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 | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 58 | 50 | 98 | 0 | 124 | 0 | 96 | 0 |
N.S. |
1 | 1.16 | 1.00 | 1.96 | 0.00 | 2.48 | 0.00 | 1.92 | 0.00 |
time (sec) |
N/A | 0.403 | 0.027 | 0.489 | 0.000 | 0.266 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | B | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 58 | 47 | 98 | 0 | 111 | 95 | 0 | 0 |
N.S. |
1 | 1.23 | 1.00 | 2.09 | 0.00 | 2.36 | 2.02 | 0.00 | 0.00 |
time (sec) |
N/A | 0.652 | 0.038 | 0.490 | 0.000 | 0.266 | 4.292 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 55 | 28 | 27 | 0 | 28 | 0 | 0 | 24 |
N.S. |
1 | 1.31 | 0.67 | 0.64 | 0.00 | 0.67 | 0.00 | 0.00 | 0.57 |
time (sec) |
N/A | 0.660 | 0.045 | 0.484 | 0.000 | 0.257 | 0.000 | 0.000 | 4.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 78 | 36 | 35 | 0 | 36 | 0 | 0 | 32 |
N.S. |
1 | 1.13 | 0.52 | 0.51 | 0.00 | 0.52 | 0.00 | 0.00 | 0.46 |
time (sec) |
N/A | 0.673 | 0.052 | 0.478 | 0.000 | 0.252 | 0.000 | 0.000 | 3.900 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 105 | 44 | 43 | 0 | 44 | 0 | 0 | 77 |
N.S. |
1 | 1.09 | 0.46 | 0.45 | 0.00 | 0.46 | 0.00 | 0.00 | 0.80 |
time (sec) |
N/A | 0.693 | 0.060 | 0.482 | 0.000 | 0.251 | 0.000 | 0.000 | 4.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 130 | 52 | 51 | 0 | 52 | 0 | 0 | 98 |
N.S. |
1 | 1.07 | 0.43 | 0.42 | 0.00 | 0.43 | 0.00 | 0.00 | 0.81 |
time (sec) |
N/A | 0.715 | 0.072 | 0.478 | 0.000 | 0.239 | 0.000 | 0.000 | 4.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 313 | 188 | 252 | 224 | 0 | 568 | 0 | 0 | 0 |
N.S. |
1 | 0.60 | 0.81 | 0.72 | 0.00 | 1.81 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.502 | 1.449 | 0.257 | 0.000 | 0.328 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 261 | 160 | 244 | 202 | 0 | 552 | 0 | 0 | 0 |
N.S. |
1 | 0.61 | 0.93 | 0.77 | 0.00 | 2.11 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.468 | 1.077 | 0.247 | 0.000 | 0.336 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 209 | 132 | 236 | 180 | 0 | 536 | 0 | 0 | 0 |
N.S. |
1 | 0.63 | 1.13 | 0.86 | 0.00 | 2.56 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.408 | 1.598 | 0.243 | 0.000 | 0.336 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 152 | 104 | 95 | 160 | 0 | 512 | 0 | 0 | 0 |
N.S. |
1 | 0.68 | 0.62 | 1.05 | 0.00 | 3.37 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.337 | 0.059 | 0.233 | 0.000 | 0.323 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 146 | 100 | 218 | 159 | 0 | 490 | 0 | 0 | 0 |
N.S. |
1 | 0.68 | 1.49 | 1.09 | 0.00 | 3.36 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.420 | 0.804 | 0.256 | 0.000 | 0.336 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 138 | 155 | 140 | 0 | 353 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 1.24 | 1.12 | 0.00 | 2.82 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.430 | 0.382 | 0.247 | 0.000 | 0.300 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 170 | 177 | 162 | 165 | 0 | 381 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.95 | 0.97 | 0.00 | 2.24 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.466 | 0.442 | 0.259 | 0.000 | 0.298 