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 | B | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 20 | 65 | 27 | 0 | 39 | 41 | 61 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 3.61 | 1.50 | 0.00 | 2.17 | 2.28 | 3.39 |
time (sec) |
N/A | 0.291 | 0.033 | 0.392 | 0.119 | 0.080 | 0.000 | 0.472 | 0.178 | 0.403 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 32 | 31 | 51 | 84 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.00 | 1.03 | 1.00 | 1.65 | 2.71 | 0.00 | 0.00 | 1.32 | 0.00 |
time (sec) |
N/A | 0.305 | 0.028 | 0.506 | 0.027 | 0.090 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 68 | 58 | 83 | 81 | 79 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.03 | 0.88 | 1.26 | 1.23 | 1.20 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.346 | 0.225 | 0.557 | 0.112 | 0.088 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 81 | 66 | 132 | 1518 | 80 | 0 | 188 | 43 | 0 |
N.S. |
1 | 0.89 | 0.73 | 1.45 | 16.68 | 0.88 | 0.00 | 2.07 | 0.47 | 0.00 |
time (sec) |
N/A | 0.552 | 0.154 | 0.555 | 0.316 | 0.096 | 0.000 | 0.526 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 55 | 43 | 106 | 527 | 67 | 0 | 158 | 43 | 0 |
N.S. |
1 | 0.89 | 0.69 | 1.71 | 8.50 | 1.08 | 0.00 | 2.55 | 0.69 | 0.00 |
time (sec) |
N/A | 0.450 | 0.052 | 0.520 | 0.168 | 0.092 | 0.000 | 0.518 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 32 | 90 | 36 | 0 | 0 | 43 | 37 |
N.S. |
1 | 1.00 | 1.00 | 1.28 | 3.60 | 1.44 | 0.00 | 0.00 | 1.72 | 1.48 |
time (sec) |
N/A | 0.381 | 0.034 | 0.503 | 0.156 | 0.079 | 0.000 | 0.000 | 0.177 | 35.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 46 | 37 | 64 | 525 | 58 | 0 | 0 | 43 | 118 |
N.S. |
1 | 0.77 | 0.62 | 1.07 | 8.75 | 0.97 | 0.00 | 0.00 | 0.72 | 1.97 |
time (sec) |
N/A | 0.407 | 0.074 | 0.510 | 0.166 | 0.082 | 0.000 | 0.000 | 0.171 | 40.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 56 | 49 | 74 | 1236 | 79 | 0 | 0 | 43 | 491 |
N.S. |
1 | 0.58 | 0.51 | 0.77 | 12.88 | 0.82 | 0.00 | 0.00 | 0.45 | 5.11 |
time (sec) |
N/A | 0.414 | 0.088 | 0.536 | 0.166 | 0.111 | 0.000 | 0.000 | 0.166 | 43.877 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 74 | 51 | 51 | 69 | 50 | 0 | 93 | 52 | 583 |
N.S. |
1 | 1.09 | 0.75 | 0.75 | 1.01 | 0.74 | 0.00 | 1.37 | 0.76 | 8.57 |
time (sec) |
N/A | 0.368 | 0.258 | 0.625 | 0.041 | 0.085 | 0.000 | 0.778 | 0.190 | 71.399 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 53 | 34 | 41 | 48 | 40 | 0 | 80 | 52 | 389 |
N.S. |
1 | 1.20 | 0.77 | 0.93 | 1.09 | 0.91 | 0.00 | 1.82 | 1.18 | 8.84 |
time (sec) |
N/A | 0.359 | 0.186 | 0.534 | 0.042 | 0.081 | 0.000 | 0.698 | 0.184 | 41.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 21 | 95 | 28 | 0 | 54 | 50 | 72 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 4.52 | 1.33 | 0.00 | 2.57 | 2.38 | 3.43 |
time (sec) |
N/A | 0.299 | 0.033 | 0.402 | 0.121 | 0.075 | 0.000 | 0.653 | 0.181 | 38.860 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 55 | 37 | 75 | 73 | 58 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.04 | 0.70 | 1.42 | 1.38 | 1.09 | 0.00 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.323 | 0.103 | 0.623 | 0.030 | 0.084 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 70 | 59 | 67 | 100 | 83 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.06 | 0.89 | 1.02 | 1.52 | 1.26 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.359 | 0.141 | 0.595 | 0.037 | 0.089 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 84 | 59 | 104 | 1532 | 77 | 0 | 99 | 52 | 0 |
N.S. |
1 | 0.79 | 0.56 | 0.98 | 14.45 | 0.73 | 0.00 | 0.93 | 0.49 | 0.00 |
time (sec) |
N/A | 0.572 | 0.108 | 0.589 | 0.315 | 0.097 | 0.000 | 0.644 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 44 | 44 | 123 | 220 | 66 | 0 | 0 | 52 | 0 |
N.S. |
1 | 0.70 | 0.70 | 1.95 | 3.49 | 1.05 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.410 | 0.091 | 0.572 | 0.175 | 0.088 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 29 | 35 | 382 | 50 | 0 | 0 | 52 | 88 |
N.S. |
1 | 1.00 | 0.76 | 0.92 | 10.05 | 1.32 | 0.00 | 0.00 | 1.37 | 2.32 |
time (sec) |
N/A | 0.397 | 0.047 | 0.563 | 0.163 | 0.078 | 0.000 | 0.000 | 0.179 | 39.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 53 | 41 | 47 | 1063 | 75 | 0 | 0 | 52 | 393 |
