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 | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 235 | 3006 | 1415 | 0 | 1496 | 0 | 0 | 1060 | 0 |
N.S. |
1 | 1.03 | 13.13 | 6.18 | 0.00 | 6.53 | 0.00 | 0.00 | 4.63 | 0.00 |
time (sec) |
N/A | 1.070 | 6.258 | 0.831 | 0.000 | 0.122 | 0.000 | 0.000 | 0.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 180 | 570 | 761 | 0 | 1348 | 0 | 0 | 115 | 0 |
N.S. |
1 | 1.00 | 3.17 | 4.23 | 0.00 | 7.49 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.769 | 5.472 | 1.445 | 0.000 | 0.105 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 266 | 3176 | 2904 | 0 | 2050 | 0 | 0 | 607 | 0 |
N.S. |
1 | 1.06 | 12.70 | 11.62 | 0.00 | 8.20 | 0.00 | 0.00 | 2.43 | 0.00 |
time (sec) |
N/A | 1.156 | 6.442 | 2.821 | 0.000 | 0.133 | 0.000 | 0.000 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 378 | 393 | 5554 | 4014 | 0 | 3989 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 14.69 | 10.62 | 0.00 | 10.55 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.843 | 6.674 | 10.754 | 0.000 | 0.316 | 0.000 | 0.000 | 0.387 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 90 | 80 | 96 | 0 | 346 | 1110 | 136 | 25 | 1143 |
N.S. |
1 | 1.07 | 0.95 | 1.14 | 0.00 | 4.12 | 13.21 | 1.62 | 0.30 | 13.61 |
time (sec) |
N/A | 0.485 | 0.731 | 0.329 | 0.000 | 0.097 | 14.811 | 0.278 | 0.167 | 23.601 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 124 | 114 | 155 | 0 | 458 | 0 | 180 | 142 | 227 |
N.S. |
1 | 1.05 | 0.97 | 1.31 | 0.00 | 3.88 | 0.00 | 1.53 | 1.20 | 1.92 |
time (sec) |
N/A | 0.556 | 0.841 | 0.391 | 0.000 | 0.093 | 0.000 | 0.283 | 0.154 | 16.238 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 205 | 174 | 373 | 0 | 880 | 0 | 571 | 418 | 557 |
N.S. |
1 | 1.11 | 0.94 | 2.02 | 0.00 | 4.76 | 0.00 | 3.09 | 2.26 | 3.01 |
time (sec) |
N/A | 0.790 | 1.145 | 0.619 | 0.000 | 0.108 | 0.000 | 0.310 | 0.176 | 17.912 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 294 | 244 | 715 | 0 | 1411 | 0 | 1281 | 954 | 1085 |
N.S. |
1 | 1.14 | 0.95 | 2.77 | 0.00 | 5.47 | 0.00 | 4.97 | 3.70 | 4.21 |
time (sec) |
N/A | 1.095 | 2.411 | 1.003 | 0.000 | 0.147 | 0.000 | 0.361 | 0.172 | 18.857 |
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 | 131 | 131 | 145 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.351 | 0.447 | 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 | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 112 | 75 | 106 | 80 | 97 | 190 | 75 | 99 | 125 |
N.S. |
1 | 1.05 | 0.70 | 0.99 | 0.75 | 0.91 | 1.78 | 0.70 | 0.93 | 1.17 |
time (sec) |
N/A | 0.383 | 0.644 | 0.076 | 0.036 | 0.079 | 0.379 | 0.295 | 0.170 | 16.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 48 | 46 | 48 | 63 | 129 | 46 | 67 | 78 |
N.S. |
1 | 1.00 | 0.79 | 0.75 | 0.79 | 1.03 | 2.11 | 0.75 | 1.10 | 1.28 |
time (sec) |
N/A | 0.249 | 0.389 | 0.774 | 0.027 | 0.072 | 0.197 | 0.310 | 0.154 | 15.447 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 38 | 19 | 18 | 22 | 24 | 18 | 22 | 22 |
N.S. |
1 | 1.00 | 1.90 | 0.95 | 0.90 | 1.10 | 1.20 | 0.90 | 1.10 | 1.10 |
time (sec) |
N/A | 0.156 | 0.029 | 0.156 | 0.033 | 0.071 | 0.090 | 0.259 | 0.150 | 16.693 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 48 | 45 | 0 | 290 | 0 | 61 | 113 | 44 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.00 | 6.04 | 0.00 | 1.27 | 2.35 | 0.92 |
time (sec) |
N/A | 0.268 | 0.227 | 0.199 | 0.000 | 0.093 | 0.000 | 0.263 | 0.157 | 17.268 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 100 | 94 | 114 | 0 | 493 | 0 | 116 | 44 | 181 |
N.S. |
1 | 1.05 | 0.99 | 1.20 | 0.00 | 5.19 | 0.00 | 1.22 | 0.46 | 1.91 |
time (sec) |
N/A | 0.404 | 0.463 | 0.512 | 0.000 | 0.099 | 0.000 | 0.270 | 0.162 | 16.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 169 | 120 | 271 | 0 | 969 | 0 | 252 | 68 | 396 |
