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 | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 92 | 85 | 78 | 92 | 113 | 0 | 142 | 189 | 0 |
N.S. |
1 | 1.14 | 1.05 | 0.96 | 1.14 | 1.40 | 0.00 | 1.75 | 2.33 | 0.00 |
time (sec) |
N/A | 0.439 | 0.379 | 1.725 | 0.130 | 0.081 | 0.000 | 0.306 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 57 | 58 | 48 | 72 | 79 | 0 | 121 | 117 | 0 |
N.S. |
1 | 1.02 | 1.04 | 0.86 | 1.29 | 1.41 | 0.00 | 2.16 | 2.09 | 0.00 |
time (sec) |
N/A | 0.310 | 0.256 | 4.145 | 0.117 | 0.077 | 0.000 | 0.248 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 148 | 96 | 92 | 0 | 141 | 0 | 176 | 286 | 0 |
N.S. |
1 | 1.35 | 0.87 | 0.84 | 0.00 | 1.28 | 0.00 | 1.60 | 2.60 | 0.00 |
time (sec) |
N/A | 0.640 | 0.468 | 2.172 | 0.000 | 0.084 | 0.000 | 0.249 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 207 | 108 | 104 | 0 | 166 | 0 | 0 | 395 | 0 |
N.S. |
1 | 1.48 | 0.77 | 0.74 | 0.00 | 1.19 | 0.00 | 0.00 | 2.82 | 0.00 |
time (sec) |
N/A | 0.768 | 0.681 | 2.128 | 0.000 | 0.083 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 235 | 113 | 97 | 0 | 191 | 0 | 284 | 504 | 0 |
N.S. |
1 | 1.44 | 0.69 | 0.60 | 0.00 | 1.17 | 0.00 | 1.74 | 3.09 | 0.00 |
time (sec) |
N/A | 0.819 | 0.711 | 2.197 | 0.000 | 0.084 | 0.000 | 0.272 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 204 | 174 | 141 | 0 | 60 | 0 | 0 | 149 | 0 |
N.S. |
1 | 1.25 | 1.07 | 0.87 | 0.00 | 0.37 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 1.069 | 32.619 | 2.155 | 0.000 | 0.075 | 0.000 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 146 | 170 | 136 | 0 | 55 | 0 | 0 | 129 | 0 |
N.S. |
1 | 1.04 | 1.21 | 0.97 | 0.00 | 0.39 | 0.00 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.507 | 29.215 | 1.887 | 0.000 | 0.071 | 0.000 | 0.000 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 141 | 164 | 131 | 0 | 50 | 0 | 0 | 109 | 0 |
N.S. |
1 | 1.04 | 1.21 | 0.97 | 0.00 | 0.37 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.491 | 27.741 | 1.876 | 0.000 | 0.073 | 0.000 | 0.000 | 0.228 | 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 | 155 | 169 | 165 | 165 | 0 | 0 | 0 | 0 | 148 | 0 |
N.S. |
1 | 1.09 | 1.06 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.909 | 20.684 | 2.621 | 0.000 | 0.000 | 0.000 | 0.000 | 7.390 | 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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 174 | 154 | 249 | 0 | 0 | 0 | 0 | 319 | 0 |
N.S. |
1 | 1.09 | 0.97 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 2.01 | 0.00 |
time (sec) |
N/A | 0.933 | 20.696 | 1.714 | 0.000 | 0.000 | 0.000 | 0.000 | 7.974 | 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 | 194 | 314 | 133 | 275 | 0 | 0 | 0 | 0 | 523 | 0 |
N.S. |
1 | 1.62 | 0.69 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 2.70 | 0.00 |
time (sec) |
N/A | 1.919 | 20.667 | 1.802 | 0.000 | 0.000 | 0.000 | 0.000 | 8.067 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 204 | 175 | 141 | 0 | 60 | 0 | 0 | 149 | 0 |
N.S. |
1 | 1.24 | 1.06 | 0.85 | 0.00 | 0.36 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 1.103 | 32.702 | 1.415 | 0.000 | 0.073 | 0.000 | 0.000 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 171 | 170 | 136 | 0 | 55 | 0 | 0 | 129 | 0 |
N.S. |