N.S. |
1 | 0.69 | 0.53 | 0.61 | 13.81 | 0.97 | 0.00 | 0.00 | 0.68 | 5.10 |
time (sec) |
N/A | 0.424 | 0.109 | 0.530 | 0.168 | 0.084 | 0.000 | 0.000 | 0.176 | 40.671 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 65 | 51 | 57 | 2026 | 100 | 0 | 0 | 52 | 589 |
N.S. |
1 | 0.57 | 0.44 | 0.50 | 17.62 | 0.87 | 0.00 | 0.00 | 0.45 | 5.12 |
time (sec) |
N/A | 0.442 | 0.149 | 0.563 | 0.197 | 0.084 | 0.000 | 0.000 | 0.183 | 71.756 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 177 | 143 | 721 | 230 | 369 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.81 | 4.07 | 1.30 | 2.08 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.349 | 0.652 | 0.622 | 0.124 | 0.560 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 113 | 84 | 403 | 127 | 249 | 0 | 959 | 24 | 0 |
N.S. |
1 | 0.96 | 0.71 | 3.42 | 1.08 | 2.11 | 0.00 | 8.13 | 0.20 | 0.00 |
time (sec) |
N/A | 0.295 | 0.465 | 0.526 | 0.114 | 0.325 | 0.000 | 0.642 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 60 | 60 | 129 | 122 | 160 | 0 | 313 | 22 | 0 |
N.S. |
1 | 1.03 | 1.03 | 2.22 | 2.10 | 2.76 | 0.00 | 5.40 | 0.38 | 0.00 |
time (sec) |
N/A | 0.242 | 0.074 | 0.470 | 0.144 | 0.211 | 0.000 | 0.452 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 56 | 51 | 58 | 43 | 154 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.04 | 0.94 | 1.07 | 0.80 | 2.85 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.260 | 0.055 | 0.467 | 0.038 | 0.465 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 100 | 77 | 122 | 113 | 256 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.91 | 0.70 | 1.11 | 1.03 | 2.33 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.287 | 0.227 | 0.454 | 0.034 | 0.730 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 152 | 103 | 212 | 215 | 432 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.92 | 0.62 | 1.28 | 1.30 | 2.62 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.321 | 0.629 | 0.520 | 0.036 | 1.023 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 243 | 198 | 380 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.03 | 0.84 | 1.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.477 | 2.663 | 5.510 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 164 | 140 | 222 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.96 | 0.82 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.363 | 0.857 | 4.120 | 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 | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 51 | 61 | 71 | 0 | 0 | 0 | 0 | 15 | 0 |
N.S. |
1 | 0.98 | 1.17 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.281 | 0.073 | 1.515 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 167 | 143 | 156 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.96 | 0.82 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.376 | 1.053 | 3.202 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 238 | 197 | 351 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.03 | 0.85 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.476 | 3.844 | 3.802 | 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 | A | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 202 | 160 | 711 | 238 | 398 | 0 | 3585 | 61 | 0 |
N.S. |
1 | 0.92 | 0.73 | 3.23 | 1.08 | 1.81 | 0.00 | 16.30 | 0.28 | 0.00 |
time (sec) |
N/A | 0.363 | 2.207 | 0.571 | 0.120 | 0.453 | 0.000 | 2.129 | 0.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 138 | 116 | 426 | 169 | 278 | 0 | 2073 | 61 | 0 |
N.S. |
1 | 0.93 | 0.78 | 2.88 | 1.14 | 1.88 | 0.00 | 14.01 | 0.41 | 0.00 |
time (sec) |
N/A | 0.308 | 0.622 | 0.517 | 0.117 | 0.303 | 0.000 | 1.306 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 85 | 79 | 211 | 157 | 199 | 0 | 1270 | 57 | 0 |
N.S. |
1 | 1.01 | 0.94 | 2.51 | 1.87 | 2.37 | 0.00 | 15.12 | 0.68 | 0.00 |
time (sec) |
N/A | 0.253 | 0.177 | 0.509 | 0.134 | 0.250 | 0.000 | 0.683 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 79 | 69 | 86 | 61 | 190 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.01 | 0.88 | 1.10 | 0.78 | 2.44 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.261 | 0.126 | 0.450 | 0.030 | 0.472 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 123 | 90 | 165 | 148 | 297 | 0 | 0 | 61 | 0 |
