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 | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 177 | 167 | 131 | 1078 | 144 | 0 | 15993 | 226 | 116 |
N.S. |
1 | 0.93 | 0.87 | 0.69 | 5.64 | 0.75 | 0.00 | 83.73 | 1.18 | 0.61 |
time (sec) |
N/A | 0.327 | 0.302 | 4.299 | 0.085 | 0.081 | 0.000 | 0.608 | 0.175 | 20.730 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 80 | 51 | 46 | 93 | 59 | 100 | 0 | 68 | 50 |
N.S. |
1 | 1.10 | 0.70 | 0.63 | 1.27 | 0.81 | 1.37 | 0.00 | 0.93 | 0.68 |
time (sec) |
N/A | 0.287 | 0.084 | 6.663 | 0.057 | 0.078 | 8.433 | 0.000 | 0.163 | 20.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 37 | 22 | 27 | 20 | 25 | 0 | 25 | 35 | 21 |
N.S. |
1 | 1.28 | 0.76 | 0.93 | 0.69 | 0.86 | 0.00 | 0.86 | 1.21 | 0.72 |
time (sec) |
N/A | 0.200 | 0.017 | 0.219 | 0.033 | 0.072 | 0.000 | 0.118 | 0.166 | 20.994 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | A | C | F | C | B | B |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 106 | 0 | 0 | 82 | 60 | 0 | 267 | 59 | 131 |
N.S. |
1 | 1.05 | 0.00 | 0.00 | 0.81 | 0.59 | 0.00 | 2.64 | 0.58 | 1.30 |
time (sec) |
N/A | 0.411 | 0.000 | 0.000 | 0.073 | 0.077 | 0.000 | 0.960 | 0.168 | 21.954 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | A | C | F | A | B | B |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 72 | 0 | 0 | 29 | 40 | 0 | 1 | 75 | 83 |
N.S. |
1 | 1.16 | 0.00 | 0.00 | 0.47 | 0.65 | 0.00 | 0.02 | 1.21 | 1.34 |
time (sec) |
N/A | 0.295 | 0.000 | 0.000 | 0.057 | 0.068 | 0.000 | 0.188 | 0.172 | 20.659 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | A | C | F | C | B | B |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 129 | 0 | 0 | 172 | 107 | 0 | 498 | 95 | 143 |
N.S. |
1 | 1.10 | 0.00 | 0.00 | 1.47 | 0.91 | 0.00 | 4.26 | 0.81 | 1.22 |
time (sec) |
N/A | 0.406 | 0.000 | 0.000 | 0.077 | 0.081 | 0.000 | 3.708 | 0.180 | 21.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | A | C | F | A | B | B |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 85 | 0 | 0 | 41 | 57 | 0 | 1 | 116 | 86 |
N.S. |
1 | 1.25 | 0.00 | 0.00 | 0.60 | 0.84 | 0.00 | 0.01 | 1.71 | 1.26 |
time (sec) |
N/A | 0.309 | 0.000 | 0.000 | 0.062 | 0.072 | 0.000 | 0.435 | 0.167 | 20.209 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 226 | 231 | 158 | 218 | 195 | 128 | 0 | 1870 | 151 | 277 |
N.S. |
1 | 1.02 | 0.70 | 0.96 | 0.86 | 0.57 | 0.00 | 8.27 | 0.67 | 1.23 |
time (sec) |
N/A | 0.404 | 0.991 | 125.530 | 0.102 | 0.078 | 0.000 | 9.583 | 0.171 | 22.371 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | A | C | F | F(-2) | B | B |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 138 | 0 | 0 | 106 | 84 | 0 | 0 | 229 | 158 |
N.S. |
1 | 1.08 | 0.00 | 0.00 | 0.83 | 0.66 | 0.00 | 0.00 | 1.79 | 1.23 |
time (sec) |
N/A | 0.350 | 0.000 | 0.000 | 0.076 | 0.073 | 0.000 | 0.000 | 0.172 | 20.295 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 377 | 0 | 0 | 0 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.00 | 3.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.308 | 3.487 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 181 | 0 | 84 | 0 | 0 | 18 | 23 |
N.S. |
1 | 1.00 | 1.00 | 7.54 | 0.00 | 3.50 | 0.00 | 0.00 | 0.75 | 0.96 |
time (sec) |
N/A | 0.217 | 0.080 | 1.157 | 0.000 | 0.078 | 0.000 | 0.000 | 0.170 | 19.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 220 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 2.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.298 | 0.858 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 61 | 54 | 247 | 0 | 107 | 0 | 0 | 29 | 56 |
N.S. |
1 | 0.97 | 0.86 | 3.92 | 0.00 | 1.70 | 0.00 | 0.00 | 0.46 | 0.89 |
