Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | A | A | F | A | B | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 269 | 196 | 374 | 0 | 284 | 357 | 0 | 428 | 323 | 299 |
N.S. |
1 | 0.73 | 1.39 | 0.00 | 1.06 | 1.33 | 0.00 | 1.59 | 1.20 | 1.11 |
time (sec) |
N/A | 0.865 | 0.391 | 0.000 | 0.050 | 0.107 | 0.000 | 0.154 | 0.158 | 25.496 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | A | A | F(-1) | B | B | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 479 | 306 | 551 | 0 | 387 | 597 | 0 | 877 | 518 | 439 |
N.S. |
1 | 0.64 | 1.15 | 0.00 | 0.81 | 1.25 | 0.00 | 1.83 | 1.08 | 0.92 |
time (sec) |
N/A | 0.976 | 0.594 | 0.000 | 0.056 | 0.117 | 0.000 | 0.169 | 0.163 | 27.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 759 | 1374 | 0 | 0 | 0 | 0 | 0 | 0 | 1132 | 0 |
N.S. |
1 | 1.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.49 | 0.00 |
time (sec) |
N/A | 10.850 | 0.000 | 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 | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 436 | 391 | 0 | 0 | 0 | 0 | 0 | 0 | 664 | 0 |
N.S. |
1 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.52 | 0.00 |
time (sec) |
N/A | 3.379 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 128 | 0 | 0 | 0 | 0 | 0 | 0 | 102 | 0 |
N.S. |
1 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.997 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 438 | 444 | 666 | 0 | 640 | 814 | 0 | 846 | 700 | 570 |
N.S. |
1 | 1.01 | 1.52 | 0.00 | 1.46 | 1.86 | 0.00 | 1.93 | 1.60 | 1.30 |
time (sec) |
N/A | 1.237 | 0.839 | 0.000 | 0.092 | 0.159 | 0.000 | 0.216 | 0.160 | 25.579 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 907 | 913 | 962 | 0 | 864 | 1404 | 0 | 1747 | 1174 | 992 |
N.S. |
1 | 1.01 | 1.06 | 0.00 | 0.95 | 1.55 | 0.00 | 1.93 | 1.29 | 1.09 |
time (sec) |
N/A | 2.274 | 1.443 | 0.000 | 0.122 | 0.138 | 0.000 | 0.230 | 0.170 | 35.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 135 | 137 | 0 | 98 | 160 | 0 | 105 | 140 | 112 |
N.S. |
1 | 0.94 | 0.96 | 0.00 | 0.69 | 1.12 | 0.00 | 0.73 | 0.98 | 0.78 |
time (sec) |
N/A | 0.530 | 0.126 | 0.000 | 0.055 | 0.099 | 0.000 | 0.185 | 0.153 | 25.588 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 111 | 65 | 0 | 0 | 399 | 0 | 103 | 114 | 0 |
N.S. |
1 | 0.92 | 0.54 | 0.00 | 0.00 | 3.30 | 0.00 | 0.85 | 0.94 | 0.00 |
time (sec) |
N/A | 0.468 | 0.019 | 0.000 | 0.000 | 0.140 | 0.000 | 0.197 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 91 | 93 | 0 | 63 | 113 | 0 | 69 | 100 | 73 |
N.S. |
1 | 0.97 | 0.99 | 0.00 | 0.67 | 1.20 | 0.00 | 0.73 | 1.06 | 0.78 |
time (sec) |
N/A | 0.442 | 0.029 | 0.000 | 0.054 | 0.099 | 0.000 | 0.192 | 0.156 | 25.446 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 53 | 154 | 0 | 279 | 61 | 60 | 68 | 51 |
N.S. |
1 | 1.00 | 0.82 | 2.37 | 0.00 | 4.29 | 0.94 | 0.92 | 1.05 | 0.78 |
time (sec) |
N/A | 0.339 | 0.017 | 1.154 | 0.000 | 0.132 | 13.836 | 0.155 | 0.170 | 25.370 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 53 | 55 | 0 | 127 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 0.96 | 1.00 | 0.00 | 2.31 | 0.00 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.452 | 0.014 | 0.000 | 0.397 | 0.000 | 0.000 | 0.000 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 86 | 80 | 0 | 0 | 235 | 0 | 78 | 80 | 0 |
N.S. |
1 | 1.12 | 1.04 | 0.00 | 0.00 | 3.05 | 0.00 | 1.01 | 1.04 | 0.00 |
time (sec) |
N/A | 0.401 | 0.054 | 0.000 | 0.000 | 0.110 | 0.000 | 0.194 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 91 | 94 | 0 | 88 | 84 | 0 | 105 | 97 | 74 |
N.S. |
1 | 1.02 | 1.06 | 0.00 | 0.99 | 0.94 | 0.00 | 1.18 | 1.09 | 0.83 |
time (sec) |
N/A | 0.452 | 0.039 | 0.000 | 0.043 | 0.088 | 0.000 | 0.197 | 0.160 | 25.320 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 145 | 129 | 0 | 0 | 339 | 0 | 111 | 123 | 0 |
N.S. |
1 | 1.10 | 0.98 | 0.00 | 0.00 | 2.57 | 0.00 | 0.84 | 0.93 | 0.00 |
time (sec) |
N/A | 0.463 | 0.180 | 0.000 | 0.000 | 0.157 | 0.000 | 0.198 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 412 | 568 | 830 | 0 | 0 | 0 | 0 | 0 | 471 | 0 |