N.S. |
1 | 1.13 | 0.81 | 1.82 | 0.00 | 6.50 | 0.00 | 1.69 | 0.46 | 2.66 |
time (sec) |
N/A | 0.588 | 0.937 | 1.404 | 0.000 | 0.120 | 0.000 | 0.287 | 0.563 | 16.540 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 265 | 260 | 202 | 1138 | 0 | 0 | 0 | 0 | 100 | 0 |
N.S. |
1 | 0.98 | 0.76 | 4.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 1.226 | 1.823 | 1.470 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 208 | 167 | 844 | 0 | 0 | 0 | 0 | 56 | 0 |
N.S. |
1 | 0.98 | 0.79 | 3.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.922 | 1.468 | 0.625 | 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 | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 75 | 312 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 0.99 | 4.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.367 | 0.323 | 0.404 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 70 | 165 | 0 | 304 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 0.92 | 2.17 | 0.00 | 4.00 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.374 | 0.346 | 0.186 | 0.000 | 0.096 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 143 | 101 | 570 | 0 | 914 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.00 | 0.71 | 3.99 | 0.00 | 6.39 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.516 | 0.651 | 0.260 | 0.000 | 0.125 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 295 | 297 | 201 | 1554 | 0 | 1506 | 0 | 0 | 86 | 0 |
N.S. |
1 | 1.01 | 0.68 | 5.27 | 0.00 | 5.11 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 1.236 | 1.555 | 0.312 | 0.000 | 0.176 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 461 | 425 | 340 | 2282 | 0 | 3308 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.92 | 0.74 | 4.95 | 0.00 | 7.18 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 1.463 | 0.685 | 0.194 | 0.000 | 0.785 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 340 | 321 | 256 | 1782 | 0 | 2492 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.94 | 0.75 | 5.24 | 0.00 | 7.33 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.134 | 0.619 | 0.158 | 0.000 | 0.725 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 229 | 788 | 1284 | 0 | 1676 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.02 | 3.50 | 5.71 | 0.00 | 7.45 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.730 | 1.157 | 0.146 | 0.000 | 0.971 | 0.000 | 0.000 | 0.179 | 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 | 14 | 14 | 16 | 14 | 16 | 15 | 14 | 16 | 30 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.07 | 1.00 | 1.14 | 2.14 | 1.14 |
time (sec) |
N/A | 0.268 | 1.941 | 0.076 | 0.177 | 0.071 | 25.746 | 0.244 | 0.164 | 15.969 |
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 | 34 | 34 | 36 | 34 | 36 | 66 | 53 | 36 | 68 | 36 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 1.94 | 1.56 | 1.06 | 2.00 | 1.06 |
time (sec) |
N/A | 0.404 | 7.616 | 0.486 | 2.403 | 0.089 | 82.531 | 0.318 | 0.202 | 16.832 |
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 | 33 | 33 | 35 | 33 | 35 | 70 | 53 | 35 | 68 | 35 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 2.12 | 1.61 | 1.06 | 2.06 | 1.06 |
time (sec) |
N/A | 0.392 | 6.591 | 0.505 | 1.949 | 0.098 | 84.534 | 0.294 | 0.170 | 18.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 244 | 198 | 508 | 0 | 186 | 0 | 7347 | 49 | 0 |
N.S. |
1 | 1.39 | 1.13 | 2.90 | 0.00 | 1.06 | 0.00 | 41.98 | 0.28 | 0.00 |
time (sec) |
N/A | 0.941 | 1.461 | 2.806 | 0.000 | 0.150 | 0.000 | 0.783 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 181 | 142 | 349 | 0 | 142 | 0 | 4175 | 49 | 0 |
N.S. |
1 | 1.38 | 1.08 | 2.66 | 0.00 | 1.08 | 0.00 | 31.87 | 0.37 | 0.00 |
time (sec) |