time (sec) |
N/A | 0.286 | 0.095 | 1.851 | 0.000 | 0.082 | 0.000 | 0.000 | 0.165 | 20.884 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-2) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 696 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 6.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.299 | 8.332 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 61 | 58 | 280 | 0 | 113 | 0 | 0 | 31 | 65 |
N.S. |
1 | 0.97 | 0.92 | 4.44 | 0.00 | 1.79 | 0.00 | 0.00 | 0.49 | 1.03 |
time (sec) |
N/A | 0.278 | 0.113 | 4.786 | 0.000 | 0.082 | 0.000 | 0.000 | 0.174 | 21.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 134 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.298 | 0.483 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 26 | 0 | 78 | 0 | 0 | 31 | 23 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 0.00 | 3.25 | 0.00 | 0.00 | 1.29 | 0.96 |
time (sec) |
N/A | 0.212 | 0.075 | 0.322 | 0.000 | 0.077 | 0.000 | 0.000 | 0.171 | 19.604 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 431 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 3.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.297 | 5.698 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 57 | 54 | 250 | 0 | 150 | 0 | 0 | 31 | 65 |
N.S. |
1 | 0.97 | 0.92 | 4.24 | 0.00 | 2.54 | 0.00 | 0.00 | 0.53 | 1.10 |
time (sec) |
N/A | 0.281 | 0.129 | 0.700 | 0.000 | 0.076 | 0.000 | 0.000 | 0.167 | 20.478 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 188 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 1.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.302 | 1.854 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 61 | 54 | 291 | 0 | 149 | 0 | 0 | 31 | 65 |
N.S. |
1 | 0.97 | 0.86 | 4.62 | 0.00 | 2.37 | 0.00 | 0.00 | 0.49 | 1.03 |
time (sec) |
N/A | 0.276 | 0.120 | 0.897 | 0.000 | 0.082 | 0.000 | 0.000 | 0.160 | 20.359 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | A | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 82 | 0 | 187 | 39 | 0 | 0 | 30 | 48 |
N.S. |
1 | 1.00 | 1.71 | 0.00 | 3.90 | 0.81 | 0.00 | 0.00 | 0.62 | 1.00 |
time (sec) |
N/A | 0.226 | 0.112 | 0.000 | 0.157 | 0.064 | 0.000 | 0.000 | 0.158 | 20.714 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 232 | 312 | 222 | 3537 | 273 | 0 | 224645 | 797 | 152 |
N.S. |
1 | 0.87 | 1.17 | 0.83 | 13.30 | 1.03 | 0.00 | 844.53 | 3.00 | 0.57 |
time (sec) |
N/A | 0.407 | 2.834 | 75.805 | 0.254 | 0.092 | 0.000 | 6.070 | 0.175 | 21.893 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 182 | 292 | 307 | 2352 | 190 | 0 | 159584 | 477 | 140 |
N.S. |
1 | 0.91 | 1.45 | 1.53 | 11.70 | 0.95 | 0.00 | 793.95 | 2.37 | 0.70 |
time (sec) |
N/A | 0.374 | 1.338 | 15.208 | 0.152 | 0.088 | 0.000 | 4.478 | 0.170 | 20.984 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 120 | 91 | 82 | 646 | 105 | 0 | 9145 | 155 | 82 |
N.S. |
1 | 1.00 | 0.76 | 0.68 | 5.38 | 0.88 | 0.00 | 76.21 | 1.29 | 0.68 |
time (sec) |
N/A | 0.245 | 0.240 | 2.706 | 0.088 | 0.077 | 0.000 | 0.563 | 0.163 | 19.921 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 53 | 63 | 313 | 58 | 0 | 5162 | 61 | 70 |
N.S. |
1 | 1.00 | 0.76 | 0.90 | 4.47 | 0.83 | 0.00 | 73.74 | 0.87 | 1.00 |
time (sec) |
N/A | 0.199 | 0.098 | 0.414 | 0.059 | 0.075 | 0.000 | 0.294 | 0.155 | 20.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 126 | 204 | 0 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 0.97 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.345 | 1.641 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 126 | 436 | 0 | 0 | 0 | 0 | 0 | 72 | 0 |
N.S. |