1 | 1.24 | 1.23 | 0.99 | 0.00 | 0.40 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.823 | 32.632 | 1.392 | 0.000 | 0.075 | 0.000 | 0.000 | 0.253 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 116 | 165 | 131 | 0 | 50 | 0 | 0 | 109 | 0 |
N.S. |
1 | 1.01 | 1.43 | 1.14 | 0.00 | 0.43 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.463 | 28.238 | 1.293 | 0.000 | 0.074 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 111 | 160 | 125 | 0 | 45 | 0 | 0 | 91 | 0 |
N.S. |
1 | 1.05 | 1.51 | 1.18 | 0.00 | 0.42 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.428 | 27.280 | 1.379 | 0.000 | 0.076 | 0.000 | 0.000 | 0.235 | 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 | 128 | 144 | 211 | 80 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.12 | 1.65 | 0.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.718 | 22.227 | 1.387 | 0.000 | 0.000 | 0.000 | 0.000 | 7.005 | 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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 176 | 154 | 249 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.09 | 0.95 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.948 | 20.785 | 1.730 | 0.000 | 0.000 | 0.000 | 0.000 | 7.815 | 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 | 194 | 316 | 134 | 275 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.63 | 0.69 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.953 | 20.756 | 1.768 | 0.000 | 0.000 | 0.000 | 0.000 | 7.493 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 330 | 427 | 641 | 307 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.29 | 1.94 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.306 | 24.431 | 5.761 | 0.000 | 0.000 | 0.000 | 0.000 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 491 | 433 | 643 | 351 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 0.88 | 1.31 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.219 | 24.031 | 3.208 | 0.000 | 0.000 | 0.000 | 0.000 | 200.024 | 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 | 132 | 156 | 98 | 81 | 112 | 90 | 0 | 87 | 125 | 0 |
N.S. |
1 | 1.18 | 0.74 | 0.61 | 0.85 | 0.68 | 0.00 | 0.66 | 0.95 | 0.00 |
time (sec) |
N/A | 0.737 | 0.469 | 1.358 | 0.113 | 0.082 | 0.000 | 0.299 | 0.155 | 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 | 111 | 132 | 93 | 76 | 99 | 85 | 0 | 82 | 111 | 0 |
N.S. |
1 | 1.19 | 0.84 | 0.68 | 0.89 | 0.77 | 0.00 | 0.74 | 1.00 | 0.00 |
time (sec) |
N/A | 0.591 | 0.441 | 1.447 | 0.116 | 0.075 | 0.000 | 0.296 | 0.157 | 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 | 95 | 111 | 88 | 71 | 87 | 80 | 0 | 77 | 97 | 0 |
N.S. |
1 | 1.17 | 0.93 | 0.75 | 0.92 | 0.84 | 0.00 | 0.81 | 1.02 | 0.00 |
time (sec) |
N/A | 0.482 | 0.375 | 1.204 | 0.116 | 0.079 | 0.000 | 0.295 | 0.155 | 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 | 90 | 106 | 83 | 66 | 74 | 75 | 0 | 72 | 83 | 0 |
N.S. |
1 | 1.18 | 0.92 | 0.73 | 0.82 | 0.83 | 0.00 | 0.80 | 0.92 | 0.00 |
time (sec) |
N/A | 0.464 | 0.295 | 1.237 | 0.120 | 0.086 | 0.000 | 0.272 | 0.148 | 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 | 118 | 174 | 108 | 91 | 104 | 118 | 0 | 122 | 119 | 0 |
N.S. |
1 | 1.47 | 0.92 | 0.77 | 0.88 | 1.00 | 0.00 | 1.03 | 1.01 | 0.00 |
time (sec) |
