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 | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 176 | 177 | 200 | 277 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 1.87 | 1.88 | 2.13 | 2.95 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.444 | 0.201 | 0.406 | 0.111 | 0.096 | 0.000 | 0.000 | 0.177 | 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 | 20 | 20 | 22 | 20 | 228 | 22 | 19 | 22 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 11.40 | 1.10 | 0.95 | 1.10 | 1.10 | 1.10 |
time (sec) |
N/A | 0.535 | 6.218 | 0.308 | 0.271 | 0.075 | 0.474 | 0.329 | 0.153 | 19.152 |
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 | 20 | 20 | 22 | 20 | 340 | 33 | 20 | 22 | 33 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 17.00 | 1.65 | 1.00 | 1.10 | 1.65 | 1.10 |
time (sec) |
N/A | 0.671 | 3.002 | 0.298 | 0.601 | 0.073 | 0.710 | 2.456 | 0.153 | 19.559 |
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 | 16 | 16 | 18 | 16 | 18 | 18 | 15 | 18 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.94 | 1.12 | 1.12 | 1.12 |
time (sec) |
N/A | 0.201 | 0.831 | 0.104 | 0.399 | 0.068 | 1.440 | 0.175 | 0.171 | 18.594 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 210 | 598 | 921 | 3242 | 856 | 0 | 0 | 677 | 0 |
N.S. |
1 | 1.35 | 3.86 | 5.94 | 20.92 | 5.52 | 0.00 | 0.00 | 4.37 | 0.00 |
time (sec) |
N/A | 0.897 | 5.311 | 0.498 | 0.448 | 0.099 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 164 | 374 | 581 | 1953 | 599 | 0 | 0 | 502 | 0 |
N.S. |
1 | 1.29 | 2.94 | 4.57 | 15.38 | 4.72 | 0.00 | 0.00 | 3.95 | 0.00 |
time (sec) |
N/A | 0.689 | 4.147 | 0.470 | 0.303 | 0.093 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 120 | 198 | 305 | 645 | 384 | 0 | 0 | 331 | 0 |
N.S. |
1 | 1.24 | 2.04 | 3.14 | 6.65 | 3.96 | 0.00 | 0.00 | 3.41 | 0.00 |
time (sec) |
N/A | 0.498 | 4.118 | 0.445 | 0.220 | 0.083 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 45 | 82 | 60 | 292 | 97 | 104 | 1151 | 105 | 67 |
N.S. |
1 | 1.05 | 1.91 | 1.40 | 6.79 | 2.26 | 2.42 | 26.77 | 2.44 | 1.56 |
time (sec) |
N/A | 0.270 | 0.380 | 0.385 | 0.117 | 0.073 | 0.209 | 0.349 | 0.155 | 19.665 |
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 | 16 | 16 | 18 | 16 | 581 | 18 | 14 | 18 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 36.31 | 1.12 | 0.88 | 1.12 | 1.12 | 1.12 |
time (sec) |
N/A | 0.205 | 4.820 | 0.246 | 0.339 | 0.062 | 0.399 | 0.155 | 0.156 | 19.079 |
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 | 16 | 16 | 18 | 16 | 813 | 29 | 15 | 18 | 29 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 50.81 | 1.81 | 0.94 | 1.12 | 1.81 | 1.12 |
time (sec) |
N/A | 0.212 | 1.635 | 0.251 | 0.973 | 0.063 | 0.637 | 2.248 | 0.157 | 18.955 |
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 | 22 | 22 | 24 | 22 | 24 | 24 | 22 | 24 | 24 | 26 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 1.00 | 1.09 | 1.09 | 1.18 |
time (sec) |
N/A | 0.309 | 24.449 | 0.117 | 0.962 | 0.071 | 5.664 | 0.158 | 0.196 | 18.899 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 416 | 742 | 854 | 1673 | 7004 | 2770 | 0 | 0 | 187 | 0 |
N.S. |
1 | 1.78 | 2.05 | 4.02 | 16.84 | 6.66 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 2.900 | 5.656 | 0.562 | 3.134 | 0.172 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 532 | 528 | 1056 | 3887 | 1742 | 0 | 0 | 150 | 0 |