1 | 0.98 | 3.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.335 | 5.936 | 0.000 | 0.000 | 0.000 | 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 | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 119 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.327 | 0.659 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 126 | 487 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 0.97 | 3.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.331 | 3.674 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 126 | 205 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 0.97 | 1.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.335 | 1.845 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 181 | 170 | 0 | 0 | 0 | 0 | 0 | 88 | 0 |
N.S. |
1 | 1.26 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.380 | 1.380 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 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 | 114 | 114 | 141 | 0 | 0 | 0 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.00 | 1.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.330 | 0.674 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 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 | 112 | 112 | 143 | 0 | 0 | 0 | 0 | 0 | 60 | 0 |
N.S. |
1 | 1.00 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.310 | 0.516 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 132 | 37 | 88 | 30 | 37 | 37 | 13 | 36 |
N.S. |
1 | 1.00 | 2.81 | 0.79 | 1.87 | 0.64 | 0.79 | 0.79 | 0.28 | 0.77 |
time (sec) |
N/A | 0.237 | 0.028 | 0.876 | 0.050 | 0.063 | 0.115 | 0.178 | 0.156 | 19.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 42 | 66 | 33 | 149 | 42 | 61 | 26 | 13 | 36 |
N.S. |
1 | 0.98 | 1.53 | 0.77 | 3.47 | 0.98 | 1.42 | 0.60 | 0.30 | 0.84 |
time (sec) |
N/A | 0.210 | 0.015 | 0.659 | 0.147 | 0.074 | 0.113 | 0.185 | 0.158 | 19.636 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 114 | 26 | 70 | 21 | 26 | 28 | 11 | 25 |
N.S. |
1 | 1.00 | 3.45 | 0.79 | 2.12 | 0.64 | 0.79 | 0.85 | 0.33 | 0.76 |
time (sec) |
N/A | 0.211 | 0.019 | 0.504 | 0.037 | 0.065 | 0.113 | 0.187 | 0.151 | 19.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 42 | 22 | 122 | 33 | 27 | 17 | 9 | 25 |
N.S. |
1 | 1.00 | 1.56 | 0.81 | 4.52 | 1.22 | 1.00 | 0.63 | 0.33 | 0.93 |
time (sec) |
N/A | 0.176 | 0.007 | 0.344 | 0.143 | 0.071 | 0.114 | 0.147 | 0.158 | 19.478 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 17 | 10 | 16 | 17 | 73 | 15 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.21 | 0.71 | 1.14 | 1.21 | 5.21 | 1.07 | 1.14 |
time (sec) |
N/A | 0.184 | 0.018 | 0.146 | 0.032 | 0.068 | 0.156 | 0.124 | 0.155 | 21.337 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 44 | 24 | 127 | 39 | 27 | 19 | 13 | 27 |
N.S. |
1 | 1.00 | 1.52 | 0.83 | 4.38 | 1.34 | 0.93 | 0.66 | 0.45 | 0.93 |
time (sec) |
N/A | 0.192 | 0.020 | 0.359 | 0.132 | 0.073 | 0.138 | 0.252 | 0.155 | 19.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 132 | 36 | 94 | 37 | 39 | 36 | 13 | 35 |
N.S. |
1 | 1.00 | 3.77 | 1.03 | 2.69 | 1.06 | 1.11 | 1.03 | 0.37 | 1.00 |
time (sec) |
N/A | 0.214 | 0.026 | 0.514 | 0.035 | 0.067 | 0.206 | 0.180 | 0.156 | 19.532 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 46 | 70 | 35 | 156 | 53 | 53 | 28 | 13 | 40 |
N.S. |
1 | 1.02 | 1.56 | 0.78 | 3.47 | 1.18 | 1.18 | 0.62 | 0.29 | 0.89 |
time (sec) |
N/A | 0.209 | 0.019 | 0.752 | 0.136 | 0.071 | 0.184 | 0.178 | 0.160 | 19.445 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 67 | 155 | 52 | 217 | 64 | 54 | 261 | 35 | 51 |
N.S. |
1 | 1.06 | 2.46 | 0.83 | 3.44 | 1.02 | 0.86 | 4.14 | 0.56 | 0.81 |
