Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 116 | 114 | 137 | 159 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.03 | 1.01 | 1.21 | 1.41 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.681 | 0.034 | 2.894 | 0.055 | 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 | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 85 | 81 | 86 | 85 | 148 | 425 | 145 | 113 | 85 |
N.S. |
1 | 1.05 | 1.00 | 1.06 | 1.05 | 1.83 | 5.25 | 1.79 | 1.40 | 1.05 |
time (sec) |
N/A | 0.486 | 0.072 | 1.204 | 0.027 | 0.134 | 2.205 | 0.129 | 0.171 | 25.796 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 123 | 113 | 120 | 160 | 428 | 3485 | 470 | 489 | 217 |
N.S. |
1 | 0.97 | 0.89 | 0.94 | 1.26 | 3.37 | 27.44 | 3.70 | 3.85 | 1.71 |
time (sec) |
N/A | 0.570 | 0.191 | 1.616 | 0.033 | 0.555 | 9.184 | 0.136 | 0.193 | 26.535 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 170 | 164 | 165 | 299 | 818 | 0 | 1097 | 984 | 662 |
N.S. |
1 | 0.97 | 0.94 | 0.94 | 1.71 | 4.67 | 0.00 | 6.27 | 5.62 | 3.78 |
time (sec) |
N/A | 0.660 | 0.276 | 2.628 | 0.042 | 3.474 | 0.000 | 0.144 | 0.176 | 27.220 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 111 | 115 | 114 | 82 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.06 | 1.10 | 1.09 | 0.78 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.689 | 0.064 | 6.255 | 0.035 | 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 | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 301 | 296 | 239 | 0 | 0 | 0 | 0 | 0 | 736 | 0 |
N.S. |
1 | 0.98 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.45 | 0.00 |
time (sec) |
N/A | 1.442 | 0.748 | 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 | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 206 | 176 | 0 | 0 | 0 | 0 | 0 | 730 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.56 | 0.00 |
time (sec) |
N/A | 0.700 | 0.267 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 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 | 89 | 89 | 77 | 0 | 0 | 0 | 0 | 0 | 743 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 8.35 | 0.00 |
time (sec) |
N/A | 0.380 | 0.062 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 123 | 0 | 0 | 0 | 0 | 0 | 453 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.36 | 0.00 |
time (sec) |
N/A | 0.481 | 0.083 | 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 | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 258 | 211 | 0 | 0 | 0 | 0 | 0 | 207 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.992 | 0.499 | 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 | N/A | N/A | N/A | N/A | N/A | F(-1) | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 100 | 22 | 0 | 0 | 800 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 5.00 | 1.10 | 0.00 | 0.00 | 40.00 | 1.10 |
time (sec) |
N/A | 0.287 | 0.566 | 0.601 | 0.145 | 0.080 | 0.000 | 0.000 | 0.206 | 25.778 |
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 | 234 | 230 | 224 | 0 | 0 | 0 | 515 | 0 | 205 | 0 |
N.S. |
1 | 0.98 | 0.96 | 0.00 | 0.00 | 0.00 | 2.20 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.868 | 0.490 | 0.000 | 0.000 | 0.000 | 13.487 | 0.000 | 0.171 | 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 | 181 | 182 | 178 | 0 | 0 | 0 | 360 | 0 | 143 | 0 |
N.S. |
1 | 1.01 | 0.98 | 0.00 | 0.00 | 0.00 | 1.99 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.739 | 0.262 | 0.000 | 0.000 | 0.000 | 8.413 | 0.000 | 0.174 | 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 | 132 | 136 | 130 | 0 | 0 | 0 | 214 | 0 | 83 | 0 |
N.S. |
1 | 1.03 | 0.98 | 0.00 | 0.00 | 0.00 | 1.62 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.644 | 0.126 | 0.000 | 0.000 | 0.000 | 5.737 | 0.000 | 0.166 | 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 | 54 | 54 | 52 | 0 | 0 | 0 | 76 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 1.41 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.322 | 0.026 | 0.000 | 0.000 | 0.000 | 1.563 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 22 | 22 | 17 | 22 | 123 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.85 | 1.10 | 6.15 | 1.10 |
time (sec) |
N/A | 0.288 | 2.493 | 0.553 | 0.144 | 0.073 | 3.269 | 0.129 | 0.187 | 25.580 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 105 | 33 | 19 | 22 | 169 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 5.25 | 1.65 | 0.95 | 1.10 | 8.45 | 1.10 |
time (sec) |
N/A | 0.283 | 0.552 | 0.602 | 0.174 | 0.078 | 45.541 | 0.148 | 0.180 | 25.665 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 174 | 44 | 0 | 22 | 401 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 8.70 | 2.20 | 0.00 | 1.10 | 20.05 | 1.10 |
time (sec) |
N/A | 0.281 | 0.587 | 0.565 | 0.176 | 0.095 | 0.000 | 0.153 | 0.179 | 25.740 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 250 | 183 | 297 | 0 | 0 | 0 | 0 | 329 | 0 |
N.S. |
1 | 1.00 | 0.73 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 1.32 | 0.00 |
