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 | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 78 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.393 | 0.235 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 133 | 134 | 0 | 0 | 0 | 165 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.05 | 0.00 | 0.00 | 0.00 | 1.29 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.472 | 0.217 | 0.000 | 0.000 | 0.000 | 27.099 | 0.000 | 0.377 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 123 | 126 | 0 | 0 | 0 | 163 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.05 | 0.00 | 0.00 | 0.00 | 1.36 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.449 | 0.155 | 0.000 | 0.000 | 0.000 | 27.352 | 0.000 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 114 | 114 | 0 | 0 | 0 | 153 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.02 | 0.00 | 0.00 | 0.00 | 1.37 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.419 | 0.070 | 0.000 | 0.000 | 0.000 | 38.168 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 120 | 0 | 0 | 0 | 150 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 1.19 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.479 | 0.113 | 0.000 | 0.000 | 0.000 | 26.854 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 131 | 0 | 0 | 0 | 160 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 1.15 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.494 | 0.115 | 0.000 | 0.000 | 0.000 | 27.203 | 0.000 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 139 | 134 | 0 | 0 | 0 | 165 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.94 | 0.00 | 0.00 | 0.00 | 1.16 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.491 | 0.109 | 0.000 | 0.000 | 0.000 | 26.735 | 0.000 | 0.326 | 0.000 |
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 | 20 | 20 | 20 | 21 | 29 | 25 | 46 | 35 | 22 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.45 | 1.25 | 2.30 | 1.75 | 1.10 | 1.10 |
time (sec) |
N/A | 0.228 | 0.035 | 0.346 | 0.074 | 0.099 | 1.313 | 0.127 | 0.195 | 3.695 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 97 | 26 | 35 | 32 | 80 | 52 | 32 | 47 |
N.S. |
1 | 1.00 | 3.59 | 0.96 | 1.30 | 1.19 | 2.96 | 1.93 | 1.19 | 1.74 |
time (sec) |
N/A | 0.243 | 0.087 | 0.811 | 0.068 | 0.117 | 43.673 | 0.131 | 0.203 | 3.755 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 97 | 26 | 35 | 32 | 0 | 56 | 32 | 47 |
N.S. |
1 | 1.00 | 3.59 | 0.96 | 1.30 | 1.19 | 0.00 | 2.07 | 1.19 | 1.74 |
time (sec) |
N/A | 0.260 | 0.092 | 1.789 | 0.067 | 0.097 | 0.000 | 0.130 | 0.207 | 4.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 101 | 60 | 39 | 35 | 116 | 66 | 32 | 54 |
N.S. |
1 | 1.00 | 3.74 | 2.22 | 1.44 | 1.30 | 4.30 | 2.44 | 1.19 | 2.00 |
time (sec) |
N/A | 0.263 | 0.134 | 2.332 | 0.094 | 0.093 | 28.267 | 0.151 | 0.190 | 3.915 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 313 | 1 | 245 | 0 | 0 | 0 | 0 | 0 | 1192 | 0 |
N.S. |
1 | 0.00 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.81 | 0.00 |
time (sec) |
N/A | 0.533 | 5.613 | 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 | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 1 | 190 | 0 | 0 | 0 | 0 | 0 | 664 | 0 |
N.S. |
1 | 0.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.95 | 0.00 |
time (sec) |
N/A | 0.272 | 5.384 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 232 | 103 | 730 | 0 | 300 | 0 | 0 | 307 | 0 |
N.S. |
1 | 1.45 | 0.64 | 4.56 | 0.00 | 1.88 | 0.00 | 0.00 | 1.92 | 0.00 |
time (sec) |
N/A | 0.764 | 0.153 | 8.196 | 0.000 | 0.130 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | B | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 164 | 106 | 488 | 0 | 221 | 648 | 0 | 196 | 0 |
N.S. |
1 | 1.20 | 0.77 | 3.56 | 0.00 | 1.61 | 4.73 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.510 | 0.189 | 2.205 | 0.000 | 0.105 | 95.260 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 114 | 64 | 0 | 0 | 155 | 464 | 0 | 106 | 0 |
N.S. |
1 | 0.98 | 0.55 | 0.00 | 0.00 | 1.34 | 4.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.397 | 0.013 | 0.000 | 0.000 | 0.100 | 42.669 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 302 | 347 | 343 | 0 | 0 | 0 | 0 | 0 | 1143 | 0 |
N.S. |
1 | 1.15 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.78 | 0.00 |
time (sec) |