time (sec) |
N/A | 0.268 | 0.133 | 1.083 | 0.040 | 0.065 | 0.181 | 0.346 | 0.162 | 19.756 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 79 | 100 | 48 | 254 | 86 | 66 | 141 | 35 | 52 |
N.S. |
1 | 1.32 | 1.67 | 0.80 | 4.23 | 1.43 | 1.10 | 2.35 | 0.58 | 0.87 |
time (sec) |
N/A | 0.264 | 0.087 | 0.748 | 0.137 | 0.079 | 0.175 | 0.388 | 0.168 | 19.375 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 53 | 135 | 42 | 185 | 54 | 42 | 221 | 33 | 41 |
N.S. |
1 | 1.04 | 2.65 | 0.82 | 3.63 | 1.06 | 0.82 | 4.33 | 0.65 | 0.80 |
time (sec) |
N/A | 0.236 | 0.083 | 0.519 | 0.040 | 0.063 | 0.161 | 0.302 | 0.161 | 19.591 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 70 | 36 | 218 | 77 | 51 | 114 | 26 | 42 |
N.S. |
1 | 1.00 | 1.52 | 0.78 | 4.74 | 1.67 | 1.11 | 2.48 | 0.57 | 0.91 |
time (sec) |
N/A | 0.211 | 0.061 | 0.482 | 0.134 | 0.071 | 0.159 | 0.213 | 0.168 | 19.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 28 | 17 | 17 | 30 | 22 | 17 | 15 | 16 |
N.S. |
1 | 1.00 | 1.56 | 0.94 | 0.94 | 1.67 | 1.22 | 0.94 | 0.83 | 0.89 |
time (sec) |
N/A | 0.206 | 0.030 | 0.214 | 0.102 | 0.077 | 0.205 | 0.144 | 0.165 | 19.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 76 | 72 | 38 | 223 | 78 | 54 | 73 | 33 | 45 |
N.S. |
1 | 1.95 | 1.85 | 0.97 | 5.72 | 2.00 | 1.38 | 1.87 | 0.85 | 1.15 |
time (sec) |
N/A | 0.249 | 0.080 | 0.378 | 0.134 | 0.075 | 0.205 | 0.309 | 0.172 | 20.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 150 | 51 | 0 | 74 | 61 | 178 | 36 | 56 |
N.S. |
1 | 1.00 | 2.73 | 0.93 | 0.00 | 1.35 | 1.11 | 3.24 | 0.65 | 1.02 |
time (sec) |
N/A | 0.251 | 0.130 | 0.542 | 0.000 | 0.067 | 0.278 | 0.285 | 0.163 | 20.400 |
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 | 71 | 71 | 124 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.00 | 1.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.261 | 0.167 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 122 | 86 | 0 | 0 | 0 | 0 | 0 | 95 | 0 |
N.S. |
1 | 1.58 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.326 | 0.188 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 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 | 126 | 225 | 125 | 0 | 0 | 0 | 0 | 0 | 103 | 0 |
N.S. |
1 | 1.79 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 0.446 | 0.205 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 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 | 142 | 142 | 330 | 0 | 0 | 0 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.00 | 2.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.304 | 0.552 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 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 | 162 | 162 | 157 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.352 | 0.548 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 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 | 120 | 120 | 240 | 0 | 0 | 0 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.00 | 2.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.276 | 0.388 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 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 | 120 | 120 | 240 | 0 | 0 | 0 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.00 | 2.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.279 | 0.391 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 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 | 120 | 120 | 240 | 0 | 0 | 0 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.00 | 2.