N.S. |
1 | 1.38 | 2.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 3.860 | 0.755 | 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 | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 232 | 542 | 0 | 0 | 0 | 0 | 0 | 276 | 0 |
N.S. |
1 | 0.97 | 2.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.15 | 0.00 |
time (sec) |
N/A | 1.623 | 0.466 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 92 | 1701 | 0 | 0 | 0 | 0 | 0 | 67 | 0 |
N.S. |
1 | 0.97 | 17.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.750 | 0.544 | 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 | A | C | F | A | A | F(-1) | F | B | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 198 | 691 | 0 | 298 | 307 | 0 | 0 | 329 | 302 |
N.S. |
1 | 0.72 | 2.50 | 0.00 | 1.08 | 1.11 | 0.00 | 0.00 | 1.19 | 1.09 |
time (sec) |
N/A | 0.860 | 0.629 | 0.000 | 0.066 | 0.109 | 0.000 | 0.000 | 0.162 | 25.554 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | A | A | F(-1) | F | B | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 482 | 308 | 988 | 0 | 397 | 513 | 0 | 0 | 524 | 440 |
N.S. |
1 | 0.64 | 2.05 | 0.00 | 0.82 | 1.06 | 0.00 | 0.00 | 1.09 | 0.91 |
time (sec) |
N/A | 0.965 | 0.912 | 0.000 | 0.067 | 0.095 | 0.000 | 0.000 | 0.163 | 27.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 490 | 441 | 735 | 0 | 0 | 0 | 0 | 0 | 429 | 0 |
N.S. |
1 | 0.90 | 1.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 1.507 | 2.406 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 309 | 295 | 523 | 0 | 0 | 0 | 0 | 0 | 228 | 0 |
N.S. |
1 | 0.95 | 1.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.967 | 1.157 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 361 | 347 | 609 | 0 | 0 | 0 | 0 | 0 | 160 | 0 |
N.S. |
1 | 0.96 | 1.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 1.261 | 1.627 | 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 | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 773 | 1384 | 5557 | 0 | 0 | 0 | 0 | 0 | 971 | 0 |
N.S. |
1 | 1.79 | 7.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.26 | 0.00 |
time (sec) |
N/A | 10.888 | 30.498 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 451 | 373 | 0 | 0 | 0 | 0 | 0 | 0 | 454 | 0 |
N.S. |
1 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 3.311 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 130 | 0 | 0 | 0 | 0 | 0 | 0 | 102 | 0 |
N.S. |
1 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.924 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 449 | 446 | 692 | 0 | 684 | 725 | 0 | 0 | 712 | 578 |
N.S. |
1 | 0.99 | 1.54 | 0.00 | 1.52 | 1.61 | 0.00 | 0.00 | 1.59 | 1.29 |
time (sec) |
N/A | 1.252 | 1.357 | 0.000 | 0.081 | 0.098 | 0.000 | 0.000 | 0.172 | 25.626 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | B | N/A | F(-2) | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 5975 | 22 | 0 | 93 | 0 | 24 | 935 | 24 |
N.S. |
1 | 1.00 | 248.96 | 0.92 | 0.00 | 3.88 | 0.00 | 1.00 | 38.96 | 1.00 |
time (sec) |
N/A | 3.152 | 29.295 | 0.175 | 0.000 | 0.096 | 0.000 | 0.524 | 0.203 | 25.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | 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 | 0 | 80 | 0 | 20 | 451 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.00 | 4.00 | 0.00 | 1.00 | 22.55 | 1.00 |
time (sec) |
N/A | 1.126 | 6.265 | 0.129 | 0.000 | 0.115 | 0.000 | 0.224 | 0.196 | 25.209 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | B | N/A | F(-2) | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 5502 | 22 | 0 | 84 | 0 | 24 | 245 | 24 |
N.S. |
1 | 1.00 | 229.25 | 0.92 | 0.00 | 3.50 | 0.00 | 1.00 | 10.21 | 1.00 |
time (sec) |
N/A | 2.236 | 19.560 | 0.175 | 0.000 | 0.081 | 0.000 | 0.529 | 0.178 | 25.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | B | N/A | F(-2) | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 6328 | 22 | 0 | 84 | 0 | 24 | 302 | 24 |
N.S. |
