00 |
time (sec) |
N/A | 0.000 | 0.224 | 0.000 | 0.000 | 0.101 | 0.000 | 0.000 | 0.293 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 0 | 130 | 0 | 0 | 373 | 0 | 0 | 536 | 0 |
N.S. |
1 | 0.00 | 0.53 | 0.00 | 0.00 | 1.52 | 0.00 | 0.00 | 2.19 | 0.00 |
time (sec) |
N/A | 0.000 | 0.255 | 0.000 | 0.000 | 0.112 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 0 | 117 | 0 | 219 | 156 | 0 | 314 | 207 | 0 |
N.S. |
1 | 0.00 | 0.50 | 0.00 | 0.93 | 0.66 | 0.00 | 1.34 | 0.88 | 0.00 |
time (sec) |
N/A | 0.000 | 0.154 | 0.000 | 0.128 | 0.081 | 0.000 | 0.127 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 0 | 93 | 0 | 171 | 118 | 0 | 230 | 153 | 0 |
N.S. |
1 | 0.00 | 0.53 | 0.00 | 0.97 | 0.67 | 0.00 | 1.30 | 0.86 | 0.00 |
time (sec) |
N/A | 0.000 | 0.118 | 0.000 | 0.116 | 0.105 | 0.000 | 0.123 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 0 | 66 | 0 | 119 | 77 | 0 | 134 | 99 | 0 |
N.S. |
1 | 0.00 | 0.56 | 0.00 | 1.02 | 0.66 | 0.00 | 1.15 | 0.85 | 0.00 |
time (sec) |
N/A | 0.000 | 0.089 | 0.000 | 0.113 | 0.113 | 0.000 | 0.122 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | F | A | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 0 | 40 | 0 | 66 | 40 | 0 | 83 | 50 | 0 |
N.S. |
1 | 0.00 | 0.70 | 0.00 | 1.16 | 0.70 | 0.00 | 1.46 | 0.88 | 0.00 |
time (sec) |
N/A | 0.000 | 0.021 | 0.000 | 0.134 | 0.092 | 0.000 | 0.122 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 0 | 104 | 0 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 0.00 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.000 | 0.108 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 0 | 273 | 0 | 0 | 0 | 0 | 0 | 73 | 0 |
N.S. |
1 | 0.00 | 1.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.000 | 0.185 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 226 | 0 | 364 | 0 | 0 | 0 | 0 | 0 | 92 | 0 |
N.S. |
1 | 0.00 | 1.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.000 | 0.287 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 568 | 0 | 477 | 0 | 0 | 0 | 0 | 0 | 70 | 0 |
N.S. |
1 | 0.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.000 | 1.589 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 0 | 378 | 0 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 0.00 | 1.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.000 | 0.490 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 0 | 61 | 0 | 63 | 139 | 0 | 0 | 90 | 0 |
N.S. |
1 | 0.00 | 0.98 | 0.00 | 1.02 | 2.24 | 0.00 | 0.00 | 1.45 | 0.00 |
time (sec) |
N/A | 0.000 | 0.145 | 0.000 | 0.119 | 0.114 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 0 | 84 | 0 | 0 | 214 | 0 | 0 | 188 | 0 |
N.S. |
1 | 0.00 | 0.68 | 0.00 | 0.00 | 1.73 | 0.00 | 0.00 | 1.52 | 0.00 |
time (sec) |
N/A | 0.000 | 0.215 | 0.000 | 0.000 | 0.095 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 0 | 108 | 0 | 0 | 292 | 0 | 0 | 293 | 0 |
N.S. |
1 | 0.00 | 0.57 | 0.00 | 0.00 | 1.54 | 0.00 | 0.00 | 1.54 | 0.00 |
time (sec) |
N/A | 0.000 | 0.267 | 0.000 | 0.000 | 0.107 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 0 | 132 | 0 | 0 | 368 | 0 | 0 | 395 | 0 |
N.S. |
1 | 0.00 | 0.52 | 0.00 | 0.00 | 1.44 | 0.00 | 0.00 | 1.54 | 0.00 |
time (sec) |
N/A | 0.000 | 0.349 | 0.000 | 0.000 | 0.129 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 0 | 139 | 0 | 227 | 182 | 360 | 253 | 347 | 0 |
N.S. |
1 | 0.00 | 0.59 | 0.00 | 0.96 | 0.77 | 1.53 | 1.07 | 1.47 | 0.00 |
time (sec) |
N/A | 0.000 | 0.174 | 0.000 | 0.042 | 0.087 | 16.288 | 0.128 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 0 | 106 | 0 | 173 | 132 | 267 | 191 | 254 | 0 |
N.S. |
1 | 0.00 | 0.61 | 0.00 | 0.99 | 0.75 | 1.53 | 1.09 | 1.45 | 0.00 |
time (sec) |
N/A | 0.000 | 0.111 | 0.000 | 0.042 | 0.085 | 5.423 | 0.124 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 0 | 69 | 0 | 115 | 80 | 173 | 129 | 161 | 0 |
N.S. |
1 | 0.00 | 0.61 | 0.00 | 1.02 | 0.71 | 1.53 | 1.14 | 1.42 | 0.00 |
time (sec) |
N/A | 0.000 | 0.078 | 0.000 | 0.040 | 0.100 | 1.692 | 0.121 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 0 | 37 | 0 | 60 | 37 | 80 | 65 | 76 | 0 |
N.S. |
1 | 0.00 | 0.70 | 0.00 | 1.13 | 0.70 | 1.51 | 1.23 | 1.43 | 0.00 |
time (sec) |
N/A | 0.000 | 0.022 | 0.000 | 0.038 | 0.077 | 0.531 | 0.117 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 0 | 120 | 0 | 0 | 0 | 0 | 0 | 92 | 0 |
N.S. |
1 | 0.00 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.000 | 0.114 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 0 | 310 | 0 | 0 | 0 | 0 | 0 | 122 | 0 |
N.S. |
1 | 0.00 | 1.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.000 | 0.211 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 0 | 412 | 0 | 0 | 0 | 0 | 0 | 145 | 0 |
N.S. |
1 | 0.00 | 1.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.000 | 0.305 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 406 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 80 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | F | B | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 0 | 81 | 0 | 0 | 139 | 0 | 152 | 195 | 0 |
N.S. |
1 | 0.00 | 1.16 | 0.00 | 0.00 | 1.99 | 0.00 | 2.17 | 2.79 | 0.00 |
time (sec) |
N/A | 0.000 | 0.147 | 0.000 | 0.000 | 0.088 | 0.000 | 0.455 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | F | B | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 0 | 111 | 0 | 0 | 229 | 0 | 263 | 322 | 0 |
N.S. |
1 | 0.00 | 0.80 | 0.00 | 0.00 | 1.65 | 0.00 | 1.89 | 2.32 | 0.00 |
time (sec) |
N/A | 0.000 | 0.222 | 0.000 | 0.000 | 0.119 | 0.000 | 0.700 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | F | B | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 0 | 147 | 0 | 0 | 328 | 0 | 383 | 448 | 0 |
N.S. |
1 | 0.00 | 0.71 | 0.00 | 0.00 | 1.58 | 0.00 | 1.84 | 2.15 | 0.00 |
time (sec) |
N/A | 0.000 | 0.236 | 0.000 | 0.000 | 0.118 | 0.000 | 0.983 | 0.185 | 0.000 |