N.S. |
1 | 1.73 | 1.71 | 3.43 | 12.62 | 5.66 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 1.914 | 3.362 | 0.443 | 0.991 | 0.136 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 324 | 471 | 546 | 1938 | 970 | 0 | 0 | 113 | 0 |
N.S. |
1 | 1.81 | 2.63 | 3.05 | 10.83 | 5.42 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 1.357 | 6.957 | 0.361 | 0.309 | 0.111 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 176 | 260 | 246 | 762 | 454 | 0 | 0 | 74 | 0 |
N.S. |
1 | 1.63 | 2.41 | 2.28 | 7.06 | 4.20 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.699 | 1.183 | 0.273 | 0.169 | 0.096 | 0.000 | 0.000 | 0.188 | 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 | 22 | 22 | 24 | 22 | 1793 | 24 | 20 | 24 | 24 | 26 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 81.50 | 1.09 | 0.91 | 1.09 | 1.09 | 1.18 |
time (sec) |
N/A | 0.301 | 29.933 | 0.174 | 2.544 | 0.082 | 1.047 | 4.681 | 0.163 | 18.747 |
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 | 22 | 22 | 24 | 22 | 2289 | 35 | 22 | 24 | 35 | 26 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 104.05 | 1.59 | 1.00 | 1.09 | 1.59 | 1.18 |
time (sec) |
N/A | 0.308 | 34.167 | 0.181 | 8.296 | 0.086 | 4.069 | 16.943 | 0.201 | 18.426 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 406 | 406 | 1445 | 476 | 547 | 341 | 0 | 2445 | 86 | 0 |
N.S. |
1 | 1.00 | 3.56 | 1.17 | 1.35 | 0.84 | 0.00 | 6.02 | 0.21 | 0.00 |
time (sec) |
N/A | 1.180 | 10.293 | 1.357 | 0.164 | 0.098 | 0.000 | 0.831 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 353 | 353 | 751 | 384 | 499 | 280 | 0 | 1515 | 52 | 0 |
N.S. |
1 | 1.00 | 2.13 | 1.09 | 1.41 | 0.79 | 0.00 | 4.29 | 0.15 | 0.00 |
time (sec) |
N/A | 0.916 | 1.047 | 0.819 | 0.157 | 0.094 | 0.000 | 0.712 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 304 | 251 | 296 | 424 | 235 | 0 | 844 | 23 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.97 | 1.39 | 0.77 | 0.00 | 2.78 | 0.08 | 0.00 |
time (sec) |
N/A | 0.757 | 0.153 | 0.782 | 0.158 | 0.086 | 0.000 | 0.392 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 304 | 251 | 296 | 424 | 235 | 0 | 844 | 23 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.97 | 1.39 | 0.77 | 0.00 | 2.78 | 0.08 | 0.00 |
time (sec) |
N/A | 0.728 | 0.144 | 0.456 | 0.160 | 0.086 | 0.000 | 0.379 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 353 | 353 | 751 | 384 | 499 | 280 | 0 | 1515 | 52 | 0 |
N.S. |
1 | 1.00 | 2.13 | 1.09 | 1.41 | 0.79 | 0.00 | 4.29 | 0.15 | 0.00 |
time (sec) |
N/A | 0.849 | 0.935 | 0.661 | 0.164 | 0.090 | 0.000 | 0.684 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 406 | 406 | 1445 | 476 | 547 | 341 | 0 | 2445 | 86 | 0 |
N.S. |
1 | 1.00 | 3.56 | 1.17 | 1.35 | 0.84 | 0.00 | 6.02 | 0.21 | 0.00 |
time (sec) |
N/A | 0.966 | 6.009 | 1.109 | 0.170 | 0.095 | 0.000 | 0.834 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 228 | 140 | 251 | 285 | 347 | 0 | 1358 | 92 | 0 |
N.S. |
1 | 1.00 | 0.61 | 1.10 | 1.25 | 1.52 | 0.00 | 5.96 | 0.40 | 0.00 |
time (sec) |
N/A | 0.715 | 0.873 | 2.796 | 0.138 | 0.098 | 0.000 | 0.888 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 140 | 206 | 264 | 249 | 0 | 833 | 56 | 0 |
N.S. |
1 | 1.00 | 0.70 | 1.03 | 1.32 | 1.24 | 0.00 | 4.16 | 0.28 | 0.00 |
time (sec) |