1 | 1.00 | 263.67 | 0.92 | 0.00 | 3.50 | 0.00 | 1.00 | 12.58 | 1.00 |
time (sec) |
N/A | 4.666 | 27.193 | 0.175 | 0.000 | 0.086 | 0.000 | 0.543 | 0.181 | 22.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 730 | 741 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.873 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.293 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 551 | 552 | 0 | 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 | 0.00 |
time (sec) |
N/A | 2.070 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.236 | 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 | 360 | 364 | 229 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.431 | 6.137 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 178 | 130 | 0 | 0 | 0 | 0 | 0 | 1228 | 0 |
N.S. |
1 | 1.02 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 7.06 | 0.00 |
time (sec) |
N/A | 0.803 | 0.064 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 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 | 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 | 23 | 0 | 22 | 224 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.05 | 0.00 | 1.00 | 10.18 | 1.00 |
time (sec) |
N/A | 0.367 | 0.173 | 0.093 | 0.140 | 0.094 | 0.000 | 0.155 | 0.307 | 25.749 |
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 | 23 | 0 | 22 | 188 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.05 | 0.00 | 1.00 | 8.55 | 1.00 |
time (sec) |
N/A | 0.376 | 0.159 | 0.089 | 0.148 | 0.101 | 0.000 | 0.166 | 0.190 | 25.469 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 907 | 896 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.042 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.345 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 677 | 679 | 0 | 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 | 0.00 |
time (sec) |
N/A | 2.200 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 445 | 442 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.532 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.235 | 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 | 213 | 216 | 182 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.865 | 0.075 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 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 | 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 | 33 | 0 | 24 | 292 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.38 | 0.00 | 1.00 | 12.17 | 1.00 |
time (sec) |
N/A | 0.388 | 0.178 | 0.095 | 0.152 | 0.086 | 0.000 | 1.154 | 0.181 | 25.492 |
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 | 33 | 0 | 24 | 257 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.38 | 0.00 | 1.00 | 10.71 | 1.00 |
time (sec) |
N/A | 0.384 | 0.179 | 0.095 | 0.154 | 0.090 | 0.000 | 1.185 | 0.207 | 25.598 |
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 | 26 | 0 | 20 | 25 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.30 | 0.00 | 1.00 | 1.25 | 1.00 |
time (sec) |
N/A | 0.371 | 1.261 | 0.142 | 0.168 | 0.111 | 0.000 | 0.195 | 0.163 | 25.468 |
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 | 18 | 18 | 20 | 16 | 18 | 24 | 0 | 18 | 23 | 18 |
N.S. |
1 | 1.00 | 1.11 | 0.89 | 1.00 | 1.33 | 0.00 | 1.00 | 1.28 | 1.00 |
time (sec) |
N/A | 0.340 | 0.051 | 0.096 | 0.182 | 0.093 | 0.000 | 0.155 | 0.157 | 25.383 |
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 | 28 | 0 | 22 | 27 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.27 | 0.00 | 1.00 | 1.23 | 1.00 |
time (sec) |
N/A | 0.379 | 0.481 | 0.017 | 0.181 | 0.086 | 0.000 | 0.185 | 0.160 | 25.392 |
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 | 175 | 178 | 131 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.821 | 0.331 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 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 | 552 | 552 | 325 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.067 | 1.318 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.270 | 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 | 926 | 929 | 525 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.344 | 5.952 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.512 | 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 | 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 | 35 | 0 | 22 | 34 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.59 | 0.00 | 1.00 | 1.55 | 1.00 |