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 209 | 221 | 170 | 187 | 0 | 397 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.81 | 0.89 | 0.00 | 1.90 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.538 | 0.437 | 0.261 | 0.000 | 0.297 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 303 | 276 | 178 | 206 | 0 | 413 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 0.59 | 0.68 | 0.00 | 1.36 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.776 | 0.496 | 0.262 | 0.000 | 0.289 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 126 | 117 | 93 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.523 | 0.073 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 164 | 177 | 147 | 133 | 0 | 337 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.90 | 0.81 | 0.00 | 2.05 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.534 | 0.899 | 0.141 | 0.000 | 0.285 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 132 | 139 | 116 | 0 | 321 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.12 | 0.94 | 0.00 | 2.59 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.422 | 1.492 | 0.137 | 0.000 | 0.284 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 87 | 65 | 101 | 0 | 297 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.82 | 1.28 | 0.00 | 3.76 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.332 | 0.044 | 0.124 | 0.000 | 0.287 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 83 | 132 | 100 | 0 | 275 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.74 | 1.32 | 0.00 | 3.62 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.397 | 0.635 | 0.135 | 0.000 | 0.279 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 78 | 46 | 54 | 0 | 59 | 0 | 0 | 54 |
N.S. |
1 | 1.11 | 0.66 | 0.77 | 0.00 | 0.84 | 0.00 | 0.00 | 0.77 |
time (sec) |
N/A | 0.364 | 0.195 | 0.124 | 0.000 | 0.247 | 0.000 | 0.000 | 4.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 120 | 58 | 62 | 0 | 69 | 0 | 0 | 62 |
N.S. |
1 | 1.06 | 0.51 | 0.55 | 0.00 | 0.61 | 0.00 | 0.00 | 0.55 |
time (sec) |
N/A | 0.385 | 0.273 | 0.116 | 0.000 | 0.269 | 0.000 | 0.000 | 3.997 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 149 | 169 | 66 | 70 | 0 | 77 | 0 | 0 | 100 |
N.S. |
1 | 1.13 | 0.44 | 0.47 | 0.00 | 0.52 | 0.00 | 0.00 | 0.67 |
time (sec) |
N/A | 0.485 | 0.240 | 0.135 | 0.000 | 0.249 | 0.000 | 0.000 | 4.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 172 | 207 | 116 | 197 | 0 | 271 | 0 | 0 | 0 |
N.S. |
1 | 1.20 | 0.67 | 1.15 | 0.00 | 1.58 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.799 | 0.166 | 0.490 | 0.000 | 0.281 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 147 | 174 | 108 | 189 | 0 | 259 | 0 | 0 | 0 |
N.S. |
1 | 1.18 | 0.73 | 1.29 | 0.00 | 1.76 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.785 | 0.117 | 0.490 | 0.000 | 0.264 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 141 | 100 | 181 | 0 | 239 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 0.82 | 1.48 | 0.00 | 1.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.625 | 0.096 | 0.484 | 0.000 | 0.271 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 108 | 92 | 168 | 0 | 219 | 0 | 0 | 0 |
N.S. |
