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 | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 60 | 70 | 0 | 165 | 0 | 128 | 239 | 60 |
N.S. |
1 | 1.00 | 0.76 | 0.89 | 0.00 | 2.09 | 0.00 | 1.62 | 3.03 | 0.76 |
time (sec) |
N/A | 0.213 | 10.055 | 1.293 | 0.000 | 0.293 | 0.000 | 0.385 | 0.206 | 5.747 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 103 | 93 | 332 | 0 | 357 | 0 | 247 | 434 | 0 |
N.S. |
1 | 1.01 | 0.91 | 3.25 | 0.00 | 3.50 | 0.00 | 2.42 | 4.25 | 0.00 |
time (sec) |
N/A | 0.248 | 0.819 | 1.220 | 0.000 | 0.191 | 0.000 | 0.389 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 40 | 41 | 0 | 47 | 92 | 48 | 51 | 40 |
N.S. |
1 | 1.00 | 0.83 | 0.85 | 0.00 | 0.98 | 1.92 | 1.00 | 1.06 | 0.83 |
time (sec) |
N/A | 0.190 | 0.452 | 1.046 | 0.000 | 0.131 | 0.110 | 0.351 | 0.202 | 5.785 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 75 | 212 | 0 | 225 | 0 | 111 | 193 | 156 |
N.S. |
1 | 1.00 | 1.14 | 3.21 | 0.00 | 3.41 | 0.00 | 1.68 | 2.92 | 2.36 |
time (sec) |
N/A | 0.199 | 0.425 | 1.058 | 0.000 | 0.131 | 0.000 | 0.417 | 0.186 | 5.775 |
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 | 17 | 17 | 16 | 16 | 15 | 15 | 17 | 15 | 26 | 15 |
N.S. |
1 | 1.00 | 0.94 | 0.94 | 0.88 | 0.88 | 1.00 | 0.88 | 1.53 | 0.88 |
time (sec) |
N/A | 0.154 | 0.021 | 0.904 | 0.041 | 0.100 | 0.091 | 0.358 | 0.192 | 5.600 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 104 | 78 | 0 | 311 | 0 | 158 | 508 | 0 |
N.S. |
1 | 1.00 | 1.21 | 0.91 | 0.00 | 3.62 | 0.00 | 1.84 | 5.91 | 0.00 |
time (sec) |
N/A | 0.237 | 0.760 | 1.131 | 0.000 | 0.158 | 0.000 | 0.364 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 463 | 68 | 0 | 155 | 0 | 266 | 227 | 188 |
N.S. |
1 | 1.00 | 6.09 | 0.89 | 0.00 | 2.04 | 0.00 | 3.50 | 2.99 | 2.47 |
time (sec) |
N/A | 0.212 | 3.055 | 1.224 | 0.000 | 0.231 | 0.000 | 0.380 | 0.187 | 5.887 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 143 | 60 | 115 | 0 | 702 | 0 | 432 | 1330 | 0 |
N.S. |
1 | 1.08 | 0.45 | 0.87 | 0.00 | 5.32 | 0.00 | 3.27 | 10.08 | 0.00 |
time (sec) |
N/A | 0.293 | 10.036 | 1.169 | 0.000 | 0.595 | 0.000 | 0.445 | 0.318 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 127 | 108 | 111 | 0 | 381 | 0 | 398 | 581 | 4588 |
N.S. |
1 | 1.08 | 0.92 | 0.94 | 0.00 | 3.23 | 0.00 | 3.37 | 4.92 | 38.88 |
time (sec) |
N/A | 0.258 | 10.059 | 1.435 | 0.000 | 1.157 | 0.000 | 0.409 | 0.221 | 6.767 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 135 | 145 | 712 | 0 | 693 | 0 | 526 | 942 | 0 |
N.S. |
1 | 0.99 | 1.07 | 5.24 | 0.00 | 5.10 | 0.00 | 3.87 | 6.93 | 0.00 |
time (sec) |
N/A | 0.286 | 1.293 | 1.549 | 0.000 | 0.484 | 0.000 | 0.376 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 80 | 91 | 70 | 0 | 140 | 702 | 386 | 132 | 118 |
N.S. |
1 | 0.95 | 1.08 | 0.83 | 0.00 | 1.67 | 8.36 | 4.60 | 1.57 | 1.40 |
time (sec) |
N/A | 0.230 | 0.908 | 1.030 | 0.000 | 0.355 | 0.475 | 0.368 | 0.208 | 6.148 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 88 | 1137 | 0 | 440 | 0 | 313 | 431 | 0 |
N.S. |
1 | 1.00 | 0.92 | 11.84 | 0.00 | 4.58 | 0.00 | 3.26 | 4.49 | 0.00 |
time (sec) |
N/A | 0.249 | 0.806 | 1.194 | 0.000 | 0.419 | 0.000 | 0.364 | 0.198 | 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 | 52 | 52 | 42 | 39 | 0 | 83 | 320 | 67 | 82 | 62 |
N.S. |