time (sec) |
N/A | 0.847 | 0.199 | 2.846 | 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 | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 127 | 213 | 0 | 0 | 0 | 0 | 231 | 0 |
N.S. |
1 | 1.00 | 0.80 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 1.45 | 0.00 |
time (sec) |
N/A | 0.659 | 0.100 | 2.666 | 0.000 | 0.000 | 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 | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 79 | 156 | 0 | 0 | 0 | 0 | 149 | 0 |
N.S. |
1 | 1.00 | 0.87 | 1.71 | 0.00 | 0.00 | 0.00 | 0.00 | 1.64 | 0.00 |
time (sec) |
N/A | 0.497 | 0.043 | 2.639 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 57 | 98 | 118 | 0 | 0 | 0 | 97 | 0 |
N.S. |
1 | 1.00 | 0.98 | 1.69 | 2.03 | 0.00 | 0.00 | 0.00 | 1.67 | 0.00 |
time (sec) |
N/A | 0.450 | 0.001 | 2.512 | 0.037 | 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 | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 98 | 156 | 123 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.01 | 1.61 | 1.27 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.539 | 0.026 | 1.027 | 0.075 | 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 | A | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 146 | 147 | 201 | 156 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 1.01 | 1.38 | 1.07 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.658 | 0.045 | 1.211 | 0.070 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 227 | 194 | 260 | 216 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.15 | 0.95 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.807 | 0.188 | 1.492 | 0.069 | 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 | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 394 | 394 | 370 | 412 | 0 | 0 | 0 | 0 | 326 | 0 |
N.S. |
1 | 1.00 | 0.94 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 1.227 | 0.356 | 2.109 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 313 | 313 | 310 | 348 | 0 | 0 | 0 | 0 | 228 | 0 |
N.S. |
1 | 1.00 | 0.99 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 1.001 | 0.147 | 1.773 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 256 | 238 | 263 | 0 | 0 | 0 | 0 | 169 | 0 |
N.S. |
1 | 1.00 | 0.93 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.854 | 0.130 | 1.694 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 213 | 201 | 196 | 0 | 0 | 0 | 0 | 108 | 0 |
N.S. |
1 | 1.06 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.744 | 0.001 | 1.468 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 247 | 230 | 311 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 0.93 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.948 | 0.096 | 1.104 | 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 | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 306 | 306 | 282 | 354 | 0 | 0 | 0 | 0 | 77 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.018 | 0.234 | 1.178 | 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 | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 371 | 371 | 347 | 410 | 0 | 0 | 0 | 0 | 196 | 0 |
N.S. |
1 | 1.00 | 0.94 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 1.169 | 0.217 | 1.750 | 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 | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 692 | 692 | 581 | 302 | 0 | 0 | 0 | 0 | 458 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 1.864 | 0.467 | 2.299 | 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 | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 643 | 643 | 504 | 250 | 0 | 0 | 0 | 0 | 372 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 1.684 | 0.449 | 2.040 | 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 | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 457 | 457 | 430 | 206 | 0 | 0 | 0 | 0 | 225 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 1.302 | 0.325 | 1.796 | 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 | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 322 | 313 | 101 | 0 | 0 | 0 | 0 | 110 | 0 |
N.S. |
1 | 1.05 | 1.02 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.984 | 0.002 | 1.533 | 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 | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 352 | 352 | 327 | 170 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.177 | 0.143 | 1.375 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 510 | 510 | 395 | 292 | 0 | 0 | 0 | 0 | 127 | 0 |
N.S. |
1 | 1.00 | 0.77 | 0.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.465 | 0.171 | 1.556 | 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 | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 674 | 674 | 542 | 421 | 0 | 0 | 0 | 0 | 245 | 0 |
N.S. |