1 | 1.17 | 1.00 | 1.83 | 0.00 | 2.38 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.451 | 0.029 | 0.481 | 0.000 | 0.273 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | B | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 104 | 86 | 165 | 0 | 203 | 141 | 0 | 0 |
N.S. |
1 | 1.21 | 1.00 | 1.92 | 0.00 | 2.36 | 1.64 | 0.00 | 0.00 |
time (sec) |
N/A | 0.710 | 0.048 | 0.523 | 0.000 | 0.263 | 4.276 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 86 | 69 | 142 | 0 | 161 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.84 | 1.73 | 0.00 | 1.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.672 | 0.075 | 0.499 | 0.000 | 0.258 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 79 | 152 | 0 | 181 | 0 | 278 | 0 |
N.S. |
1 | 1.00 | 0.70 | 1.35 | 0.00 | 1.60 | 0.00 | 2.46 | 0.00 |
time (sec) |
N/A | 0.696 | 0.092 | 0.517 | 0.000 | 0.251 | 0.000 | 0.638 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 117 | 87 | 160 | 0 | 201 | 0 | 356 | 0 |
N.S. |
1 | 1.04 | 0.77 | 1.42 | 0.00 | 1.78 | 0.00 | 3.15 | 0.00 |
time (sec) |
N/A | 0.731 | 0.146 | 0.510 | 0.000 | 0.255 | 0.000 | 0.742 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 163 | 167 | 95 | 168 | 0 | 213 | 0 | 434 | 0 |
N.S. |
1 | 1.02 | 0.58 | 1.03 | 0.00 | 1.31 | 0.00 | 2.66 | 0.00 |
time (sec) |
N/A | 0.762 | 0.161 | 0.505 | 0.000 | 0.252 | 0.000 | 0.879 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 303 | 172 | 167 | 197 | 0 | 353 | 0 | 0 | 0 |
N.S. |
1 | 0.57 | 0.55 | 0.65 | 0.00 | 1.17 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.449 | 1.115 | 0.144 | 0.000 | 0.291 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 251 | 144 | 159 | 180 | 0 | 337 | 0 | 0 | 0 |
N.S. |
1 | 0.57 | 0.63 | 0.72 | 0.00 | 1.34 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.435 | 0.951 | 0.146 | 0.000 | 0.293 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 199 | 116 | 151 | 163 | 0 | 321 | 0 | 0 | 0 |
N.S. |
1 | 0.58 | 0.76 | 0.82 | 0.00 | 1.61 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.374 | 1.614 | 0.143 | 0.000 | 0.282 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 92 | 67 | 146 | 0 | 299 | 0 | 0 | 0 |
N.S. |
1 | 0.66 | 0.48 | 1.04 | 0.00 | 2.14 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.325 | 0.047 | 0.124 | 0.000 | 0.280 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 90 | 131 | 151 | 0 | 277 | 0 | 0 | 0 |
N.S. |
1 | 0.67 | 0.98 | 1.13 | 0.00 | 2.07 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.407 | 0.831 | 0.151 | 0.000 | 0.269 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 115 | 58 | 62 | 0 | 59 | 0 | 0 | 54 |
N.S. |
1 | 1.06 | 0.53 | 0.57 | 0.00 | 0.54 | 0.00 | 0.00 | 0.50 |
time (sec) |
N/A | 0.408 | 0.217 | 0.154 | 0.000 | 0.263 | 0.000 | 0.000 | 4.193 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 150 | 157 | 70 | 70 | 0 | 69 | 0 | 0 | 62 |
N.S. |
1 | 1.05 | 0.47 | 0.47 | 0.00 | 0.46 | 0.00 | 0.00 | 0.41 |
time (sec) |
N/A | 0.432 | 0.274 | 0.151 | 0.000 | 0.258 | 0.000 | 0.000 | 4.247 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 188 | 205 | 78 | 78 | 0 | 77 | 0 | 0 | 100 |
N.S. |
1 | 1.09 | 0.41 | 0.41 | 0.00 | 0.41 | 0.00 | 0.00 | 0.53 |
time (sec) |