N.S. |
1 | 0.88 | 0.64 | 1.18 | 1.06 | 2.12 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.299 | 0.519 | 0.477 | 0.038 | 0.764 | 0.000 | 0.000 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 177 | 123 | 257 | 272 | 457 | 0 | 0 | 61 | 0 |
N.S. |
1 | 0.85 | 0.59 | 1.24 | 1.31 | 2.20 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.343 | 0.888 | 0.494 | 0.040 | 1.047 | 0.000 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 283 | 211 | 419 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.03 | 0.77 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.542 | 3.529 | 6.672 | 0.000 | 0.000 | 0.000 | 0.000 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 223 | 174 | 389 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.00 | 0.78 | 1.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.422 | 3.371 | 5.928 | 0.000 | 0.000 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 155 | 156 | 266 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 0.99 | 1.00 | 1.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.807 | 0.796 | 2.613 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 224 | 173 | 204 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.437 | 2.782 | 4.890 | 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 | A | F | F | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 282 | 218 | 419 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.02 | 0.79 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.549 | 5.612 | 4.700 | 0.000 | 0.000 | 0.000 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 149 | 108 | 644 | 248 | 343 | 0 | 2448 | 38 | 0 |
N.S. |
1 | 1.11 | 0.81 | 4.81 | 1.85 | 2.56 | 0.00 | 18.27 | 0.28 | 0.00 |
time (sec) |
N/A | 0.329 | 0.551 | 0.554 | 0.123 | 0.293 | 0.000 | 0.560 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 83 | 77 | 353 | 124 | 235 | 0 | 753 | 38 | 0 |
N.S. |
1 | 1.02 | 0.95 | 4.36 | 1.53 | 2.90 | 0.00 | 9.30 | 0.47 | 0.00 |
time (sec) |
N/A | 0.282 | 0.262 | 0.538 | 0.122 | 0.162 | 0.000 | 0.451 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 38 | 103 | 106 | 125 | 0 | 94 | 36 | 0 |
N.S. |
1 | 1.00 | 1.06 | 2.86 | 2.94 | 3.47 | 0.00 | 2.61 | 1.00 | 0.00 |
time (sec) |
N/A | 0.240 | 0.063 | 0.460 | 0.135 | 0.130 | 0.000 | 0.305 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 42 | 25 | 117 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.27 | 0.76 | 3.55 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.247 | 0.041 | 0.485 | 0.030 | 0.132 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 71 | 71 | 109 | 77 | 235 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.95 | 0.95 | 1.45 | 1.03 | 3.13 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.274 | 0.182 | 0.515 | 0.035 | 0.159 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 127 | 101 | 205 | 158 | 403 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.01 | 0.80 | 1.63 | 1.25 | 3.20 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.320 | 0.405 | 0.539 | 0.038 | 0.161 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 249 | 188 | 377 | 0 | 845 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.01 | 0.76 | 1.53 | 0.00 | 3.43 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.487 | 2.751 | 4.244 | 0.000 | 0.146 | 0.000 | 0.000 | 0.180 | 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 | 109 | 123 | 100 | 222 | 0 | 730 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.13 | 0.92 | 2.04 | 0.00 | 6.70 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.318 | 0.782 | 2.418 | 0.000 | 0.122 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 51 | 60 | 52 | 0 | 305 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.98 | 1.15 | 1.00 | 0.00 | 5.87 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.291 | 0.060 | 0.372 | 0.000 | 0.104 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 120 | 101 | 120 | 0 | 723 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.13 | 0.95 | 1.13 | 0.00 | 6.82 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.327 | 0.807 | 1.819 | 0.000 | 0.120 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 243 | 186 | 351 | 0 | 1045 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.01 | 0.78 | 1.46 | 0.00 | 4.35 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.490 | 4.754 | 2.322 | 0.000 | 0.130 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 182 | 107 | 3767 | 334 | 606 | 0 | 2644 | 54 | 0 |
