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 | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 33 | 32 | 32 | 34 | 32 | 35 | 32 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.84 | 0.84 | 0.89 | 0.84 | 0.92 | 0.84 |
time (sec) |
N/A | 0.253 | 0.002 | 0.382 | 0.026 | 0.061 | 0.020 | 0.120 | 0.226 | 0.023 |
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 | 25 | 25 | 25 | 22 | 21 | 21 | 20 | 21 | 24 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.84 | 0.84 | 0.80 | 0.84 | 0.96 | 0.84 |
time (sec) |
N/A | 0.234 | 0.002 | 0.369 | 0.037 | 0.060 | 0.019 | 0.120 | 0.253 | 0.017 |
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 | 12 | 12 | 12 | 11 | 10 | 10 | 8 | 10 | 12 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.83 | 1.00 | 0.83 |
time (sec) |
N/A | 0.207 | 0.000 | 0.035 | 0.028 | 0.065 | 0.017 | 0.118 | 0.292 | 0.009 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 301 | 317 | 311 | 27 | 239 | 1130235 | 20 | 275 | 11 | 235 |
N.S. |
1 | 1.05 | 1.03 | 0.09 | 0.79 | 3754.93 | 0.07 | 0.91 | 0.04 | 0.78 |
time (sec) |
N/A | 0.942 | 0.125 | 0.467 | 0.116 | 9.463 | 0.095 | 0.120 | 0.210 | 0.353 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 169 | 144 | 32 | 144 | 128 | 34 | 112 | 9 | 182 |
N.S. |
1 | 1.01 | 0.86 | 0.19 | 0.86 | 0.76 | 0.20 | 0.67 | 0.05 | 1.08 |
time (sec) |
N/A | 0.561 | 0.079 | 0.400 | 0.109 | 0.080 | 0.901 | 0.127 | 0.193 | 0.179 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 89 | 47 | 0 | 0 | 0 | 37 | 0 | 52 | 37 |
N.S. |
1 | 1.89 | 1.00 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 | 1.11 | 0.79 |
time (sec) |
N/A | 0.294 | 7.105 | 0.000 | 0.000 | 0.000 | 0.527 | 0.000 | 0.213 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 67 | 46 | 0 | 0 | 0 | 37 | 0 | 35 | 37 |
N.S. |
1 | 1.46 | 1.00 | 0.00 | 0.00 | 0.00 | 0.80 | 0.00 | 0.76 | 0.80 |
time (sec) |
N/A | 0.267 | 5.815 | 0.000 | 0.000 | 0.000 | 0.474 | 0.000 | 0.228 | 0.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 0 | 0 | 0 | 36 | 0 | 20 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 | 0.43 | 0.80 |
time (sec) |
N/A | 0.255 | 10.024 | 0.000 | 0.000 | 0.000 | 0.447 | 0.000 | 0.209 | 0.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 72 | 56 | 0 | 0 | 0 | 36 | 0 | 31 | 37 |
N.S. |
1 | 1.47 | 1.14 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 | 0.63 | 0.76 |
time (sec) |
N/A | 0.274 | 6.534 | 0.000 | 0.000 | 0.000 | 0.508 | 0.000 | 0.200 | 0.181 |
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 | 51 | 51 | 51 | 44 | 43 | 43 | 49 | 43 | 46 | 43 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.84 | 0.84 | 0.96 | 0.84 | 0.90 | 0.84 |
time (sec) |
N/A | 0.280 | 0.002 | 0.341 | 0.028 | 0.066 | 0.031 | 0.127 | 0.223 | 0.024 |
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 | 38 | 38 | 38 | 33 | 32 | 32 | 36 | 32 | 35 | 32 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.84 | 0.84 | 0.95 | 0.84 | 0.92 | 0.84 |
time (sec) |
N/A | 0.256 | 0.002 | 0.339 | 0.029 | 0.066 | 0.021 | 0.122 | 0.218 | 0.041 |
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 | 25 | 25 | 25 | 22 | 21 | 21 | 22 | 21 | 24 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.84 | 0.84 | 0.88 | 0.84 | 0.96 | 0.84 |
time (sec) |
N/A | 0.236 | 0.002 | 0.336 | 0.050 | 0.059 | 0.024 | 0.121 | 0.208 | 0.031 |