N/A | 0.679 | 0.448 | 1.437 | 0.126 | 0.078 | 0.000 | 0.339 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 181 | 115 | 108 | 0 | 147 | 0 | 349 | 226 | 0 |
N.S. |
1 | 1.46 | 0.93 | 0.87 | 0.00 | 1.19 | 0.00 | 2.81 | 1.82 | 0.00 |
time (sec) |
N/A | 0.724 | 0.552 | 1.449 | 0.000 | 0.087 | 0.000 | 0.420 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 268 | 115 | 108 | 0 | 171 | 0 | 197 | 347 | 0 |
N.S. |
1 | 2.05 | 0.88 | 0.82 | 0.00 | 1.31 | 0.00 | 1.50 | 2.65 | 0.00 |
time (sec) |
N/A | 0.863 | 0.690 | 1.477 | 0.000 | 0.091 | 0.000 | 0.320 | 0.157 | 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 | 139 | 226 | 118 | 101 | 129 | 128 | 0 | 132 | 147 | 0 |
N.S. |
1 | 1.63 | 0.85 | 0.73 | 0.93 | 0.92 | 0.00 | 0.95 | 1.06 | 0.00 |
time (sec) |
N/A | 0.816 | 0.542 | 1.443 | 0.125 | 0.087 | 0.000 | 0.285 | 0.150 | 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 | 109 | 123 | 83 | 66 | 77 | 75 | 0 | 72 | 83 | 0 |
N.S. |
1 | 1.13 | 0.76 | 0.61 | 0.71 | 0.69 | 0.00 | 0.66 | 0.76 | 0.00 |
time (sec) |
N/A | 0.743 | 0.416 | 1.410 | 0.117 | 0.081 | 0.000 | 0.293 | 0.147 | 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 | 90 | 99 | 78 | 61 | 62 | 70 | 0 | 67 | 69 | 0 |
N.S. |
1 | 1.10 | 0.87 | 0.68 | 0.69 | 0.78 | 0.00 | 0.74 | 0.77 | 0.00 |
time (sec) |
N/A | 0.567 | 0.367 | 1.426 | 0.109 | 0.088 | 0.000 | 0.296 | 0.172 | 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 | 69 | 80 | 73 | 56 | 49 | 65 | 0 | 62 | 57 | 0 |
N.S. |
1 | 1.16 | 1.06 | 0.81 | 0.71 | 0.94 | 0.00 | 0.90 | 0.83 | 0.00 |
time (sec) |
N/A | 0.435 | 0.295 | 1.391 | 0.111 | 0.082 | 0.000 | 0.270 | 0.161 | 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 | 53 | 59 | 57 | 44 | 37 | 53 | 0 | 50 | 46 | 0 |
N.S. |
1 | 1.11 | 1.08 | 0.83 | 0.70 | 1.00 | 0.00 | 0.94 | 0.87 | 0.00 |
time (sec) |
N/A | 0.352 | 0.199 | 1.247 | 0.115 | 0.079 | 0.000 | 0.291 | 0.156 | 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 | 28 | 29 | 31 | 25 | 16 | 31 | 0 | 27 | 25 | 0 |
N.S. |
1 | 1.04 | 1.11 | 0.89 | 0.57 | 1.11 | 0.00 | 0.96 | 0.89 | 0.00 |
time (sec) |
N/A | 0.260 | 0.155 | 1.253 | 0.110 | 0.077 | 0.000 | 1.180 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 69 | 68 | 58 | 0 | 81 | 0 | 84 | 77 | 0 |
N.S. |
1 | 1.08 | 1.06 | 0.91 | 0.00 | 1.27 | 0.00 | 1.31 | 1.20 | 0.00 |
time (sec) |
N/A | 0.386 | 0.286 | 1.414 | 0.000 | 0.085 | 0.000 | 0.285 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 92 | 91 | 77 | 0 | 116 | 0 | 213 | 175 | 0 |
N.S. |
1 | 1.06 | 1.05 | 0.89 | 0.00 | 1.33 | 0.00 | 2.45 | 2.01 | 0.00 |
time (sec) |
N/A | 0.432 | 0.423 | 1.466 | 0.000 | 0.086 | 0.000 | 0.303 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 115 | 96 | 92 | 0 | 141 | 0 | 176 | 286 | 0 |
N.S. |
1 | 1.05 | 0.87 | 0.84 | 0.00 | 1.28 | 0.00 | 1.60 | 2.60 | 0.00 |
time (sec) |
N/A | 0.522 | 0.525 | 1.409 | 0.000 | 0.081 | 0.000 | 0.240 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 123 | 90 | 83 | 81 | 98 | 0 | 422 | 138 | 0 |
N.S. |
1 | 1.13 | 0.83 | 0.76 | 0.74 | 0.90 | 0.00 | 3.87 | 1.27 | 0.00 |
time (sec) |
N/A | 0.718 | 0.517 | 1.473 | 0.115 | 0.117 | 0.000 | 0.395 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 101 | 85 | 75 | 68 | 93 | 0 | 326 | 124 | 0 |
N.S. |
1 | 1.10 | 0.92 | 0.82 | 0.74 | 1.01 | 0.00 | 3.54 | 1.35 | 0.00 |