N/A | 0.497 | 0.261 | 0.153 | 0.000 | 0.251 | 0.000 | 0.000 | 4.447 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 289 | 253 | 86 | 86 | 0 | 85 | 0 | 0 | 108 |
N.S. |
1 | 0.88 | 0.30 | 0.30 | 0.00 | 0.29 | 0.00 | 0.00 | 0.37 |
time (sec) |
N/A | 0.756 | 0.330 | 0.139 | 0.000 | 0.269 | 0.000 | 0.000 | 4.162 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 185 | 187 | 155 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.335 | 0.379 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 97 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.286 | 0.466 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 166 | 163 | 113 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.338 | 0.075 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F(-1) | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.415 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F(-1) | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.414 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F(-1) | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.400 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F(-1) | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.423 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.369 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 67 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.334 | 0.034 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.360 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 57 | 69 | 46 | 0 | 0 | 0 | 269 | 0 | 0 |
N.S. |
1 | 1.21 | 0.81 | 0.00 | 0.00 | 0.00 | 4.72 | 0.00 | 0.00 |
time (sec) |
N/A | 0.365 | 0.033 | 0.000 | 0.000 | 0.000 | 4.895 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.343 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.341 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 114 | 124 | 87 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.417 | 0.060 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 393 | 0 | 111 | 160 | 415 | 169 | 0 | 218 | 362 |
N.S. |
1 | 0.00 | 0.28 | 0.41 | 1.06 | 0.43 | 0.00 | 0.55 | 0.92 |
time (sec) |
N/A | 0.000 | 0.208 | 0.478 | 0.202 | 0.259 | 0.000 | 0.307 | 4.413 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 313 | 0 | 95 | 144 | 337 | 148 | 0 | 178 | 289 |
N.S. |
1 | 0.00 | 0.30 | 0.46 | 1.08 | 0.47 | 0.00 | 0.57 | 0.92 |
time (sec) |
N/A | 0.000 | 0.203 | 0.489 | 0.207 | 0.248 | 0.000 | 0.293 | 3.960 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 233 | 0 | 79 | 128 | 259 | 125 | 0 | 137 | 214 |
N.S. |
1 | 0.00 | 0.34 | 0.55 | 1.11 | 0.54 | 0.00 | 0.59 | 0.92 |
time (sec) |
N/A | 0.000 | 0.136 | 0.489 | 0.204 | 0.260 | 0.000 | 0.287 | 3.885 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 145 | 0 | 61 | 108 | 171 | 91 | 0 | 90 | 131 |
N.S. |
1 | 0.00 | 0.42 | 0.74 | 1.18 | 0.63 | 0.00 | 0.62 | 0.90 |
time (sec) |
N/A | 0.000 | 0.110 | 0.062 | 0.201 | 0.248 | 0.000 | 0.278 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 23 | 22 | 34 | 0 | 0 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.77 | 1.69 | 2.62 | 0.00 | 0.00 | 1.69 |
time (sec) |
N/A | 0.192 | 0.153 | 0.496 | 0.213 | 0.247 | 0.000 | 0.000 | 3.834 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 50 | 47 | 65 | 58 | 0 | 0 | 50 |