N/A | 1.040 | 1.238 | 1.393 | 0.000 | 0.102 | 0.000 | 0.508 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 101 | 77 | 196 | 0 | 77 | 0 | 1033 | 49 | 0 |
N.S. |
1 | 1.26 | 0.96 | 2.45 | 0.00 | 0.96 | 0.00 | 12.91 | 0.61 | 0.00 |
time (sec) |
N/A | 0.520 | 1.273 | 1.141 | 0.000 | 0.101 | 0.000 | 0.436 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-2) | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 69 | 160 | 120 | 0 | 45 | 0 | 496 | 47 | 0 |
N.S. |
1 | 1.23 | 2.86 | 2.14 | 0.00 | 0.80 | 0.00 | 8.86 | 0.84 | 0.00 |
time (sec) |
N/A | 0.454 | 1.780 | 0.567 | 0.000 | 0.084 | 0.000 | 0.351 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 24 | 25 | 114 | 24 | 20 | 39 | 24 | 24 |
N.S. |
1 | 1.00 | 0.69 | 0.71 | 3.26 | 0.69 | 0.57 | 1.11 | 0.69 | 0.69 |
time (sec) |
N/A | 0.192 | 0.305 | 0.649 | 0.033 | 0.076 | 1.946 | 0.246 | 0.158 | 18.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 21 | 20 | 21 | 19 | 42 | 20 | 23 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.00 | 1.05 | 0.95 | 2.10 | 1.00 | 1.15 |
time (sec) |
N/A | 0.209 | 0.022 | 0.168 | 0.029 | 0.068 | 2.093 | 0.271 | 0.151 | 0.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 32 | 33 | 100 | 34 | 112 | 53 | 32 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.94 | 2.86 | 0.97 | 3.20 | 1.51 | 0.91 | 0.00 |
time (sec) |
N/A | 0.259 | 1.353 | 0.371 | 0.030 | 0.068 | 2.841 | 0.258 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 119 | 157 | 0 | 0 | 295 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.14 | 1.51 | 0.00 | 0.00 | 2.84 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.493 | 0.845 | 0.000 | 0.000 | 0.093 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 158 | 102 | 172 | 594 | 410 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.24 | 0.80 | 1.35 | 4.68 | 3.23 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.815 | 1.224 | 0.468 | 0.071 | 0.095 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 245 | 194 | 509 | 0 | 162 | 0 | 7279 | 49 | 0 |
N.S. |
1 | 1.39 | 1.10 | 2.89 | 0.00 | 0.92 | 0.00 | 41.36 | 0.28 | 0.00 |
time (sec) |
N/A | 0.964 | 1.001 | 2.314 | 0.000 | 0.110 | 0.000 | 0.707 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 179 | 136 | 367 | 0 | 135 | 0 | 3130 | 49 | 0 |
N.S. |
1 | 1.36 | 1.03 | 2.78 | 0.00 | 1.02 | 0.00 | 23.71 | 0.37 | 0.00 |
time (sec) |
N/A | 1.046 | 0.714 | 1.135 | 0.000 | 0.092 | 0.000 | 0.517 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 101 | 71 | 197 | 0 | 73 | 0 | 997 | 49 | 0 |
N.S. |
1 | 1.26 | 0.89 | 2.46 | 0.00 | 0.91 | 0.00 | 12.46 | 0.61 | 0.00 |
time (sec) |
N/A | 0.523 | 0.966 | 0.863 | 0.000 | 0.090 | 0.000 | 0.370 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-2) | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 67 | 181 | 119 | 0 | 43 | 0 | 366 | 47 | 0 |
N.S. |
1 | 1.20 | 3.23 | 2.12 | 0.00 | 0.77 | 0.00 | 6.54 | 0.84 | 0.00 |
time (sec) |
N/A | 0.443 | 1.659 | 0.460 | 0.000 | 0.074 | 0.000 | 0.339 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 22 | 23 | 114 | 23 | 20 | 32 | 22 | 22 |
N.S. |
1 | 1.00 | 0.65 | 0.68 | 3.35 | 0.68 | 0.59 | 0.94 | 0.65 | 0.65 |
time (sec) |
N/A | 0.192 | 0.212 | 0.544 | 0.035 | 0.074 | 2.202 | 0.263 | 0.202 | 0.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 20 | 19 | 22 | 20 | 40 | 19 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.00 | 1.16 | 1.05 | 2.11 | 1.00 | 1.16 |
time (sec) |
N/A | 0.220 | 0.016 | 0.191 | 0.031 | 0.068 | 2.236 | 0.247 | 0.155 | 0.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 31 | 32 | 100 | 36 | 109 | 52 | 31 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.97 | 3.03 | 1.09 | 3.30 | 1.58 | 0.94 | 0.00 |
time (sec) |