time (sec) |
N/A | 0.567 | 0.468 | 1.454 | 0.121 | 0.080 | 0.000 | 0.427 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 87 | 80 | 63 | 56 | 88 | 0 | 176 | 112 | 0 |
N.S. |
1 | 1.14 | 1.05 | 0.83 | 0.74 | 1.16 | 0.00 | 2.32 | 1.47 | 0.00 |
time (sec) |
N/A | 0.437 | 0.390 | 1.428 | 0.123 | 0.078 | 0.000 | 0.447 | 0.184 | 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 | 55 | 56 | 57 | 47 | 36 | 63 | 0 | 83 | 73 | 0 |
N.S. |
1 | 1.02 | 1.04 | 0.85 | 0.65 | 1.15 | 0.00 | 1.51 | 1.33 | 0.00 |
time (sec) |
N/A | 0.308 | 0.282 | 1.270 | 0.113 | 0.075 | 0.000 | 0.285 | 0.182 | 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 | 55 | 56 | 57 | 47 | 36 | 62 | 0 | 81 | 73 | 0 |
N.S. |
1 | 1.02 | 1.04 | 0.85 | 0.65 | 1.13 | 0.00 | 1.47 | 1.33 | 0.00 |
time (sec) |
N/A | 0.307 | 0.224 | 1.303 | 0.112 | 0.077 | 0.000 | 0.325 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 124 | 91 | 77 | 0 | 116 | 0 | 244 | 175 | 0 |
N.S. |
1 | 1.43 | 1.05 | 0.89 | 0.00 | 1.33 | 0.00 | 2.80 | 2.01 | 0.00 |
time (sec) |
N/A | 0.475 | 0.430 | 1.470 | 0.000 | 0.089 | 0.000 | 0.282 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 147 | 103 | 87 | 0 | 141 | 0 | 455 | 286 | 0 |
N.S. |
1 | 1.34 | 0.94 | 0.79 | 0.00 | 1.28 | 0.00 | 4.14 | 2.60 | 0.00 |
time (sec) |
N/A | 0.529 | 0.590 | 1.412 | 0.000 | 0.084 | 0.000 | 0.407 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 170 | 108 | 104 | 0 | 166 | 0 | 549 | 395 | 0 |
N.S. |
1 | 1.28 | 0.81 | 0.78 | 0.00 | 1.25 | 0.00 | 4.13 | 2.97 | 0.00 |
time (sec) |
N/A | 0.606 | 0.673 | 1.506 | 0.000 | 0.090 | 0.000 | 0.399 | 0.195 | 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 | 115 | 132 | 90 | 83 | 92 | 118 | 0 | 154 | 203 | 0 |
N.S. |
1 | 1.15 | 0.78 | 0.72 | 0.80 | 1.03 | 0.00 | 1.34 | 1.77 | 0.00 |
time (sec) |
N/A | 0.754 | 0.465 | 1.401 | 0.114 | 0.087 | 0.000 | 0.277 | 0.186 | 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 | 99 | 115 | 85 | 78 | 80 | 113 | 0 | 142 | 189 | 0 |
N.S. |
1 | 1.16 | 0.86 | 0.79 | 0.81 | 1.14 | 0.00 | 1.43 | 1.91 | 0.00 |
time (sec) |
N/A | 0.584 | 0.472 | 1.441 | 0.112 | 0.079 | 0.000 | 0.262 | 0.187 | 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 | 78 | 84 | 62 | 62 | 60 | 83 | 0 | 121 | 128 | 0 |
N.S. |
1 | 1.08 | 0.79 | 0.79 | 0.77 | 1.06 | 0.00 | 1.55 | 1.64 | 0.00 |
time (sec) |
N/A | 0.396 | 0.391 | 1.344 | 0.111 | 0.080 | 0.000 | 0.241 | 0.190 | 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 | 78 | 84 | 62 | 62 | 60 | 83 | 0 | 121 | 128 | 0 |
N.S. |
1 | 1.08 | 0.79 | 0.79 | 0.77 | 1.06 | 0.00 | 1.55 | 1.64 | 0.00 |
time (sec) |
N/A | 0.366 | 0.379 | 1.260 | 0.115 | 0.075 | 0.000 | 0.257 | 0.237 | 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 | 78 | 84 | 62 | 62 | 60 | 83 | 0 | 121 | 128 | 0 |
N.S. |
1 | 1.08 | 0.79 | 0.79 | 0.77 | 1.06 | 0.00 | 1.55 | 1.64 | 0.00 |
time (sec) |
N/A | 0.364 | 0.353 | 1.177 | 0.109 | 0.076 | 0.000 | 0.249 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 147 | 96 | 92 | 0 | 141 | 0 | 176 | 286 | 0 |
N.S. |
1 | 1.34 | 0.87 | 0.84 | 0.00 | 1.28 | 0.00 | 1.60 | 2.60 | 0.00 |
time (sec) |
N/A | 0.529 | 0.540 | 1.377 | 0.000 | 0.082 | 0.000 | 0.310 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 170 | 108 | 104 | 0 | 166 | 0 | 0 | 395 | 0 |