N.S. |
1 | 1.03 | 0.60 | 21.28 | 1.89 | 3.42 | 0.00 | 14.94 | 0.31 | 0.00 |
time (sec) |
N/A | 0.377 | 0.547 | 0.823 | 0.123 | 0.266 | 0.000 | 1.108 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 75 | 2541 | 193 | 458 | 0 | 967 | 54 | 0 |
N.S. |
1 | 1.00 | 0.64 | 21.53 | 1.64 | 3.88 | 0.00 | 8.19 | 0.46 | 0.00 |
time (sec) |
N/A | 0.311 | 0.126 | 0.655 | 0.119 | 0.193 | 0.000 | 0.627 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 65 | 54 | 1317 | 143 | 293 | 0 | 242 | 52 | 0 |
N.S. |
1 | 1.03 | 0.86 | 20.90 | 2.27 | 4.65 | 0.00 | 3.84 | 0.83 | 0.00 |
time (sec) |
N/A | 0.265 | 0.093 | 0.640 | 0.134 | 0.133 | 0.000 | 0.450 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 59 | 46 | 62 | 46 | 241 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.04 | 0.81 | 1.09 | 0.81 | 4.23 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.278 | 0.065 | 0.502 | 0.033 | 0.154 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 103 | 70 | 148 | 117 | 421 | 0 | 0 | 54 | 0 |
N.S. |
1 | 0.94 | 0.64 | 1.35 | 1.06 | 3.83 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.305 | 0.116 | 0.471 | 0.036 | 0.168 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 158 | 94 | 265 | 219 | 667 | 0 | 0 | 54 | 0 |
N.S. |
1 | 0.95 | 0.56 | 1.59 | 1.31 | 3.99 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.352 | 0.357 | 0.537 | 0.042 | 0.177 | 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(-1) | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 311 | 197 | 368 | 0 | 1228 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.07 | 0.67 | 1.26 | 0.00 | 4.21 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.522 | 3.022 | 5.812 | 0.000 | 0.185 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 233 | 145 | 278 | 0 | 1048 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.04 | 0.65 | 1.24 | 0.00 | 4.68 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.450 | 1.335 | 3.931 | 0.000 | 0.143 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 101 | 90 | 103 | 0 | 938 | 0 | 0 | 46 | 0 |
N.S. |
1 | 0.99 | 0.88 | 1.01 | 0.00 | 9.20 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.426 | 0.149 | 0.888 | 0.000 | 0.127 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 222 | 142 | 141 | 0 | 996 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.06 | 0.68 | 0.67 | 0.00 | 4.77 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.453 | 1.240 | 3.271 | 0.000 | 0.157 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 312 | 199 | 353 | 0 | 1465 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.05 | 0.67 | 1.19 | 0.00 | 4.93 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.602 | 4.624 | 3.931 | 0.000 | 0.160 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 212 | 107 | 1909 | 424 | 1008 | 0 | 3688 | 70 | 0 |
N.S. |
1 | 0.97 | 0.49 | 8.76 | 1.94 | 4.62 | 0.00 | 16.92 | 0.32 | 0.00 |
time (sec) |
N/A | 0.394 | 0.527 | 0.638 | 0.123 | 0.320 | 0.000 | 1.465 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 150 | 76 | 834 | 262 | 782 | 0 | 1746 | 70 | 0 |
N.S. |
1 | 0.98 | 0.50 | 5.45 | 1.71 | 5.11 | 0.00 | 11.41 | 0.46 | 0.00 |
time (sec) |
N/A | 0.326 | 0.135 | 0.623 | 0.119 | 0.230 | 0.000 | 0.926 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 97 | 56 | 963 | 203 | 534 | 0 | 832 | 68 | 0 |
N.S. |
1 | 1.07 | 0.62 | 10.58 | 2.23 | 5.87 | 0.00 | 9.14 | 0.75 | 0.00 |
time (sec) |
N/A | 0.282 | 0.089 | 0.574 | 0.150 | 0.166 | 0.000 | 0.645 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 87 | 49 | 260 | 66 | 397 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.05 | 0.59 | 3.13 | 0.80 | 4.78 | 0.00 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 0.280 | 0.068 | 0.566 | 0.037 | 0.166 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 131 | 69 | 1038 | 156 | 681 | 0 | 0 | 70 | 0 |
N.S. |