N/A | 0.257 | 0.942 | 0.369 | 0.033 | 0.069 | 2.551 | 0.270 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 126 | 176 | 0 | 0 | 290 | 0 | 0 | 1013 | 0 |
N.S. |
1 | 1.15 | 1.60 | 0.00 | 0.00 | 2.64 | 0.00 | 0.00 | 9.21 | 0.00 |
time (sec) |
N/A | 0.497 | 1.073 | 0.000 | 0.000 | 0.092 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 156 | 130 | 141 | 372 | 382 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.26 | 1.05 | 1.14 | 3.00 | 3.08 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.815 | 1.648 | 0.583 | 0.138 | 0.103 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 173 | 64 | 90 | 0 | 106 | 0 | 0 | 34 | 463 |
N.S. |
1 | 1.10 | 0.41 | 0.57 | 0.00 | 0.68 | 0.00 | 0.00 | 0.22 | 2.95 |
time (sec) |
N/A | 1.012 | 1.021 | 1.330 | 0.000 | 0.077 | 0.000 | 0.000 | 0.197 | 22.299 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 121 | 62 | 80 | 0 | 84 | 0 | 0 | 34 | 148 |
N.S. |
1 | 1.10 | 0.56 | 0.73 | 0.00 | 0.76 | 0.00 | 0.00 | 0.31 | 1.35 |
time (sec) |
N/A | 0.716 | 0.657 | 1.107 | 0.000 | 0.079 | 0.000 | 0.000 | 0.193 | 27.282 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 44 | 70 | 0 | 64 | 0 | 0 | 34 | 129 |
N.S. |
1 | 1.00 | 0.61 | 0.97 | 0.00 | 0.89 | 0.00 | 0.00 | 0.47 | 1.79 |
time (sec) |
N/A | 0.505 | 0.495 | 1.149 | 0.000 | 0.076 | 0.000 | 0.000 | 0.221 | 21.350 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 30 | 44 | 0 | 40 | 0 | 0 | 32 | 87 |
N.S. |
1 | 1.00 | 0.91 | 1.33 | 0.00 | 1.21 | 0.00 | 0.00 | 0.97 | 2.64 |
time (sec) |
N/A | 0.312 | 0.271 | 0.998 | 0.000 | 0.074 | 0.000 | 0.000 | 0.217 | 18.316 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 73 | 122 | 430 | 201 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.62 | 2.71 | 9.56 | 4.47 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.272 | 0.200 | 1.134 | 0.165 | 0.106 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 92 | 268 | 1049 | 351 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.10 | 3.19 | 12.49 | 4.18 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.460 | 0.414 | 1.203 | 0.239 | 0.115 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 134 | 105 | 427 | 1421 | 419 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.04 | 0.81 | 3.31 | 11.02 | 3.25 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.637 | 0.707 | 1.418 | 0.282 | 0.105 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 186 | 116 | 596 | 2333 | 481 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.06 | 0.66 | 3.39 | 13.26 | 2.73 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.836 | 1.057 | 1.756 | 0.585 | 0.119 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 228 | 85 | 101 | 0 | 132 | 0 | 9119 | 50 | 594 |
N.S. |
1 | 1.10 | 0.41 | 0.49 | 0.00 | 0.63 | 0.00 | 43.84 | 0.24 | 2.86 |
time (sec) |
N/A | 1.235 | 1.176 | 1.253 | 0.000 | 0.079 | 0.000 | 12.573 | 0.220 | 23.987 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 163 | 73 | 91 | 0 | 111 | 0 | 5862 | 50 | 479 |
N.S. |
1 | 1.10 | 0.49 | 0.61 | 0.00 | 0.75 | 0.00 | 39.61 | 0.34 | 3.24 |
time (sec) |
N/A | 0.893 | 0.701 | 1.172 | 0.000 | 0.080 | 0.000 | 8.671 | 0.219 | 23.546 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 115 | 59 | 81 | 0 | 88 | 0 | 3323 | 50 | 149 |
N.S. |
1 | 1.05 | 0.54 | 0.74 | 0.00 | 0.80 | 0.00 | 30.21 | 0.45 | 1.35 |
time (sec) |
N/A | 0.650 | 0.628 | 1.089 | 0.000 | 0.077 | 0.000 | 7.459 | 0.218 | 27.930 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 51 | 71 | 0 | 67 | 0 | 1285 | 48 | 158 |
N.S. |
1 | 1.00 | 0.68 | 0.95 | 0.00 | 0.89 | 0.00 | 17.13 | 0.64 | 2.11 |
time (sec) |
