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 | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 91 | 48 | 61 | 0 | 74 | 0 | 121 | 45 | 116 |
N.S. |
1 | 1.06 | 0.56 | 0.71 | 0.00 | 0.86 | 0.00 | 1.41 | 0.52 | 1.35 |
time (sec) |
N/A | 0.474 | 0.092 | 1.301 | 0.000 | 0.102 | 0.000 | 0.385 | 0.173 | 12.993 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 38 | 47 | 0 | 61 | 0 | 93 | 43 | 111 |
N.S. |
1 | 1.00 | 0.64 | 0.80 | 0.00 | 1.03 | 0.00 | 1.58 | 0.73 | 1.88 |
time (sec) |
N/A | 0.336 | 0.063 | 1.140 | 0.000 | 0.078 | 0.000 | 0.358 | 0.189 | 1.171 |
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 | 66 | 66 | 75 | 124 | 997 | 235 | 0 | 195 | 34 | 0 |
N.S. |
1 | 1.00 | 1.14 | 1.88 | 15.11 | 3.56 | 0.00 | 2.95 | 0.52 | 0.00 |
time (sec) |
N/A | 0.302 | 0.168 | 2.276 | 0.213 | 0.090 | 0.000 | 0.393 | 0.175 | 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 | 65 | 94 | 82 | 132 | 803 | 248 | 0 | 278 | 47 | 0 |
N.S. |
1 | 1.45 | 1.26 | 2.03 | 12.35 | 3.82 | 0.00 | 4.28 | 0.72 | 0.00 |
time (sec) |
N/A | 0.471 | 0.150 | 2.980 | 0.238 | 0.091 | 0.000 | 0.388 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 104 | 108 | 137 | 0 | 278 | 0 | 0 | 51 | 0 |
N.S. |
1 | 0.98 | 1.02 | 1.29 | 0.00 | 2.62 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.501 | 0.248 | 3.230 | 0.000 | 0.106 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 145 | 120 | 148 | 0 | 300 | 0 | 535 | 51 | 0 |
N.S. |
1 | 1.01 | 0.83 | 1.03 | 0.00 | 2.08 | 0.00 | 3.72 | 0.35 | 0.00 |
time (sec) |
N/A | 0.668 | 0.360 | 3.240 | 0.000 | 0.097 | 0.000 | 0.659 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 226 | 80 | 95 | 0 | 121 | 0 | 209 | 69 | 542 |
N.S. |
1 | 1.11 | 0.39 | 0.47 | 0.00 | 0.60 | 0.00 | 1.03 | 0.34 | 2.67 |
time (sec) |
N/A | 1.221 | 0.152 | 47.621 | 0.000 | 0.081 | 0.000 | 0.531 | 0.183 | 20.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 165 | 70 | 85 | 0 | 108 | 0 | 180 | 69 | 456 |
N.S. |
1 | 1.13 | 0.48 | 0.58 | 0.00 | 0.74 | 0.00 | 1.23 | 0.47 | 3.12 |
time (sec) |
N/A | 0.846 | 0.313 | 17.394 | 0.000 | 0.090 | 0.000 | 0.622 | 0.213 | 16.734 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 125 | 60 | 75 | 0 | 95 | 0 | 151 | 69 | 349 |
N.S. |
1 | 1.08 | 0.52 | 0.65 | 0.00 | 0.82 | 0.00 | 1.30 | 0.59 | 3.01 |
time (sec) |
N/A | 0.615 | 0.127 | 6.151 | 0.000 | 0.086 | 0.000 | 0.491 | 0.186 | 13.221 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 93 | 50 | 63 | 0 | 82 | 0 | 122 | 67 | 146 |
N.S. |
1 | 1.04 | 0.56 | 0.71 | 0.00 | 0.92 | 0.00 | 1.37 | 0.75 | 1.64 |
time (sec) |
N/A | 0.455 | 0.068 | 2.600 | 0.000 | 0.079 | 0.000 | 0.560 | 0.214 | 13.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | F | B | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 102 | 360 | 135 | 1395 | 310 | 0 | 225 | 58 | 0 |
N.S. |
1 | 1.04 | 3.67 | 1.38 | 14.23 | 3.16 | 0.00 | 2.30 | 0.59 | 0.00 |
time (sec) |
N/A | 0.542 | 8.928 | 2.796 | 0.234 | 0.097 | 0.000 | 0.481 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 97 | 82 | 137 | 1383 | 276 | 0 | 368 | 77 | 0 |
N.S. |
1 | 1.03 | 0.87 | 1.46 | 14.71 | 2.94 | 0.00 | 3.91 | 0.82 | 0.00 |
time (sec) |
N/A | 0.513 | 0.227 | 10.618 | 0.241 | 0.097 | 0.000 | 0.673 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 108 | 150 | 139 | 0 | 294 | 0 | 364 | 83 | 0 |
N.S. |
1 | 1.02 | 1.42 | 1.31 | 0.00 | 2.77 | 0.00 | 3.43 | 0.78 | 0.00 |
time (sec) |
N/A | 0.547 | 0.357 | 33.093 | 0.000 | 0.099 | 0.000 | 0.518 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 148 | 151 | 150 | 0 | 320 | 0 | 539 | 83 | 0 |
N.S. |
1 | 1.03 | 1.05 | 1.04 | 0.00 | 2.22 | 0.00 | 3.74 | 0.58 | 0.00 |
time (sec) |
N/A | 0.761 | 0.535 | 125.655 | 0.000 | 0.099 | 0.000 | 0.735 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 189 | 92 | 160 | 0 | 346 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.04 | 0.51 | 0.88 | 0.00 | 1.90 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.969 | 0.615 | 1.379 | 0.000 | 0.098 | 0.000 | 0.000 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 30 | 38 | 0 | 44 | 0 | 57 | 23 | 36 |
N.S. |
1 | 1.00 | 1.11 | 1.41 | 0.00 | 1.63 | 0.00 | 2.11 | 0.85 | 1.33 |