time (sec) |
N/A | 0.374 | 0.388 | 0.189 | 0.175 | 0.119 | 0.000 | 1.825 | 0.155 | 25.779 |
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 | 33 | 0 | 20 | 32 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.65 | 0.00 | 1.00 | 1.60 | 1.00 |
time (sec) |
N/A | 0.348 | 0.053 | 0.098 | 0.177 | 0.097 | 0.000 | 1.041 | 0.154 | 25.644 |
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 | 37 | 0 | 24 | 36 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.54 | 0.00 | 1.00 | 1.50 | 1.00 |
time (sec) |
N/A | 0.397 | 0.242 | 0.100 | 0.175 | 0.084 | 0.000 | 1.873 | 0.185 | 25.532 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 216 | 0 | 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 | 0.00 |
time (sec) |
N/A | 0.900 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 676 | 679 | 0 | 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 | 0.00 |
time (sec) |
N/A | 2.283 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.350 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1141 | 1143 | 0 | 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 | 0.00 |
time (sec) |
N/A | 3.632 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.541 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1121 | 1115 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 4.041 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.480 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 831 | 836 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.444 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 553 | 552 | 0 | 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 | 0.00 |
time (sec) |
N/A | 2.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 269 | 174 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.127 | 0.036 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 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 | 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 | 23 | 0 | 22 | 130 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.05 | 0.00 | 1.00 | 5.91 | 1.00 |
time (sec) |
N/A | 0.377 | 0.159 | 0.092 | 0.144 | 0.091 | 0.000 | 0.160 | 0.264 | 25.331 |
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 | 23 | 0 | 22 | 532 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.05 | 0.00 | 1.00 | 24.18 | 1.00 |
time (sec) |
N/A | 0.373 | 0.155 | 0.093 | 0.148 | 0.097 | 0.000 | 0.165 | 0.197 | 25.431 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1363 | 1375 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 4.414 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.771 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1035 | 1039 | 0 | 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 | 0.00 |
time (sec) |
N/A | 3.352 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.489 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 673 | 679 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.231 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.326 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 338 | 344 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.253 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.237 | 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 | 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 | 35 | 0 | 24 | 193 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.46 | 0.00 | 1.00 | 8.04 | 1.00 |
time (sec) |
N/A | 0.381 | 0.190 | 0.093 | 0.165 | 0.113 | 0.000 | 1.728 | 0.285 | 25.506 |
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 | 35 | 0 | 24 | 773 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.46 | 0.00 | 1.00 | 32.21 | 1.00 |