N/A | 0.425 | 0.396 | 1.084 | 0.000 | 0.079 | 0.000 | 6.118 | 0.242 | 21.853 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 86 | 224 | 1317 | 296 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.00 | 1.08 | 2.80 | 16.46 | 3.70 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.377 | 0.283 | 1.582 | 0.245 | 0.111 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 124 | 93 | 384 | 1058 | 369 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.44 | 1.08 | 4.47 | 12.30 | 4.29 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.638 | 0.571 | 1.354 | 0.252 | 0.108 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 137 | 105 | 558 | 0 | 437 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.03 | 0.79 | 4.20 | 0.00 | 3.29 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.723 | 0.975 | 1.633 | 0.000 | 0.114 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 189 | 117 | 740 | 0 | 503 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.04 | 0.64 | 4.07 | 0.00 | 2.76 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.904 | 1.141 | 2.016 | 0.000 | 0.114 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 189 | 112 | 435 | 0 | 380 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.08 | 0.64 | 2.49 | 0.00 | 2.17 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 1.148 | 1.611 | 1.655 | 0.000 | 0.108 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 136 | 89 | 355 | 0 | 294 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.05 | 0.69 | 2.75 | 0.00 | 2.28 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.786 | 0.979 | 1.600 | 0.000 | 0.105 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 67 | 439 | 0 | 245 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.00 | 0.76 | 4.99 | 0.00 | 2.78 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.563 | 0.702 | 1.098 | 0.000 | 0.100 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 64 | 208 | 0 | 146 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.00 | 1.16 | 3.78 | 0.00 | 2.65 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.323 | 0.370 | 1.041 | 0.000 | 0.104 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 96 | 259 | 1685 | 309 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 0.96 | 2.59 | 16.85 | 3.09 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.475 | 0.439 | 1.067 | 0.410 | 0.085 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 163 | 563 | 0 | 481 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.00 | 1.18 | 4.08 | 0.00 | 3.49 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.685 | 2.248 | 1.066 | 0.000 | 0.093 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 197 | 186 | 886 | 0 | 569 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.08 | 1.02 | 4.87 | 0.00 | 3.13 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 1.040 | 3.685 | 1.306 | 0.000 | 0.096 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 189 | 100 | 398 | 0 | 350 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.05 | 0.56 | 2.21 | 0.00 | 1.94 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 1.073 | 2.692 | 1.734 | 0.000 | 0.116 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 133 | 94 | 286 | 0 | 276 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.04 | 0.73 | 2.23 | 0.00 | 2.16 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.734 | 1.525 | 1.263 | 0.000 | 0.102 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 84 | 340 | 0 | 272 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.00 | 0.90 | 3.66 | 0.00 | 2.92 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.534 | 1.425 | 1.233 | 0.000 | 0.100 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 83 | 393 | 0 | 269 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.00 | 0.89 | 4.23 | 0.00 | 2.89 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.447 | 0.914 | 1.462 | 0.000 | 0.103 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 