1 | 1.00 | 0.80 | 0.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 1.801 | 0.498 | 2.405 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 297 | 308 | 301 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 1.04 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.007 | 0.163 | 3.100 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 219 | 229 | 240 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 1.05 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.849 | 0.099 | 2.827 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 151 | 165 | 188 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 1.09 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.732 | 0.052 | 2.629 | 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 | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 116 | 114 | 137 | 159 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.03 | 1.01 | 1.21 | 1.41 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.685 | 0.001 | 2.693 | 0.035 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 161 | 209 | 179 | 0 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.00 | 1.01 | 1.31 | 1.13 | 0.00 | 0.00 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 0.810 | 0.051 | 1.180 | 0.070 | 0.000 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 198 | 200 | 264 | 230 | 0 | 0 | 0 | 181 | 0 |
N.S. |
1 | 1.00 | 1.01 | 1.33 | 1.16 | 0.00 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.891 | 0.083 | 1.286 | 0.075 | 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 | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 287 | 263 | 345 | 307 | 0 | 0 | 0 | 271 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.20 | 1.07 | 0.00 | 0.00 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 1.090 | 0.252 | 1.619 | 0.075 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 421 | 421 | 404 | 411 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.455 | 0.278 | 2.435 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 353 | 353 | 349 | 362 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 0.99 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.191 | 0.196 | 2.169 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 291 | 291 | 271 | 296 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 0.93 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 1.048 | 0.175 | 1.914 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 249 | 242 | 234 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.03 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.004 | 0.070 | 2.016 | 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 | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 287 | 289 | 362 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.01 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.128 | 0.100 | 1.506 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 357 | 357 | 327 | 418 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 1.252 | 0.227 | 1.648 | 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 | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 414 | 414 | 384 | 488 | 0 | 0 | 0 | 0 | 211 | 0 |
N.S. |
1 | 1.00 | 0.93 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 1.340 | 0.300 | 2.078 | 0.000 | 0.000 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 714 | 714 | 536 | 301 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 0.75 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 2.091 | 0.364 | 3.093 | 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 | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 666 | 666 | 483 | 269 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 0.73 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.791 | 0.250 | 2.603 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 488 | 488 | 403 | 238 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.490 | 0.228 | 2.531 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 344 | 354 | 350 | 142 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.03 | 1.02 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.183 | 0.169 | 2.268 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 388 | 388 | 395 | 220 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.356 | 0.176 | 1.883 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 557 | 557 | 463 | 345 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.637 | 0.199 | 2.326 | 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 | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 737 | 737 | 535 | 489 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 0.73 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.991 | 0.259 | 3.190 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 749 | 706 | 867 | 272 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.94 | 1.16 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 1.995 | 0.841 | 1.906 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 533 | 506 | 564 | 449 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.95 | 