1 | 1.00 | 0.81 | 0.75 | 0.00 | 1.60 | 6.15 | 1.29 | 1.58 | 1.19 |
time (sec) |
N/A | 0.198 | 0.835 | 0.926 | 0.000 | 0.256 | 0.469 | 0.389 | 0.191 | 6.370 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 38 | 38 | 0 | 146 | 0 | 195 | 237 | 67 |
N.S. |
1 | 1.00 | 0.97 | 0.97 | 0.00 | 3.74 | 0.00 | 5.00 | 6.08 | 1.72 |
time (sec) |
N/A | 0.171 | 0.619 | 0.953 | 0.000 | 0.277 | 0.000 | 0.379 | 0.207 | 6.398 |
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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 18 | 16 | 15 | 52 | 82 | 30 | 57 | 15 |
N.S. |
1 | 1.00 | 0.95 | 0.84 | 0.79 | 2.74 | 4.32 | 1.58 | 3.00 | 0.79 |
time (sec) |
N/A | 0.153 | 0.022 | 0.824 | 0.035 | 0.240 | 0.428 | 0.324 | 0.186 | 6.527 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 128 | 1624 | 132 | 0 | 620 | 0 | 906 | 1193 | 0 |
N.S. |
1 | 1.08 | 13.76 | 1.12 | 0.00 | 5.25 | 0.00 | 7.68 | 10.11 | 0.00 |
time (sec) |
N/A | 0.285 | 6.707 | 1.032 | 0.000 | 0.438 | 0.000 | 0.351 | 0.313 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 128 | 108 | 132 | 0 | 374 | 0 | 374 | 579 | 110 |
N.S. |
1 | 1.05 | 0.89 | 1.08 | 0.00 | 3.07 | 0.00 | 3.07 | 4.75 | 0.90 |
time (sec) |
N/A | 0.259 | 10.068 | 1.081 | 0.000 | 1.097 | 0.000 | 0.364 | 0.206 | 6.364 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 195 | 62 | 194 | 0 | 1287 | 0 | 1443 | 2452 | 0 |
N.S. |
1 | 1.11 | 0.35 | 1.10 | 0.00 | 7.31 | 0.00 | 8.20 | 13.93 | 0.00 |
time (sec) |
N/A | 0.343 | 10.042 | 1.040 | 0.000 | 1.970 | 0.000 | 0.525 | 1.331 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 177 | 178 | 187 | 0 | 677 | 0 | 1389 | 1084 | 5604 |
N.S. |
1 | 1.09 | 1.10 | 1.15 | 0.00 | 4.18 | 0.00 | 8.57 | 6.69 | 34.59 |
time (sec) |
N/A | 0.322 | 10.079 | 1.265 | 0.000 | 3.682 | 0.000 | 0.461 | 0.224 | 7.303 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 294 | 24 | 14 | 66 | 0 | 89 | 57 | 0 |
N.S. |
1 | 1.00 | 10.89 | 0.89 | 0.52 | 2.44 | 0.00 | 3.30 | 2.11 | 0.00 |
time (sec) |
N/A | 0.174 | 0.421 | 1.398 | 0.108 | 0.082 | 0.000 | 0.371 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 77 | 53 | 0 | 175 | 0 | 66 | 129 | 0 |
N.S. |
1 | 1.00 | 1.38 | 0.95 | 0.00 | 3.12 | 0.00 | 1.18 | 2.30 | 0.00 |
time (sec) |
N/A | 0.200 | 0.375 | 1.019 | 0.000 | 0.107 | 0.000 | 0.393 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 21 | 12 | 9 | 18 | 0 | 18 | 15 | 0 |
N.S. |
1 | 1.00 | 1.62 | 0.92 | 0.69 | 1.38 | 0.00 | 1.38 | 1.15 | 0.00 |
time (sec) |
N/A | 0.156 | 0.089 | 1.075 | 0.116 | 0.081 | 0.000 | 0.360 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 233 | 155 | 555 | 0 | 199 | 0 | 0 | 1425 | 0 |
N.S. |
1 | 1.03 | 0.68 | 2.44 | 0.00 | 0.88 | 0.00 | 0.00 | 6.28 | 0.00 |
time (sec) |
N/A | 0.467 | 10.294 | 2.641 | 0.000 | 0.083 | 0.000 | 0.000 | 0.696 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 185 | 110 | 490 | 0 | 121 | 0 | 0 | 779 | 0 |
N.S. |
1 | 1.03 | 0.61 | 2.72 | 0.00 | 0.67 | 0.00 | 0.00 | 4.33 | 0.00 |
time (sec) |
N/A | 0.384 | 10.134 | 1.356 | 0.000 | 0.081 | 0.000 | 0.000 | 0.497 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 137 | 91 | 364 | 0 | 82 | 0 | 0 | 674 | 0 |
N.S. |
1 | 1.00 | 0.66 | 2.66 | 0.00 | 0.60 | 0.00 | 0.00 | 4.92 | 0.00 |
time (sec) |