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 | 12 | 12 | 12 | 11 | 10 | 10 | 8 | 10 | 12 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.83 | 1.00 | 0.83 |
time (sec) |
N/A | 0.206 | 0.000 | 0.035 | 0.027 | 0.061 | 0.018 | 0.123 | 0.221 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 210 | 154 | 27 | 184 | 216 | 20 | 190 | 124 | 219 |
N.S. |
1 | 1.40 | 1.03 | 0.18 | 1.23 | 1.44 | 0.13 | 1.27 | 0.83 | 1.46 |
time (sec) |
N/A | 0.636 | 0.039 | 0.429 | 0.113 | 0.082 | 0.089 | 0.124 | 0.222 | 0.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 235 | 192 | 46 | 204 | 351 | 39 | 205 | 330 | 242 |
N.S. |
1 | 1.41 | 1.15 | 0.28 | 1.22 | 2.10 | 0.23 | 1.23 | 1.98 | 1.45 |
time (sec) |
N/A | 0.651 | 0.080 | 0.582 | 0.127 | 0.072 | 0.177 | 0.117 | 0.262 | 0.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 166 | 162 | 24 | 224 | 127 | 15 | 114 | 433 | 164 |
N.S. |
1 | 1.27 | 1.24 | 0.18 | 1.71 | 0.97 | 0.11 | 0.87 | 3.31 | 1.25 |
time (sec) |
N/A | 0.574 | 0.052 | 0.415 | 0.119 | 0.071 | 0.336 | 0.130 | 0.419 | 0.226 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 179 | 24 | 17 | 0 | 0 | 36 | 0 | 28 | 15 |
N.S. |
1 | 1.00 | 0.13 | 0.09 | 0.00 | 0.00 | 0.20 | 0.00 | 0.16 | 0.08 |
time (sec) |
N/A | 0.366 | 8.884 | 0.751 | 0.000 | 0.000 | 0.406 | 0.000 | 0.218 | 0.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 164 | 24 | 18 | 0 | 0 | 34 | 0 | 16 | 16 |
N.S. |
1 | 1.00 | 0.15 | 0.11 | 0.00 | 0.00 | 0.21 | 0.00 | 0.10 | 0.10 |
time (sec) |
N/A | 0.314 | 10.021 | 0.536 | 0.000 | 0.000 | 0.391 | 0.000 | 0.215 | 0.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 179 | 38 | 18 | 0 | 0 | 34 | 0 | 21 | 16 |
N.S. |
1 | 1.00 | 0.21 | 0.10 | 0.00 | 0.00 | 0.19 | 0.00 | 0.12 | 0.09 |
time (sec) |
N/A | 0.338 | 9.906 | 0.609 | 0.000 | 0.000 | 0.431 | 0.000 | 0.205 | 0.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | A | A | F | B |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 191 | 166 | 44 | 0 | 65 | 46 | 127 | 11 | 103 |
N.S. |
1 | 1.15 | 1.00 | 0.27 | 0.00 | 0.39 | 0.28 | 0.77 | 0.07 | 0.62 |
time (sec) |
N/A | 0.645 | 0.005 | 0.377 | 0.000 | 2.898 | 0.118 | 0.121 | 0.205 | 0.465 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | A | A | F | B |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 189 | 166 | 38 | 0 | 65 | 44 | 129 | 9 | 103 |
N.S. |
1 | 1.14 | 1.00 | 0.23 | 0.00 | 0.39 | 0.27 | 0.78 | 0.05 | 0.62 |
time (sec) |
N/A | 0.595 | 0.005 | 0.371 | 0.000 | 2.764 | 0.125 | 0.121 | 0.207 | 0.448 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 316 | 357 | 47 | 0 | 0 | 0 | 37 | 0 | 45 | 37 |
N.S. |
1 | 1.13 | 0.15 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 | 0.14 | 0.12 |
time (sec) |
N/A | 0.502 | 10.012 | 0.000 | 0.000 | 0.000 | 0.534 | 0.000 | 0.246 | 0.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 335 | 46 | 0 | 0 | 0 | 37 | 0 | 27 | 37 |
N.S. |
1 | 1.12 | 0.15 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 | 0.09 | 0.12 |
time (sec) |
N/A | 0.432 | 10.008 | 0.000 | 0.000 | 0.000 | 0.483 | 0.000 | 0.251 | 0.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 284 | 317 | 46 | 0 | 0 | 0 | 36 | 0 | 11 | 37 |
N.S. |
1 | 1.12 | 0.16 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 | 0.04 | 0.13 |
time (sec) |
N/A | 0.397 | 10.010 | 0.000 | 0.000 | 0.000 | 0.480 | 0.000 | 0.199 | 0.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 340 | 56 | 0 | 0 | 0 | 36 | 0 | 30 | 37 |