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.278 | 0.397 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 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 | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 107 | 146 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.51 | 2.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.297 | 5.068 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 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 | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 111 | 155 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.48 | 2.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.307 | 4.409 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 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 | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 105 | 146 | 0 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.52 | 2.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.305 | 4.453 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 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 | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 101 | 153 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.51 | 2.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.289 | 7.234 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 25 | 30 | 24 | 35 | 44 | 0 | 30 | 38 |
N.S. |
1 | 1.00 | 0.96 | 1.15 | 0.92 | 1.35 | 1.69 | 0.00 | 1.15 | 1.46 |
time (sec) |
N/A | 0.213 | 0.042 | 0.171 | 0.029 | 0.072 | 1.475 | 0.000 | 0.167 | 22.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 105 | 153 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.48 | 2.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.308 | 3.050 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 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 | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 105 | 147 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.52 | 2.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.300 | 2.684 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 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 | 159 | 213 | 179 | 0 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.34 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.471 | 5.243 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 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 | 163 | 217 | 189 | 0 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.33 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.455 | 4.616 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 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 | 159 | 213 | 179 | 0 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.34 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.456 | 4.675 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 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 | 154 | 207 | 185 | 0 | 0 | 0 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.34 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.444 | 7.479 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 34 | 51 | 35 | 320 | 85 | 0 | 0 | 35 | 39 |
N.S. |
1 | 1.17 | 1.76 | 1.21 | 11.03 | 2.93 | 0.00 | 0.00 | 1.21 | 1.34 |
time (sec) |
N/A | 0.227 | 0.077 | 0.160 | 0.053 | 0.074 | 0.000 | 0.000 | 0.165 | 21.730 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 212 | 184 | 0 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.35 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.454 | 3.173 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 213 | 179 | 0 | 0 | 0 | 0 | 0 | 60 | 0 |
N.S. |
1 | 1.37 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.456 | 2.888 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 41 | 38 | 41 | 1242 | 69 | 63 | 0 | 40 | 105 |