time (sec) |
N/A | 0.225 | 0.120 | 0.951 | 0.000 | 0.074 | 0.000 | 0.194 | 0.177 | 9.442 |
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 | 38 | 38 | 85 | 81 | 146 | 182 | 0 | 65 | 16 | 0 |
N.S. |
1 | 1.00 | 2.24 | 2.13 | 3.84 | 4.79 | 0.00 | 1.71 | 0.42 | 0.00 |
time (sec) |
N/A | 0.210 | 0.391 | 1.035 | 0.240 | 0.108 | 0.000 | 0.248 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 77 | 95 | 791 | 294 | 0 | 134 | 23 | 0 |
N.S. |
1 | 1.00 | 1.18 | 1.46 | 12.17 | 4.52 | 0.00 | 2.06 | 0.35 | 0.00 |
time (sec) |
N/A | 0.332 | 0.204 | 2.616 | 0.293 | 0.113 | 0.000 | 0.197 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 154 | 106 | 131 | 0 | 347 | 0 | 150 | 36 | 0 |
N.S. |
1 | 1.10 | 0.76 | 0.94 | 0.00 | 2.48 | 0.00 | 1.07 | 0.26 | 0.00 |
time (sec) |
N/A | 0.832 | 0.148 | 1.026 | 0.000 | 0.108 | 0.000 | 0.406 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 112 | 86 | 117 | 0 | 316 | 0 | 113 | 36 | 0 |
N.S. |
1 | 1.08 | 0.83 | 1.12 | 0.00 | 3.04 | 0.00 | 1.09 | 0.35 | 0.00 |
time (sec) |
N/A | 0.533 | 0.104 | 0.988 | 0.000 | 0.104 | 0.000 | 0.395 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 83 | 95 | 0 | 262 | 0 | 108 | 36 | 0 |
N.S. |
1 | 1.00 | 1.14 | 1.30 | 0.00 | 3.59 | 0.00 | 1.48 | 0.49 | 0.00 |
time (sec) |
N/A | 0.350 | 0.055 | 0.858 | 0.000 | 0.100 | 0.000 | 0.377 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 64 | 76 | 0 | 158 | 0 | 59 | 34 | 0 |
N.S. |
1 | 1.00 | 1.39 | 1.65 | 0.00 | 3.43 | 0.00 | 1.28 | 0.74 | 0.00 |
time (sec) |
N/A | 0.232 | 0.037 | 0.868 | 0.000 | 0.129 | 0.000 | 0.208 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 130 | 131 | 698 | 294 | 0 | 69 | 28 | 0 |
N.S. |
1 | 1.00 | 1.53 | 1.54 | 8.21 | 3.46 | 0.00 | 0.81 | 0.33 | 0.00 |
time (sec) |
N/A | 0.398 | 0.499 | 0.827 | 0.389 | 0.105 | 0.000 | 0.364 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 109 | 105 | 199 | 0 | 417 | 0 | 326 | 34 | 0 |
N.S. |
1 | 1.01 | 0.97 | 1.84 | 0.00 | 3.86 | 0.00 | 3.02 | 0.31 | 0.00 |
time (sec) |
N/A | 0.534 | 0.093 | 2.476 | 0.000 | 0.113 | 0.000 | 0.396 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 159 | 118 | 208 | 0 | 446 | 0 | 423 | 36 | 0 |
N.S. |
1 | 1.08 | 0.80 | 1.41 | 0.00 | 3.03 | 0.00 | 2.88 | 0.24 | 0.00 |
time (sec) |
N/A | 0.857 | 0.165 | 2.616 | 0.000 | 0.118 | 0.000 | 0.419 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 199 | 124 | 165 | 0 | 414 | 0 | 210 | 46 | 0 |
N.S. |
1 | 1.09 | 0.68 | 0.90 | 0.00 | 2.26 | 0.00 | 1.15 | 0.25 | 0.00 |
time (sec) |
N/A | 1.073 | 0.272 | 1.670 | 0.000 | 0.118 | 0.000 | 0.463 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 154 | 114 | 149 | 0 | 387 | 0 | 179 | 46 | 0 |
N.S. |
1 | 1.06 | 0.79 | 1.03 | 0.00 | 2.67 | 0.00 | 1.23 | 0.32 | 0.00 |
time (sec) |
N/A | 0.805 | 0.208 | 1.685 | 0.000 | 0.155 | 0.000 | 0.566 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 109 | 104 | 120 | 0 | 336 | 0 | 157 | 46 | 0 |
N.S. |
1 | 1.04 | 0.99 | 1.14 | 0.00 | 3.20 | 0.00 | 1.50 | 0.44 | 0.00 |
time (sec) |
N/A | 0.546 | 0.210 | 1.465 | 0.000 | 0.117 | 0.000 | 0.472 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 94 | 115 | 0 | 329 | 0 | 108 | 46 | 0 |
N.S. |
1 | 1.00 | 1.22 | 1.49 | 0.00 | 4.27 | 0.00 | 1.40 | 0.60 | 0.00 |
time (sec) |
N/A | 0.364 | 0.136 | 1.340 | 0.000 | 0.104 | 0.000 | 0.418 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 93 | 114 | 0 | 327 | 0 | 108 | 44 | 0 |
N.S. |
1 | 1.00 | 1.21 | 1.48 | 0.00 | 4.25 | 0.00 | 1.40 | 0.57 | 0.00 |
time (sec) |
N/A | 0.353 | 0.077 | 1.290 | 0.000 | 0.108 | 0.000 | 0.324 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 120 | 181 | 169 | 0 | 491 | 0 | 47 | 38 | 0 |
N.S. |
1 | 1.05 | 1.59 | 1.48 | 0.00 | 4.31 | 0.00 | 0.41 | 0.33 | 0.00 |
time (sec) |
N/A | 0.585 | 1.681 | 1.368 | 0.000 | 0.140 | 0.000 | 0.310 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 152 | 129 | 240 | 0 | 518 | 0 | 387 | 44 | 0 |
N.S. |
1 | 1.06 | 0.90 | 1.67 | 0.00 | 3.60 | 0.00 | 2.69 | 0.31 | 0.00 |
time (sec) |
N/A | 0.825 | 0.590 | 3.127 | 0.000 | 0.150 | 0.000 | 0.511 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 200 | 177 | 250 | 0 | 536 | 0 | 473 | 46 | 0 |