N/A | 0.341 | 10.047 | 1.181 | 0.000 | 0.081 | 0.000 | 0.000 | 0.374 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 137 | 91 | 319 | 0 | 119 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.66 | 2.33 | 0.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.326 | 10.049 | 1.662 | 0.000 | 0.104 | 0.000 | 0.000 | 0.586 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 192 | 99 | 547 | 0 | 250 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.54 | 2.97 | 0.00 | 1.36 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.408 | 10.060 | 2.380 | 0.000 | 0.105 | 0.000 | 0.000 | 0.848 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 254 | 99 | 613 | 0 | 452 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.43 | 2.65 | 0.00 | 1.96 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.477 | 10.058 | 2.861 | 0.000 | 0.107 | 0.000 | 0.000 | 1.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 279 | 249 | 110 | 703 | 0 | 166 | 0 | 0 | 624 | 0 |
N.S. |
1 | 0.89 | 0.39 | 2.52 | 0.00 | 0.59 | 0.00 | 0.00 | 2.24 | 0.00 |
time (sec) |
N/A | 0.574 | 10.155 | 2.548 | 0.000 | 0.090 | 0.000 | 0.000 | 0.503 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 203 | 91 | 492 | 0 | 98 | 0 | 0 | 379 | 0 |
N.S. |
1 | 0.86 | 0.39 | 2.08 | 0.00 | 0.42 | 0.00 | 0.00 | 1.61 | 0.00 |
time (sec) |
N/A | 0.480 | 10.038 | 1.625 | 0.000 | 0.088 | 0.000 | 0.000 | 0.515 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 190 | 91 | 325 | 0 | 104 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.83 | 0.40 | 1.42 | 0.00 | 0.45 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.468 | 10.034 | 1.335 | 0.000 | 0.084 | 0.000 | 0.000 | 0.613 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 256 | 91 | 874 | 0 | 224 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 0.32 | 3.09 | 0.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.540 | 10.054 | 2.093 | 0.000 | 0.092 | 0.000 | 0.000 | 1.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 274 | 286 | 161 | 642 | 0 | 292 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.59 | 2.34 | 0.00 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.515 | 10.440 | 4.852 | 0.000 | 0.096 | 0.000 | 0.000 | 1.042 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 238 | 117 | 555 | 0 | 186 | 0 | 0 | 1425 | 0 |
N.S. |
1 | 1.05 | 0.52 | 2.44 | 0.00 | 0.82 | 0.00 | 0.00 | 6.28 | 0.00 |
time (sec) |
N/A | 0.453 | 10.065 | 2.481 | 0.000 | 0.100 | 0.000 | 0.000 | 0.707 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 190 | 99 | 486 | 0 | 119 | 0 | 0 | 809 | 0 |
N.S. |
1 | 1.04 | 0.54 | 2.67 | 0.00 | 0.65 | 0.00 | 0.00 | 4.45 | 0.00 |
time (sec) |
N/A | 0.390 | 10.055 | 1.940 | 0.000 | 0.084 | 0.000 | 0.000 | 0.536 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 185 | 99 | 573 | 0 | 173 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.57 | 3.29 | 0.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.388 | 10.059 | 4.571 | 0.000 | 0.094 | 0.000 | 0.000 | 0.863 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 185 | 107 | 533 | 0 | 194 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.61 | 3.06 | 0.00 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.381 | 10.062 | 6.520 | 0.000 | 0.096 | 0.000 | 0.000 | 1.409 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 240 | 107 | 611 | 0 | 374 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.48 | 2.76 | 0.00 | 1.69 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.468 | 10.117 | 7.924 | 0.000 | 0.111 | 0.000 | 0.000 | 2.