1.06 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.318 | 0.411 | 1.770 | 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 | C | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 229 | 178 | 392 | 309 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 0.78 | 1.71 | 1.35 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.790 | 0.132 | 1.271 | 0.145 | 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 | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 360 | 326 | 373 | 0 | 377 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 0.91 | 1.04 | 0.00 | 1.05 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.006 | 0.263 | 0.000 | 0.156 | 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 | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 597 | 557 | 706 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 0.93 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.563 | 0.481 | 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 | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 541 | 543 | 422 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.722 | 0.307 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 561 | 563 | 912 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 2.159 | 0.605 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.018 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 338 | 338 | 215 | 258 | 0 | 596 | 697 | 268 | 329 | 298 |
N.S. |
1 | 1.00 | 0.64 | 0.76 | 0.00 | 1.76 | 2.06 | 0.79 | 0.97 | 0.88 |
time (sec) |
N/A | 0.880 | 0.257 | 3.895 | 0.000 | 0.102 | 125.043 | 0.129 | 0.159 | 26.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 221 | 151 | 167 | 0 | 404 | 478 | 174 | 212 | 193 |
N.S. |
1 | 1.00 | 0.68 | 0.76 | 0.00 | 1.83 | 2.16 | 0.79 | 0.96 | 0.87 |
time (sec) |
N/A | 0.641 | 0.122 | 1.813 | 0.000 | 0.118 | 32.846 | 0.121 | 0.164 | 26.618 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 117 | 89 | 0 | 220 | 260 | 94 | 113 | 97 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.00 | 1.88 | 2.22 | 0.80 | 0.97 | 0.83 |
time (sec) |
N/A | 0.464 | 0.045 | 0.882 | 0.000 | 0.095 | 8.270 | 0.124 | 0.146 | 25.950 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 533 | 506 | 564 | 449 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.95 | 1.06 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.242 | 0.121 | 0.915 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 751 | 751 | 877 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.907 | 1.471 | 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 | A | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 945 | 945 | 435 | 1077 | 0 | 0 | 0 | 0 | 478 | 0 |
N.S. |
1 | 1.00 | 0.46 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 2.545 | 0.538 | 2.423 | 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 | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 548 | 548 | 281 | 729 | 0 | 0 | 0 | 0 | 252 | 0 |
N.S. |
1 | 1.00 | 0.51 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 1.591 | 0.295 | 1.151 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 26 | 26 | 20 | 26 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.83 | 1.08 | 1.08 | 1.08 |
time (sec) |
N/A | 0.313 | 3.866 | 0.625 | 0.847 | 0.105 | 10.155 | 0.124 | 0.148 | 25.978 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 0 | 37 | 0 | 26 | 37 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 0.00 | 1.54 | 0.00 | 1.08 | 1.54 | 1.08 |
time (sec) |
N/A | 0.308 | 10.962 | 0.681 | 0.000 | 0.079 | 0.000 | 0.125 | 0.175 | 25.692 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | B | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 1772 | 22 | 0 | 24 | 20 | 24 | 397 | 24 |
N.S. |
1 | 1.00 | 80.55 | 1.00 | 0.00 | 1.09 | 0.91 | 1.09 | 18.05 | 1.09 |
time (sec) |
N/A | 2.542 | 12.979 | 0.082 | 0.000 | 0.072 | 10.183 | 0.182 | 0.159 | 25.744 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 26 | 26 | 20 | 26 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.83 | 1.08 | 1.08 | 1.08 |
time (sec) |
N/A | 0.313 | 6.563 | 0.575 | 1.751 | 0.135 | 14.270 | 0.146 | 0.154 | 25.613 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 0 | 37 | 0 | 26 | 37 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 0.00 | 1.54 | 0.00 | 1.08 | 1.54 | 1.08 |
time (sec) |
N/A | 0.314 | 10.948 | 1.063 | 0.000 | 0.087 | 0.000 | 0.148 | 0.183 | 25.457 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 26 | 35 | 20 | 26 | 69 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.46 | 0.83 | 1.08 | 2.88 | 1.08 |
time (sec) |
N/A | 0.308 | 0.426 | 0.266 | 0.130 | 0.097 | 8.438 | 0.125 | 0.158 | 25.527 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 24 | 24 | 19 | 24 | 41 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.86 | 1.09 | 1.86 | 1.09 |
time (sec) |