N/A | 7.059 | 4.371 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 507 | 556 | 544 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 9.068 | 5.788 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.564 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 1 | 194 | 0 | 0 | 0 | 0 | 0 | 698 | 0 |
N.S. |
1 | 0.01 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.75 | 0.00 |
time (sec) |
N/A | 0.418 | 5.271 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 1 | 147 | 0 | 0 | 0 | 0 | 0 | 308 | 0 |
N.S. |
1 | 0.01 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.12 | 0.00 |
time (sec) |
N/A | 0.268 | 5.218 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | B | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 114 | 93 | 269 | 0 | 131 | 184 | 0 | 110 | 0 |
N.S. |
1 | 1.41 | 1.15 | 3.32 | 0.00 | 1.62 | 2.27 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.419 | 0.185 | 2.079 | 0.000 | 0.098 | 91.045 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 64 | 0 | 0 | 99 | 109 | 0 | 66 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 1.41 | 1.56 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.309 | 0.014 | 0.000 | 0.000 | 0.098 | 42.269 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 230 | 227 | 0 | 0 | 0 | 0 | 0 | 662 | 0 |
N.S. |
1 | 1.32 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.80 | 0.00 |
time (sec) |
N/A | 2.920 | 1.994 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 314 | 403 | 395 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.746 | 2.080 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.327 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 263 | 195 | 0 | 0 | 0 | 0 | 0 | 583 | 0 |
N.S. |
1 | 1.25 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.78 | 0.00 |
time (sec) |
N/A | 0.892 | 5.389 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 154 | 149 | 0 | 0 | 0 | 0 | 0 | 349 | 0 |
N.S. |
1 | 1.15 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.60 | 0.00 |
time (sec) |
N/A | 0.557 | 5.210 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 101 | 87 | 0 | 0 | 0 | 82 | 0 | 118 | 0 |
N.S. |
1 | 1.09 | 0.94 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.392 | 0.071 | 0.000 | 0.000 | 0.000 | 84.949 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 70 | 0 | 53 | 31 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.19 | 0.00 | 1.66 | 0.97 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 0.243 | 0.011 | 0.532 | 0.000 | 0.100 | 41.899 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 143 | 140 | 0 | 0 | 0 | 0 | 0 | 351 | 0 |
N.S. |
1 | 1.49 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.66 | 0.00 |
time (sec) |
N/A | 1.166 | 0.659 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 297 | 283 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.55 | 1.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.601 | 0.778 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 2724 | 2698 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 8.84 | 8.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 5.646 | 1.841 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 6.415 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 264 | 203 | 0 | 0 | 0 | 0 | 0 | 570 | 0 |
N.S. |
1 | 1.06 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.28 | 0.00 |
time (sec) |
N/A | 0.884 | 5.202 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 160 | 148 | 0 | 0 | 0 | 0 | 0 | 299 | 0 |
N.S. |
1 | 0.94 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.75 | 0.00 |
time (sec) |
N/A | 0.614 | 5.177 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 84 | 98 | 0 | 0 | 0 | 100 | 0 | 136 | 0 |
N.S. |
1 | 0.88 | 1.03 | 0.00 | 0.00 | 0.00 | 1.05 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.385 | 0.124 | 0.000 | 0.000 | 0.000 | 25.860 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 47 | 58 | 0 | 0 | 0 | 37 | 0 | 22 | 0 |
N.S. |
1 | 0.81 | 1.00 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.295 | 0.008 | 0.000 | 0.000 | 0.000 | 3.176 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 96 | 88 | 0 | 0 | 0 | 0 | 0 | 175 | 0 |
N.S. |
1 | 1.60 | 1.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.92 | 0.00 |
time (sec) |
N/A | 0.392 | 0.087 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 114 | 110 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.522 | 0.207 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 226 | 196 | 192 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.87 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.862 | 0.324 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.692 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 186 | 156 | 0 | 0 | 0 | 0 | 0 | 474 | 0 |