N.S. |
1 | 1.00 | 0.98 | 0.92 | 1.27 | 1.14 | 0.00 | 0.00 | 0.98 |
time (sec) |
N/A | 0.306 | 0.301 | 0.474 | 0.208 | 0.247 | 0.000 | 0.000 | 0.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 87 | 66 | 65 | 99 | 86 | 0 | 0 | 60 |
N.S. |
1 | 1.02 | 0.78 | 0.76 | 1.16 | 1.01 | 0.00 | 0.00 | 0.71 |
time (sec) |
N/A | 0.433 | 0.377 | 0.482 | 0.197 | 0.262 | 0.000 | 0.000 | 4.298 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 123 | 82 | 81 | 132 | 134 | 0 | 0 | 142 |
N.S. |
1 | 1.03 | 0.69 | 0.68 | 1.11 | 1.13 | 0.00 | 0.00 | 1.19 |
time (sec) |
N/A | 0.566 | 0.456 | 0.485 | 0.210 | 0.241 | 0.000 | 0.000 | 0.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 74 | 47 | 85 | 113 | 113 | 119 | 113 | 113 |
N.S. |
1 | 0.88 | 0.56 | 1.01 | 1.35 | 1.35 | 1.42 | 1.35 | 1.35 |
time (sec) |
N/A | 0.365 | 0.045 | 0.647 | 0.204 | 0.244 | 0.042 | 0.281 | 3.900 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 62 | 39 | 61 | 82 | 82 | 87 | 82 | 82 |
N.S. |
1 | 0.90 | 0.57 | 0.88 | 1.19 | 1.19 | 1.26 | 1.19 | 1.19 |
time (sec) |
N/A | 0.342 | 0.036 | 0.625 | 0.201 | 0.232 | 0.038 | 0.260 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 48 | 31 | 53 | 70 | 70 | 70 | 70 | 70 |
N.S. |
1 | 0.92 | 0.60 | 1.02 | 1.35 | 1.35 | 1.35 | 1.35 | 1.35 |
time (sec) |
N/A | 0.324 | 0.029 | 0.634 | 0.195 | 0.236 | 0.033 | 0.284 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 34 | 23 | 29 | 38 | 38 | 36 | 38 | 38 |
N.S. |
1 | 0.97 | 0.66 | 0.83 | 1.09 | 1.09 | 1.03 | 1.09 | 1.09 |
time (sec) |
N/A | 0.308 | 0.020 | 0.592 | 0.194 | 0.243 | 0.028 | 0.284 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 20 | 14 | 21 | 21 | 20 | 21 | 17 |
N.S. |
1 | 1.00 | 1.33 | 0.93 | 1.40 | 1.40 | 1.33 | 1.40 | 1.13 |
time (sec) |
N/A | 0.245 | 0.016 | 0.490 | 0.199 | 0.238 | 0.025 | 0.268 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 13 | 13 | 13 | 10 | 14 | 14 |
N.S. |
1 | 1.00 | 1.12 | 0.81 | 0.81 | 0.81 | 0.62 | 0.88 | 0.88 |
time (sec) |
N/A | 0.279 | 0.061 | 0.574 | 0.196 | 0.235 | 0.058 | 0.280 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 47 | 35 | 51 | 63 | 76 | 54 | 51 | 46 |
N.S. |
1 | 0.92 | 0.69 | 1.00 | 1.24 | 1.49 | 1.06 | 1.00 | 0.90 |
time (sec) |
N/A | 0.323 | 0.032 | 0.574 | 0.187 | 0.233 | 0.147 | 0.282 | 3.895 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 76 | 63 | 76 | 91 | 121 | 85 | 74 | 73 |
N.S. |
1 | 0.88 | 0.73 | 0.88 | 1.06 | 1.41 | 0.99 | 0.86 | 0.85 |
time (sec) |
N/A | 0.351 | 0.045 | 0.612 | 0.214 | 0.244 | 0.221 | 0.267 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 105 | 82 | 92 | 140 | 217 | 141 | 91 | 121 |
N.S. |
1 | 0.87 | 0.68 | 0.76 | 1.16 | 1.79 | 1.17 | 0.75 | 1.00 |
time (sec) |
N/A | 0.383 | 0.071 | 0.618 | 0.204 | 0.252 | 0.334 | 0.267 | 4.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 393 | 0 | 111 | 160 | 415 | 170 | 0 | 216 | 362 |
N.S. |
1 | 0.00 | 0.28 | 0.41 | 1.06 | 0.43 | 0.00 | 0.55 | 0.92 |
time (sec) |
N/A | 0.000 | 0.207 | 0.504 | 0.212 | 0.257 | 0.000 | 0.320 | 4.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 313 | 0 | 95 | 144 | 337 | 147 | 0 | 177 | 289 |
N.S. |
1 | 0.00 | 0.30 | 0.46 | 1.08 | 0.47 | 0.00 | 0.57 | 0.92 |