N/A | 0.289 | 0.252 | 0.092 | 0.134 | 0.109 | 4.498 | 0.118 | 0.154 | 25.573 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 26 | 26 | 20 | 26 | 36 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.83 | 1.08 | 1.50 | 1.08 |
time (sec) |
N/A | 0.313 | 0.748 | 0.983 | 0.095 | 0.091 | 15.427 | 0.112 | 0.159 | 25.539 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 26 | 37 | 22 | 26 | 59 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.54 | 0.92 | 1.08 | 2.46 | 1.08 |
time (sec) |
N/A | 0.309 | 1.829 | 0.935 | 0.101 | 0.088 | 167.597 | 0.116 | 0.159 | 25.559 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 148 | 35 | 22 | 26 | 69 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 6.17 | 1.46 | 0.92 | 1.08 | 2.88 | 1.08 |
time (sec) |
N/A | 0.309 | 0.924 | 0.092 | 0.164 | 0.118 | 13.084 | 0.118 | 0.149 | 25.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 101 | 24 | 20 | 24 | 41 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 4.59 | 1.09 | 0.91 | 1.09 | 1.86 | 1.09 |
time (sec) |
N/A | 0.282 | 0.488 | 0.089 | 0.154 | 0.072 | 7.664 | 0.118 | 0.155 | 25.618 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 157 | 26 | 22 | 26 | 40 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 6.54 | 1.08 | 0.92 | 1.08 | 1.67 | 1.08 |
time (sec) |
N/A | 0.303 | 3.349 | 0.091 | 0.108 | 0.084 | 22.363 | 0.124 | 0.150 | 25.558 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 214 | 37 | 0 | 26 | 65 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 8.92 | 1.54 | 0.00 | 1.08 | 2.71 | 1.08 |
time (sec) |
N/A | 0.303 | 6.530 | 0.007 | 0.110 | 0.080 | 0.000 | 0.136 | 0.160 | 25.436 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 366 | 366 | 258 | 309 | 0 | 708 | 0 | 325 | 356 | 316 |
N.S. |
1 | 1.00 | 0.70 | 0.84 | 0.00 | 1.93 | 0.00 | 0.89 | 0.97 | 0.86 |
time (sec) |
N/A | 0.970 | 0.257 | 16.825 | 0.000 | 0.090 | 0.000 | 0.137 | 0.155 | 28.876 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 231 | 178 | 195 | 0 | 454 | 440 | 204 | 228 | 317 |
N.S. |
1 | 1.00 | 0.77 | 0.84 | 0.00 | 1.97 | 1.90 | 0.88 | 0.99 | 1.37 |
time (sec) |
N/A | 0.686 | 0.208 | 5.223 | 0.000 | 0.090 | 126.468 | 0.131 | 0.151 | 28.454 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 110 | 104 | 0 | 250 | 214 | 98 | 112 | 94 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.00 | 2.27 | 1.95 | 0.89 | 1.02 | 0.85 |
time (sec) |
N/A | 0.484 | 0.051 | 1.865 | 0.000 | 0.080 | 16.777 | 0.124 | 0.145 | 26.495 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1165 | 1165 | 990 | 577 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.02 | 0.00 |
time (sec) |
N/A | 3.197 | 0.967 | 3.458 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1865 | 1867 | 2168 | 0 | 0 | 0 | 0 | 0 | 884 | 0 |
N.S. |
1 | 1.00 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 5.066 | 7.284 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1221 | 1221 | 780 | 1584 | 0 | 0 | 0 | 0 | 819 | 0 |
N.S. |
1 | 1.00 | 0.64 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 3.375 | 1.334 | 21.773 | 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 | A | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 835 | 835 | 475 | 1127 | 0 | 0 | 0 | 0 | 513 | 0 |
N.S. |
1 | 1.00 | 0.57 | 1.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 2.278 | 0.617 | 7.054 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 395 | 395 | 398 | 724 | 0 | 0 | 0 | 0 | 239 | 0 |
N.S. |
1 | 1.00 | 1.01 | 1.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 1.268 | 0.143 | 2.378 | 0.000 | 0.000 | 0.000 | 0.000 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 26 | 26 | 0 | 26 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.00 | 1.08 | 1.08 | 1.08 |
time (sec) |
N/A | 0.303 | 22.033 | 2.203 | 0.866 | 0.104 | 0.000 | 0.131 | 0.157 | 25.823 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 0 | 37 | 0 | 26 | 2374 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 0.00 | 1.54 | 0.00 | 1.08 | 98.92 | 1.08 |
time (sec) |
N/A | 0.306 | 31.521 | 6.498 | 0.000 | 0.090 | 0.000 | 0.139 | 0.495 | 25.949 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | B | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 2385 | 24 | 0 | 35 | 22 | 26 | 812 | 26 |
N.S. |
1 | 1.00 | 99.38 | 1.00 | 0.00 | 1.46 | 0.92 | 1.08 | 33.83 | 1.08 |
time (sec) |
N/A | 4.239 | 10.961 | 1.742 | 0.000 | 0.094 | 33.140 | 0.200 | 0.158 | 26.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | B | N/A | F(-2) | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 1051 | 22 | 0 | 24 | 20 | 24 | 374 | 24 |
N.S. |
1 | 1.00 | 47.77 | 1.00 | 0.00 | 1.09 | 0.91 | 1.09 | 17.00 | 1.09 |
time (sec) |
N/A | 1.683 | 2.339 | 2.313 | 0.000 | 0.109 | 10.116 | 0.152 | 0.160 | 25.958 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 26 | 26 | 0 | 26 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.00 | 1.08 | 1.08 | 1.08 |
time (sec) |
N/A | 0.313 | 32.223 | 2.149 | 1.290 | 0.069 | 0.000 | 0.156 | 0.155 | 25.913 |