N.S. |
1 | 1.12 | 0.18 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 | 0.10 | 0.12 |
time (sec) |
N/A | 0.423 | 10.015 | 0.000 | 0.000 | 0.000 | 0.481 | 0.000 | 0.194 | 0.188 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 47 | 0 | 0 | 0 | 37 | 0 | 45 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 | 0.96 | 0.79 |
time (sec) |
N/A | 0.244 | 10.015 | 0.000 | 0.000 | 0.000 | 0.615 | 0.000 | 0.262 | 0.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 0 | 0 | 0 | 37 | 0 | 27 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.80 | 0.00 | 0.59 | 0.80 |
time (sec) |
N/A | 0.242 | 10.009 | 0.000 | 0.000 | 0.000 | 0.528 | 0.000 | 0.242 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 0 | 0 | 0 | 36 | 0 | 11 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 | 0.24 | 0.80 |
time (sec) |
N/A | 0.245 | 10.013 | 0.000 | 0.000 | 0.000 | 0.430 | 0.000 | 0.206 | 0.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 0 | 0 | 0 | 36 | 0 | 30 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 | 0.61 | 0.76 |
time (sec) |
N/A | 0.244 | 10.012 | 0.000 | 0.000 | 0.000 | 0.522 | 0.000 | 0.202 | 0.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 310 | 324 | 27 | 0 | 248 | 20 | 437 | 321 | 110 |
N.S. |
1 | 1.48 | 1.54 | 0.13 | 0.00 | 1.18 | 0.10 | 2.08 | 1.53 | 0.52 |
time (sec) |
N/A | 0.874 | 0.183 | 0.403 | 0.000 | 0.073 | 0.093 | 0.134 | 0.217 | 0.226 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 274 | 198 | 29 | 0 | 232 | 22 | 461 | 171 | 94 |
N.S. |
1 | 1.46 | 1.05 | 0.15 | 0.00 | 1.23 | 0.12 | 2.45 | 0.91 | 0.50 |
time (sec) |
N/A | 0.732 | 0.049 | 0.405 | 0.000 | 0.075 | 0.104 | 0.135 | 0.222 | 0.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 397 | 403 | 46 | 0 | 0 | 0 | 37 | 0 | 35 | 37 |
N.S. |
1 | 1.02 | 0.12 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 | 0.09 | 0.09 |
time (sec) |
N/A | 0.675 | 10.011 | 0.000 | 0.000 | 0.000 | 0.496 | 0.000 | 0.288 | 0.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 379 | 381 | 46 | 0 | 0 | 0 | 36 | 0 | 20 | 37 |
N.S. |
1 | 1.01 | 0.12 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 | 0.05 | 0.10 |
time (sec) |
N/A | 0.582 | 10.009 | 0.000 | 0.000 | 0.000 | 0.449 | 0.000 | 0.204 | 0.146 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 404 | 408 | 56 | 0 | 0 | 0 | 36 | 0 | 31 | 37 |
N.S. |
1 | 1.01 | 0.14 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 | 0.08 | 0.09 |
time (sec) |
N/A | 0.640 | 10.029 | 0.000 | 0.000 | 0.000 | 0.521 | 0.000 | 0.283 | 0.200 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 325 | 289 | 66 | 0 | 251 | 70 | 223 | 11 | 852 |
N.S. |
1 | 1.99 | 1.77 | 0.40 | 0.00 | 1.54 | 0.43 | 1.37 | 0.07 | 5.23 |
time (sec) |
N/A | 0.843 | 0.139 | 0.412 | 0.000 | 0.077 | 3.672 | 0.125 | 0.185 | 0.333 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 203 | 0 | 0 | 0 | 34 | 0 | 94 | 41 |
N.S. |
1 | 1.00 | 4.61 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 | 2.14 | 0.93 |
time (sec) |
N/A | 0.257 | 0.095 | 0.000 | 0.000 | 0.000 | 5.397 | 0.000 | 0.189 | 0.162 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 44 | 0 | 0 | 0 | 22 | 0 | 94 | 41 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 2.14 | 0.93 |
time (sec) |
N/A | 0.243 | 0.041 | 0.000 | 0.000 | 0.000 | 1.193 | 0.000 | 0.203 | 0.753 |