144 | 198 | 411 | 0 | 438 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.04 | 1.43 | 2.98 | 0.00 | 3.17 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.652 | 2.969 | 1.236 | 0.000 | 0.092 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 182 | 217 | 737 | 0 | 528 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.02 | 1.22 | 4.14 | 0.00 | 2.97 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.994 | 5.823 | 1.342 | 0.000 | 0.094 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 247 | 357 | 1072 | 0 | 616 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.06 | 1.53 | 4.58 | 0.00 | 2.63 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 1.400 | 7.288 | 1.644 | 0.000 | 0.095 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 121 | 0 | 29 | 0 | 0 | 18 | 14 |
N.S. |
1 | 1.00 | 1.00 | 7.56 | 0.00 | 1.81 | 0.00 | 0.00 | 1.12 | 0.88 |
time (sec) |
N/A | 0.274 | 0.041 | 0.239 | 0.000 | 0.081 | 0.000 | 0.000 | 0.153 | 16.738 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | B | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 55 | 80 | 396 | 0 | 120 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.80 | 1.16 | 5.74 | 0.00 | 1.74 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.597 | 1.043 | 0.406 | 0.000 | 0.086 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-1) | A | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 57 | 122 | 396 | 0 | 120 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.72 | 1.54 | 5.01 | 0.00 | 1.52 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.767 | 1.741 | 0.488 | 0.000 | 0.084 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-1) | A | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 65 | 92 | 653 | 0 | 136 | 0 | 0 | 39 | 0 |
N.S. |
1 | 0.68 | 0.97 | 6.87 | 0.00 | 1.43 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.795 | 4.097 | 0.845 | 0.000 | 0.088 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 31 | 30 | 59 | 138 | 85 | 45 | 63 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.00 | 1.97 | 4.60 | 2.83 | 1.50 | 2.10 |
time (sec) |
N/A | 0.262 | 5.331 | 0.129 | 0.027 | 0.108 | 20.706 | 0.805 | 0.176 | 18.874 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 938 | 137 | 24 | 122 | 129 | 164 | 94 | 185 |
N.S. |
1 | 1.00 | 36.08 | 5.27 | 0.92 | 4.69 | 4.96 | 6.31 | 3.62 | 7.12 |
time (sec) |
N/A | 0.235 | 12.186 | 0.413 | 0.037 | 0.092 | 2.628 | 0.392 | 0.153 | 16.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 152 | 24 | 92 | 100 | 321 | 70 | 100 |
N.S. |
1 | 1.00 | 1.00 | 5.85 | 0.92 | 3.54 | 3.85 | 12.35 | 2.69 | 3.85 |
time (sec) |
N/A | 0.235 | 5.953 | 61.833 | 0.038 | 0.081 | 1.096 | 0.418 | 0.151 | 17.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 67 | 57 | 24 | 61 | 73 | 51 | 47 | 61 |
N.S. |
1 | 1.00 | 2.58 | 2.19 | 0.92 | 2.35 | 2.81 | 1.96 | 1.81 | 2.35 |
time (sec) |
N/A | 0.221 | 0.048 | 7.270 | 0.031 | 0.077 | 0.439 | 0.268 | 0.149 | 16.915 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 29 | 23 | 22 | 33 | 63 | 42 | 22 | 133 |
N.S. |
1 | 1.00 | 1.32 | 1.05 | 1.00 | 1.50 | 2.86 | 1.91 | 1.00 | 6.05 |
time (sec) |
N/A | 0.237 | 2.980 | 1.204 | 0.039 | 0.098 | 4.038 | 0.206 | 0.192 | 17.399 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 27 | 25 | 24 | 29 | 49 | 108 | 24 | 47 |
N.S. |
1 | 1.00 | 1.12 | 1.04 | 1.00 | 1.21 | 2.04 | 4.50 | 1.00 | 1.96 |
time (sec) |
N/A | 0.240 | 1.506 | 3.738 | 0.025 | 0.073 | 12.331 | 0.334 | 0.149 | 16.414 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 29 | 25 | 24 | 63 | 80 | 37 | 48 | 291 |
N.S. |
1 | 1.00 | 1.12 | 0.96 | 0.92 | 2.42 | 3.08 | 1.42 | 1.85 | 11.19 |
time (sec) |
N/A | 0.238 | 3.765 | 20.707 | 0.056 | 0.079 | 26.498 | 0.209 | 0.147 | 19.768 |