N.S. |
1 | 0.99 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.52 | 0.00 |
time (sec) |
N/A | 0.615 | 5.170 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 109 | 106 | 0 | 0 | 0 | 122 | 0 | 212 | 0 |
N.S. |
1 | 0.92 | 0.90 | 0.00 | 0.00 | 0.00 | 1.03 | 0.00 | 1.80 | 0.00 |
time (sec) |
N/A | 0.417 | 0.124 | 0.000 | 0.000 | 0.000 | 33.492 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 57 | 63 | 0 | 0 | 0 | 39 | 0 | 70 | 0 |
N.S. |
1 | 0.86 | 0.95 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.302 | 0.019 | 0.000 | 0.000 | 0.000 | 10.065 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 78 | 78 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.64 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.370 | 0.055 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 105 | 103 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.48 | 1.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.408 | 0.090 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 166 | 162 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.20 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.556 | 0.164 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.667 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 507 | 502 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 2.09 | 2.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.076 | 0.235 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 35.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 191 | 156 | 0 | 0 | 0 | 0 | 0 | 785 | 0 |
N.S. |
1 | 1.02 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.18 | 0.00 |
time (sec) |
N/A | 0.630 | 5.217 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 113 | 106 | 0 | 0 | 0 | 124 | 0 | 384 | 0 |
N.S. |
1 | 0.96 | 0.90 | 0.00 | 0.00 | 0.00 | 1.05 | 0.00 | 3.25 | 0.00 |
time (sec) |
N/A | 0.426 | 0.205 | 0.000 | 0.000 | 0.000 | 86.897 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 61 | 64 | 0 | 0 | 0 | 41 | 0 | 144 | 0 |
N.S. |
1 | 0.92 | 0.97 | 0.00 | 0.00 | 0.00 | 0.62 | 0.00 | 2.18 | 0.00 |
time (sec) |
N/A | 0.310 | 0.077 | 0.000 | 0.000 | 0.000 | 29.250 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 79 | 78 | 0 | 0 | 0 | 0 | 0 | 356 | 0 |
N.S. |
1 | 0.41 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.85 | 0.00 |
time (sec) |
N/A | 0.377 | 0.179 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 79 | 78 | 0 | 0 | 0 | 0 | 0 | 56 | 0 |
N.S. |
1 | 0.40 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.389 | 0.176 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 106 | 103 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.45 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.423 | 0.156 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.928 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 313 | 304 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 2.24 | 2.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.987 | 0.416 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 30.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 733 | 722 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 2.99 | 2.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.205 | 0.978 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 152.068 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 191 | 156 | 0 | 0 | 0 | 0 | 0 | 1177 | 0 |
N.S. |
1 | 1.02 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 6.26 | 0.00 |
time (sec) |
N/A | 0.623 | 5.248 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 113 | 106 | 0 | 0 | 0 | 0 | 0 | 602 | 0 |
N.S. |
1 | 0.96 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.10 | 0.00 |
time (sec) |
N/A | 0.428 | 0.200 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 61 | 64 | 0 | 0 | 0 | 41 | 0 | 237 | 0 |
N.S. |
1 | 0.92 | 0.97 | 0.00 | 0.00 | 0.00 | 0.62 | 0.00 | 3.59 | 0.00 |
time (sec) |
N/A | 0.305 | 0.070 | 0.000 | 0.000 | 0.000 | 60.180 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 79 | 78 | 0 | 0 | 0 | 0 | 0 | 765 | 0 |
N.S. |
1 | 0.30 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.87 | 0.00 |
time (sec) |
N/A | 0.376 | 0.191 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 79 | 78 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.30 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.390 | 0.181 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 79 | 78 | 0 | 0 | 0 | 0 | 0 | 74 | 0 |