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 | 18 | 18 | 18 | 19 | 18 | 20 | 20 | 18 | 21 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.11 | 1.11 | 1.00 | 1.17 | 1.00 |
time (sec) |
N/A | 0.214 | 0.005 | 0.406 | 0.047 | 0.080 | 0.018 | 0.119 | 0.234 | 0.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 50 | 0 | 0 | 0 | 34 | 0 | 46 | 51 |
N.S. |
1 | 1.00 | 1.25 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 | 1.15 | 1.28 |
time (sec) |
N/A | 0.238 | 0.071 | 0.000 | 0.000 | 0.000 | 0.979 | 0.000 | 0.174 | 0.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 60 | 0 | 0 | 0 | 24 | 0 | 61 | 57 |
N.S. |
1 | 1.00 | 1.36 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 | 1.39 | 1.30 |
time (sec) |
N/A | 0.263 | 0.033 | 0.000 | 0.000 | 0.000 | 1.514 | 0.000 | 0.186 | 0.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 60 | 0 | 0 | 0 | 39 | 0 | 61 | 57 |
N.S. |
1 | 1.00 | 1.36 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 | 1.39 | 1.30 |
time (sec) |
N/A | 0.282 | 0.037 | 0.000 | 0.000 | 0.000 | 6.293 | 0.000 | 0.227 | 0.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 19 | 0 | 0 | 20 | 0 | 91 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.50 | 0.00 | 0.00 | 0.53 | 0.00 | 2.39 | 0.45 |
time (sec) |
N/A | 0.228 | 0.062 | 0.423 | 0.000 | 0.000 | 0.774 | 0.000 | 0.203 | 0.431 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 19 | 0 | 0 | 20 | 0 | 91 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.50 | 0.00 | 0.00 | 0.53 | 0.00 | 2.39 | 0.45 |
time (sec) |
N/A | 0.236 | 0.052 | 0.402 | 0.000 | 0.000 | 0.700 | 0.000 | 0.182 | 0.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 35 | 19 | 0 | 0 | 19 | 0 | 84 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.54 | 0.00 | 0.00 | 0.54 | 0.00 | 2.40 | 0.49 |
time (sec) |
N/A | 0.233 | 0.025 | 0.423 | 0.000 | 0.000 | 0.417 | 0.000 | 0.193 | 0.311 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 0 | 0 | 0 | 20 | 0 | 87 | 33 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 | 2.42 | 0.92 |
time (sec) |
N/A | 0.231 | 0.061 | 0.000 | 0.000 | 0.000 | 0.485 | 0.000 | 0.197 | 0.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 0 | 0 | 0 | 22 | 0 | 91 | 35 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.58 | 0.00 | 2.39 | 0.92 |
time (sec) |
N/A | 0.242 | 0.067 | 0.000 | 0.000 | 0.000 | 0.824 | 0.000 | 0.187 | 0.435 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 0 | 0 | 0 | 22 | 0 | 91 | 35 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.58 | 0.00 | 2.39 | 0.92 |
time (sec) |
N/A | 0.237 | 0.064 | 0.000 | 0.000 | 0.000 | 0.868 | 0.000 | 0.181 | 0.439 |
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 | 38 | 40 | 65 | 55 | 54 | 58 | 66 | 54 | 56 | 54 |
N.S. |
1 | 1.05 | 1.71 | 1.45 | 1.42 | 1.53 | 1.74 | 1.42 | 1.47 | 1.42 |
time (sec) |
N/A | 0.253 | 0.019 | 0.741 | 0.033 | 0.064 | 0.350 | 0.119 | 0.182 | 0.036 |
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 | 38 | 40 | 52 | 44 | 43 | 47 | 51 | 43 | 43 | 43 |
N.S. |
1 | 1.05 | 1.37 | 1.16 | 1.13 | 1.24 | 1.34 | 1.13 | 1.13 | 1.13 |
time (sec) |
N/A | 0.265 | 0.015 | 0.568 | 0.043 | 0.061 | 0.092 | 0.117 | 0.236 | 0.026 |
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 | 38 | 40 | 41 | 33 | 32 | 35 | 39 | 32 | 32 | 32 |
N.S. |
1 | 1.05 | 1.08 | 0.87 | 0.84 | 0.92 | 1.03 | 0.84 | 0.84 | 0.84 |
time (sec) |
N/A | 0.262 | 0.017 | 0.474 | 0.025 | 0.062 | 0.317 | 0.119 | 0.197 | 0.047 |