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 302 | 107 | 677 | 0 | 620 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 0.40 | 2.53 | 0.00 | 2.31 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.551 | 5.029 | 8.527 | 0.000 | 0.147 | 0.000 | 0.000 | 3.019 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 326 | 302 | 117 | 938 | 0 | 246 | 0 | 0 | 927 | 0 |
N.S. |
1 | 0.93 | 0.36 | 2.88 | 0.00 | 0.75 | 0.00 | 0.00 | 2.84 | 0.00 |
time (sec) |
N/A | 0.615 | 10.139 | 4.142 | 0.000 | 0.089 | 0.000 | 0.000 | 0.868 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 281 | 256 | 99 | 700 | 0 | 149 | 0 | 0 | 620 | 0 |
N.S. |
1 | 0.91 | 0.35 | 2.49 | 0.00 | 0.53 | 0.00 | 0.00 | 2.21 | 0.00 |
time (sec) |
N/A | 0.555 | 10.052 | 2.277 | 0.000 | 0.084 | 0.000 | 0.000 | 0.619 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 249 | 99 | 504 | 0 | 150 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.37 | 1.86 | 0.00 | 0.55 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.552 | 10.048 | 3.582 | 0.000 | 0.095 | 0.000 | 0.000 | 0.716 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 238 | 99 | 893 | 0 | 182 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.87 | 0.36 | 3.27 | 0.00 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.522 | 10.052 | 4.085 | 0.000 | 0.104 | 0.000 | 0.000 | 1.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 320 | 304 | 107 | 1161 | 0 | 350 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.33 | 3.63 | 0.00 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.616 | 10.070 | 7.589 | 0.000 | 0.103 | 0.000 | 0.000 | 1.626 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 321 | 339 | 161 | 761 | 0 | 404 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.50 | 2.37 | 0.00 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.584 | 10.278 | 9.922 | 0.000 | 0.095 | 0.000 | 0.000 | 1.624 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 274 | 291 | 117 | 642 | 0 | 275 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.43 | 2.34 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.537 | 10.062 | 4.986 | 0.000 | 0.091 | 0.000 | 0.000 | 1.115 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 243 | 101 | 549 | 0 | 183 | 0 | 0 | 1453 | 0 |
N.S. |
1 | 1.06 | 0.44 | 2.40 | 0.00 | 0.80 | 0.00 | 0.00 | 6.34 | 0.00 |
time (sec) |
N/A | 0.475 | 10.098 | 3.907 | 0.000 | 0.085 | 0.000 | 0.000 | 0.755 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 238 | 101 | 1000 | 0 | 259 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.46 | 4.57 | 0.00 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.452 | 10.049 | 5.318 | 0.000 | 0.092 | 0.000 | 0.000 | 1.373 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 233 | 109 | 646 | 0 | 299 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.52 | 3.06 | 0.00 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.434 | 10.060 | 11.405 | 0.000 | 0.103 | 0.000 | 0.000 | 2.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 233 | 109 | 606 | 0 | 298 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.52 | 2.87 | 0.00 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.434 | 10.070 | 8.892 | 0.000 | 0.103 | 0.000 | 0.000 | 3.