time (sec) |
N/A | 0.383 | 0.180 | 0.092 | 0.159 | 0.120 | 0.000 | 1.646 | 0.239 | 25.320 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 557 | 554 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.127 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 271 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.114 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.220 | 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 | 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 | 23 | 0 | 22 | 133 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.05 | 0.00 | 1.00 | 6.05 | 1.00 |
time (sec) |
N/A | 0.385 | 0.197 | 0.094 | 0.167 | 0.096 | 0.000 | 0.174 | 0.228 | 25.368 |
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 | 23 | 0 | 22 | 533 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.05 | 0.00 | 1.00 | 24.23 | 1.00 |
time (sec) |
N/A | 0.385 | 0.211 | 0.090 | 0.156 | 0.101 | 0.000 | 0.178 | 0.604 | 25.373 |
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 | 23 | 0 | 22 | 1475 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.05 | 0.00 | 1.00 | 67.05 | 1.00 |
time (sec) |
N/A | 0.388 | 0.201 | 0.092 | 0.157 | 0.119 | 0.000 | 0.184 | 0.326 | 25.216 |
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 | 18 | 18 | 20 | 16 | 18 | 19 | 0 | 18 | 578 | 18 |
N.S. |
1 | 1.00 | 1.11 | 0.89 | 1.00 | 1.06 | 0.00 | 1.00 | 32.11 | 1.00 |
time (sec) |
N/A | 0.356 | 0.045 | 0.092 | 0.156 | 0.118 | 0.000 | 0.154 | 0.224 | 25.236 |
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 | 23 | 0 | 22 | 100 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.05 | 0.00 | 1.00 | 4.55 | 1.00 |
time (sec) |
N/A | 0.377 | 0.170 | 0.092 | 0.150 | 0.106 | 0.000 | 0.172 | 0.371 | 25.235 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 678 | 681 | 0 | 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 | 0.00 |
time (sec) |
N/A | 2.202 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.379 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 350 | 346 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.211 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.255 | 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 | 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 | 35 | 0 | 24 | 193 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.46 | 0.00 | 1.00 | 8.04 | 1.00 |
time (sec) |
N/A | 0.389 | 0.248 | 0.095 | 0.155 | 0.106 | 0.000 | 1.978 | 0.187 | 25.396 |
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 | 35 | 0 | 24 | 773 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.46 | 0.00 | 1.00 | 32.21 | 1.00 |
time (sec) |
N/A | 0.396 | 0.323 | 0.093 | 0.158 | 0.097 | 0.000 | 1.956 | 0.730 | 25.500 |
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 | 35 | 0 | 24 | 2087 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.46 | 0.00 | 1.00 | 86.96 | 1.00 |
time (sec) |
N/A | 0.398 | 0.241 | 0.092 | 0.154 | 0.149 | 0.000 | 1.957 | 0.437 | 25.350 |
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 | 31 | 0 | 20 | 830 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.55 | 0.00 | 1.00 | 41.50 | 1.00 |
time (sec) |
N/A | 0.349 | 0.054 | 0.092 | 0.152 | 0.146 | 0.000 | 1.099 | 0.294 | 25.219 |
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 | 35 | 0 | 24 | 148 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.46 | 0.00 | 1.00 | 6.17 | 1.00 |
time (sec) |
N/A | 0.389 | 0.200 | 0.091 | 0.152 | 0.118 | 0.000 | 1.965 | 0.450 | 25.341 |
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 | 26 | 0 | 20 | 25 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.30 | 0.00 | 1.00 | 1.25 | 1.00 |
time (sec) |
N/A | 0.362 | 1.628 | 0.144 | 0.168 | 0.125 | 0.000 | 0.188 | 0.184 | 25.770 |
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 | 18 | 18 | 20 | 16 | 18 | 24 | 0 | 18 | 23 | 18 |
N.S. |
1 | 1.00 | 1.11 | 0.89 | 1.00 | 1.33 | 0.00 | 1.00 | 1.28 | 1.00 |
time (sec) |