N.S. |
1 | 0.95 | 0.88 | 0.95 | 28.88 | 1.60 | 1.47 | 0.00 | 0.93 | 2.44 |
time (sec) |
N/A | 0.272 | 0.130 | 0.250 | 0.066 | 0.074 | 0.852 | 0.000 | 0.188 | 22.515 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 47 | 62 | 44 | 2171 | 140 | 65 | 0 | 44 | 183 |
N.S. |
1 | 1.04 | 1.38 | 0.98 | 48.24 | 3.11 | 1.44 | 0.00 | 0.98 | 4.07 |
time (sec) |
N/A | 0.283 | 0.077 | 0.357 | 0.094 | 0.074 | 1.943 | 0.000 | 0.165 | 27.957 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 62 | 65 | 57 | 4466 | 129 | 82 | 0 | 55 | 247 |
N.S. |
1 | 0.93 | 0.97 | 0.85 | 66.66 | 1.93 | 1.22 | 0.00 | 0.82 | 3.69 |
time (sec) |
N/A | 0.345 | 0.102 | 0.645 | 0.131 | 0.076 | 4.095 | 0.000 | 0.165 | 24.253 |
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 | 101 | 137 | 186 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.36 | 1.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.335 | 11.585 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 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 | 196 | 243 | 349 | 0 | 0 | 0 | 0 | 0 | 137 | 0 |
N.S. |
1 | 1.24 | 1.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.508 | 15.001 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 351 | 410 | 642 | 0 | 0 | 0 | 0 | 0 | 186 | 0 |
N.S. |
1 | 1.17 | 1.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.777 | 15.574 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 190 | 458 | 0 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 2.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.461 | 1.025 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 210 | 205 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.492 | 0.903 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 194 | 121 | 139 | 0 | 526 | 0 | 0 | 31 | 79 |
N.S. |
1 | 1.30 | 0.81 | 0.93 | 0.00 | 3.53 | 0.00 | 0.00 | 0.21 | 0.53 |
time (sec) |
N/A | 0.461 | 0.259 | 0.563 | 0.000 | 0.084 | 0.000 | 0.000 | 0.161 | 21.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 192 | 176 | 139 | 0 | 406 | 0 | 0 | 57 | 78 |
N.S. |
1 | 1.30 | 1.19 | 0.94 | 0.00 | 2.74 | 0.00 | 0.00 | 0.39 | 0.53 |
time (sec) |
N/A | 0.439 | 0.221 | 0.466 | 0.000 | 0.084 | 0.000 | 0.000 | 0.179 | 21.607 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 170 | 82 | 122 | 0 | 365 | 0 | 0 | 18 | 131 |
N.S. |
1 | 1.36 | 0.66 | 0.98 | 0.00 | 2.92 | 0.00 | 0.00 | 0.14 | 1.05 |
time (sec) |
N/A | 0.359 | 0.102 | 0.476 | 0.000 | 0.080 | 0.000 | 0.000 | 0.166 | 20.638 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 170 | 142 | 122 | 0 | 365 | 0 | 0 | 31 | 59 |
N.S. |
1 | 1.37 | 1.15 | 0.98 | 0.00 | 2.94 | 0.00 | 0.00 | 0.25 | 0.48 |
time (sec) |
N/A | 0.376 | 0.137 | 0.467 | 0.000 | 0.080 | 0.000 | 0.000 | 0.171 | 20.713 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 192 | 105 | 139 | 0 | 506 | 0 | 0 | 31 | 79 |
N.S. |
1 | 1.31 | 0.71 | 0.95 | 0.00 | 3.44 | 0.00 | 0.00 | 0.21 | 0.54 |
time (sec) |
N/A | 0.439 | 0.182 | 0.459 | 0.000 | 0.089 | 0.000 | 0.000 | 0.162 | 20.849 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 194 | 109 | 139 | 0 | 537 | 0 | 0 | 31 | 78 |
N.S. |
1 | 1.29 | 0.73 | 0.93 | 0.00 | 3.58 | 0.00 | 0.00 | 0.21 | 0.52 |
time (sec) |
N/A | 0.446 | 0.209 | 0.459 | 0.000 | 0.089 | 0.000 | 0.000 | 0.188 | 22.559 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 137 | 39 | 131 | 32 | 39 | 50 | 13 | 38 |
N.S. |
1 | 1.00 | 2.80 | 0.80 | 2.67 | 0.65 | 0.80 | 1.02 | 0.27 | 0.78 |
time (sec) |
N/A | 0.242 | 0.029 | 0.402 | 0.045 | 0.062 | 0.172 | 0.132 | 0.179 | 19.987 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 66 | 33 | 126 | 78 | 63 | 41 | 13 | 40 |
