Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 50 | 137 | 146 | 138 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 1.35 | 3.70 | 3.95 | 3.73 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.245 | 0.055 | 10.928 | 0.212 | 0.091 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 39 | 50 | 98 | 49 | 0 | 58 | 30 | 41 |
N.S. |
1 | 1.00 | 1.08 | 1.39 | 2.72 | 1.36 | 0.00 | 1.61 | 0.83 | 1.14 |
time (sec) |
N/A | 0.240 | 0.055 | 8.698 | 0.135 | 0.079 | 0.000 | 0.379 | 0.177 | 41.166 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 51 | 76 | 190 | 61 | 0 | 87 | 30 | 82 |
N.S. |
1 | 1.00 | 0.66 | 0.99 | 2.47 | 0.79 | 0.00 | 1.13 | 0.39 | 1.06 |
time (sec) |
N/A | 0.367 | 0.096 | 8.330 | 0.139 | 0.081 | 0.000 | 0.444 | 0.184 | 41.596 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 120 | 61 | 78 | 237 | 71 | 0 | 116 | 30 | 132 |
N.S. |
1 | 1.04 | 0.53 | 0.68 | 2.06 | 0.62 | 0.00 | 1.01 | 0.26 | 1.15 |
time (sec) |
N/A | 0.514 | 0.127 | 8.698 | 0.151 | 0.086 | 0.000 | 0.481 | 0.169 | 42.783 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 163 | 71 | 91 | 283 | 81 | 0 | 143 | 30 | 415 |
N.S. |
1 | 1.07 | 0.46 | 0.59 | 1.85 | 0.53 | 0.00 | 0.93 | 0.20 | 2.71 |
time (sec) |
N/A | 0.686 | 0.188 | 10.741 | 0.152 | 0.106 | 0.000 | 0.543 | 0.163 | 48.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 161 | 106 | 138 | 1942 | 133 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.01 | 0.66 | 0.86 | 12.14 | 0.83 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.720 | 0.392 | 8.428 | 0.349 | 0.098 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 118 | 92 | 124 | 1080 | 122 | 0 | 0 | 49 | 0 |
N.S. |
1 | 0.98 | 0.77 | 1.03 | 9.00 | 1.02 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.564 | 0.234 | 8.557 | 0.245 | 0.088 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 79 | 104 | 803 | 109 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.00 | 1.05 | 1.39 | 10.71 | 1.45 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.414 | 0.109 | 10.996 | 0.246 | 0.083 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 85 | 99 | 997 | 127 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.00 | 1.12 | 1.30 | 13.12 | 1.67 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.386 | 0.163 | 5.922 | 0.233 | 0.098 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 52 | 57 | 125 | 62 | 0 | 0 | 59 | 89 |
N.S. |
1 | 1.00 | 0.64 | 0.70 | 1.54 | 0.77 | 0.00 | 0.00 | 0.73 | 1.10 |
time (sec) |
N/A | 0.389 | 0.113 | 5.763 | 0.215 | 0.081 | 0.000 | 0.000 | 0.179 | 41.337 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 123 | 62 | 69 | 217 | 73 | 0 | 0 | 59 | 133 |
N.S. |
1 | 1.02 | 0.51 | 0.57 | 1.79 | 0.60 | 0.00 | 0.00 | 0.49 | 1.10 |
time (sec) |
N/A | 0.528 | 0.156 | 5.668 | 0.137 | 0.105 | 0.000 | 0.000 | 0.178 | 42.340 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 166 | 72 | 79 | 263 | 86 | 0 | 0 | 59 | 157 |
N.S. |
1 | 1.03 | 0.45 | 0.49 | 1.63 | 0.53 | 0.00 | 0.00 | 0.37 | 0.98 |
time (sec) |
N/A | 0.691 | 0.232 | 5.561 | 0.147 | 0.080 | 0.000 | 0.000 | 0.179 | 47.983 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 208 | 182 | 150 | 7450 | 156 | 0 | 0 | 88 | 0 |
N.S. |
1 | 1.04 | 0.91 | 0.75 | 37.25 | 0.78 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.955 | 4.638 | 8.037 | 0.550 | 0.092 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 165 | 182 | 140 | 1964 | 143 | 0 | 0 | 80 | 0 |
N.S. |
1 | 1.03 | 1.14 | 0.88 | 12.28 | 0.89 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.778 | 4.513 | 8.134 | 0.325 | 0.093 | 0.000 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 121 | 182 | 119 | 1106 | 130 | 0 | 0 | 80 | 0 |
N.S. |
1 | 1.01 | 1.52 | 0.99 | 9.22 | 1.08 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.606 | 4.381 | 11.054 | 0.287 | 0.092 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 117 | 182 | 114 | 973 | 146 | 0 | 0 | 82 | 0 |
N.S. |
1 | 1.03 | 1.60 | 1.00 | 8.54 | 1.28 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.594 | 4.357 | 10.643 | 0.294 | 0.091 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 122 | 356 | 123 | 1395 | 150 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.03 | 3.02 | 1.04 | 11.82 | 1.27 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.588 | 10.792 | 5.856 | 0.276 | 0.125 | 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 | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 127 | 64 | 65 | 151 | 81 | 0 | 0 | 90 | 135 |