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 | 27 | 32 | 26 | 22 | 21 | 21 | 24 | 21 | 21 | 21 |
N.S. |
1 | 1.19 | 0.96 | 0.81 | 0.78 | 0.78 | 0.89 | 0.78 | 0.78 | 0.78 |
time (sec) |
N/A | 0.260 | 0.020 | 0.395 | 0.025 | 0.072 | 0.067 | 0.114 | 0.188 | 0.039 |
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 | 14 | 14 | 14 | 11 | 10 | 10 | 12 | 10 | 12 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.71 | 0.71 | 0.86 | 0.71 | 0.86 | 0.71 |
time (sec) |
N/A | 0.214 | 0.001 | 0.069 | 0.031 | 0.064 | 0.018 | 0.121 | 0.184 | 0.029 |
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 | 27 | 28 | 27 | 24 | 27 | 22 | 27 | 24 | 20 | 23 |
N.S. |
1 | 1.04 | 1.00 | 0.89 | 1.00 | 0.81 | 1.00 | 0.89 | 0.74 | 0.85 |
time (sec) |
N/A | 0.252 | 0.020 | 0.356 | 0.032 | 0.064 | 0.147 | 0.122 | 0.221 | 0.068 |
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 | 33 | 33 | 29 | 30 | 29 | 50 | 80 | 30 | 39 | 29 |
N.S. |
1 | 1.00 | 0.88 | 0.91 | 0.88 | 1.52 | 2.42 | 0.91 | 1.18 | 0.88 |
time (sec) |
N/A | 0.265 | 0.026 | 0.357 | 0.031 | 0.073 | 0.209 | 0.122 | 0.193 | 0.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 27 | 30 | 29 | 47 | 63 | 22 | 22 | 34 |
N.S. |
1 | 1.00 | 1.69 | 1.88 | 1.81 | 2.94 | 3.94 | 1.38 | 1.38 | 2.12 |
time (sec) |
N/A | 0.212 | 0.033 | 0.355 | 0.039 | 0.069 | 0.347 | 0.114 | 0.185 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 40 | 30 | 31 | 30 | 72 | 97 | 22 | 42 | 45 |
N.S. |
1 | 1.11 | 0.83 | 0.86 | 0.83 | 2.00 | 2.69 | 0.61 | 1.17 | 1.25 |
time (sec) |
N/A | 0.266 | 0.028 | 0.353 | 0.034 | 0.073 | 0.461 | 0.119 | 0.184 | 0.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 40 | 30 | 31 | 30 | 96 | 136 | 22 | 53 | 57 |
N.S. |
1 | 1.05 | 0.79 | 0.82 | 0.79 | 2.53 | 3.58 | 0.58 | 1.39 | 1.50 |
time (sec) |
N/A | 0.269 | 0.028 | 0.356 | 0.044 | 0.071 | 0.698 | 0.119 | 0.243 | 0.193 |
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 | 42 | 47 | 41 | 33 | 32 | 38 | 41 | 32 | 37 | 32 |
N.S. |
1 | 1.12 | 0.98 | 0.79 | 0.76 | 0.90 | 0.98 | 0.76 | 0.88 | 0.76 |
time (sec) |
N/A | 0.284 | 0.016 | 0.488 | 0.032 | 0.062 | 0.450 | 0.118 | 0.177 | 0.051 |
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 | 27 | 32 | 28 | 22 | 21 | 21 | 24 | 21 | 24 | 21 |
N.S. |
1 | 1.19 | 1.04 | 0.81 | 0.78 | 0.78 | 0.89 | 0.78 | 0.89 | 0.78 |
time (sec) |
N/A | 0.269 | 0.014 | 0.393 | 0.028 | 0.083 | 0.111 | 0.125 | 0.180 | 0.036 |
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 | 14 | 14 | 14 | 11 | 10 | 10 | 12 | 10 | 13 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.71 | 0.71 | 0.86 | 0.71 | 0.93 | 0.71 |
time (sec) |
N/A | 0.212 | 0.001 | 0.068 | 0.032 | 0.061 | 0.023 | 0.124 | 0.182 | 0.026 |
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 | 125 | 128 | 99 | 95 | 102 | 386 | 138 | 116 | 66 | 121 |
N.S. |
1 | 1.02 | 0.79 | 0.76 | 0.82 | 3.09 | 1.10 | 0.93 | 0.53 | 0.97 |
time (sec) |
N/A | 0.426 | 0.075 | 0.357 | 0.111 | 0.085 | 1.256 | 0.130 | 0.256 | 0.136 |
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 | 146 | 155 | 129 | 116 | 126 | 509 | 459 | 131 | 158 | 150 |
N.S. |
1 | 1.06 | 0.88 | 0.79 | 0.86 | 3.49 | 3.14 | 0.90 | 1.08 | 1.03 |
time (sec) |
N/A | 0.466 | 0.175 | 0.361 | 0.113 | 0.082 | 18.987 | 0.133 | 0.184 | 0.352 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 182 | 142 | 137 | 149 | 664 | 896 | 141 | 270 | 167 |
N.S. |