time (sec) |
N/A | 0.000 | 0.172 | 0.492 | 0.225 | 0.243 | 0.000 | 0.298 | 4.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 233 | 0 | 79 | 128 | 259 | 126 | 0 | 138 | 214 |
N.S. |
1 | 0.00 | 0.34 | 0.55 | 1.11 | 0.54 | 0.00 | 0.59 | 0.92 |
time (sec) |
N/A | 0.000 | 0.137 | 0.489 | 0.187 | 0.247 | 0.000 | 0.289 | 3.985 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 145 | 0 | 61 | 108 | 171 | 91 | 0 | 90 | 133 |
N.S. |
1 | 0.00 | 0.42 | 0.74 | 1.18 | 0.63 | 0.00 | 0.62 | 0.92 |
time (sec) |
N/A | 0.000 | 0.103 | 0.126 | 0.202 | 0.248 | 0.000 | 0.279 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 24 | 23 | 51 | 0 | 49 | 23 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.28 | 2.83 | 0.00 | 2.72 | 1.28 |
time (sec) |
N/A | 0.195 | 0.177 | 0.513 | 0.189 | 0.240 | 0.000 | 0.285 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 43 | 49 | 55 | 77 | 0 | 65 | 55 |
N.S. |
1 | 1.00 | 0.78 | 0.89 | 1.00 | 1.40 | 0.00 | 1.18 | 1.00 |
time (sec) |
N/A | 0.313 | 0.342 | 0.499 | 0.194 | 0.245 | 0.000 | 0.311 | 4.370 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 93 | 66 | 63 | 97 | 96 | 0 | 0 | 60 |
N.S. |
1 | 1.02 | 0.73 | 0.69 | 1.07 | 1.05 | 0.00 | 0.00 | 0.66 |
time (sec) |
N/A | 0.434 | 0.410 | 0.504 | 0.191 | 0.244 | 0.000 | 0.000 | 4.310 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 131 | 82 | 81 | 131 | 124 | 0 | 0 | 76 |
N.S. |
1 | 1.03 | 0.65 | 0.64 | 1.03 | 0.98 | 0.00 | 0.00 | 0.60 |
time (sec) |
N/A | 0.592 | 0.489 | 0.489 | 0.192 | 0.250 | 0.000 | 0.000 | 3.981 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 58 | 39 | 75 | 101 | 101 | 109 | 102 | 101 |
N.S. |
1 | 0.88 | 0.59 | 1.14 | 1.53 | 1.53 | 1.65 | 1.55 | 1.53 |
time (sec) |
N/A | 0.345 | 0.039 | 0.689 | 0.197 | 0.235 | 0.049 | 0.265 | 3.968 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 47 | 31 | 69 | 92 | 92 | 100 | 90 | 92 |
N.S. |
1 | 0.90 | 0.60 | 1.33 | 1.77 | 1.77 | 1.92 | 1.73 | 1.77 |
time (sec) |
N/A | 0.319 | 0.032 | 0.655 | 0.190 | 0.242 | 0.043 | 0.268 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 33 | 23 | 45 | 59 | 59 | 63 | 78 | 59 |
N.S. |
1 | 0.94 | 0.66 | 1.29 | 1.69 | 1.69 | 1.80 | 2.23 | 1.69 |
time (sec) |
N/A | 0.305 | 0.025 | 0.654 | 0.191 | 0.234 | 0.036 | 0.264 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 37 | 16 | 47 | 47 | 48 | 64 | 47 |
N.S. |
1 | 1.00 | 2.18 | 0.94 | 2.76 | 2.76 | 2.82 | 3.76 | 2.76 |
time (sec) |
N/A | 0.289 | 0.024 | 0.624 | 0.185 | 0.224 | 0.034 | 0.270 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 44 | 38 | 32 | 33 | 37 | 36 | 60 | 33 |
N.S. |
1 | 0.96 | 0.83 | 0.70 | 0.72 | 0.80 | 0.78 | 1.30 | 0.72 |
time (sec) |
N/A | 0.290 | 0.020 | 0.595 | 0.193 | 0.249 | 0.066 | 0.259 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 25 | 13 | 19 | 19 | 17 | 27 | 12 |
N.S. |
1 | 1.00 | 1.92 | 1.00 | 1.46 | 1.46 | 1.31 | 2.08 | 0.92 |
time (sec) |
N/A | 0.279 | 0.014 | 0.647 | 0.194 | 0.239 | 0.092 | 0.275 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 16 | 41 | 41 | 42 | 15 | 40 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 2.28 | 2.28 | 2.33 | 0.83 | 2.22 |
time (sec) |