N.S. |
1 | 1.05 | 0.53 | 0.54 | 1.25 | 0.67 | 0.00 | 0.00 | 0.74 | 1.12 |
time (sec) |
N/A | 0.587 | 0.229 | 5.538 | 0.140 | 0.175 | 0.000 | 0.000 | 0.293 | 41.432 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 165 | 74 | 75 | 243 | 94 | 0 | 0 | 90 | 163 |
N.S. |
1 | 1.02 | 0.46 | 0.47 | 1.51 | 0.58 | 0.00 | 0.00 | 0.56 | 1.01 |
time (sec) |
N/A | 0.761 | 5.287 | 5.736 | 0.167 | 0.090 | 0.000 | 0.000 | 0.296 | 46.983 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 212 | 84 | 85 | 289 | 107 | 0 | 0 | 90 | 279 |
N.S. |
1 | 1.05 | 0.42 | 0.42 | 1.44 | 0.53 | 0.00 | 0.00 | 0.45 | 1.39 |
time (sec) |
N/A | 0.961 | 5.334 | 5.632 | 0.179 | 0.086 | 0.000 | 0.000 | 0.180 | 52.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | A | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 51 | 0 | 121 | 50 | 0 | 0 | 45 | 42 |
N.S. |
1 | 1.00 | 1.34 | 0.00 | 3.18 | 1.32 | 0.00 | 0.00 | 1.18 | 1.11 |
time (sec) |
N/A | 0.253 | 0.100 | 0.000 | 0.182 | 0.090 | 0.000 | 0.000 | 0.181 | 0.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 50 | 137 | 146 | 138 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 1.35 | 3.70 | 3.95 | 3.73 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.250 | 0.073 | 10.152 | 0.206 | 0.093 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 55 | 153 | 420 | 164 | 0 | 83 | 34 | 0 |
N.S. |
1 | 1.00 | 1.45 | 4.03 | 11.05 | 4.32 | 0.00 | 2.18 | 0.89 | 0.00 |
time (sec) |
N/A | 0.263 | 0.189 | 7.826 | 0.256 | 0.115 | 0.000 | 0.477 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 184 | 151 | 153 | 0 | 190 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.08 | 0.88 | 0.89 | 0.00 | 1.11 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.007 | 0.311 | 9.423 | 0.000 | 0.176 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 137 | 122 | 141 | 0 | 180 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.07 | 0.95 | 1.10 | 0.00 | 1.41 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.699 | 0.253 | 11.648 | 0.000 | 0.117 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 89 | 108 | 698 | 125 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 0.94 | 1.14 | 7.35 | 1.32 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.480 | 0.147 | 4.329 | 0.516 | 0.109 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 51 | 67 | 522 | 159 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 0.91 | 1.20 | 9.32 | 2.84 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.251 | 0.057 | 7.230 | 0.477 | 0.104 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 180 | 96 | 665 | 132 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 1.94 | 1.03 | 7.15 | 1.42 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.379 | 2.498 | 6.850 | 0.451 | 0.101 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 139 | 473 | 116 | 818 | 145 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.06 | 3.61 | 0.89 | 6.24 | 1.11 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.609 | 7.820 | 6.789 | 0.428 | 0.113 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 187 | 1540 | 130 | 1006 | 157 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.11 | 9.11 | 0.77 | 5.95 | 0.93 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.870 | 10.196 | 6.465 | 0.436 | 0.151 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 132 | 135 | 153 | 0 | 166 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.05 | 1.07 | 1.21 | 0.00 | 1.32 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.804 | 0.272 | 9.056 | 0.000 | 0.098 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 91 | 106 | 143 | 0 | 154 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.07 | 1.25 | 1.68 | 0.00 | 1.81 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.590 | 0.192 | 9.005 | 0.000 | 0.088 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 101 | 99 | 689 | 102 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 1.87 | 1.83 | 12.76 | 1.89 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.396 | 0.160 | 2.968 | 0.439 | 0.094 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 49 | 62 | 505 | 54 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 1.81 | 2.30 | 18.70 | 2.00 | 0.00 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.225 | 0.057 | 5.678 | 0.400 | 0.098 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | C | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 178 | 107 | 648 | 121 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 2.87 | 1.73 | 10.45 | 1.95 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.338 | 2.143 | 5.764 | 0.362 | 0.098 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 102 | 471 | 124 | 801 | 134 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.04 | 4.81 | 1.27 | 8.17 | 1.37 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.512 | 6.744 | 5.784 | 0.377 | 0.099 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | C | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 142 | 1538 | 183 | 989 | 146 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.06 | 11.48 | 1.37 | 7.38 | 1.09 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.698 | 7.896 | 5.865 | 0.399 | 0.131 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 182 | 212 | 182 | 0 | 231 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.05 | 1.22 | 1.05 | 0.00 | 1.33 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.971 | 0.476 | 9.585 | 0.000 | 0.176 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 140 | 158 | 173 | 0 | 221 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.04 | 1.18 | 1.29 | 0.00 | 1.65 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.706 | 0.575 | 3.796 | 0.000 | 0.152 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 118 | 131 | 0 | 145 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 1.22 | 1.35 | 0.00 | 1.49 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.386 | 0.343 | 3.960 | 0.000 | 0.102 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 106 | 108 | 0 | 146 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 1.09 | 1.11 | 0.00 | 1.51 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.392 | 0.542 | 6.862 | 0.000 | 0.102 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 139 | 456 | 119 | 0 | 171 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.01 | 3.33 | 0.87 | 0.00 | 1.25 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.631 | 7.201 | 6.605 | 0.000 | 0.104 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 187 | 589 | 138 | 0 | 185 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.06 | 3.33 | 0.78 | 0.00 | 1.05 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.907 | 9.405 | 6.814 | 0.000 | 0.108 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 230 | 217 | 220 | 0 | 275 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.07 | 1.01 | 1.03 | 0.00 | 1.29 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 1.292 | 1.118 | 9.803 | 0.000 | 0.238 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 186 | 191 | 210 | 0 | 265 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.07 | 1.10 | 1.21 | 0.00 | 1.52 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.987 | 0.871 | 3.735 | 0.000 | 0.230 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 143 | 149 | 158 | 0 | 180 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.04 | 1.09 | 1.15 | 0.00 | 1.31 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.601 | 0.866 | 3.722 | 0.000 | 0.104 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 143 | 122 | 156 | 0 | 178 | 0 | 0 | 55 | 0 |
N.S. |
1 | 1.04 | 0.89 | 1.14 | 0.00 | 1.30 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.613 | 1.165 | 3.992 | 0.000 | 0.106 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 143 | 134 | 153 | 0 | 180 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.04 | 0.98 | 1.12 | 0.00 | 1.31 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.611 | 1.261 | 6.905 | 0.000 | 0.117 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 187 | 506 | 159 | 0 | 205 | 0 | 0 | 64 | 0 |
N.S. |
1 | 1.06 | 2.86 | 0.90 | 0.00 | 1.16 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.901 | 6.878 | 6.450 | 0.000 | 0.121 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 235 | 154 | 178 | 0 | 219 | 0 | 0 | 64 | 0 |