1 | 1.10 | 0.86 | 0.83 | 0.90 | 4.02 | 5.43 | 0.85 | 1.64 | 1.01 |
time (sec) |
N/A | 0.516 | 0.205 | 0.372 | 0.110 | 0.097 | 108.281 | 0.135 | 0.201 | 0.282 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 209 | 153 | 158 | 171 | 787 | 0 | 152 | 386 | 195 |
N.S. |
1 | 1.14 | 0.83 | 0.86 | 0.93 | 4.28 | 0.00 | 0.83 | 2.10 | 1.06 |
time (sec) |
N/A | 0.567 | 0.213 | 0.360 | 0.112 | 0.106 | 0.000 | 0.138 | 0.198 | 0.296 |
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 | 46 | 57 | 46 | 43 | 42 | 48 | 44 | 44 | 54 | 45 |
N.S. |
1 | 1.24 | 1.00 | 0.93 | 0.91 | 1.04 | 0.96 | 0.96 | 1.17 | 0.98 |
time (sec) |
N/A | 0.300 | 0.030 | 0.586 | 0.027 | 0.087 | 0.186 | 0.125 | 0.222 | 0.057 |
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 | 35 | 44 | 35 | 32 | 31 | 41 | 36 | 32 | 35 | 33 |
N.S. |
1 | 1.26 | 1.00 | 0.91 | 0.89 | 1.17 | 1.03 | 0.91 | 1.00 | 0.94 |
time (sec) |
N/A | 0.281 | 0.025 | 0.486 | 0.038 | 0.069 | 0.184 | 0.118 | 0.184 | 0.043 |
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 | 21 | 30 | 21 | 20 | 19 | 22 | 20 | 20 | 18 | 22 |
N.S. |
1 | 1.43 | 1.00 | 0.95 | 0.90 | 1.05 | 0.95 | 0.95 | 0.86 | 1.05 |
time (sec) |
N/A | 0.254 | 0.016 | 0.426 | 0.032 | 0.065 | 0.085 | 0.120 | 0.193 | 0.050 |
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 | 12 | 12 | 12 | 11 | 10 | 10 | 10 | 10 | 9 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.83 | 0.83 | 0.75 | 0.83 |
time (sec) |
N/A | 0.210 | 0.001 | 0.072 | 0.034 | 0.063 | 0.022 | 0.122 | 0.215 | 0.031 |
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 | 35 | 39 | 34 | 34 | 39 | 30 | 42 | 32 | 28 | 30 |
N.S. |
1 | 1.11 | 0.97 | 0.97 | 1.11 | 0.86 | 1.20 | 0.91 | 0.80 | 0.86 |
time (sec) |
N/A | 0.278 | 0.020 | 0.368 | 0.027 | 0.068 | 0.181 | 0.128 | 0.223 | 0.049 |
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 | 54 | 58 | 67 | 51 | 65 | 82 | 134 | 52 | 62 | 54 |
N.S. |
1 | 1.07 | 1.24 | 0.94 | 1.20 | 1.52 | 2.48 | 0.96 | 1.15 | 1.00 |
time (sec) |
N/A | 0.310 | 0.037 | 0.386 | 0.032 | 0.072 | 0.268 | 0.122 | 0.183 | 0.105 |
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 | 73 | 80 | 78 | 68 | 87 | 123 | 270 | 65 | 95 | 73 |
N.S. |
1 | 1.10 | 1.07 | 0.93 | 1.19 | 1.68 | 3.70 | 0.89 | 1.30 | 1.00 |
time (sec) |
N/A | 0.338 | 0.070 | 0.368 | 0.041 | 0.075 | 0.413 | 0.121 | 0.172 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 101 | 95 | 85 | 112 | 172 | 503 | 75 | 138 | 91 |
N.S. |
1 | 1.07 | 1.01 | 0.90 | 1.19 | 1.83 | 5.35 | 0.80 | 1.47 | 0.97 |
time (sec) |
N/A | 0.370 | 0.089 | 0.369 | 0.035 | 0.077 | 0.519 | 0.119 | 0.219 | 0.117 |
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 | 51 | 58 | 51 | 44 | 43 | 51 | 49 | 46 | 58 | 46 |
N.S. |
1 | 1.14 | 1.00 | 0.86 | 0.84 | 1.00 | 0.96 | 0.90 | 1.14 | 0.90 |
time (sec) |
N/A | 0.321 | 0.029 | 0.630 | 0.028 | 0.069 | 0.402 | 0.115 | 0.201 | 0.121 |
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 | 40 | 45 | 40 | 33 | 32 | 41 | 39 | 35 | 43 | 35 |
N.S. |
1 | 1.12 | 1.00 | 0.82 | 0.80 | 1.02 | 0.98 | 0.88 | 1.08 | 0.88 |
time (sec) |
N/A | 0.290 | 0.026 | 0.523 | 0.032 | 0.068 | 0.285 | 0.115 | 0.194 | 0.047 |
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 | 25 | 30 | 25 | 22 | 21 | 26 | 22 | 22 | 34 | 24 |
N.S. |
1 | 1.20 | 1.00 | 0.88 | 0.84 | 1.04 | 0.88 | 0.88 | 1.36 | 0.96 |
time (sec) |
N/A | 0.278 | 0.023 | 0.419 | 0.029 | 0.069 | 0.225 | 0.124 | 0.186 | 0.102 |
