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 | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 160 | 113 | 162 | 131 | 146 | 0 | 0 | 73 | 0 |
N.S. |
1 | 0.99 | 0.70 | 1.00 | 0.81 | 0.90 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.540 | 0.228 | 0.446 | 0.131 | 0.100 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 132 | 141 | 300 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 0.96 | 1.02 | 2.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.588 | 0.587 | 0.270 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 72 | 85 | 134 | 63 | 117 | 0 | 0 | 49 | 0 |
N.S. |
1 | 0.97 | 1.15 | 1.81 | 0.85 | 1.58 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.441 | 0.186 | 0.335 | 0.041 | 0.088 | 0.000 | 0.000 | 0.214 | 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 | 56 | 53 | 53 | 89 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.95 | 0.95 | 1.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.376 | 0.013 | 0.154 | 0.000 | 0.000 | 0.000 | 0.000 | 0.211 | 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 | 160 | 86 | 153 | 326 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 0.54 | 0.96 | 2.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.733 | 0.282 | 0.382 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 71 | 71 | 208 | 116 | 266 | 0 | 0 | 49 | 0 |
N.S. |
1 | 0.97 | 0.97 | 2.85 | 1.59 | 3.64 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.483 | 0.060 | 0.398 | 0.115 | 0.134 | 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 | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 168 | 309 | 431 | 0 | 0 | 0 | 0 | 69 | 0 |
N.S. |
1 | 0.67 | 1.23 | 1.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.766 | 0.824 | 0.434 | 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 | A | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 154 | 174 | 192 | 134 | 480 | 0 | 0 | 73 | 0 |
N.S. |
1 | 0.96 | 1.08 | 1.19 | 0.83 | 2.98 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.494 | 0.306 | 0.451 | 0.112 | 0.141 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 162 | 145 | 325 | 0 | 489 | 0 | 0 | 108 | 0 |
N.S. |
1 | 0.70 | 0.62 | 1.40 | 0.00 | 2.11 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.501 | 0.076 | 0.452 | 0.000 | 0.130 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 226 | 243 | 192 | 301 | 0 | 0 | 0 | 0 | 119 | 0 |
N.S. |
1 | 1.08 | 0.85 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.824 | 1.175 | 0.421 | 0.000 | 0.000 | 0.000 | 0.000 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 113 | 97 | 255 | 157 | 429 | 0 | 0 | 98 | 0 |
N.S. |
1 | 0.76 | 0.66 | 1.72 | 1.06 | 2.90 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.407 | 0.060 | 0.369 | 0.125 | 0.132 | 0.000 | 0.000 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 143 | 159 | 279 | 0 | 0 | 0 | 0 | 108 | 0 |
N.S. |
1 | 1.00 | 1.11 | 1.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.482 | 0.597 | 0.426 | 0.000 | 0.000 | 0.000 | 0.000 | 0.266 | 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 | 76 | 76 | 136 | 135 | 0 | 327 | 0 | 0 | 85 | 0 |
N.S. |
1 | 1.00 | 1.79 | 1.78 | 0.00 | 4.30 | 0.00 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.295 | 0.376 | 0.345 | 0.000 | 0.122 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 72 | 180 | 70 | 0 | 0 | 0 | 80 | 0 |
N.S. |
1 | 1.00 | 0.86 | 2.14 | 0.83 | 0.00 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.254 | 0.020 | 0.335 | 0.035 | 0.000 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 159 | 337 | 483 | 0 | 0 | 0 | 0 | 114 | 0 |
N.S. |
1 | 0.69 | 1.47 | 2.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.792 | 2.025 | 0.538 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 122 | 114 | 266 | 144 | 0 | 0 | 0 | 96 | 0 |
N.S. |
1 | 0.78 | 0.73 | 1.69 | 0.92 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.673 | 0.068 | 0.474 | 0.042 | 0.000 | 0.000 | 0.000 | 0.236 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 329 | 254 | 439 | 588 | 0 | 0 | 0 | 0 | 147 | 0 |