N/A | 0.610 | 0.623 | 0.812 | 0.135 | 0.090 | 0.000 | 0.624 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 174 | 120 | 159 | 219 | 175 | 0 | 460 | 25 | 0 |
N.S. |
1 | 1.00 | 0.69 | 0.91 | 1.26 | 1.01 | 0.00 | 2.64 | 0.14 | 0.00 |
time (sec) |
N/A | 0.521 | 0.554 | 0.741 | 0.149 | 0.089 | 0.000 | 0.417 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 174 | 120 | 159 | 219 | 175 | 0 | 460 | 25 | 0 |
N.S. |
1 | 1.00 | 0.69 | 0.91 | 1.26 | 1.01 | 0.00 | 2.64 | 0.14 | 0.00 |
time (sec) |
N/A | 0.517 | 0.012 | 0.481 | 0.135 | 0.088 | 0.000 | 0.403 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 140 | 206 | 264 | 249 | 0 | 833 | 56 | 0 |
N.S. |
1 | 1.00 | 0.70 | 1.03 | 1.32 | 1.24 | 0.00 | 4.16 | 0.28 | 0.00 |
time (sec) |
N/A | 0.556 | 0.031 | 0.553 | 0.141 | 0.098 | 0.000 | 0.637 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 228 | 140 | 251 | 285 | 347 | 0 | 1358 | 92 | 0 |
N.S. |
1 | 1.00 | 0.61 | 1.10 | 1.25 | 1.52 | 0.00 | 5.96 | 0.40 | 0.00 |
time (sec) |
N/A | 0.621 | 0.089 | 2.608 | 0.145 | 0.097 | 0.000 | 0.965 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 615 | 615 | 2177 | 719 | 826 | 521 | 0 | 3673 | 92 | 0 |
N.S. |
1 | 1.00 | 3.54 | 1.17 | 1.34 | 0.85 | 0.00 | 5.97 | 0.15 | 0.00 |
time (sec) |
N/A | 1.621 | 13.098 | 9.487 | 0.196 | 0.113 | 0.000 | 1.583 | 0.271 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 534 | 534 | 1126 | 580 | 760 | 427 | 0 | 2279 | 56 | 0 |
N.S. |
1 | 1.00 | 2.11 | 1.09 | 1.42 | 0.80 | 0.00 | 4.27 | 0.10 | 0.00 |
time (sec) |
N/A | 1.285 | 2.223 | 2.312 | 0.189 | 0.108 | 0.000 | 1.039 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 459 | 459 | 372 | 447 | 680 | 356 | 0 | 1270 | 25 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.97 | 1.48 | 0.78 | 0.00 | 2.77 | 0.05 | 0.00 |
time (sec) |
N/A | 1.031 | 0.219 | 2.203 | 0.171 | 0.101 | 0.000 | 0.629 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 459 | 459 | 372 | 447 | 680 | 356 | 0 | 1270 | 25 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.97 | 1.48 | 0.78 | 0.00 | 2.77 | 0.05 | 0.00 |
time (sec) |
N/A | 0.979 | 0.202 | 1.431 | 0.174 | 0.100 | 0.000 | 0.648 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 534 | 534 | 1126 | 580 | 760 | 427 | 0 | 2279 | 56 | 0 |
N.S. |
1 | 1.00 | 2.11 | 1.09 | 1.42 | 0.80 | 0.00 | 4.27 | 0.10 | 0.00 |
time (sec) |
N/A | 1.210 | 1.619 | 1.940 | 0.182 | 0.109 | 0.000 | 1.036 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 615 | 615 | 2177 | 719 | 826 | 521 | 0 | 3673 | 92 | 0 |
N.S. |
1 | 1.00 | 3.54 | 1.17 | 1.34 | 0.85 | 0.00 | 5.97 | 0.15 | 0.00 |
time (sec) |
N/A | 1.381 | 6.011 | 9.107 | 0.193 | 0.116 | 0.000 | 1.548 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 273 | 245 | 0 | 0 | 188 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.69 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.525 | 0.176 | 0.000 | 0.000 | 0.085 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 325 | 158 | 187 | 967 | 378 | 935 | 361 | 698 | 576 |
N.S. |
1 | 1.29 | 0.63 | 0.74 | 3.84 | 1.50 | 3.71 | 1.43 | 2.77 | 2.29 |
time (sec) |
N/A | 1.006 | 1.194 | 2.280 | 0.079 | 0.086 | 0.927 | 0.144 | 0.174 | 19.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 243 | 135 | 148 | 549 | 238 | 602 | 241 | 441 | 366 |
N.S. |
1 | 1.24 | 0.69 | 0.76 | 2.80 | 1.21 | 3.07 | 1.23 | 2.25 | 1.87 |
time (sec) |