N/A | 0.274 | 0.088 | 0.625 | 0.190 | 0.232 | 0.107 | 0.263 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 76 | 52 | 65 | 102 | 147 | 99 | 91 | 83 |
N.S. |
1 | 0.87 | 0.60 | 0.75 | 1.17 | 1.69 | 1.14 | 1.05 | 0.95 |
time (sec) |
N/A | 0.342 | 0.042 | 0.621 | 0.188 | 0.252 | 0.253 | 0.276 | 0.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 105 | 80 | 92 | 130 | 191 | 129 | 127 | 111 |
N.S. |
1 | 0.86 | 0.66 | 0.75 | 1.07 | 1.57 | 1.06 | 1.04 | 0.91 |
time (sec) |
N/A | 0.375 | 0.066 | 0.632 | 0.195 | 0.250 | 0.294 | 0.267 | 3.960 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 393 | 0 | 111 | 160 | 415 | 170 | 0 | 196 | 362 |
N.S. |
1 | 0.00 | 0.28 | 0.41 | 1.06 | 0.43 | 0.00 | 0.50 | 0.92 |
time (sec) |
N/A | 0.000 | 0.219 | 0.487 | 0.195 | 0.249 | 0.000 | 0.303 | 4.435 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 313 | 0 | 95 | 144 | 337 | 147 | 0 | 161 | 289 |
N.S. |
1 | 0.00 | 0.30 | 0.46 | 1.08 | 0.47 | 0.00 | 0.51 | 0.92 |
time (sec) |
N/A | 0.000 | 0.207 | 0.493 | 0.205 | 0.257 | 0.000 | 0.289 | 0.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 233 | 0 | 79 | 128 | 259 | 126 | 0 | 126 | 214 |
N.S. |
1 | 0.00 | 0.34 | 0.55 | 1.11 | 0.54 | 0.00 | 0.54 | 0.92 |
time (sec) |
N/A | 0.000 | 0.134 | 0.489 | 0.204 | 0.255 | 0.000 | 0.287 | 3.967 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 145 | 0 | 61 | 108 | 171 | 91 | 0 | 82 | 132 |
N.S. |
1 | 0.00 | 0.42 | 0.74 | 1.18 | 0.63 | 0.00 | 0.57 | 0.91 |
time (sec) |
N/A | 0.000 | 0.116 | 0.066 | 0.200 | 0.243 | 0.000 | 0.287 | 3.893 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 24 | 23 | 23 | 0 | 0 | 23 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 1.44 | 1.44 | 0.00 | 0.00 | 1.44 |
time (sec) |
N/A | 0.195 | 0.165 | 0.497 | 0.202 | 0.256 | 0.000 | 0.000 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 48 | 49 | 67 | 50 | 0 | 0 | 55 |
N.S. |
1 | 1.00 | 0.87 | 0.89 | 1.22 | 0.91 | 0.00 | 0.00 | 1.00 |
time (sec) |
N/A | 0.309 | 0.304 | 0.500 | 0.202 | 0.238 | 0.000 | 0.000 | 0.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 93 | 64 | 65 | 102 | 76 | 0 | 0 | 109 |
N.S. |
1 | 1.02 | 0.70 | 0.71 | 1.12 | 0.84 | 0.00 | 0.00 | 1.20 |
time (sec) |
N/A | 0.425 | 0.386 | 0.504 | 0.204 | 0.256 | 0.000 | 0.000 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 131 | 80 | 81 | 135 | 104 | 0 | 0 | 148 |
N.S. |
1 | 1.03 | 0.63 | 0.64 | 1.06 | 0.82 | 0.00 | 0.00 | 1.17 |
time (sec) |
N/A | 0.573 | 0.471 | 0.507 | 0.197 | 0.262 | 0.000 | 0.000 | 4.235 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 66 | 39 | 61 | 80 | 80 | 87 | 80 | 80 |
N.S. |
1 | 0.90 | 0.53 | 0.84 | 1.10 | 1.10 | 1.19 | 1.10 | 1.10 |
time (sec) |
N/A | 0.342 | 0.037 | 0.620 | 0.204 | 0.237 | 0.041 | 0.259 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 51 | 31 | 53 | 70 | 70 | 70 | 70 | 70 |
N.S. |
1 | 0.93 | 0.56 | 0.96 | 1.27 | 1.27 | 1.27 | 1.27 | 1.27 |
time (sec) |
N/A | 0.332 | 0.030 | 0.631 | 0.193 | 0.238 | 0.037 | 0.272 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 36 | 30 | 29 | 37 | 37 | 36 | 37 | 37 |
N.S. |
1 | 0.97 | 0.81 | 0.78 | 1.00 | 1.00 | 0.97 | 1.00 | 1.00 |
time (sec) |
N/A | 0.300 | 0.022 | 0.627 | 0.197 | 0.236 | 0.029 | 0.267 | 0.055 |