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 | 18 | 18 | 20 | 18 | 20 | 20 | 15 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.83 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.209 | 0.050 | 0.026 | 0.136 | 0.063 | 0.462 | 0.136 | 0.163 | 16.664 |
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 | 18 | 18 | 20 | 18 | 20 | 20 | 15 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.83 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.212 | 0.055 | 0.025 | 0.137 | 0.061 | 0.523 | 0.140 | 0.159 | 16.854 |
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 | 20 | 20 | 22 | 20 | 22 | 22 | 17 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.85 | 1.10 | 1.10 | 1.10 |
time (sec) |
N/A | 0.217 | 0.081 | 0.043 | 0.110 | 0.067 | 0.388 | 0.227 | 0.158 | 16.958 |
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 | 20 | 20 | 22 | 20 | 22 | 22 | 17 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.85 | 1.10 | 1.10 | 1.10 |
time (sec) |
N/A | 0.218 | 0.090 | 0.044 | 0.139 | 0.067 | 3.451 | 0.134 | 0.158 | 16.489 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 13 | 12 | 15 | 17 | 13 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.25 | 1.42 | 1.08 | 1.00 | 1.00 |
time (sec) |
N/A | 0.182 | 0.027 | 0.195 | 0.028 | 0.079 | 0.094 | 0.133 | 0.160 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 21 | 20 | 23 | 63 | 20 | 24 | 20 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.00 | 1.15 | 3.15 | 1.00 | 1.20 | 1.00 |
time (sec) |
N/A | 0.187 | 0.021 | 1.178 | 0.067 | 0.077 | 0.568 | 0.126 | 0.152 | 16.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 5 | 5 | 16 | 6 | 5 | 36 | 0 | 14 | 20 | 5 |
N.S. |
1 | 1.00 | 3.20 | 1.20 | 1.00 | 7.20 | 0.00 | 2.80 | 4.00 | 1.00 |
time (sec) |
N/A | 0.185 | 0.038 | 0.126 | 0.110 | 0.077 | 0.000 | 0.116 | 0.158 | 15.885 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 5 | 5 | 5 | 6 | 5 | 20 | 5 | 5 | 5 | 5 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 1.00 | 4.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.195 | 2.879 | 0.142 | 0.029 | 0.071 | 0.162 | 0.122 | 0.186 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 33 | 21 | 23 | 17 | 73 | 34 | 17 | 27 | 22 |
N.S. |
1 | 1.18 | 0.75 | 0.82 | 0.61 | 2.61 | 1.21 | 0.61 | 0.96 | 0.79 |
time (sec) |
N/A | 0.245 | 1.501 | 0.425 | 0.033 | 0.071 | 0.604 | 0.132 | 0.163 | 16.293 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 21 | 20 | 168 | 54 | 20 | 15 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.77 | 6.46 | 2.08 | 0.77 | 0.58 | 0.77 |
time (sec) |
N/A | 0.253 | 3.818 | 5.064 | 0.037 | 0.089 | 3.005 | 0.141 | 0.195 | 16.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 40 | 137 | 40 | 103 | 39 | 46 | 39 | 41 | 39 |
N.S. |
1 | 1.11 | 3.81 | 1.11 | 2.86 | 1.08 | 1.28 | 1.08 | 1.14 | 1.08 |
time (sec) |
N/A | 0.272 | 0.275 | 229.003 | 0.030 | 0.090 | 1.027 | 0.129 | 0.152 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 8 | 7 | 22 | 7 | 7 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.78 | 2.44 | 0.78 | 0.78 | 0.78 | 0.78 |
time (sec) |
N/A | 0.195 | 1.916 | 0.146 | 0.027 | 0.071 | 0.148 | 0.142 | 0.154 | 16.909 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 29 | 24 | 18 | 17 | 17 | 26 | 17 | 20 | 17 |
N.S. |
1 | 0.94 | 0.77 | 0.58 | 0.55 | 0.55 | 0.84 | 0.55 | 0.65 | 0.55 |
time (sec) |
N/A | 0.214 | 0.088 | 0.208 | 0.036 | 0.068 | 0.155 | 0.135 | 0.155 | 0.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | B | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 162 | 0 | 18 | 29 | 0 | 7 | 28 | 0 |
N.S. |
1 | 1.00 | 18.00 | 0.00 | 2.00 | 3.22 | 0.00 | 0.78 | 3.11 | 0.00 |
time (sec) |
N/A | 0.245 | 1.888 | 0.000 | 0.128 | 0.114 | 0.000 | 0.131 | 0.162 | 0.000 |