N.S. |
1 | 0.77 | 1.33 | 1.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 1.531 | 3.427 | 0.544 | 0.000 | 0.000 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 177 | 161 | 367 | 0 | 0 | 0 | 0 | 108 | 0 |
N.S. |
1 | 0.72 | 0.65 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.573 | 0.089 | 0.532 | 0.000 | 0.000 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 175 | 167 | 398 | 0 | 529 | 0 | 0 | 217 | 0 |
N.S. |
1 | 0.75 | 0.72 | 1.72 | 0.00 | 2.28 | 0.00 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.484 | 0.120 | 0.471 | 0.000 | 0.161 | 0.000 | 0.000 | 0.268 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 264 | 225 | 366 | 0 | 0 | 0 | 0 | 252 | 0 |
N.S. |
1 | 1.18 | 1.00 | 1.63 | 0.00 | 0.00 | 0.00 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.894 | 0.644 | 0.505 | 0.000 | 0.000 | 0.000 | 0.000 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 138 | 122 | 257 | 175 | 469 | 0 | 0 | 208 | 0 |
N.S. |
1 | 0.87 | 0.77 | 1.63 | 1.11 | 2.97 | 0.00 | 0.00 | 1.32 | 0.00 |
time (sec) |
N/A | 0.405 | 0.107 | 0.418 | 0.046 | 0.151 | 0.000 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 108 | 101 | 458 | 169 | 0 | 0 | 0 | 196 | 0 |
N.S. |
1 | 0.81 | 0.76 | 3.44 | 1.27 | 0.00 | 0.00 | 0.00 | 1.47 | 0.00 |
time (sec) |
N/A | 0.373 | 0.141 | 0.491 | 0.043 | 0.000 | 0.000 | 0.000 | 0.230 | 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 | 127 | 107 | 162 | 220 | 0 | 421 | 0 | 0 | 195 | 0 |
N.S. |
1 | 0.84 | 1.28 | 1.73 | 0.00 | 3.31 | 0.00 | 0.00 | 1.54 | 0.00 |
time (sec) |
N/A | 0.308 | 0.395 | 0.427 | 0.000 | 0.130 | 0.000 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 179 | 132 | 477 | 157 | 0 | 0 | 0 | 197 | 0 |
N.S. |
1 | 1.10 | 0.81 | 2.94 | 0.97 | 0.00 | 0.00 | 0.00 | 1.22 | 0.00 |
time (sec) |
N/A | 0.440 | 0.054 | 0.000 | 0.041 | 0.000 | 0.000 | 0.000 | 0.227 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 305 | 265 | 376 | 560 | 0 | 0 | 0 | 0 | 284 | 0 |
N.S. |
1 | 0.87 | 1.23 | 1.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 1.167 | 6.449 | 0.535 | 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 | A | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 237 | 173 | 173 | 434 | 0 | 0 | 0 | 0 | 217 | 0 |
N.S. |
1 | 0.73 | 0.73 | 1.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.506 | 0.254 | 0.534 | 0.000 | 0.000 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 410 | 384 | 502 | 655 | 0 | 0 | 0 | 0 | 315 | 0 |
N.S. |
1 | 0.94 | 1.22 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 2.072 | 7.104 | 0.581 | 0.000 | 0.000 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 324 | 226 | 237 | 403 | 276 | 0 | 0 | 0 | 226 | 0 |
N.S. |
1 | 0.70 | 0.73 | 1.24 | 0.85 | 0.00 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 1.131 | 0.156 | 0.530 | 0.053 | 0.000 | 0.000 | 0.000 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 153 | 93 | 456 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.06 | 0.64 | 3.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.586 | 0.323 | 0.475 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 114 | 74 | 144 | 62 | 101 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.04 | 0.67 | 1.31 | 0.56 | 0.92 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.387 | 0.093 | 0.418 | 0.138 | 0.101 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 75 | 223 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.85 | 2.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.360 | 0.145 | 0.282 | 0.000 | 0.000 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 49 | 55 | 65 | 28 | 72 | 0 | 40 | 21 | 0 |
N.S. |
1 | 1.02 | 1.15 | 1.35 | 0.58 | 1.50 | 0.00 | 0.83 | 0.44 | 0.00 |
time (sec) |