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 288 | 109 | 684 | 0 | 521 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.12 | 0.42 | 2.65 | 0.00 | 2.02 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.519 | 5.566 | 10.228 | 0.000 | 0.228 | 0.000 | 0.000 | 5.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 305 | 350 | 109 | 750 | 0 | 810 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 0.36 | 2.46 | 0.00 | 2.66 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.617 | 5.280 | 10.964 | 0.000 | 0.250 | 0.000 | 0.000 | 7.514 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 373 | 355 | 117 | 1190 | 0 | 346 | 0 | 0 | 1296 | 0 |
N.S. |
1 | 0.95 | 0.31 | 3.19 | 0.00 | 0.93 | 0.00 | 0.00 | 3.47 | 0.00 |
time (sec) |
N/A | 0.710 | 10.132 | 8.977 | 0.000 | 0.107 | 0.000 | 0.000 | 1.127 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 328 | 309 | 101 | 924 | 0 | 221 | 0 | 0 | 925 | 0 |
N.S. |
1 | 0.94 | 0.31 | 2.82 | 0.00 | 0.67 | 0.00 | 0.00 | 2.82 | 0.00 |
time (sec) |
N/A | 0.618 | 10.048 | 3.883 | 0.000 | 0.100 | 0.000 | 0.000 | 0.741 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 316 | 302 | 101 | 700 | 0 | 223 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.32 | 2.22 | 0.00 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.607 | 10.056 | 5.621 | 0.000 | 0.101 | 0.000 | 0.000 | 1.100 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 310 | 297 | 101 | 1295 | 0 | 274 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.33 | 4.18 | 0.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.610 | 10.085 | 9.437 | 0.000 | 0.106 | 0.000 | 0.000 | 2.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 310 | 286 | 109 | 1144 | 0 | 284 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.35 | 3.69 | 0.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.588 | 10.065 | 8.476 | 0.000 | 0.109 | 0.000 | 0.000 | 2.562 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 357 | 352 | 109 | 1234 | 0 | 496 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.31 | 3.46 | 0.00 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.693 | 10.073 | 9.926 | 0.000 | 0.119 | 0.000 | 0.000 | 3.884 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 180 | 166 | 488 | 0 | 131 | 0 | 0 | 818 | 0 |
N.S. |
1 | 1.03 | 0.95 | 2.80 | 0.00 | 0.75 | 0.00 | 0.00 | 4.70 | 0.00 |
time (sec) |
N/A | 0.391 | 10.212 | 2.578 | 0.000 | 0.083 | 0.000 | 0.000 | 0.561 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 132 | 111 | 362 | 0 | 80 | 0 | 0 | 681 | 0 |
N.S. |
1 | 1.00 | 0.84 | 2.74 | 0.00 | 0.61 | 0.00 | 0.00 | 5.16 | 0.00 |
time (sec) |
N/A | 0.322 | 10.079 | 1.394 | 0.000 | 0.080 | 0.000 | 0.000 | 0.391 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 89 | 189 | 0 | 42 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.95 | 0.00 | 0.43 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.272 | 10.101 | 2.666 | 0.000 | 0.078 | 0.000 | 0.000 | 0.302 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 144 | 91 | 362 | 0 | 151 | 0 | 0 | 104 | 0 |
N.S. |
1 | 1.00 | 0.63 | 2.51 | 0.00 | 1.05 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.338 | 10.040 | 4.267 | 0.000 | 0.082 | 0.000 | 0.000 | 0.440 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 206 | 99 | 556 | 0 | 306 | 0 | 0 | 150 | 0 |