N/A | 0.818 | 0.591 | 1.741 | 0.053 | 0.079 | 0.645 | 0.138 | 0.170 | 19.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 133 | 89 | 109 | 263 | 130 | 320 | 145 | 247 | 202 |
N.S. |
1 | 1.06 | 0.71 | 0.87 | 2.10 | 1.04 | 2.56 | 1.16 | 1.98 | 1.62 |
time (sec) |
N/A | 0.419 | 0.308 | 1.457 | 0.042 | 0.074 | 0.457 | 0.131 | 0.167 | 18.663 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 80 | 75 | 68 | 92 | 58 | 138 | 75 | 101 | 94 |
N.S. |
1 | 1.11 | 1.04 | 0.94 | 1.28 | 0.81 | 1.92 | 1.04 | 1.40 | 1.31 |
time (sec) |
N/A | 0.327 | 0.090 | 1.172 | 0.038 | 0.069 | 0.319 | 0.147 | 0.215 | 0.329 |
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 | 129 | 129 | 110 | 178 | 281 | 124 | 0 | 6046 | 24 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.38 | 2.18 | 0.96 | 0.00 | 46.87 | 0.19 | 0.00 |
time (sec) |
N/A | 0.442 | 0.159 | 1.030 | 0.113 | 0.067 | 0.000 | 0.352 | 0.170 | 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 | 179 | 179 | 151 | 256 | 308 | 183 | 0 | 63510 | 35 | 0 |
N.S. |
1 | 1.00 | 0.84 | 1.43 | 1.72 | 1.02 | 0.00 | 354.80 | 0.20 | 0.00 |
time (sec) |
N/A | 0.483 | 1.115 | 1.269 | 0.157 | 0.082 | 0.000 | 2.555 | 0.170 | 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 | 231 | 231 | 197 | 329 | 343 | 309 | 0 | 111694 | 46 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.42 | 1.48 | 1.34 | 0.00 | 483.52 | 0.20 | 0.00 |
time (sec) |
N/A | 0.574 | 2.645 | 1.602 | 0.256 | 0.088 | 0.000 | 3.039 | 0.192 | 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 | 287 | 287 | 316 | 404 | 393 | 455 | 0 | 157526 | 0 | 0 |
N.S. |
1 | 1.00 | 1.10 | 1.41 | 1.37 | 1.59 | 0.00 | 548.87 | 0.00 | 0.00 |
time (sec) |
N/A | 0.655 | 1.493 | 2.237 | 0.430 | 0.097 | 0.000 | 4.179 | 0.351 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 419 | 419 | 409 | 0 | 0 | 280 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.67 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.695 | 0.598 | 0.000 | 0.000 | 0.090 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 330 | 330 | 563 | 253 | 1339 | 527 | 1098 | 531 | 807 | 816 |
N.S. |
1 | 1.00 | 1.71 | 0.77 | 4.06 | 1.60 | 3.33 | 1.61 | 2.45 | 2.47 |
time (sec) |
N/A | 0.675 | 2.415 | 3.398 | 0.107 | 0.094 | 1.152 | 0.165 | 0.164 | 21.869 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 259 | 259 | 195 | 205 | 766 | 342 | 690 | 351 | 501 | 516 |
N.S. |
1 | 1.00 | 0.75 | 0.79 | 2.96 | 1.32 | 2.66 | 1.36 | 1.93 | 1.99 |
time (sec) |
N/A | 0.525 | 1.481 | 3.069 | 0.076 | 0.083 | 0.862 | 0.140 | 0.161 | 2.559 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 184 | 252 | 144 | 375 | 193 | 382 | 209 | 260 | 295 |
N.S. |
1 | 1.00 | 1.37 | 0.78 | 2.04 | 1.05 | 2.08 | 1.14 | 1.41 | 1.60 |
time (sec) |
N/A | 0.423 | 0.597 | 3.233 | 0.051 | 0.075 | 0.615 | 0.154 | 0.160 | 0.938 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 110 | 91 | 139 | 91 | 163 | 106 | 102 | 119 |
N.S. |
1 | 1.00 | 1.01 | 0.83 | 1.28 | 0.83 | 1.50 | 0.97 | 0.94 | 1.09 |
time (sec) |
N/A | 0.295 | 0.232 | 2.430 | 0.041 | 0.072 | 0.415 | 0.145 | 0.158 | 0.458 |
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 | 185 | 185 | 154 | 257 | 413 | 182 | 0 | 44961 | 26 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.39 | 2.23 | 0.98 | 0.00 | 243.03 | 0.14 | 0.00 |
time (sec) |