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 | 12 | 12 | 12 | 11 | 10 | 16 | 10 | 10 | 14 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 1.33 | 0.83 | 0.83 | 1.17 | 0.83 |
time (sec) |
N/A | 0.210 | 0.002 | 0.079 | 0.048 | 0.078 | 0.021 | 0.123 | 0.201 | 0.034 |
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 | 130 | 143 | 119 | 107 | 107 | 124 | 151 | 115 | 82 | 128 |
N.S. |
1 | 1.10 | 0.92 | 0.82 | 0.82 | 0.95 | 1.16 | 0.88 | 0.63 | 0.98 |
time (sec) |
N/A | 0.472 | 0.087 | 0.374 | 0.114 | 0.073 | 1.237 | 0.134 | 0.192 | 0.167 |
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 | 152 | 174 | 142 | 119 | 132 | 197 | 620 | 131 | 186 | 150 |
N.S. |
1 | 1.14 | 0.93 | 0.78 | 0.87 | 1.30 | 4.08 | 0.86 | 1.22 | 0.99 |
time (sec) |
N/A | 0.523 | 0.205 | 0.375 | 0.111 | 0.077 | 19.937 | 0.126 | 0.174 | 0.259 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 203 | 153 | 128 | 154 | 262 | 1255 | 143 | 296 | 170 |
N.S. |
1 | 1.17 | 0.88 | 0.74 | 0.89 | 1.51 | 7.21 | 0.82 | 1.70 | 0.98 |
time (sec) |
N/A | 0.572 | 0.270 | 0.377 | 0.109 | 0.078 | 111.682 | 0.130 | 0.184 | 0.270 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 50 | 0 | 0 | 0 | 0 | 0 | 239 | 41 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.78 | 0.82 |
time (sec) |
N/A | 0.272 | 0.073 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.217 | 0.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 50 | 0 | 0 | 0 | 37 | 0 | 225 | 41 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 | 4.50 | 0.82 |
time (sec) |
N/A | 0.271 | 0.096 | 0.000 | 0.000 | 0.000 | 26.417 | 0.000 | 0.260 | 0.217 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 49 | 42 | 0 | 45 | 56 | 445 | 94 | 46 | 41 |
N.S. |
1 | 1.02 | 0.88 | 0.00 | 0.94 | 1.17 | 9.27 | 1.96 | 0.96 | 0.85 |
time (sec) |
N/A | 0.271 | 0.062 | 0.000 | 0.036 | 0.095 | 0.948 | 0.123 | 0.187 | 0.220 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 0 | 0 | 0 | 41 | 0 | 263 | 57 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 | 5.72 | 1.24 |
time (sec) |
N/A | 0.259 | 0.112 | 0.000 | 0.000 | 0.000 | 2.955 | 0.000 | 0.227 | 0.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 52 | 50 | 0 | 0 | 0 | 0 | 0 | 120 | 41 |
N.S. |
1 | 1.04 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.40 | 0.82 |
time (sec) |
N/A | 0.293 | 0.216 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.285 | 0.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 52 | 50 | 0 | 0 | 0 | 0 | 0 | 128 | 41 |
N.S. |
1 | 1.04 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.56 | 0.82 |
time (sec) |
N/A | 0.301 | 0.180 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.304 |
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 | 59 | 61 | 78 | 66 | 47 | 72 | 80 | 65 | 66 | 65 |
N.S. |
1 | 1.03 | 1.32 | 1.12 | 0.80 | 1.22 | 1.36 | 1.10 | 1.12 | 1.10 |
time (sec) |
N/A | 0.301 | 0.023 | 1.189 | 0.043 | 0.072 | 0.402 | 0.121 | 0.208 | 0.039 |
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 | 59 | 61 | 67 | 55 | 54 | 61 | 68 | 54 | 55 | 54 |
N.S. |
1 | 1.03 | 1.14 | 0.93 | 0.92 | 1.03 | 1.15 | 0.92 | 0.93 | 0.92 |
time (sec) |
N/A | 0.299 | 0.020 | 0.881 | 0.032 | 0.068 | 0.447 | 0.114 | 0.218 | 0.029 |
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 | 57 | 61 | 54 | 44 | 43 | 46 | 53 | 43 | 44 | 43 |
N.S. |