N.S. |
1 | 1.28 | 0.81 | 0.78 | 0.00 | 1.25 | 0.00 | 0.00 | 2.97 | 0.00 |
time (sec) |
N/A | 0.595 | 0.645 | 1.387 | 0.000 | 0.082 | 0.000 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 193 | 113 | 97 | 0 | 191 | 0 | 284 | 504 | 0 |
N.S. |
1 | 1.24 | 0.72 | 0.62 | 0.00 | 1.22 | 0.00 | 1.82 | 3.23 | 0.00 |
time (sec) |
N/A | 0.684 | 0.695 | 1.492 | 0.000 | 0.118 | 0.000 | 0.313 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 174 | 170 | 136 | 0 | 55 | 0 | 0 | 129 | 0 |
N.S. |
1 | 1.09 | 1.06 | 0.85 | 0.00 | 0.34 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.850 | 32.715 | 1.434 | 0.000 | 0.082 | 0.000 | 0.000 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 144 | 164 | 131 | 0 | 50 | 0 | 0 | 109 | 0 |
N.S. |
1 | 1.07 | 1.21 | 0.97 | 0.00 | 0.37 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.650 | 32.590 | 1.436 | 0.000 | 0.071 | 0.000 | 0.000 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 155 | 88 | 0 | 45 | 0 | 0 | 91 | 0 |
N.S. |
1 | 1.00 | 2.07 | 1.17 | 0.00 | 0.60 | 0.00 | 0.00 | 1.21 | 0.00 |
time (sec) |
N/A | 0.337 | 31.437 | 1.300 | 0.000 | 0.075 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 71 | 59 | 0 | 26 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 1.78 | 1.48 | 0.00 | 0.65 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.278 | 30.091 | 1.204 | 0.000 | 0.080 | 0.000 | 0.000 | 0.213 | 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 | 88 | 99 | 76 | 61 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.12 | 0.86 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.531 | 20.755 | 1.338 | 0.000 | 0.000 | 0.000 | 0.000 | 4.785 | 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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 176 | 154 | 249 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.09 | 0.95 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.969 | 20.746 | 1.745 | 0.000 | 0.000 | 0.000 | 0.000 | 5.017 | 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 | 194 | 316 | 133 | 275 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.63 | 0.69 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.972 | 20.702 | 1.706 | 0.000 | 0.000 | 0.000 | 0.000 | 5.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 201 | 175 | 141 | 0 | 60 | 0 | 0 | 149 | 0 |
N.S. |
1 | 1.09 | 0.95 | 0.76 | 0.00 | 0.32 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.803 | 32.869 | 1.421 | 0.000 | 0.092 | 0.000 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 171 | 170 | 136 | 0 | 55 | 0 | 0 | 129 | 0 |
N.S. |
1 | 1.07 | 1.06 | 0.85 | 0.00 | 0.34 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.614 | 32.689 | 1.407 | 0.000 | 0.073 | 0.000 | 0.000 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 141 | 165 | 131 | 0 | 50 | 0 | 0 | 109 | 0 |
N.S. |
1 | 1.04 | 1.22 | 0.97 | 0.00 | 0.37 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.520 | 31.357 | 1.347 | 0.000 | 0.078 | 0.000 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 111 | 160 | 126 | 0 | 45 | 0 | 0 | 91 | 0 |
N.S. |