N/A | 0.532 | 0.262 | 2.053 | 0.151 | 0.074 | 0.000 | 1.499 | 0.156 | 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 | 257 | 257 | 212 | 372 | 446 | 264 | 0 | 1022022 | 37 | 0 |
N.S. |
1 | 1.00 | 0.82 | 1.45 | 1.74 | 1.03 | 0.00 | 3976.74 | 0.14 | 0.00 |
time (sec) |
N/A | 0.641 | 1.290 | 2.288 | 0.227 | 0.092 | 0.000 | 40.171 | 0.160 | 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 | 338 | 338 | 283 | 478 | 481 | 438 | 0 | 1708998 | 48 | 0 |
N.S. |
1 | 1.00 | 0.84 | 1.41 | 1.42 | 1.30 | 0.00 | 5056.21 | 0.14 | 0.00 |
time (sec) |
N/A | 0.773 | 1.920 | 3.008 | 0.349 | 0.099 | 0.000 | 79.752 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 413 | 413 | 451 | 588 | 531 | 640 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.00 | 1.09 | 1.42 | 1.29 | 1.55 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.879 | 1.612 | 4.087 | 0.587 | 0.124 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 285 | 255 | 0 | 0 | 190 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.67 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.552 | 1.442 | 0.000 | 0.000 | 0.089 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 233 | 153 | 185 | 1033 | 546 | 1334 | 359 | 919 | 576 |
N.S. |
1 | 1.00 | 0.66 | 0.79 | 4.43 | 2.34 | 5.73 | 1.54 | 3.94 | 2.47 |
time (sec) |
N/A | 0.504 | 0.892 | 3.424 | 0.076 | 0.092 | 1.597 | 0.196 | 0.158 | 21.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 181 | 132 | 148 | 602 | 349 | 857 | 241 | 569 | 366 |
N.S. |
1 | 1.00 | 0.73 | 0.82 | 3.33 | 1.93 | 4.73 | 1.33 | 3.14 | 2.02 |
time (sec) |
N/A | 0.434 | 1.582 | 2.818 | 0.060 | 0.083 | 1.118 | 0.185 | 0.155 | 1.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 91 | 111 | 303 | 194 | 461 | 145 | 293 | 202 |
N.S. |
1 | 1.00 | 0.71 | 0.86 | 2.35 | 1.50 | 3.57 | 1.12 | 2.27 | 1.57 |
time (sec) |
N/A | 0.340 | 0.355 | 2.330 | 0.040 | 0.076 | 0.808 | 0.149 | 0.159 | 0.892 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 63 | 69 | 119 | 87 | 201 | 75 | 118 | 84 |
N.S. |
1 | 1.00 | 0.82 | 0.90 | 1.55 | 1.13 | 2.61 | 0.97 | 1.53 | 1.09 |
time (sec) |
N/A | 0.258 | 0.319 | 2.319 | 0.033 | 0.075 | 0.541 | 0.135 | 0.149 | 0.805 |
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 | 129 | 129 | 110 | 178 | 281 | 126 | 0 | 6046 | 26 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.38 | 2.18 | 0.98 | 0.00 | 46.87 | 0.20 | 0.00 |
time (sec) |
N/A | 0.454 | 0.187 | 2.076 | 0.109 | 0.073 | 0.000 | 0.341 | 0.182 | 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 | 179 | 179 | 189 | 256 | 308 | 198 | 0 | 63798 | 37 | 0 |
N.S. |
1 | 1.00 | 1.06 | 1.43 | 1.72 | 1.11 | 0.00 | 356.41 | 0.21 | 0.00 |
time (sec) |
N/A | 0.536 | 0.648 | 2.354 | 0.160 | 0.086 | 0.000 | 2.989 | 0.151 | 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 | 235 | 235 | 239 | 329 | 343 | 348 | 0 | 111694 | 48 | 0 |
N.S. |
1 | 1.00 | 1.02 | 1.40 | 1.46 | 1.48 | 0.00 | 475.29 | 0.20 | 0.00 |
time (sec) |
N/A | 0.604 | 0.716 | 2.765 | 0.257 | 0.099 | 0.000 | 3.021 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 287 | 554 | 404 | 393 | 524 | 0 | 157526 | 0 | 0 |
N.S. |
1 | 1.00 | 1.93 | 1.41 | 1.37 | 1.83 | 0.00 | 548.87 | 0.00 | 0.00 |
time (sec) |