N.S. |
1 | 1.08 | 0.71 | 0.82 | 0.00 | 1.01 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 1.206 | 6.364 | 6.640 | 0.000 | 0.108 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 278 | 256 | 259 | 0 | 319 | 0 | 0 | 73 | 0 |
N.S. |
1 | 1.09 | 1.01 | 1.02 | 0.00 | 1.26 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 1.627 | 1.739 | 9.707 | 0.000 | 0.317 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 234 | 230 | 249 | 0 | 309 | 0 | 0 | 73 | 0 |
N.S. |
1 | 1.09 | 1.07 | 1.16 | 0.00 | 1.44 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 1.265 | 1.623 | 3.592 | 0.000 | 0.364 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 191 | 176 | 188 | 0 | 214 | 0 | 0 | 73 | 0 |
N.S. |
1 | 1.08 | 0.99 | 1.06 | 0.00 | 1.21 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.897 | 2.945 | 3.467 | 0.000 | 0.133 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 191 | 148 | 188 | 0 | 214 | 0 | 0 | 71 | 0 |
N.S. |
1 | 1.08 | 0.84 | 1.06 | 0.00 | 1.21 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.878 | 2.101 | 3.603 | 0.000 | 0.108 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 191 | 149 | 188 | 0 | 214 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.08 | 0.84 | 1.06 | 0.00 | 1.21 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.892 | 3.020 | 4.003 | 0.000 | 0.109 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 191 | 148 | 185 | 0 | 214 | 0 | 0 | 72 | 0 |
N.S. |
1 | 1.08 | 0.84 | 1.05 | 0.00 | 1.21 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.881 | 2.047 | 6.359 | 0.000 | 0.108 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 235 | 559 | 189 | 0 | 239 | 0 | 0 | 74 | 0 |
N.S. |
1 | 1.08 | 2.58 | 0.87 | 0.00 | 1.10 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 1.175 | 8.886 | 6.750 | 0.000 | 0.107 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 279 | 694 | 208 | 0 | 253 | 0 | 0 | 74 | 0 |
N.S. |
1 | 1.09 | 2.70 | 0.81 | 0.00 | 0.98 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 1.513 | 8.882 | 6.530 | 0.000 | 0.120 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 239 | 474 | 218 | 0 | 248 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.10 | 2.18 | 1.00 | 0.00 | 1.14 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 1.180 | 6.075 | 3.770 | 0.000 | 0.116 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 239 | 158 | 218 | 0 | 248 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.10 | 0.73 | 1.00 | 0.00 | 1.14 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 1.189 | 2.379 | 4.142 | 0.000 | 0.119 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 30 | 35 | 306 | 31 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 1.88 | 2.19 | 19.12 | 1.94 | 0.00 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.219 | 0.031 | 1.817 | 0.365 | 0.089 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 32 | 40 | 323 | 105 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.98 | 7.88 | 2.56 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.256 | 0.023 | 1.661 | 0.427 | 0.096 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 186 | 241 | 1063 | 155 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 1.44 | 1.87 | 8.24 | 1.20 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.574 | 1.201 | 8.273 | 0.355 | 0.113 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 152 | 214 | 795 | 142 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.79 | 2.52 | 9.35 | 1.67 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.394 | 0.889 | 8.214 | 0.285 | 0.102 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 125 | 151 | 148 | 155 | 0 | 122 | 32 | 0 |
N.S. |
1 | 1.00 | 2.60 | 3.15 | 3.08 | 3.23 | 0.00 | 2.54 | 0.67 | 0.00 |
time (sec) |
N/A | 0.255 | 0.686 | 8.302 | 0.238 | 0.106 | 0.000 | 0.772 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 40 | 52 | 82 | 42 | 0 | 62 | 32 | 42 |
N.S. |
1 | 1.00 | 1.08 | 1.41 | 2.22 | 1.14 | 0.00 | 1.68 | 0.86 | 1.14 |
time (sec) |
N/A | 0.243 | 0.051 | 5.669 | 0.150 | 0.084 | 0.000 | 0.528 | 0.167 | 40.357 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 52 | 68 | 174 | 52 | 0 | 90 | 32 | 85 |
N.S. |