N.S. |
1 | 0.29 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.383 | 0.216 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 106 | 103 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.45 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.432 | 0.162 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.519 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 430 | 421 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 3.07 | 3.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.378 | 0.575 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 168.113 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 977 | 966 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 3.99 | 3.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 3.180 | 1.410 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.046 | 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 | 55 | 55 | 56 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.308 | 0.162 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 98 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.437 | 0.254 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.333 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.445 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 112 | 107 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.477 | 0.167 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 97 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.445 | 0.195 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 102 | 98 | 0 | 0 | 0 | 0 | 0 | 998 | 0 |
N.S. |
1 | 0.99 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 9.69 | 0.00 |
time (sec) |
N/A | 0.503 | 0.188 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 232 | 195 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.652 | 0.520 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.831 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 145 | 118 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.437 | 0.240 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.423 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 85 | 84 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.21 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.360 | 0.153 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.269 | 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 | 97 | 98 | 103 | 0 | 0 | 0 | 0 | 0 | 937 | 0 |
N.S. |
1 | 1.01 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 9.66 | 0.00 |
time (sec) |
N/A | 0.392 | 0.145 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 98 | 110 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.402 | 0.354 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.417 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 101 | 110 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.404 | 0.522 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.817 | 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 | 78 | 78 | 80 | 0 | 0 | 0 | 0 | 0 | 178 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.28 | 0.00 |
time (sec) |
N/A | 0.379 | 0.070 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.234 | 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 | 70 | 70 | 72 | 0 | 0 | 0 | 0 | 0 | 170 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.43 | 0.00 |
time (sec) |
N/A | 0.346 | 0.052 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 73 | 0 | 0 | 0 | 0 | 0 | 168 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.30 | 0.00 |
time (sec) |
N/A | 0.339 | 0.046 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 | 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 | 72 | 73 | 73 | 0 | 0 | 0 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.01 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 0.357 | 0.063 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.209 | 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 | 76 | 76 | 78 | 0 | 0 | 0 | 0 | 0 | 196 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.58 | 0.00 |
time (sec) |
N/A | 0.352 | 0.056 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 290 | 183 | 203 | 290 | 675 | 0 | 376 | 358 | 1044 |
N.S. |
1 | 1.14 | 0.72 | 0.80 | 1.14 | 2.65 | 0.00 | 1.47 | 1.40 | 4.09 |
time (sec) |