N/A | 0.663 | 4.150 | 3.570 | 0.410 | 0.108 | 0.000 | 4.291 | 0.445 | 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 | 22 | 22 | 24 | 22 | 24 | 24 | 22 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 1.00 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.581 | 7.834 | 0.236 | 0.487 | 0.071 | 25.952 | 0.126 | 0.154 | 18.232 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 372 | 2918 | 1335 | 1654 | 1453 | 0 | 0 | 160 | 0 |
N.S. |
1 | 1.24 | 9.76 | 4.46 | 5.53 | 4.86 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 1.787 | 6.293 | 2.751 | 0.281 | 0.166 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 298 | 1956 | 908 | 979 | 984 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.21 | 7.95 | 3.69 | 3.98 | 4.00 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 1.424 | 6.242 | 1.757 | 0.200 | 0.144 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 207 | 564 | 544 | 529 | 594 | 0 | 0 | 102 | 0 |
N.S. |
1 | 1.20 | 3.28 | 3.16 | 3.08 | 3.45 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 1.010 | 1.987 | 1.266 | 0.141 | 0.118 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 134 | 131 | 249 | 223 | 292 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.18 | 1.15 | 2.18 | 1.96 | 2.56 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.635 | 0.453 | 0.988 | 0.144 | 0.105 | 0.000 | 0.000 | 0.160 | 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 | 22 | 22 | 24 | 22 | 231 | 24 | 20 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 10.50 | 1.09 | 0.91 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.637 | 0.539 | 0.366 | 0.350 | 0.072 | 0.962 | 0.136 | 0.142 | 18.823 |
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 | 22 | 22 | 24 | 22 | 343 | 35 | 22 | 24 | 35 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 15.59 | 1.59 | 1.00 | 1.09 | 1.59 | 1.09 |
time (sec) |
N/A | 0.758 | 1.805 | 0.378 | 0.723 | 0.071 | 1.255 | 2.415 | 0.168 | 19.895 |
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 | 22 | 22 | 24 | 22 | 24 | 24 | 22 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 1.00 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.633 | 8.258 | 0.118 | 0.992 | 0.072 | 20.707 | 0.141 | 0.174 | 19.515 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 329 | 798 | 1056 | 17589 | 1233 | 0 | 0 | 805 | 0 |
N.S. |
1 | 1.10 | 2.67 | 3.53 | 58.83 | 4.12 | 0.00 | 0.00 | 2.69 | 0.00 |
time (sec) |
N/A | 1.763 | 1.223 | 2.178 | 4.432 | 0.142 | 0.000 | 0.000 | 1.471 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 232 | 539 | 649 | 10994 | 797 | 0 | 0 | 544 | 0 |
N.S. |
1 | 1.07 | 2.50 | 3.00 | 50.90 | 3.69 | 0.00 | 0.00 | 2.52 | 0.00 |
time (sec) |
N/A | 1.207 | 0.950 | 1.144 | 1.101 | 0.129 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 144 | 310 | 332 | 3199 | 448 | 0 | 0 | 295 | 0 |
N.S. |
1 | 1.04 | 2.23 | 2.39 | 23.01 | 3.22 | 0.00 | 0.00 | 2.12 | 0.00 |
time (sec) |
N/A | 0.809 | 2.786 | 0.686 | 0.958 | 0.099 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 104 | 124 | 2110 | 95 | 0 | 1759 | 88 | 162 |
N.S. |
1 | 1.00 | 1.79 | 2.14 | 36.38 | 1.64 | 0.00 | 30.33 | 1.52 | 2.79 |
time (sec) |
N/A | 0.463 | 0.689 | 0.507 | 0.065 | 0.083 | 0.000 | 0.662 | 0.151 | 19.058 |
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 | 22 | 22 | 24 | 22 | 1438 | 24 | 20 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 65.36 | 1.09 | 0.91 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.700 | 2.479 | 0.180 | 0.479 | 0.074 | 0.661 | 0.902 | 0.153 | 18.170 |