N/A | 0.344 | 0.052 | 0.095 | 0.166 | 0.097 | 0.000 | 0.158 | 0.165 | 25.476 |
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 | 28 | 0 | 22 | 27 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.27 | 0.00 | 1.00 | 1.23 | 1.00 |
time (sec) |
N/A | 0.375 | 0.407 | 0.100 | 0.175 | 0.137 | 0.000 | 0.196 | 0.170 | 25.413 |
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 | 267 | 269 | 175 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.050 | 0.433 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.229 | 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 | 554 | 552 | 325 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.008 | 1.326 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.365 | 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 | 832 | 836 | 502 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.921 | 1.431 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.466 | 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 | 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 | 38 | 0 | 22 | 37 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.73 | 0.00 | 1.00 | 1.68 | 1.00 |
time (sec) |
N/A | 0.370 | 0.401 | 0.189 | 0.174 | 0.111 | 0.000 | 1.095 | 0.169 | 25.434 |
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 | 36 | 0 | 20 | 35 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.80 | 0.00 | 1.00 | 1.75 | 1.00 |
time (sec) |
N/A | 0.367 | 0.058 | 0.098 | 0.173 | 0.123 | 0.000 | 0.628 | 0.186 | 25.416 |
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 | 40 | 0 | 24 | 39 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.67 | 0.00 | 1.00 | 1.62 | 1.00 |
time (sec) |
N/A | 0.395 | 0.249 | 0.099 | 0.178 | 0.131 | 0.000 | 1.080 | 0.161 | 25.331 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 342 | 344 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.277 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 673 | 679 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.206 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.561 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1036 | 1039 | 0 | 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 | 0.00 |
time (sec) |
N/A | 3.388 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.644 | 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 | 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 | 28 | 0 | 22 | 27 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.27 | 0.00 | 1.00 | 1.23 | 1.00 |
time (sec) |
N/A | 0.376 | 0.403 | 0.141 | 0.174 | 0.164 | 0.000 | 0.243 | 0.160 | 25.374 |
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 | 28 | 0 | 22 | 27 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.27 | 0.00 | 1.00 | 1.23 | 1.00 |
time (sec) |
N/A | 0.376 | 0.227 | 0.095 | 0.177 | 0.095 | 0.000 | 0.239 | 0.178 | 25.126 |
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 | 26 | 0 | 20 | 25 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.30 | 0.00 | 1.00 | 1.25 | 1.00 |
time (sec) |
N/A | 0.368 | 0.268 | 0.095 | 0.176 | 0.129 | 0.000 | 0.233 | 0.156 | 25.265 |
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 | 18 | 18 | 20 | 16 | 18 | 24 | 0 | 18 | 23 | 18 |
N.S. |
1 | 1.00 | 1.11 | 0.89 | 1.00 | 1.33 | 0.00 | 1.00 | 1.28 | 1.00 |
time (sec) |
N/A | 0.348 | 0.052 | 0.094 | 0.170 | 0.108 | 0.000 | 0.187 | 0.162 | 25.192 |
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 | 28 | 0 | 22 | 27 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.27 | 0.00 | 1.00 | 1.23 | 1.00 |
time (sec) |
N/A | 0.373 | 0.222 | 0.102 | 0.175 | 0.151 | 0.000 | 0.243 | 0.165 | 25.254 |
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 | 28 | 0 | 22 | 116 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.27 | 0.00 | 1.00 | 5.27 | 1.00 |
time (sec) |
N/A | 0.373 | 0.188 | 0.096 | 0.179 | 0.104 | 0.000 | 0.254 | 0.199 | 25.247 |
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 | 0.382 | 0.478 | 0.190 | 0.180 | 0.108 | 0.000 | 1.731 | 0.191 | 25.449 |