N.S. |
1 | 1.00 | 1.53 | 0.77 | 2.93 | 1.81 | 1.47 | 0.95 | 0.30 | 0.93 |
time (sec) |
N/A | 0.214 | 0.016 | 0.378 | 0.038 | 0.068 | 0.118 | 0.152 | 0.173 | 19.422 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 118 | 28 | 109 | 23 | 27 | 41 | 11 | 27 |
N.S. |
1 | 1.00 | 3.37 | 0.80 | 3.11 | 0.66 | 0.77 | 1.17 | 0.31 | 0.77 |
time (sec) |
N/A | 0.216 | 0.018 | 0.358 | 0.037 | 0.063 | 0.120 | 0.128 | 0.174 | 19.537 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 42 | 22 | 94 | 49 | 29 | 32 | 9 | 29 |
N.S. |
1 | 1.00 | 1.56 | 0.81 | 3.48 | 1.81 | 1.07 | 1.19 | 0.33 | 1.07 |
time (sec) |
N/A | 0.179 | 0.007 | 0.263 | 0.035 | 0.071 | 0.105 | 0.133 | 0.200 | 20.544 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 16 | 14 | 17 | 10 | 18 | 17 | 75 | 31 | 21 |
N.S. |
1 | 1.14 | 1.00 | 1.21 | 0.71 | 1.29 | 1.21 | 5.36 | 2.21 | 1.50 |
time (sec) |
N/A | 0.197 | 0.015 | 0.349 | 0.024 | 0.065 | 0.162 | 0.142 | 0.171 | 19.520 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 44 | 24 | 99 | 36 | 29 | 34 | 13 | 31 |
N.S. |
1 | 1.00 | 1.52 | 0.83 | 3.41 | 1.24 | 1.00 | 1.17 | 0.45 | 1.07 |
time (sec) |
N/A | 0.199 | 0.018 | 0.194 | 0.041 | 0.067 | 0.138 | 0.131 | 0.189 | 19.935 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 136 | 38 | 135 | 39 | 39 | 49 | 13 | 37 |
N.S. |
1 | 1.00 | 3.78 | 1.06 | 3.75 | 1.08 | 1.08 | 1.36 | 0.36 | 1.03 |
time (sec) |
N/A | 0.215 | 0.025 | 0.198 | 0.042 | 0.067 | 0.200 | 0.142 | 0.192 | 19.713 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 70 | 35 | 139 | 55 | 54 | 43 | 13 | 44 |
N.S. |
1 | 1.00 | 1.56 | 0.78 | 3.09 | 1.22 | 1.20 | 0.96 | 0.29 | 0.98 |
time (sec) |
N/A | 0.213 | 0.020 | 0.211 | 0.043 | 0.072 | 0.174 | 0.138 | 0.184 | 19.933 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 71 | 162 | 54 | 345 | 70 | 54 | 139 | 15 | 55 |
N.S. |
1 | 1.06 | 2.42 | 0.81 | 5.15 | 1.04 | 0.81 | 2.07 | 0.22 | 0.82 |
time (sec) |
N/A | 0.273 | 0.141 | 0.754 | 0.046 | 0.064 | 0.191 | 0.180 | 0.184 | 19.823 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 82 | 100 | 48 | 335 | 102 | 60 | 83 | 15 | 57 |
N.S. |
1 | 1.32 | 1.61 | 0.77 | 5.40 | 1.65 | 0.97 | 1.34 | 0.24 | 0.92 |
time (sec) |
N/A | 0.270 | 0.101 | 0.501 | 0.048 | 0.074 | 0.198 | 0.175 | 0.167 | 20.655 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 57 | 142 | 44 | 290 | 61 | 42 | 118 | 13 | 45 |
N.S. |
1 | 1.04 | 2.58 | 0.80 | 5.27 | 1.11 | 0.76 | 2.15 | 0.24 | 0.82 |
time (sec) |
N/A | 0.257 | 0.097 | 0.520 | 0.050 | 0.064 | 0.191 | 0.181 | 0.169 | 20.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 70 | 36 | 270 | 72 | 42 | 79 | 11 | 44 |
N.S. |
1 | 1.00 | 1.46 | 0.75 | 5.62 | 1.50 | 0.88 | 1.65 | 0.23 | 0.92 |
time (sec) |
N/A | 0.217 | 0.059 | 0.634 | 0.044 | 0.065 | 0.154 | 0.145 | 0.194 | 19.283 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 34 | 17 | 19 | 34 | 20 | 32 | 14 | 16 |
N.S. |
1 | 1.00 | 1.89 | 0.94 | 1.06 | 1.89 | 1.11 | 1.78 | 0.78 | 0.89 |
time (sec) |
N/A | 0.204 | 0.051 | 0.431 | 0.106 | 0.066 | 0.184 | 0.122 | 0.171 | 21.446 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 81 | 72 | 38 | 276 | 74 | 46 | 87 | 15 | 47 |
N.S. |
1 | 1.98 | 1.76 | 0.93 | 6.73 | 1.80 | 1.12 | 2.12 | 0.37 | 1.15 |
time (sec) |
N/A | 0.253 | 0.088 | 0.930 | 0.051 | 0.069 | 0.227 | 0.187 | 0.190 | 21.841 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 153 | 53 | 0 | 81 | 60 | 190 | 15 | 60 |
N.S. |
1 | 1.00 | 2.68 | 0.93 | 0.00 | 1.42 | 1.05 | 3.33 | 0.26 | 1.05 |
time (sec) |
N/A | 0.248 | 0.176 | 1.490 | 0.000 | 0.067 | 0.284 | 0.165 | 0.194 | 22.355 |