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 | 22 | 22 | 24 | 22 | 1678 | 35 | 22 | 24 | 35 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 76.27 | 1.59 | 1.00 | 1.09 | 1.59 | 1.09 |
time (sec) |
N/A | 0.860 | 2.597 | 0.197 | 1.208 | 0.072 | 0.929 | 6.214 | 0.185 | 18.730 |
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 | 16 | 16 | 18 | 16 | 18 | 18 | 15 | 18 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.94 | 1.12 | 1.12 | 1.12 |
time (sec) |
N/A | 0.219 | 9.571 | 0.112 | 0.524 | 0.069 | 1.963 | 0.139 | 0.187 | 18.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 302 | 407 | 1632 | 1877 | 7158 | 1751 | 0 | 0 | 196 | 0 |
N.S. |
1 | 1.35 | 5.40 | 6.22 | 23.70 | 5.80 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 2.229 | 6.700 | 0.473 | 3.256 | 0.121 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 321 | 1032 | 1203 | 3958 | 1139 | 0 | 0 | 165 | 0 |
N.S. |
1 | 1.25 | 4.03 | 4.70 | 15.46 | 4.45 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 1.591 | 6.569 | 0.428 | 0.959 | 0.103 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 197 | 548 | 644 | 1966 | 657 | 0 | 0 | 134 | 0 |
N.S. |
1 | 1.22 | 3.40 | 4.00 | 12.21 | 4.08 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.979 | 6.490 | 0.374 | 0.298 | 0.093 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 124 | 234 | 281 | 830 | 339 | 0 | 0 | 97 | 0 |
N.S. |
1 | 1.14 | 2.15 | 2.58 | 7.61 | 3.11 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.542 | 5.368 | 0.257 | 0.188 | 0.083 | 0.000 | 0.000 | 0.154 | 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 | 16 | 16 | 18 | 16 | 1636 | 18 | 14 | 18 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 102.25 | 1.12 | 0.88 | 1.12 | 1.12 | 1.12 |
time (sec) |
N/A | 0.207 | 6.114 | 0.151 | 2.684 | 0.072 | 0.424 | 0.190 | 0.151 | 17.970 |
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 | 16 | 16 | 18 | 16 | 2124 | 29 | 15 | 18 | 29 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 132.75 | 1.81 | 0.94 | 1.12 | 1.81 | 1.12 |
time (sec) |
N/A | 0.211 | 7.504 | 0.162 | 11.378 | 0.067 | 0.670 | 2.001 | 0.200 | 18.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 407 | 407 | 1332 | 470 | 551 | 376 | 0 | 2412 | 86 | 0 |
N.S. |
1 | 1.00 | 3.27 | 1.15 | 1.35 | 0.92 | 0.00 | 5.93 | 0.21 | 0.00 |
time (sec) |
N/A | 1.087 | 7.837 | 3.038 | 0.175 | 0.100 | 0.000 | 0.919 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 351 | 351 | 693 | 376 | 503 | 294 | 0 | 1490 | 52 | 0 |
N.S. |
1 | 1.00 | 1.97 | 1.07 | 1.43 | 0.84 | 0.00 | 4.25 | 0.15 | 0.00 |
time (sec) |
N/A | 0.840 | 1.049 | 0.959 | 0.166 | 0.097 | 0.000 | 0.632 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 299 | 252 | 286 | 429 | 233 | 0 | 826 | 23 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.96 | 1.43 | 0.78 | 0.00 | 2.76 | 0.08 | 0.00 |
time (sec) |
N/A | 0.685 | 0.248 | 0.957 | 0.154 | 0.087 | 0.000 | 0.411 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 299 | 252 | 286 | 429 | 233 | 0 | 826 | 23 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.96 | 1.43 | 0.78 | 0.00 | 2.76 | 0.08 | 0.00 |
time (sec) |
N/A | 0.688 | 0.109 | 0.574 | 0.150 | 0.088 | 0.000 | 0.419 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 351 | 351 | 693 | 376 | 503 | 294 | 0 | 1490 | 52 | 0 |
N.S. |