1 | 1.07 | 0.95 | 0.77 | 0.75 | 0.81 | 0.93 | 0.75 | 0.77 | 0.75 |
time (sec) |
N/A | 0.287 | 0.018 | 0.648 | 0.030 | 0.070 | 0.355 | 0.123 | 0.190 | 0.027 |
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 | 42 | 47 | 41 | 33 | 32 | 32 | 39 | 32 | 33 | 32 |
N.S. |
1 | 1.12 | 0.98 | 0.79 | 0.76 | 0.76 | 0.93 | 0.76 | 0.79 | 0.76 |
time (sec) |
N/A | 0.276 | 0.014 | 0.501 | 0.033 | 0.064 | 0.375 | 0.120 | 0.170 | 0.045 |
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 | 29 | 34 | 30 | 22 | 21 | 21 | 27 | 21 | 24 | 21 |
N.S. |
1 | 1.17 | 1.03 | 0.76 | 0.72 | 0.72 | 0.93 | 0.72 | 0.83 | 0.72 |
time (sec) |
N/A | 0.261 | 0.013 | 0.420 | 0.027 | 0.064 | 0.334 | 0.116 | 0.209 | 0.042 |
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 | 14 | 14 | 14 | 11 | 10 | 10 | 12 | 10 | 13 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.71 | 0.71 | 0.86 | 0.71 | 0.93 | 0.71 |
time (sec) |
N/A | 0.211 | 0.001 | 0.078 | 0.026 | 0.064 | 0.023 | 0.126 | 0.213 | 0.028 |
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 | 42 | 43 | 42 | 35 | 44 | 33 | 42 | 35 | 33 | 34 |
N.S. |
1 | 1.02 | 1.00 | 0.83 | 1.05 | 0.79 | 1.00 | 0.83 | 0.79 | 0.81 |
time (sec) |
N/A | 0.272 | 0.025 | 0.374 | 0.027 | 0.065 | 0.169 | 0.121 | 0.201 | 0.112 |
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 | 46 | 47 | 56 | 41 | 44 | 68 | 109 | 41 | 57 | 43 |
N.S. |
1 | 1.02 | 1.22 | 0.89 | 0.96 | 1.48 | 2.37 | 0.89 | 1.24 | 0.93 |
time (sec) |
N/A | 0.279 | 0.040 | 0.391 | 0.045 | 0.069 | 0.225 | 0.121 | 0.189 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 55 | 47 | 47 | 46 | 113 | 228 | 44 | 81 | 53 |
N.S. |
1 | 1.02 | 0.87 | 0.87 | 0.85 | 2.09 | 4.22 | 0.81 | 1.50 | 0.98 |
time (sec) |
N/A | 0.293 | 0.043 | 0.382 | 0.034 | 0.088 | 0.342 | 0.124 | 0.221 | 0.148 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 40 | 48 | 47 | 109 | 141 | 33 | 34 | 56 |
N.S. |
1 | 1.00 | 2.50 | 3.00 | 2.94 | 6.81 | 8.81 | 2.06 | 2.12 | 3.50 |
time (sec) |
N/A | 0.206 | 0.032 | 0.375 | 0.033 | 0.072 | 0.515 | 0.124 | 0.192 | 0.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 61 | 43 | 48 | 47 | 136 | 207 | 33 | 66 | 69 |
N.S. |
1 | 1.56 | 1.10 | 1.23 | 1.21 | 3.49 | 5.31 | 0.85 | 1.69 | 1.77 |
time (sec) |
N/A | 0.289 | 0.031 | 0.375 | 0.028 | 0.080 | 0.728 | 0.124 | 0.199 | 0.123 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 61 | 43 | 48 | 47 | 176 | 233 | 33 | 77 | 80 |
N.S. |
1 | 1.07 | 0.75 | 0.84 | 0.82 | 3.09 | 4.09 | 0.58 | 1.35 | 1.40 |
time (sec) |
N/A | 0.288 | 0.032 | 0.388 | 0.038 | 0.086 | 1.030 | 0.120 | 0.176 | 0.082 |
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 | 42 | 47 | 41 | 33 | 32 | 32 | 39 | 32 | 35 | 32 |
N.S. |
1 | 1.12 | 0.98 | 0.79 | 0.76 | 0.76 | 0.93 | 0.76 | 0.83 | 0.76 |
time (sec) |
N/A | 0.267 | 0.016 | 0.545 | 0.026 | 0.061 | 0.119 | 0.120 | 0.229 | 0.051 |
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 | 29 | 34 | 30 | 22 | 21 | 21 | 27 | 21 | 24 | 21 |
N.S. |
1 | 1.17 | 1.03 | 0.76 | 0.72 | 0.72 | 0.93 | 0.72 | 0.83 | 0.72 |
time (sec) |
N/A | 0.256 | 0.013 | 0.431 | 0.035 | 0.061 | 0.330 | 0.124 | 0.229 | 0.039 |
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 | 14 | 14 | 14 | 11 | 10 | 10 | 12 | 10 | 13 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.71 | 0.71 | 0.86 | 0.71 | 0.93 | 0.71 |
time (sec) |
N/A | 0.211 | 0.001 | 0.148 | 0.025 | 0.057 | 0.025 | 0.120 | 0.194 | 0.028 |