N.S. |
1 | 1.08 | 0.96 | 1.35 | 0.00 | 2.90 | 0.00 | 2.56 | 0.25 | 0.00 |
time (sec) |
N/A | 1.192 | 1.181 | 3.605 | 0.000 | 0.139 | 0.000 | 0.563 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 199 | 135 | 179 | 0 | 455 | 0 | 219 | 56 | 0 |
N.S. |
1 | 1.09 | 0.74 | 0.98 | 0.00 | 2.49 | 0.00 | 1.20 | 0.31 | 0.00 |
time (sec) |
N/A | 1.115 | 0.918 | 1.594 | 0.000 | 0.112 | 0.000 | 0.481 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 155 | 125 | 142 | 0 | 404 | 0 | 188 | 56 | 0 |
N.S. |
1 | 1.07 | 0.86 | 0.98 | 0.00 | 2.79 | 0.00 | 1.30 | 0.39 | 0.00 |
time (sec) |
N/A | 0.804 | 0.505 | 1.441 | 0.000 | 0.135 | 0.000 | 0.425 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 113 | 116 | 162 | 0 | 403 | 0 | 139 | 56 | 0 |
N.S. |
1 | 1.06 | 1.08 | 1.51 | 0.00 | 3.77 | 0.00 | 1.30 | 0.52 | 0.00 |
time (sec) |
N/A | 0.558 | 0.454 | 1.405 | 0.000 | 0.113 | 0.000 | 0.545 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 112 | 115 | 192 | 0 | 399 | 0 | 139 | 56 | 0 |
N.S. |
1 | 1.05 | 1.07 | 1.79 | 0.00 | 3.73 | 0.00 | 1.30 | 0.52 | 0.00 |
time (sec) |
N/A | 0.496 | 0.450 | 1.421 | 0.000 | 0.108 | 0.000 | 0.597 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 112 | 52 | 192 | 0 | 403 | 0 | 139 | 54 | 0 |
N.S. |
1 | 1.05 | 0.49 | 1.79 | 0.00 | 3.77 | 0.00 | 1.30 | 0.50 | 0.00 |
time (sec) |
N/A | 0.479 | 0.047 | 1.473 | 0.000 | 0.112 | 0.000 | 0.438 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 156 | 211 | 212 | 0 | 585 | 0 | 78 | 48 | 0 |
N.S. |
1 | 1.08 | 1.47 | 1.47 | 0.00 | 4.06 | 0.00 | 0.54 | 0.33 | 0.00 |
time (sec) |
N/A | 0.753 | 4.158 | 1.616 | 0.000 | 0.268 | 0.000 | 0.422 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 190 | 169 | 280 | 0 | 606 | 0 | 424 | 54 | 0 |
N.S. |
1 | 1.09 | 0.97 | 1.61 | 0.00 | 3.48 | 0.00 | 2.44 | 0.31 | 0.00 |
time (sec) |
N/A | 1.114 | 1.305 | 3.463 | 0.000 | 0.181 | 0.000 | 0.639 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 62 | 0 | 0 | 161 | 0 | 67 | 37 | 0 |
N.S. |
1 | 1.00 | 1.29 | 0.00 | 0.00 | 3.35 | 0.00 | 1.40 | 0.77 | 0.00 |
time (sec) |
N/A | 0.227 | 0.132 | 0.000 | 0.000 | 0.109 | 0.000 | 0.208 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | C | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 127 | 0 | 698 | 301 | 0 | 69 | 31 | 0 |
N.S. |
1 | 1.00 | 1.46 | 0.00 | 8.02 | 3.46 | 0.00 | 0.79 | 0.36 | 0.00 |
time (sec) |
N/A | 0.405 | 0.490 | 0.000 | 0.382 | 0.096 | 0.000 | 0.264 | 0.181 | 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 | 383 | 421 | 105 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.10 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.835 | 0.184 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 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 | 353 | 381 | 85 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.08 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.578 | 0.093 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 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 | 326 | 351 | 66 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.08 | 0.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.429 | 0.037 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 691 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 8.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.344 | 3.531 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 2700 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 35.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.418 | 14.499 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 413 | 458 | 96 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.11 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.825 | 0.225 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 383 | 417 | 106 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.09 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.602 | 0.310 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.221 | 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 | 356 | 387 | 66 | 0 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.09 | 0.