1 | 1.05 | 1.51 | 1.19 | 0.00 | 0.42 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.439 | 31.333 | 1.347 | 0.000 | 0.072 | 0.000 | 0.000 | 0.224 | 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 | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 139 | 114 | 80 | 0 | 0 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.09 | 0.89 | 0.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.553 | 10.553 | 1.395 | 0.000 | 0.000 | 0.000 | 0.000 | 8.548 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 0 | 154 | 249 | 0 | 0 | 0 | 0 | 86 | 0 |
N.S. |
1 | 0.00 | 0.95 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.000 | 20.990 | 1.799 | 0.000 | 0.000 | 0.000 | 0.000 | 9.334 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 0 | 180 | 275 | 0 | 0 | 0 | 0 | 96 | 0 |
N.S. |
1 | 0.00 | 0.93 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.000 | 20.883 | 1.779 | 0.000 | 0.000 | 0.000 | 0.000 | 8.986 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 199 | 174 | 141 | 0 | 60 | 0 | 0 | 149 | 0 |
N.S. |
1 | 1.09 | 0.95 | 0.77 | 0.00 | 0.33 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.701 | 32.774 | 1.460 | 0.000 | 0.074 | 0.000 | 0.000 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 171 | 170 | 136 | 0 | 55 | 0 | 0 | 129 | 0 |
N.S. |
1 | 1.07 | 1.06 | 0.85 | 0.00 | 0.34 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.590 | 31.395 | 1.635 | 0.000 | 0.070 | 0.000 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 141 | 165 | 131 | 0 | 50 | 0 | 0 | 109 | 0 |
N.S. |
1 | 1.04 | 1.22 | 0.97 | 0.00 | 0.37 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.500 | 31.378 | 1.314 | 0.000 | 0.072 | 0.000 | 0.000 | 0.252 | 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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 166 | 165 | 165 | 0 | 0 | 0 | 0 | 148 | 0 |
N.S. |
1 | 1.07 | 1.06 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.692 | 20.814 | 1.748 | 0.000 | 0.000 | 0.000 | 0.000 | 10.348 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 0 | 169 | 249 | 0 | 0 | 0 | 0 | 319 | 0 |
N.S. |
1 | 0.00 | 1.04 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 1.97 | 0.00 |
time (sec) |
N/A | 0.000 | 20.818 | 1.780 | 0.000 | 0.000 | 0.000 | 0.000 | 10.671 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 0 | 133 | 275 | 0 | 0 | 0 | 0 | 523 | 0 |
N.S. |
1 | 0.00 | 0.69 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 2.70 | 0.00 |
time (sec) |
N/A | 0.000 | 20.838 | 1.812 | 0.000 | 0.000 | 0.000 | 0.000 | 10.711 | 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 | 610 | 670 | 1217 | 1153 | 0 | 1186 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.10 | 2.00 | 1.89 | 0.00 | 1.94 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 2.503 | 35.092 | 12.504 | 0.000 | 0.122 | 0.000 | 0.000 | 200.029 | 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 | 487 | 525 | 770 | 989 | 0 | 772 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.08 | 1.58 | 2.03 | 0.00 | 1.59 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.414 | 29.241 | 6.327 | 0.000 | 0.099 | 0.000 | 0.000 | 200.031 | 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 | 439 | 477 | 551 | 913 | 0 | 548 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.09 | 1.26 | 2.08 | 0.00 | 1.25 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.094 | 25.789 | 6.046 | 0.000 | 0.095 | 0.000 | 0.000 | 200.023 | 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 | 238 | 248 | 408 | 872 | 0 | 459 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.04 | 1.71 | 3.66 | 0.00 | 1.93 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.558 | 11.949 | 5.523 | 0.000 | 0.085 | 0.000 | 0.000 | 200.