N/A | 0.241 | 0.066 | 0.349 | 0.037 | 0.088 | 0.000 | 0.133 | 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 | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 45 | 51 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 1.41 | 1.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.203 | 0.015 | 0.142 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 66 | 113 | 270 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 0.64 | 1.10 | 2.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.383 | 0.134 | 0.418 | 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 | A | B | C | B | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 48 | 57 | 168 | 73 | 88 | 0 | 80 | 23 | 0 |
N.S. |
1 | 1.02 | 1.21 | 3.57 | 1.55 | 1.87 | 0.00 | 1.70 | 0.49 | 0.00 |
time (sec) |
N/A | 0.251 | 0.023 | 0.398 | 0.116 | 0.099 | 0.000 | 0.135 | 0.203 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 125 | 234 | 349 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 0.74 | 1.39 | 2.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.583 | 0.260 | 0.436 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 108 | 117 | 137 | 126 | 169 | 0 | 169 | 23 | 0 |
N.S. |
1 | 0.99 | 1.07 | 1.26 | 1.16 | 1.55 | 0.00 | 1.55 | 0.21 | 0.00 |
time (sec) |
N/A | 0.396 | 1.132 | 0.454 | 0.111 | 0.107 | 0.000 | 0.175 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 100 | 0 | 0 | 0 | 0 | 0 | 95 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.309 | 0.078 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.857 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 141 | 115 | 0 | 0 | 0 | 0 | 0 | 100 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.344 | 0.059 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.926 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 385 | 423 | 387 | 0 | 0 | 0 | 0 | 0 | 616 | 0 |
N.S. |
1 | 1.10 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.60 | 0.00 |
time (sec) |
N/A | 2.245 | 0.681 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.399 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 274 | 306 | 290 | 0 | 0 | 0 | 0 | 0 | 349 | 0 |
N.S. |
1 | 1.12 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 1.006 | 0.278 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 195 | 191 | 0 | 0 | 0 | 0 | 0 | 158 | 0 |
N.S. |
1 | 1.14 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.771 | 0.153 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 27 | 32 | 31 | 41 | 31 | 51 | 29 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.19 | 1.15 | 1.52 | 1.15 | 1.89 | 1.07 |
time (sec) |
N/A | 0.324 | 3.396 | 0.525 | 0.140 | 0.106 | 3.442 | 0.136 | 0.222 | 3.499 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 27 | 30 | 43 | 58 | 30 | 66 | 29 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.11 | 1.59 | 2.15 | 1.11 | 2.44 | 1.07 |
time (sec) |
N/A | 0.789 | 8.418 | 0.499 | 0.143 | 0.095 | 50.763 | 0.129 | 0.236 | 3.429 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 27 | 32 | 57 | 0 | 31 | 83 | 29 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.19 | 2.11 | 0.00 | 1.15 | 3.07 | 1.07 |
time (sec) |
N/A | 0.886 | 11.172 | 0.490 | 0.151 | 0.094 | 0.000 | 0.139 | 0.272 | 3.626 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 718 | 548 | 350 | 0 | 0 | 0 | 0 | 0 | 162 | 0 |
N.S. |
1 | 0.76 | 0.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.716 | 0.853 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.449 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 454 | 396 | 274 | 0 | 0 | 0 | 0 | 0 | 106 | 0 |
N.S. |
1 | 0.87 | 0.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.171 | 0.502 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.325 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 274 | 265 | 223 | 0 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 0.97 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.795 | 0.179 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 176 | 147 | 0 | 0 | 0 | 0 | 0 | 55 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.347 | 0.055 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 300 | 297 | 216 | 0 | 0 | 0 | 0 | 0 | 101 | 0 |