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.447 | 0.053 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 86 | 2694 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.10 | 34.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.343 | 14.393 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 86 | 2700 | 0 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.10 | 34.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.415 | 14.523 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 371 | 390 | 155 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.05 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.092 | 0.262 | 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 | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 336 | 346 | 95 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.03 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.756 | 0.147 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 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 | 306 | 306 | 85 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.564 | 0.077 | 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 | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 276 | 65 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.431 | 0.046 | 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 | B | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 718 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 9.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.338 | 3.094 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 240 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 3.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.404 | 1.275 | 0.000 | 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 | C | F | F(-1) | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 766 | 781 | 111 | 0 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.02 | 0.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.422 | 0.378 | 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 | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 731 | 734 | 98 | 0 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 0.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.991 | 0.185 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 731 | 736 | 90 | 0 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.01 | 0.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.834 | 0.223 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 744 | 741 | 68 | 0 | 0 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.00 | 0.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.680 | 0.047 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 100 | 3007 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.22 | 36.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.340 | 14.836 | 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 | B | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 100 | 3011 | 0 | 0 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.22 | 36.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.443 | 14.821 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 153 | 115 | 384 | 0 | 188 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.01 | 0.76 | 2.54 | 0.00 | 1.25 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.650 | 0.268 | 3.989 | 0.000 | 0.100 | 0.000 | 0.000 | 0.185 | 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 | 123 | 125 | 83 | 368 | 0 | 167 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.02 | 0.67 | 2.99 | 0.00 | 1.36 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.535 | 0.208 | 2.047 | 0.000 | 0.091 | 0.000 | 0.000 | 0.175 | 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 | 97 | 98 | 68 | 148 | 0 | 124 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.01 | 0.70 | 1.53 | 0.00 | 1.28 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.516 | 0.151 | 1.312 | 0.000 | 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 | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 49 | 150 | 0 | 107 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 0.65 | 2.00 | 0.00 | 1.43 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.381 | 0.115 | 1.337 | 0.000 | 0.089 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 102 | 73 | 225 | 0 | 125 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.01 | 0.72 | 2.23 | 0.00 | 1.24 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.491 | 0.161 | 3.584 | 0.000 | 0.099 | 0.000 | 0.000 | 0.177 | 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 | 127 | 129 | 93 | 219 | 0 | 145 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.02 | 0.73 | 1.72 | 0.00 | 1.14 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.530 | 0.206 | 6.123 | 0.000 | 0.092 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 157 | 103 | 270 | 0 | 156 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.04 | 0.68 | 1.79 | 0.00 | 1.03 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.653 | 0.261 | 9.613 | 0.000 | 0.096 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 187 | 287 | 439 | 0 | 215 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.00 | 1.53 | 2.35 | 0.00 | 1.15 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 1.066 | 1.961 | 7.721 | 0.000 | 0.095 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 159 | 269 | 386 | 0 | 202 | 0 | 0 | 59 | 0 |
N.S. |
1 | 0.99 | 1.67 | 2.40 | 0.00 | 1.25 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.890 | 1.629 | 3.542 | 0.000 | 0.141 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 264 | 371 | 0 | 179 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.00 | 2.02 | 2.83 | 0.00 | 1.37 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.762 | 1.405 | 2.238 | 0.000 | 0.097 | 0.000 | 0.000 | 0.199 | 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 | 64 | 64 | 48 | 185 | 0 | 77 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.00 | 0.75 | 2.89 | 0.00 | 1.20 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.448 | 0.684 | 2.265 | 0.000 | 0.089 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 156 | 228 | 0 | 134 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 1.46 | 2.13 | 0.00 | 1.25 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.629 | 1.361 | 2.163 | 0.000 | 0.087 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 136 | 250 | 0 | 157 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.00 | 1.01 | 1.85 | 0.00 | 1.16 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.772 | 1.646 | 6.296 | 0.000 | 0.093 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 163 | 149 | 272 | 0 | 170 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.01 | 0.93 | 1.69 | 0.00 | 1.06 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.884 | 1.896 | 10.057 | 0.000 | 0.091 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 187 | 287 | 439 | 0 | 215 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.00 | 1.53 | 2.35 | 0.00 | 1.15 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.450 | 2.879 | 6.077 | 0.000 | 0.093 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 157 | 267 | 386 | 0 | 200 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.00 | 1.70 | 2.46 | 0.00 | 1.27 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.393 | 2.620 | 3.790 | 0.000 | 0.093 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 187 | 371 | 0 | 179 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.00 | 1.43 | 2.83 | 0.00 | 1.37 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.375 | 2.307 | 3.234 | 0.000 | 0.094 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 169 | 172 | 0 | 148 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.00 | 1.29 | 1.31 | 0.00 | 1.13 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.376 | 2.143 | 3.447 | 0.000 | 0.094 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 171 | 250 | 0 | 156 | 0 | 0 | 72 | 0 |
N.S. |
1 | 1.00 | 1.31 | 1.91 | 0.00 | 1.19 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.369 | 1.887 | 4.017 | 0.000 | 0.088 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 146 | 272 | 0 | 170 | 0 | 0 | 81 | 0 |
N.S. |