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 511 | 552 | 949 | 1264 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.08 | 1.86 | 2.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 2.403 | 28.003 | 7.957 | 0.000 | 0.000 | 0.000 | 0.000 | 200.023 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 885 | 0 | 14907 | 1574 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 0.00 | 16.84 | 1.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 0.000 | 37.177 | 12.931 | 0.000 | 0.000 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 141 | 165 | 131 | 0 | 48 | 0 | 0 | 109 | 0 |
N.S. |
1 | 1.04 | 1.22 | 0.97 | 0.00 | 0.36 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.623 | 32.688 | 1.463 | 0.000 | 0.088 | 0.000 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 111 | 160 | 126 | 0 | 45 | 0 | 0 | 91 | 0 |
N.S. |
1 | 1.05 | 1.51 | 1.19 | 0.00 | 0.42 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.540 | 32.575 | 1.417 | 0.000 | 0.073 | 0.000 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 150 | 62 | 0 | 26 | 0 | 0 | 72 | 0 |
N.S. |
1 | 1.00 | 1.81 | 0.75 | 0.00 | 0.31 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.376 | 31.493 | 1.240 | 0.000 | 0.074 | 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 | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 65 | 42 | 0 | 11 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.55 | 1.00 | 0.00 | 0.26 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.276 | 31.100 | 1.221 | 0.000 | 0.084 | 0.000 | 0.000 | 0.210 | 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 | 45 | 56 | 87 | 43 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.24 | 1.93 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.348 | 21.696 | 1.371 | 0.000 | 0.000 | 0.000 | 0.000 | 6.617 | 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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 176 | 169 | 249 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.09 | 1.04 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.916 | 20.742 | 1.744 | 0.000 | 0.000 | 0.000 | 0.000 | 6.814 | 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 | 194 | 314 | 133 | 275 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.62 | 0.69 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 1.921 | 20.839 | 1.733 | 0.000 | 0.000 | 0.000 | 0.000 | 7.111 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 137 | 155 | 126 | 0 | 69 | 0 | 0 | 220 | 0 |
N.S. |
1 | 1.01 | 1.15 | 0.93 | 0.00 | 0.51 | 0.00 | 0.00 | 1.63 | 0.00 |
time (sec) |
N/A | 0.617 | 32.801 | 1.328 | 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 | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 111 | 150 | 121 | 0 | 64 | 0 | 0 | 202 | 0 |
N.S. |
1 | 1.03 | 1.39 | 1.12 | 0.00 | 0.59 | 0.00 | 0.00 | 1.87 | 0.00 |
time (sec) |
N/A | 0.446 | 32.698 | 1.362 | 0.000 | 0.075 | 0.000 | 0.000 | 0.271 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 111 | 86 | 121 | 0 | 64 | 0 | 0 | 86 | 0 |
N.S. |