N.S. |
1 | 0.99 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.622 | 0.164 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 450 | 430 | 319 | 0 | 0 | 0 | 0 | 0 | 134 | 0 |
N.S. |
1 | 0.96 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.964 | 0.470 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 864 | 596 | 387 | 0 | 0 | 0 | 0 | 0 | 179 | 0 |
N.S. |
1 | 0.69 | 0.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 3.659 | 1.496 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.512 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 546 | 428 | 288 | 0 | 0 | 0 | 0 | 0 | 117 | 0 |
N.S. |
1 | 0.78 | 0.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 1.586 | 0.635 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.498 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 283 | 229 | 0 | 0 | 0 | 0 | 0 | 55 | 0 |
N.S. |
1 | 0.92 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.928 | 0.140 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 188 | 153 | 0 | 0 | 0 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.602 | 0.302 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 342 | 330 | 225 | 0 | 0 | 0 | 0 | 0 | 116 | 0 |
N.S. |
1 | 0.96 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 1.568 | 0.288 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.260 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 526 | 484 | 413 | 0 | 0 | 0 | 0 | 0 | 155 | 0 |
N.S. |
1 | 0.92 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 2.363 | 0.667 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.287 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 128 | 124 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 0.99 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.315 | 0.060 | 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 | A | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 330 | 425 | 237 | 557 | 326 | 349 | 0 | 0 | 127 | 0 |
N.S. |
1 | 1.29 | 0.72 | 1.69 | 0.99 | 1.06 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 2.495 | 0.392 | 0.860 | 0.136 | 0.103 | 0.000 | 0.000 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 319 | 328 | 241 | 678 | 0 | 0 | 0 | 0 | 115 | 0 |
N.S. |
1 | 1.03 | 0.76 | 2.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 2.672 | 1.943 | 0.356 | 0.000 | 0.000 | 0.000 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 163 | 181 | 489 | 204 | 280 | 0 | 0 | 100 | 0 |
N.S. |
1 | 0.88 | 0.97 | 2.63 | 1.10 | 1.51 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.704 | 0.517 | 0.457 | 0.062 | 0.101 | 0.000 | 0.000 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 181 | 235 | 527 | 0 | 0 | 0 | 0 | 82 | 0 |
N.S. |
1 | 0.89 | 1.15 | 2.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.752 | 0.684 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 402 | 238 | 449 | 0 | 0 | 0 | 0 | 0 | 88 | 0 |
N.S. |
1 | 0.59 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.370 | 1.084 | 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 | C | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 186 | 270 | 582 | 0 | 0 | 0 | 0 | 88 | 0 |
N.S. |
1 | 0.79 | 1.15 | 2.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 1.822 | 1.483 | 0.474 | 0.000 | 0.000 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 427 | 250 | 5035 | 0 | 0 | 0 | 0 | 0 | 102 | 0 |
N.S. |
1 | 0.59 | 11.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 2.024 | 62.667 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 326 | 213 | 304 | 1751 | 0 | 0 | 0 | 0 | 104 | 0 |
N.S. |
1 | 0.65 | 0.93 | 5.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 1.238 | 0.860 | 0.536 | 0.000 | 0.000 | 0.000 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 453 | 663 | 262 | 582 | 388 | 432 | 0 | 0 | 209 | 0 |
N.S. |