1 | 1.00 | 0.66 | 0.86 | 2.20 | 0.66 | 0.00 | 1.14 | 0.41 | 1.08 |
time (sec) |
N/A | 0.375 | 0.523 | 5.799 | 0.153 | 0.107 | 0.000 | 0.510 | 0.167 | 40.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 123 | 62 | 81 | 221 | 64 | 0 | 120 | 32 | 158 |
N.S. |
1 | 1.04 | 0.53 | 0.69 | 1.87 | 0.54 | 0.00 | 1.02 | 0.27 | 1.34 |
time (sec) |
N/A | 0.520 | 0.637 | 5.823 | 0.163 | 0.081 | 0.000 | 0.611 | 0.173 | 41.682 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 181 | 123 | 1305 | 124 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.00 | 1.59 | 1.08 | 11.45 | 1.09 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.485 | 0.442 | 8.987 | 0.294 | 0.098 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 155 | 108 | 966 | 111 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 2.15 | 1.50 | 13.42 | 1.54 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.345 | 0.552 | 9.594 | 0.246 | 0.102 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | B | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 124 | 75 | 221 | 64 | 0 | 119 | 29 | 0 |
N.S. |
1 | 1.00 | 3.35 | 2.03 | 5.97 | 1.73 | 0.00 | 3.22 | 0.78 | 0.00 |
time (sec) |
N/A | 0.228 | 0.325 | 5.824 | 0.211 | 0.119 | 0.000 | 0.576 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 39 | 36 | 75 | 41 | 0 | 59 | 29 | 31 |
N.S. |
1 | 1.00 | 1.11 | 1.03 | 2.14 | 1.17 | 0.00 | 1.69 | 0.83 | 0.89 |
time (sec) |
N/A | 0.224 | 0.041 | 5.602 | 0.153 | 0.079 | 0.000 | 0.631 | 0.169 | 40.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 51 | 64 | 164 | 51 | 0 | 87 | 29 | 84 |
N.S. |
1 | 1.00 | 0.68 | 0.85 | 2.19 | 0.68 | 0.00 | 1.16 | 0.39 | 1.12 |
time (sec) |
N/A | 0.336 | 0.255 | 5.614 | 0.136 | 0.078 | 0.000 | 0.706 | 0.174 | 40.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 117 | 61 | 77 | 209 | 63 | 0 | 117 | 29 | 156 |
N.S. |
1 | 1.04 | 0.54 | 0.69 | 1.87 | 0.56 | 0.00 | 1.04 | 0.26 | 1.39 |
time (sec) |
N/A | 0.462 | 0.302 | 5.652 | 0.166 | 0.148 | 0.000 | 0.737 | 0.162 | 41.188 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 197 | 256 | 405 | 0 | 226 | 0 | 779 | 46 | 0 |
N.S. |
1 | 1.06 | 1.38 | 2.19 | 0.00 | 1.22 | 0.00 | 4.21 | 0.25 | 0.00 |
time (sec) |
N/A | 0.993 | 1.871 | 6.681 | 0.000 | 0.092 | 0.000 | 7.214 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 150 | 228 | 376 | 0 | 212 | 0 | 581 | 44 | 0 |
N.S. |
1 | 1.06 | 1.62 | 2.67 | 0.00 | 1.50 | 0.00 | 4.12 | 0.31 | 0.00 |
time (sec) |
N/A | 0.730 | 1.496 | 6.666 | 0.000 | 0.093 | 0.000 | 5.370 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 161 | 322 | 0 | 162 | 0 | 269 | 38 | 0 |
N.S. |
1 | 1.00 | 1.50 | 3.01 | 0.00 | 1.51 | 0.00 | 2.51 | 0.36 | 0.00 |
time (sec) |
N/A | 0.506 | 0.857 | 6.816 | 0.000 | 0.091 | 0.000 | 0.791 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | C | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 118 | 258 | 209 | 144 | 0 | 162 | 47 | 0 |
N.S. |
1 | 1.00 | 2.03 | 4.45 | 3.60 | 2.48 | 0.00 | 2.79 | 0.81 | 0.00 |
time (sec) |
N/A | 0.259 | 0.769 | 5.269 | 0.264 | 0.102 | 0.000 | 0.640 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | C | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 157 | 379 | 351 | 152 | 0 | 279 | 49 | 0 |
N.S. |
1 | 1.00 | 1.65 | 3.99 | 3.69 | 1.60 | 0.00 | 2.94 | 0.52 | 0.00 |
time (sec) |
N/A | 0.399 | 0.820 | 5.256 | 0.277 | 0.108 | 0.000 | 0.552 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | C | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 142 | 171 | 387 | 504 | 165 | 0 | 235 | 49 | 0 |
N.S. |
1 | 1.05 | 1.27 | 2.87 | 3.73 | 1.22 | 0.00 | 1.74 | 0.36 | 0.00 |
time (sec) |
N/A | 0.620 | 0.768 | 13.647 | 0.272 | 0.105 | 0.000 | 0.758 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | C | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 191 | 218 | 494 | 692 | 177 | 0 | 265 | 49 | 0 |
N.S. |
1 | 1.10 | 1.26 | 2.86 | 4.00 | 1.02 | 0.00 | 1.53 | 0.28 | 0.00 |
time (sec) |
N/A | 0.911 | 1.163 | 13.118 | 0.273 | 0.143 | 0.000 | 0.527 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 166 | 255 | 147 | 0 | 239 | 0 | 747 | 41 | 0 |
N.S. |
1 | 1.03 | 1.58 | 0.91 | 0.00 | 1.48 | 0.00 | 4.64 | 0.25 | 0.00 |
time (sec) |