N.S. |
1 | 1.10 | 0.53 | 2.96 | 0.00 | 1.63 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.411 | 10.056 | 8.108 | 0.000 | 0.100 | 0.000 | 0.000 | 0.617 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 244 | 167 | 703 | 0 | 166 | 0 | 0 | 621 | 0 |
N.S. |
1 | 0.89 | 0.61 | 2.58 | 0.00 | 0.61 | 0.00 | 0.00 | 2.27 | 0.00 |
time (sec) |
N/A | 0.530 | 10.135 | 4.032 | 0.000 | 0.086 | 0.000 | 0.000 | 0.544 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 196 | 111 | 496 | 0 | 109 | 0 | 0 | 378 | 0 |
N.S. |
1 | 0.85 | 0.48 | 2.15 | 0.00 | 0.47 | 0.00 | 0.00 | 1.64 | 0.00 |
time (sec) |
N/A | 0.478 | 10.138 | 2.781 | 0.000 | 0.086 | 0.000 | 0.000 | 0.413 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 155 | 91 | 186 | 0 | 54 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.79 | 0.47 | 0.95 | 0.00 | 0.28 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.408 | 10.047 | 1.057 | 0.000 | 0.083 | 0.000 | 0.000 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 237 | 208 | 89 | 336 | 0 | 125 | 0 | 0 | 81 | 0 |
N.S. |
1 | 0.88 | 0.38 | 1.42 | 0.00 | 0.53 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.488 | 10.042 | 3.374 | 0.000 | 0.087 | 0.000 | 0.000 | 0.366 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 270 | 91 | 874 | 0 | 268 | 0 | 0 | 1013 | 0 |
N.S. |
1 | 0.94 | 0.32 | 3.05 | 0.00 | 0.93 | 0.00 | 0.00 | 3.53 | 0.00 |
time (sec) |
N/A | 0.567 | 10.048 | 7.096 | 0.000 | 0.090 | 0.000 | 0.000 | 0.818 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 76 | 118 | 0 | 31 | 0 | 0 | 96 | 0 |
N.S. |
1 | 1.00 | 0.96 | 1.49 | 0.00 | 0.39 | 0.00 | 0.00 | 1.22 | 0.00 |
time (sec) |
N/A | 0.245 | 10.028 | 0.953 | 0.000 | 0.074 | 0.000 | 0.000 | 0.349 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 63 | 102 | 0 | 11 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 1.24 | 2.00 | 0.00 | 0.22 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.200 | 10.018 | 0.837 | 0.000 | 0.074 | 0.000 | 0.000 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 65 | 142 | 0 | 54 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 0.82 | 1.80 | 0.00 | 0.68 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.233 | 10.028 | 0.854 | 0.000 | 0.079 | 0.000 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 104 | 76 | 127 | 0 | 39 | 0 | 0 | 113 | 0 |
N.S. |
1 | 0.81 | 0.59 | 0.99 | 0.00 | 0.30 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.306 | 10.028 | 0.956 | 0.000 | 0.077 | 0.000 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 78 | 65 | 105 | 0 | 14 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.76 | 0.63 | 1.02 | 0.00 | 0.14 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.250 | 10.049 | 0.835 | 0.000 | 0.091 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 106 | 63 | 116 | 0 | 47 | 0 | 0 | 40 | 0 |
N.S. |