N/A | 0.835 | 0.310 | 1.299 | 0.115 | 0.118 | 0.000 | 0.139 | 0.203 | 3.858 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 344 | 183 | 203 | 290 | 675 | 0 | 376 | 358 | 1044 |
N.S. |
1 | 1.35 | 0.72 | 0.80 | 1.14 | 2.65 | 0.00 | 1.47 | 1.40 | 4.09 |
time (sec) |
N/A | 1.695 | 0.007 | 0.263 | 0.114 | 0.099 | 0.000 | 0.135 | 0.202 | 0.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 344 | 183 | 203 | 290 | 675 | 0 | 376 | 358 | 1044 |
N.S. |
1 | 1.35 | 0.72 | 0.80 | 1.14 | 2.65 | 0.00 | 1.47 | 1.40 | 4.09 |
time (sec) |
N/A | 1.623 | 0.006 | 0.260 | 0.116 | 0.097 | 0.000 | 0.141 | 0.216 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 344 | 183 | 203 | 290 | 675 | 0 | 376 | 358 | 1044 |
N.S. |
1 | 1.35 | 0.72 | 0.80 | 1.14 | 2.65 | 0.00 | 1.47 | 1.40 | 4.09 |
time (sec) |
N/A | 1.408 | 0.006 | 0.254 | 0.112 | 0.120 | 0.000 | 0.141 | 0.243 | 3.469 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 235 | 88 | 795 | 0 | 0 | 0 | 0 | 334 | 0 |
N.S. |
1 | 0.96 | 0.36 | 3.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.461 | 15.080 | 2.652 | 0.000 | 0.000 | 0.000 | 0.000 | 0.503 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 289 | 88 | 795 | 0 | 0 | 0 | 0 | 334 | 0 |
N.S. |
1 | 1.17 | 0.36 | 3.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.858 | 0.059 | 0.671 | 0.000 | 0.000 | 0.000 | 0.000 | 0.482 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 289 | 88 | 795 | 0 | 0 | 0 | 0 | 334 | 0 |
N.S. |
1 | 1.17 | 0.36 | 3.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.846 | 0.058 | 0.619 | 0.000 | 0.000 | 0.000 | 0.000 | 0.501 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 289 | 88 | 795 | 0 | 0 | 0 | 0 | 334 | 0 |
N.S. |
1 | 1.17 | 0.36 | 3.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 1.132 | 0.060 | 0.617 | 0.000 | 0.000 | 0.000 | 0.000 | 0.510 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 35 | 32 | 15 | 44 | 0 | 0 | 66 | 32 |
N.S. |
1 | 1.00 | 0.97 | 0.89 | 0.42 | 1.22 | 0.00 | 0.00 | 1.83 | 0.89 |
time (sec) |
N/A | 0.304 | 1.203 | 0.129 | 0.055 | 0.095 | 0.000 | 0.000 | 0.201 | 3.787 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 24 | 5 | 35 | 0 | 12 | 8 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.17 | 1.21 | 0.00 | 0.41 | 0.28 | 0.79 |
time (sec) |
N/A | 0.286 | 9.524 | 0.094 | 0.055 | 0.122 | 0.000 | 0.123 | 0.202 | 3.896 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 27 | 24 | 5 | 35 | 0 | 10 | 6 | 23 |
N.S. |
1 | 1.00 | 0.93 | 0.83 | 0.17 | 1.21 | 0.00 | 0.34 | 0.21 | 0.79 |
time (sec) |
N/A | 0.269 | 5.778 | 0.092 | 0.051 | 0.107 | 0.000 | 0.123 | 0.253 | 3.797 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 24 | 22 | 5 | 33 | 0 | 9 | 5 | 21 |
N.S. |
1 | 1.00 | 0.96 | 0.88 | 0.20 | 1.32 | 0.00 | 0.36 | 0.20 | 0.84 |
time (sec) |
N/A | 0.253 | 5.074 | 0.094 | 0.048 | 0.078 | 0.000 | 0.127 | 0.206 | 3.731 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 21 | 5 | 32 | 0 | 9 | 8 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.21 | 1.33 | 0.00 | 0.38 | 0.33 | 0.83 |
time (sec) |
N/A | 0.278 | 1.749 | 0.096 | 0.053 | 0.081 | 0.000 | 0.114 | 0.198 | 3.828 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 26 | 24 | 5 | 35 | 0 | 12 | 8 | 23 |
N.S. |
1 | 1.00 | 0.90 | 0.83 | 0.17 | 1.21 | 0.00 | 0.41 | 0.28 | 0.79 |
time (sec) |
N/A | 0.273 | 3.370 | 0.095 | 0.051 | 0.076 | 0.000 | 0.120 | 0.196 | 3.836 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.356 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 237 | 175 | 0 | 0 | 0 | 162 | 0 | 664 | 0 |
N.S. |
1 | 1.27 | 0.94 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 | 3.55 | 0.00 |
time (sec) |
N/A | 0.652 | 0.193 | 0.000 | 0.000 | 0.000 | 155.514 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 143 | 112 | 0 | 0 | 0 | 117 | 0 | 351 | 0 |
N.S. |
1 | 1.07 | 0.84 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 | 2.62 | 0.00 |
time (sec) |
N/A | 0.469 | 0.154 | 0.000 | 0.000 | 0.000 | 19.931 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 73 | 0 | 0 | 0 | 73 | 0 | 150 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 | 1.90 | 0.00 |
time (sec) |
N/A | 0.334 | 0.108 | 0.000 | 0.000 | 0.000 | 4.887 | 0.000 | 0.204 | 0.000 |
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 | 0.267 | 0.050 | 0.000 | 0.000 | 0.000 | 1.389 | 0.000 | 0.235 | 3.659 |
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 | 101 | 97 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.397 | 0.143 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 0.000 |