1 | 0.92 | 0.48 | 7.26 | 1.09 | 4.76 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.316 | 0.283 | 0.600 | 0.036 | 0.174 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 186 | 117 | 988 | 280 | 999 | 0 | 0 | 70 | 0 |
N.S. |
1 | 0.89 | 0.56 | 4.75 | 1.35 | 4.80 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.356 | 0.901 | 0.580 | 0.039 | 0.210 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 348 | 380 | 235 | 667 | 0 | 1730 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.09 | 0.68 | 1.92 | 0.00 | 4.97 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.628 | 4.427 | 7.406 | 0.000 | 0.291 | 0.000 | 0.000 | 0.190 | 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 | 292 | 310 | 199 | 851 | 0 | 1632 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.06 | 0.68 | 2.91 | 0.00 | 5.59 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.520 | 3.464 | 6.351 | 0.000 | 0.206 | 0.000 | 0.000 | 0.191 | 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 | 225 | 228 | 172 | 547 | 0 | 1531 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.01 | 0.76 | 2.43 | 0.00 | 6.80 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 1.190 | 1.436 | 1.281 | 0.000 | 0.179 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 282 | 308 | 209 | 411 | 0 | 1595 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.09 | 0.74 | 1.46 | 0.00 | 5.66 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.583 | 3.500 | 5.559 | 0.000 | 0.199 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | C | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 344 | 375 | 226 | 633 | 0 | 1971 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.09 | 0.66 | 1.84 | 0.00 | 5.73 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.698 | 3.994 | 5.352 | 0.000 | 0.219 | 0.000 | 0.000 | 0.170 | 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 | 120 | 147 | 121 | 0 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.22 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.392 | 1.324 | 0.000 | 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 | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 104 | 83 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.02 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.282 | 0.288 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 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 | 59 | 59 | 61 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.230 | 0.093 | 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 | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 54 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.241 | 0.074 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 91 | 73 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.96 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.260 | 0.569 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 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 | 101 | 101 | 102 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.294 | 7.992 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.231 | 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 | 101 | 101 | 102 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.290 | 0.766 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 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 | 97 | 97 | 98 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.289 | 0.625 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.185 | 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 | 101 | 101 | 102 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.290 | 3.743 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 153 | 143 | 110 | 152 | 874 | 0 | 144 | 508 | 2003 |
N.S. |
1 | 1.00 | 0.93 | 0.72 | 0.99 | 5.71 | 0.00 | 0.94 | 3.32 | 13.09 |
time (sec) |
N/A | 0.443 | 0.359 | 3.234 | 0.111 | 0.818 | 0.000 | 0.121 | 0.194 | 38.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | F(-1) | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 45 | 0 | 52 | 0 | 0 | 38 | 14 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 1.16 | 0.00 | 0.00 | 0.84 | 0.31 | 0.00 |
time (sec) |