1 | 0.83 | 0.49 | 0.91 | 0.00 | 0.37 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.286 | 10.014 | 0.842 | 0.000 | 0.086 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 217 | 172 | 569 | 0 | 262 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.84 | 2.78 | 0.00 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.432 | 10.180 | 7.895 | 0.000 | 0.089 | 0.000 | 0.000 | 1.471 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 169 | 122 | 366 | 0 | 171 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.75 | 2.26 | 0.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.379 | 10.193 | 7.955 | 0.000 | 0.087 | 0.000 | 0.000 | 0.976 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 125 | 88 | 194 | 0 | 97 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.70 | 1.55 | 0.00 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.317 | 10.064 | 2.102 | 0.000 | 0.083 | 0.000 | 0.000 | 0.690 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 137 | 100 | 206 | 0 | 129 | 0 | 0 | 99 | 0 |
N.S. |
1 | 1.00 | 0.73 | 1.50 | 0.00 | 0.94 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.334 | 10.073 | 4.848 | 0.000 | 0.087 | 0.000 | 0.000 | 0.459 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 200 | 98 | 365 | 0 | 330 | 0 | 0 | 173 | 0 |
N.S. |
1 | 1.09 | 0.53 | 1.98 | 0.00 | 1.79 | 0.00 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.413 | 10.091 | 7.954 | 0.000 | 0.114 | 0.000 | 0.000 | 0.734 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 233 | 122 | 498 | 0 | 199 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 0.47 | 1.93 | 0.00 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.531 | 10.126 | 8.194 | 0.000 | 0.093 | 0.000 | 0.000 | 0.924 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 181 | 88 | 323 | 0 | 123 | 0 | 0 | 1337 | 0 |
N.S. |
1 | 0.83 | 0.40 | 1.47 | 0.00 | 0.56 | 0.00 | 0.00 | 6.11 | 0.00 |
time (sec) |
N/A | 0.450 | 10.056 | 4.012 | 0.000 | 0.088 | 0.000 | 0.000 | 0.647 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 205 | 98 | 332 | 0 | 135 | 0 | 0 | 63 | 0 |
N.S. |
1 | 0.89 | 0.42 | 1.44 | 0.00 | 0.58 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.478 | 10.088 | 1.455 | 0.000 | 0.086 | 0.000 | 0.000 | 0.416 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 274 | 264 | 96 | 339 | 0 | 248 | 0 | 0 | 1050 | 0 |
N.S. |
1 | 0.96 | 0.35 | 1.24 | 0.00 | 0.91 | 0.00 | 0.00 | 3.83 | 0.00 |
time (sec) |
N/A | 0.565 | 10.043 | 5.739 | 0.000 | 0.090 | 0.000 | 0.000 | 0.750 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 325 | 326 | 98 | 876 | 0 | 517 | 0 | 0 | 210 | 0 |
N.S. |
1 | 1.00 | 0.30 | 2.70 | 0.00 | 1.59 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.654 | 10.054 | 8.513 | 0.000 | 0.104 | 0.000 | 0.000 | 0.843 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 258 | 252 | 1473 | 0 | 424 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.02 | 5.96 | 0.00 | 1.72 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.491 | 10.376 | 15.680 | 0.000 | 0.115 | 0.000 | 0.000 | 4.486 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 208 | 179 | 657 | 0 | 297 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.91 | 3.35 | 0.00 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.427 | 10.166 | 12.649 | 0.000 | 0.114 | 0.000 | 0.000 | 2.964 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 166 | 122 | 479 | 0 | 185 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.74 | 2.90 | 0.00 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.367 | 10.171 | 7.990 | 0.000 | 0.104 | 0.000 | 0.000 | 1.936 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 178 | 129 | 487 | 0 | 222 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.75 | 2.82 | 0.00 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.388 | 10.112 | 2.849 | 0.000 | 0.100 | 0.000 | 0.000 | 1.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 197 | 132 | 491 | 0 | 264 | 0 | 0 | 154 | 0 |