1 | 1.00 | 1.97 | 1.07 | 1.43 | 0.84 | 0.00 | 4.25 | 0.15 | 0.00 |
time (sec) |
N/A | 0.793 | 1.039 | 0.695 | 0.154 | 0.097 | 0.000 | 0.636 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 407 | 407 | 1332 | 470 | 551 | 376 | 0 | 2412 | 86 | 0 |
N.S. |
1 | 1.00 | 3.27 | 1.15 | 1.35 | 0.92 | 0.00 | 5.93 | 0.21 | 0.00 |
time (sec) |
N/A | 0.896 | 6.015 | 2.827 | 0.164 | 0.102 | 0.000 | 0.924 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 615 | 615 | 2130 | 716 | 826 | 548 | 0 | 3677 | 92 | 0 |
N.S. |
1 | 1.00 | 3.46 | 1.16 | 1.34 | 0.89 | 0.00 | 5.98 | 0.15 | 0.00 |
time (sec) |
N/A | 1.697 | 11.109 | 9.493 | 0.188 | 0.119 | 0.000 | 1.487 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 534 | 534 | 1088 | 583 | 760 | 446 | 0 | 2278 | 56 | 0 |
N.S. |
1 | 1.00 | 2.04 | 1.09 | 1.42 | 0.84 | 0.00 | 4.27 | 0.10 | 0.00 |
time (sec) |
N/A | 1.412 | 1.809 | 2.365 | 0.173 | 0.111 | 0.000 | 1.007 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 459 | 459 | 374 | 444 | 680 | 365 | 0 | 1270 | 25 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.97 | 1.48 | 0.80 | 0.00 | 2.77 | 0.05 | 0.00 |
time (sec) |
N/A | 1.045 | 0.266 | 2.239 | 0.166 | 0.102 | 0.000 | 0.611 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 459 | 459 | 374 | 444 | 680 | 365 | 0 | 1270 | 25 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.97 | 1.48 | 0.80 | 0.00 | 2.77 | 0.05 | 0.00 |
time (sec) |
N/A | 1.024 | 0.198 | 1.443 | 0.166 | 0.102 | 0.000 | 0.622 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 534 | 534 | 1088 | 583 | 760 | 446 | 0 | 2278 | 56 | 0 |
N.S. |
1 | 1.00 | 2.04 | 1.09 | 1.42 | 0.84 | 0.00 | 4.27 | 0.10 | 0.00 |
time (sec) |
N/A | 1.216 | 1.261 | 1.992 | 0.182 | 0.108 | 0.000 | 1.012 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 615 | 615 | 2130 | 716 | 826 | 548 | 0 | 3677 | 92 | 0 |
N.S. |
1 | 1.00 | 3.46 | 1.16 | 1.34 | 0.89 | 0.00 | 5.98 | 0.15 | 0.00 |
time (sec) |
N/A | 1.415 | 4.063 | 9.066 | 0.191 | 0.116 | 0.000 | 1.475 | 0.293 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 407 | 407 | 257 | 477 | 561 | 445 | 0 | 2411 | 92 | 0 |
N.S. |
1 | 1.00 | 0.63 | 1.17 | 1.38 | 1.09 | 0.00 | 5.92 | 0.23 | 0.00 |
time (sec) |
N/A | 1.110 | 2.208 | 23.117 | 0.159 | 0.110 | 0.000 | 2.444 | 0.302 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 351 | 351 | 259 | 383 | 511 | 326 | 0 | 1489 | 56 | 0 |
N.S. |
1 | 1.00 | 0.74 | 1.09 | 1.46 | 0.93 | 0.00 | 4.24 | 0.16 | 0.00 |
time (sec) |
N/A | 0.911 | 1.840 | 1.841 | 0.164 | 0.102 | 0.000 | 1.599 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 299 | 256 | 293 | 439 | 242 | 0 | 826 | 25 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.98 | 1.47 | 0.81 | 0.00 | 2.76 | 0.08 | 0.00 |
time (sec) |
N/A | 0.688 | 1.063 | 1.792 | 0.164 | 0.093 | 0.000 | 0.941 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 299 | 256 | 293 | 439 | 242 | 0 | 826 | 25 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.98 | 1.47 | 0.81 | 0.00 | 2.76 | 0.08 | 0.00 |
time (sec) |
N/A | 0.664 | 0.181 | 1.168 | 0.155 | 0.092 | 0.000 | 1.025 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 351 | 351 | 259 | 383 | 511 | 326 | 0 | 1489 | 56 | 0 |
N.S. |
1 | 1.00 | 0.74 | 1.09 | 1.46 | 0.93 | 0.00 | 4.24 | 0.16 | 0.00 |
time (sec) |
N/A | 0.783 | 0.295 | 1.598 | 0.180 | 0.099 | 0.000 | 1.576 | 0.245 | 0.000 |