1 | 1.03 | 0.80 | 1.12 | 0.00 | 0.59 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.429 | 31.247 | 1.247 | 0.000 | 0.077 | 0.000 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 119 | 120 | 0 | 64 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 1.75 | 1.76 | 0.00 | 0.94 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.324 | 20.135 | 1.215 | 0.000 | 0.075 | 0.000 | 0.000 | 0.209 | 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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 124 | 154 | 160 | 0 | 0 | 0 | 0 | 421 | 0 |
N.S. |
1 | 1.10 | 1.36 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 3.73 | 0.00 |
time (sec) |
N/A | 0.493 | 21.016 | 1.366 | 0.000 | 0.000 | 0.000 | 0.000 | 7.516 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 0 | 134 | 277 | 0 | 0 | 0 | 0 | 50 | 0 |
N.S. |
1 | 0.00 | 0.72 | 1.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.000 | 20.939 | 1.368 | 0.000 | 0.000 | 0.000 | 0.000 | 5.066 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 0 | 139 | 303 | 0 | 0 | 0 | 0 | 55 | 0 |
N.S. |
1 | 0.00 | 0.63 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.000 | 20.937 | 1.375 | 0.000 | 0.000 | 0.000 | 0.000 | 5.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 141 | 157 | 189 | 0 | 84 | 0 | 0 | 348 | 0 |
N.S. |
1 | 1.04 | 1.16 | 1.40 | 0.00 | 0.62 | 0.00 | 0.00 | 2.58 | 0.00 |
time (sec) |
N/A | 0.620 | 32.831 | 1.410 | 0.000 | 0.077 | 0.000 | 0.000 | 0.356 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 141 | 150 | 189 | 0 | 84 | 0 | 0 | 330 | 0 |
N.S. |
1 | 1.04 | 1.11 | 1.40 | 0.00 | 0.62 | 0.00 | 0.00 | 2.44 | 0.00 |
time (sec) |
N/A | 0.526 | 32.735 | 1.354 | 0.000 | 0.076 | 0.000 | 0.000 | 0.324 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 141 | 150 | 189 | 0 | 84 | 0 | 0 | 96 | 0 |
N.S. |
1 | 1.04 | 1.11 | 1.40 | 0.00 | 0.62 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.500 | 31.420 | 1.267 | 0.000 | 0.080 | 0.000 | 0.000 | 0.320 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 141 | 150 | 189 | 0 | 84 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.04 | 1.11 | 1.40 | 0.00 | 0.62 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.496 | 20.302 | 1.289 | 0.000 | 0.083 | 0.000 | 0.000 | 0.267 | 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 | 180 | 191 | 128 | 268 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.06 | 0.71 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.646 | 21.181 | 1.704 | 0.000 | 0.000 | 0.000 | 0.000 | 6.815 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 0 | 139 | 301 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.00 | 0.66 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.000 | 20.934 | 1.358 | 0.000 | 0.000 | 0.000 | 0.000 | 7.053 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 0 | 144 | 327 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 0.00 | 0.59 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.000 | 20.892 | 1.429 | 0.000 | 0.000 | 0.000 | 0.000 | 7.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 575 | 0 | 820 | 939 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 0.00 | 1.43 | 1.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.000 | 34.598 | 6.101 | 0.000 | 0.000 | 0.000 | 0.000 | 200.025 | 0.000 |