N/A | 0.848 | 0.757 | 8.556 | 0.000 | 0.100 | 0.000 | 6.897 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 124 | 227 | 135 | 0 | 225 | 0 | 560 | 39 | 0 |
N.S. |
1 | 1.05 | 1.92 | 1.14 | 0.00 | 1.91 | 0.00 | 4.75 | 0.33 | 0.00 |
time (sec) |
N/A | 0.613 | 0.501 | 8.615 | 0.000 | 0.088 | 0.000 | 5.189 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 160 | 103 | 0 | 170 | 0 | 266 | 33 | 0 |
N.S. |
1 | 1.00 | 1.88 | 1.21 | 0.00 | 2.00 | 0.00 | 3.13 | 0.39 | 0.00 |
time (sec) |
N/A | 0.416 | 0.275 | 3.274 | 0.000 | 0.086 | 0.000 | 0.459 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | C | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 110 | 77 | 248 | 84 | 0 | 159 | 42 | 0 |
N.S. |
1 | 1.00 | 2.34 | 1.64 | 5.28 | 1.79 | 0.00 | 3.38 | 0.89 | 0.00 |
time (sec) |
N/A | 0.229 | 0.296 | 5.862 | 0.260 | 0.101 | 0.000 | 0.437 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | C | A | F | B | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 152 | 95 | 400 | 144 | 0 | 264 | 44 | 0 |
N.S. |
1 | 1.00 | 1.83 | 1.14 | 4.82 | 1.73 | 0.00 | 3.18 | 0.53 | 0.00 |
time (sec) |
N/A | 0.348 | 0.615 | 5.994 | 0.261 | 0.098 | 0.000 | 0.505 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | C | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 125 | 170 | 110 | 563 | 157 | 0 | 232 | 44 | 0 |
N.S. |
1 | 1.02 | 1.39 | 0.90 | 4.61 | 1.29 | 0.00 | 1.90 | 0.36 | 0.00 |
time (sec) |
N/A | 0.528 | 0.556 | 6.031 | 0.261 | 0.099 | 0.000 | 0.479 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.386 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F(-1) | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.384 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.390 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 153 | 268 | 384 | 0 | 188 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.01 | 1.77 | 2.54 | 0.00 | 1.25 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.776 | 2.064 | 8.513 | 0.000 | 0.092 | 0.000 | 0.000 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 125 | 255 | 368 | 0 | 167 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.02 | 2.07 | 2.99 | 0.00 | 1.36 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.627 | 1.418 | 6.830 | 0.000 | 0.103 | 0.000 | 0.000 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 98 | 124 | 148 | 0 | 124 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.01 | 1.28 | 1.53 | 0.00 | 1.28 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.569 | 0.940 | 2.922 | 0.000 | 0.085 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 141 | 150 | 0 | 107 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 1.88 | 2.00 | 0.00 | 1.43 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.473 | 0.965 | 2.672 | 0.000 | 0.084 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 102 | 140 | 225 | 0 | 125 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.01 | 1.39 | 2.23 | 0.00 | 1.24 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.595 | 1.499 | 5.914 | 0.000 | 0.091 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 129 | 224 | 219 | 0 | 145 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.02 | 1.76 | 1.72 | 0.00 | 1.14 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.643 | 1.220 | 8.530 | 0.000 | 0.120 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 157 | 198 | 270 | 0 | 156 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.04 | 1.31 | 1.79 | 0.00 | 1.03 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.771 | 2.703 | 9.822 | 0.000 | 0.087 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 159 | 261 | 386 | 0 | 202 | 0 | 0 | 75 | 0 |
N.S. |
1 | 0.99 | 1.62 | 2.40 | 0.00 | 1.25 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.990 | 2.469 | 20.761 | 0.000 | 0.097 | 0.000 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 250 | 371 | 0 | 179 | 0 | 0 | 75 | 0 |
N.S. |
1 | 1.00 | 1.91 | 2.83 | 0.00 | 1.37 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.870 | 1.792 | 19.629 | 0.000 | 0.096 | 0.000 | 0.000 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 48 | 185 | 0 | 77 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.00 | 0.75 | 2.89 | 0.00 | 1.20 | 0.00 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.542 | 1.191 | 4.102 | 0.000 | 0.087 | 0.000 | 0.000 | 0.252 | 0.000 |