1 | 1.00 | 0.91 | 1.69 | 0.00 | 1.06 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.402 | 2.287 | 9.759 | 0.000 | 0.093 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 187 | 156 | 260 | 0 | 183 | 0 | 0 | 81 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.39 | 0.00 | 0.98 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.432 | 2.688 | 15.688 | 0.000 | 0.114 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 213 | 289 | 492 | 0 | 228 | 0 | 0 | 99 | 0 |
N.S. |
1 | 1.00 | 1.36 | 2.31 | 0.00 | 1.07 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.499 | 5.008 | 8.237 | 0.000 | 0.098 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 187 | 279 | 439 | 0 | 215 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.00 | 1.49 | 2.35 | 0.00 | 1.15 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.446 | 4.168 | 6.104 | 0.000 | 0.106 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 286 | 386 | 0 | 202 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.00 | 1.78 | 2.40 | 0.00 | 1.25 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.423 | 4.495 | 4.954 | 0.000 | 0.097 | 0.000 | 0.000 | 0.217 | 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 | 118 | 118 | 70 | 292 | 0 | 121 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.00 | 0.59 | 2.47 | 0.00 | 1.03 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.398 | 2.193 | 4.161 | 0.000 | 0.096 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 184 | 194 | 0 | 162 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.00 | 1.16 | 1.22 | 0.00 | 1.02 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.400 | 3.217 | 5.972 | 0.000 | 0.099 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 180 | 272 | 0 | 170 | 0 | 0 | 92 | 0 |
N.S. |
1 | 1.00 | 1.12 | 1.69 | 0.00 | 1.06 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.412 | 3.144 | 6.996 | 0.000 | 0.102 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 187 | 156 | 260 | 0 | 183 | 0 | 0 | 101 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.39 | 0.00 | 0.98 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.458 | 3.356 | 15.516 | 0.000 | 0.097 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 213 | 306 | 273 | 0 | 196 | 0 | 0 | 101 | 0 |
N.S. |
1 | 1.00 | 1.44 | 1.28 | 0.00 | 0.92 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.507 | 3.981 | 22.154 | 0.000 | 0.100 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 168 | 291 | 413 | 0 | 248 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.02 | 1.77 | 2.52 | 0.00 | 1.51 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.735 | 3.063 | 3.758 | 0.000 | 0.096 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 140 | 262 | 253 | 0 | 196 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.03 | 1.93 | 1.86 | 0.00 | 1.44 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.695 | 2.056 | 2.676 | 0.000 | 0.105 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 116 | 201 | 200 | 0 | 184 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.05 | 1.83 | 1.82 | 0.00 | 1.67 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.586 | 1.278 | 0.527 | 0.000 | 0.098 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 115 | 202 | 198 | 0 | 184 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.05 | 1.84 | 1.80 | 0.00 | 1.67 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.564 | 1.017 | 1.309 | 0.000 | 0.088 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 116 | 317 | 199 | 0 | 186 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.04 | 2.83 | 1.78 | 0.00 | 1.66 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.566 | 1.663 | 1.573 | 0.000 | 0.093 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 144 | 318 | 215 | 0 | 207 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.03 | 2.27 | 1.54 | 0.00 | 1.48 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.721 | 3.436 | 2.267 | 0.000 | 0.090 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 172 | 347 | 229 | 0 | 217 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.02 | 2.07 | 1.36 | 0.00 | 1.29 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.771 | 2.506 | 3.391 | 0.000 | 0.101 | 0.000 | 0.000 | 0.165 | 0.000 |