1 | 1.46 | 0.58 | 1.28 | 0.86 | 0.95 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 3.895 | 0.494 | 0.694 | 0.135 | 0.110 | 0.000 | 0.000 | 0.353 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 441 | 550 | 485 | 1721 | 0 | 0 | 0 | 0 | 198 | 0 |
N.S. |
1 | 1.25 | 1.10 | 3.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 4.774 | 4.678 | 0.501 | 0.000 | 0.000 | 0.000 | 0.000 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 295 | 221 | 208 | 515 | 278 | 367 | 0 | 0 | 183 | 0 |
N.S. |
1 | 0.75 | 0.71 | 1.75 | 0.94 | 1.24 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.804 | 1.441 | 0.773 | 0.059 | 0.099 | 0.000 | 0.000 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 324 | 356 | 374 | 1061 | 0 | 0 | 0 | 0 | 166 | 0 |
N.S. |
1 | 1.10 | 1.15 | 3.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 1.536 | 1.830 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 573 | 396 | 650 | 0 | 0 | 0 | 0 | 0 | 170 | 0 |
N.S. |
1 | 0.69 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 2.450 | 2.042 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 444 | 393 | 433 | 464 | 0 | 0 | 0 | 0 | 168 | 0 |
N.S. |
1 | 0.89 | 0.98 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 2.402 | 4.091 | 0.515 | 0.000 | 0.000 | 0.000 | 0.000 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 630 | 387 | 5444 | 0 | 0 | 0 | 0 | 0 | 201 | 0 |
N.S. |
1 | 0.61 | 8.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 2.518 | 62.100 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 416 | 403 | 583 | 500 | 0 | 0 | 0 | 0 | 186 | 0 |
N.S. |
1 | 0.97 | 1.40 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 5.676 | 1.771 | 0.565 | 0.000 | 0.000 | 0.000 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 731 | 0 | 288 | 648 | 471 | 558 | 0 | 0 | 292 | 0 |
N.S. |
1 | 0.00 | 0.39 | 0.89 | 0.64 | 0.76 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.000 | 0.573 | 0.714 | 0.146 | 0.107 | 0.000 | 0.000 | 0.395 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 653 | 0 | 910 | 2528 | 0 | 0 | 0 | 0 | 281 | 0 |
N.S. |
1 | 0.00 | 1.39 | 3.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.000 | 5.761 | 0.588 | 0.000 | 0.000 | 0.000 | 0.000 | 0.392 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 405 | 259 | 234 | 581 | 337 | 477 | 0 | 0 | 265 | 0 |
N.S. |
1 | 0.64 | 0.58 | 1.43 | 0.83 | 1.18 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 1.528 | 1.475 | 0.766 | 0.059 | 0.114 | 0.000 | 0.000 | 0.364 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 462 | 561 | 740 | 1737 | 0 | 0 | 0 | 0 | 249 | 0 |
N.S. |
1 | 1.21 | 1.60 | 3.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 2.467 | 3.555 | 0.503 | 0.000 | 0.000 | 0.000 | 0.000 | 0.320 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 758 | 613 | 963 | 0 | 0 | 0 | 0 | 0 | 253 | 0 |
N.S. |
1 | 0.81 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 4.756 | 5.640 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.287 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 586 | 663 | 554 | 589 | 0 | 0 | 0 | 0 | 253 | 0 |
N.S. |
1 | 1.13 | 0.95 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 4.654 | 4.988 | 0.595 | 0.000 | 0.000 | 0.000 | 0.000 | 0.318 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 777 | 609 | 5694 | 0 | 0 | 0 | 0 | 0 | 286 | 0 |
N.S. |
1 | 0.78 | 7.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 5.456 | 62.956 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.300 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 616 | 0 | 803 | 652 | 0 | 0 | 0 | 0 | 269 | 0 |
N.S. |
1 | 0.00 | 1.30 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.000 | 2.611 | 0.628 | 0.000 | 0.000 | 0.000 | 0.000 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 365 | 470 | 255 | 561 | 407 | 348 | 0 | 0 | 133 | 0 |
N.S. |