N/A | 0.255 | 0.032 | 0.000 | 0.111 | 0.000 | 0.000 | 0.113 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | F(-2) | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 0 | 39 | 0 | 0 | 24 | 24 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 1.39 | 0.00 | 0.00 | 0.86 | 0.86 | 0.00 |
time (sec) |
N/A | 0.248 | 0.019 | 0.000 | 0.110 | 0.000 | 0.000 | 0.110 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 56 | 54 | 60 | 68 | 192 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.95 | 0.92 | 1.02 | 1.15 | 3.25 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.268 | 0.067 | 0.533 | 0.104 | 0.168 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 93 | 89 | 0 | 0 | 361 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.04 | 1.00 | 0.00 | 0.00 | 4.06 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.304 | 0.216 | 0.000 | 0.000 | 0.182 | 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 | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 54 | 65 | 72 | 0 | 240 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.06 | 1.27 | 1.41 | 0.00 | 4.71 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.242 | 0.110 | 1.711 | 0.000 | 0.165 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 35 | 42 | 50 | 137 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 1.43 | 3.91 | 0.00 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.261 | 0.031 | 0.565 | 0.109 | 0.137 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 66 | 66 | 0 | 79 | 244 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.94 | 0.94 | 0.00 | 1.13 | 3.49 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.292 | 0.103 | 0.000 | 0.113 | 0.151 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 109 | 141 | 0 | 166 | 368 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.01 | 1.31 | 0.00 | 1.54 | 3.41 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.331 | 3.291 | 0.000 | 0.112 | 0.164 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 409 | 454 | 291 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.11 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.578 | 5.434 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 162 | 195 | 396 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 1.20 | 2.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.295 | 0.500 | 2.341 | 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 | C | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 470 | 502 | 378 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.07 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.582 | 10.285 | 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 | 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 | 23 | 23 | 25 | 23 | 25 | 37 | 0 | 25 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.61 | 0.00 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.214 | 6.128 | 1.858 | 1.829 | 1.313 | 0.000 | 2.752 | 0.193 | 41.803 |
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 | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 279 | 265 | 810 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.95 | 2.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.453 | 14.815 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 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 | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 139 | 466 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 0.99 | 3.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.305 | 7.881 | 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 | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 54 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.246 | 0.125 | 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 | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 126 | 119 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.99 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.301 | 0.621 | 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 | 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 | 23 | 23 | 25 | 23 | 25 | 37 | 0 | 25 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.61 | 0.00 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.218 | 22.693 | 1.578 | 13.356 | 0.147 | 0.000 | 1.144 | 0.200 | 39.242 |