N.S. |
1 | 1.05 | 0.71 | 2.63 | 0.00 | 1.41 | 0.00 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 0.406 | 10.131 | 9.178 | 0.000 | 0.091 | 0.000 | 0.000 | 0.776 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 258 | 99 | 664 | 0 | 597 | 0 | 0 | 256 | 0 |
N.S. |
1 | 1.13 | 0.43 | 2.91 | 0.00 | 2.62 | 0.00 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.498 | 10.056 | 10.460 | 0.000 | 0.115 | 0.000 | 0.000 | 1.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 274 | 180 | 1328 | 0 | 362 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.60 | 4.44 | 0.00 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.588 | 10.156 | 15.080 | 0.000 | 0.125 | 0.000 | 0.000 | 3.075 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 222 | 122 | 859 | 0 | 230 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.86 | 0.47 | 3.33 | 0.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.509 | 10.119 | 8.237 | 0.000 | 0.096 | 0.000 | 0.000 | 1.921 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 244 | 116 | 871 | 0 | 283 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.44 | 3.30 | 0.00 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.533 | 10.084 | 7.812 | 0.000 | 0.096 | 0.000 | 0.000 | 1.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 263 | 99 | 866 | 0 | 300 | 0 | 0 | 104 | 0 |
N.S. |
1 | 0.95 | 0.36 | 3.12 | 0.00 | 1.08 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.557 | 10.041 | 1.727 | 0.000 | 0.105 | 0.000 | 0.000 | 0.741 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 325 | 324 | 97 | 877 | 0 | 514 | 0 | 0 | 205 | 0 |
N.S. |
1 | 1.00 | 0.30 | 2.70 | 0.00 | 1.58 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.647 | 10.050 | 9.431 | 0.000 | 0.107 | 0.000 | 0.000 | 0.877 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 182 | 125 | 285 | 0 | 147 | 0 | 0 | 909 | 0 |
N.S. |
1 | 1.07 | 0.74 | 1.68 | 0.00 | 0.86 | 0.00 | 0.00 | 5.35 | 0.00 |
time (sec) |
N/A | 0.386 | 10.076 | 4.421 | 0.000 | 0.095 | 0.000 | 0.000 | 0.320 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 130 | 86 | 212 | 0 | 104 | 0 | 0 | 658 | 0 |
N.S. |
1 | 1.05 | 0.69 | 1.71 | 0.00 | 0.84 | 0.00 | 0.00 | 5.31 | 0.00 |
time (sec) |
N/A | 0.300 | 10.059 | 2.572 | 0.000 | 0.088 | 0.000 | 0.000 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 54 | 158 | 0 | 69 | 0 | 0 | 484 | 0 |
N.S. |
1 | 1.00 | 0.69 | 2.03 | 0.00 | 0.88 | 0.00 | 0.00 | 6.21 | 0.00 |
time (sec) |
N/A | 0.235 | 10.028 | 2.022 | 0.000 | 0.088 | 0.000 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 38 | 121 | 0 | 32 | 0 | 0 | 73 | 0 |
N.S. |
1 | 1.00 | 1.23 | 3.90 | 0.00 | 1.03 | 0.00 | 0.00 | 2.35 | 0.00 |
time (sec) |
N/A | 0.183 | 10.025 | 2.414 | 0.000 | 0.082 | 0.000 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 40 | 164 | 0 | 113 | 0 | 0 | 117 | 0 |
N.S. |
1 | 1.00 | 0.50 | 2.05 | 0.00 | 1.41 | 0.00 | 0.00 | 1.46 | 0.00 |
time (sec) |
N/A | 0.234 | 10.032 | 3.868 | 0.000 | 0.078 | 0.000 | 0.000 | 0.298 | 0.000 |