1 | 1.29 | 0.70 | 1.54 | 1.12 | 0.95 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 1.664 | 0.462 | 0.773 | 0.137 | 0.117 | 0.000 | 0.000 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 351 | 372 | 295 | 1092 | 0 | 0 | 0 | 0 | 122 | 0 |
N.S. |
1 | 1.06 | 0.84 | 3.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 1.845 | 1.511 | 0.466 | 0.000 | 0.000 | 0.000 | 0.000 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 271 | 201 | 533 | 279 | 282 | 0 | 0 | 111 | 0 |
N.S. |
1 | 1.12 | 0.83 | 2.21 | 1.16 | 1.17 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 1.203 | 0.407 | 0.586 | 0.143 | 0.097 | 0.000 | 0.000 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 189 | 228 | 563 | 0 | 0 | 0 | 0 | 99 | 0 |
N.S. |
1 | 0.83 | 1.00 | 2.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.678 | 1.237 | 0.365 | 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 | A | B | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 108 | 149 | 314 | 145 | 218 | 0 | 0 | 83 | 0 |
N.S. |
1 | 0.97 | 1.34 | 2.83 | 1.31 | 1.96 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.358 | 0.708 | 0.464 | 0.052 | 0.090 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 53 | 53 | 149 | 0 | 0 | 0 | 0 | 69 | 0 |
N.S. |
1 | 0.95 | 0.95 | 2.66 | 0.00 | 0.00 | 0.00 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.247 | 0.014 | 0.203 | 0.000 | 0.000 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 288 | 138 | 315 | 0 | 0 | 0 | 0 | 0 | 74 | 0 |
N.S. |
1 | 0.48 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.659 | 0.655 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 138 | 237 | 476 | 0 | 0 | 0 | 0 | 83 | 0 |
N.S. |
1 | 0.71 | 1.22 | 2.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.747 | 0.889 | 0.575 | 0.000 | 0.000 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 452 | 254 | 5036 | 0 | 0 | 0 | 0 | 0 | 107 | 0 |
N.S. |
1 | 0.56 | 11.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 1.406 | 61.281 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 332 | 263 | 370 | 1520 | 0 | 0 | 0 | 0 | 111 | 0 |
N.S. |
1 | 0.79 | 1.11 | 4.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 2.196 | 0.932 | 0.668 | 0.000 | 0.000 | 0.000 | 0.000 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 440 | 412 | 343 | 756 | 0 | 0 | 0 | 0 | 191 | 0 |
N.S. |
1 | 0.94 | 0.78 | 1.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 2.530 | 1.578 | 0.620 | 0.000 | 0.000 | 0.000 | 0.000 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 346 | 287 | 319 | 648 | 0 | 0 | 0 | 0 | 168 | 0 |
N.S. |
1 | 0.83 | 0.92 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 2.447 | 1.364 | 0.553 | 0.000 | 0.000 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 199 | 270 | 738 | 0 | 0 | 0 | 0 | 178 | 0 |
N.S. |
1 | 0.77 | 1.05 | 2.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 1.687 | 1.969 | 0.641 | 0.000 | 0.000 | 0.000 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 125 | 219 | 341 | 0 | 0 | 0 | 0 | 151 | 0 |
N.S. |
1 | 0.64 | 1.12 | 1.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.804 | 1.346 | 0.507 | 0.000 | 0.000 | 0.000 | 0.000 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 140 | 126 | 578 | 0 | 0 | 0 | 0 | 142 | 0 |
N.S. |
1 | 0.71 | 0.64 | 2.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.664 | 0.262 | 0.533 | 0.000 | 0.000 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 471 | 260 | 613 | 0 | 0 | 0 | 0 | 0 | 181 | 0 |
N.S. |
1 | 0.55 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 2.337 | 3.035 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 341 | 279 | 127 | 1271 | 0 | 0 | 0 | 0 | 164 | 0 |
N.S. |
1 | 0.82 | 0.37 | 3.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 2.440 | 0.490 | 0.674 | 0.000 | 0.000 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 650 | 433 | 5362 | 0 | 0 | 0 | 0 | 0 | 221 | 0 |
N.S. |
1 | 0.67 | 8.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 6.152 | 64.729 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.251 | 0.000 |