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 | C | F | F | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 205 | 106 | 0 | 0 | 184 | 0 | 0 | 211 | 0 |
N.S. |
1 | 1.01 | 0.52 | 0.00 | 0.00 | 0.91 | 0.00 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.524 | 0.042 | 0.000 | 0.000 | 0.114 | 0.000 | 0.000 | 0.522 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 240 | 118 | 0 | 0 | 192 | 0 | 0 | 241 | 0 |
N.S. |
1 | 1.03 | 0.51 | 0.00 | 0.00 | 0.82 | 0.00 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.578 | 0.051 | 0.000 | 0.000 | 0.112 | 0.000 | 0.000 | 0.613 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 291 | 330 | 127 | 0 | 0 | 255 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.13 | 0.44 | 0.00 | 0.00 | 0.88 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.779 | 0.140 | 0.000 | 0.000 | 0.134 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 317 | 73 | 0 | 0 | 247 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.18 | 0.27 | 0.00 | 0.00 | 0.92 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.753 | 0.043 | 0.000 | 0.000 | 0.156 | 0.000 | 0.000 | 200.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 226 | 280 | 63 | 0 | 0 | 238 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.24 | 0.28 | 0.00 | 0.00 | 1.05 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.685 | 0.022 | 0.000 | 0.000 | 0.135 | 0.000 | 0.000 | 200.032 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 239 | 41 | 0 | 0 | 213 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.23 | 0.21 | 0.00 | 0.00 | 1.09 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.599 | 0.044 | 0.000 | 0.000 | 0.129 | 0.000 | 0.000 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 266 | 96 | 0 | 0 | 243 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.31 | 0.47 | 0.00 | 0.00 | 1.20 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.733 | 0.035 | 0.000 | 0.000 | 0.126 | 0.000 | 0.000 | 200.034 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 96 | 69 | 0 | 0 | 156 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.04 | 0.75 | 0.00 | 0.00 | 1.70 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.386 | 0.022 | 0.000 | 0.000 | 0.146 | 0.000 | 0.000 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 135 | 81 | 0 | 0 | 178 | 0 | 0 | 89 | 0 |
N.S. |
1 | 1.02 | 0.61 | 0.00 | 0.00 | 1.35 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.403 | 0.026 | 0.000 | 0.000 | 0.149 | 0.000 | 0.000 | 0.347 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 172 | 92 | 0 | 0 | 187 | 0 | 0 | 116 | 0 |
N.S. |
1 | 1.01 | 0.54 | 0.00 | 0.00 | 1.10 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.487 | 0.032 | 0.000 | 0.000 | 0.122 | 0.000 | 0.000 | 0.354 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 209 | 99 | 0 | 0 | 195 | 0 | 0 | 145 | 0 |
N.S. |
1 | 1.03 | 0.49 | 0.00 | 0.00 | 0.97 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.526 | 0.043 | 0.000 | 0.000 | 0.146 | 0.000 | 0.000 | 0.375 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 291 | 330 | 127 | 0 | 0 | 251 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.13 | 0.44 | 0.00 | 0.00 | 0.86 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.813 | 0.143 | 0.000 | 0.000 | 0.087 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 317 | 73 | 0 | 0 | 243 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.18 | 0.27 | 0.00 | 0.00 | 0.91 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.770 | 0.040 | 0.000 | 0.000 | 0.115 | 0.000 | 0.000 | 200.033 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 226 | 280 | 63 | 0 | 0 | 236 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.24 | 0.28 | 0.00 | 0.00 | 1.04 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.693 | 0.023 | 0.000 | 0.000 | 0.086 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 239 | 39 | 0 | 0 | 209 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.23 | 0.20 | 0.00 | 0.00 | 1.07 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.636 | 0.057 | 0.000 | 0.000 | 0.110 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 266 | 97 | 0 | 0 | 243 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.30 | 0.48 | 0.00 | 0.00 | 1.19 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.718 | 0.032 | 0.000 | 0.000 | 0.088 | 0.000 | 0.000 | 200.028 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 96 | 69 | 0 | 0 | 152 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.04 | 0.75 | 0.00 | 0.00 | 1.65 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.371 | 0.020 | 0.000 | 0.000 | 0.083 | 0.000 | 0.000 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 135 | 81 | 0 | 0 | 176 | 0 | 0 | 101 | 0 |
N.S. |
1 | 1.02 | 0.61 | 0.00 | 0.00 | 1.33 | 0.00 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.398 | 0.025 | 0.000 | 0.000 | 0.085 | 0.000 | 0.000 | 1.618 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 172 | 93 | 0 | 0 | 184 | 0 | 0 | 113 | 0 |
N.S. |
1 | 1.01 | 0.55 | 0.00 | 0.00 | 1.08 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.472 | 0.031 | 0.000 | 0.000 | 0.130 | 0.000 | 0.000 | 2.019 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 207 | 99 | 0 | 0 | 192 | 0 | 0 | 101 | 0 |
N.S. |
1 | 1.02 | 0.49 | 0.00 | 0.00 | 0.95 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.522 | 0.048 | 0.000 | 0.000 | 0.127 | 0.000 | 0.000 | 2.364 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 325 | 372 | 100 | 0 | 0 | 304 | 0 | 0 | 118 | 0 |
N.S. |
1 | 1.14 | 0.31 | 0.00 | 0.00 | 0.94 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.878 | 0.062 | 0.000 | 0.000 | 0.124 | 0.000 | 0.000 | 0.782 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 300 | 354 | 91 | 0 | 0 | 296 | 0 | 0 | 118 | 0 |
N.S. |
1 | 1.18 | 0.30 | 0.00 | 0.00 | 0.99 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.810 | 0.044 | 0.000 | 0.000 | 0.138 | 0.000 | 0.000 | 0.995 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 314 | 63 | 0 | 0 | 289 | 0 | 0 | 116 | 0 |
N.S. |
1 | 1.23 | 0.25 | 0.00 | 0.00 | 1.13 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.729 | 0.037 | 0.000 | 0.000 | 0.122 | 0.000 | 0.000 | 0.746 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 226 | 273 | 39 | 0 | 0 | 261 | 0 | 0 | 115 | 0 |
N.S. |
1 | 1.21 | 0.17 | 0.00 | 0.00 | 1.15 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.673 | 0.070 | 0.000 | 0.000 | 0.121 | 0.000 | 0.000 | 0.714 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 230 | 292 | 106 | 0 | 0 | 329 | 0 | 0 | 116 | 0 |
N.S. |
1 | 1.27 | 0.46 | 0.00 | 0.00 | 1.43 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.796 | 0.073 | 0.000 | 0.000 | 0.119 | 0.000 | 0.000 | 0.790 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 127 | 69 | 0 | 0 | 212 | 0 | 0 | 117 | 0 |
N.S. |
1 | 1.05 | 0.57 | 0.00 | 0.00 | 1.75 | 0.00 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.416 | 0.024 | 0.000 | 0.000 | 0.129 | 0.000 | 0.000 | 0.574 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 166 | 81 | 0 | 0 | 238 | 0 | 0 | 120 | 0 |
N.S. |
1 | 1.02 | 0.50 | 0.00 | 0.00 | 1.46 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.439 | 0.030 | 0.000 | 0.000 | 0.112 | 0.000 | 0.000 | 1.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 205 | 93 | 0 | 0 | 246 | 0 | 0 | 122 | 0 |
N.S. |
1 | 1.01 | 0.46 | 0.00 | 0.00 | 1.21 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.543 | 0.036 | 0.000 | 0.000 | 0.156 | 0.000 | 0.000 | 15.842 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 240 | 99 | 0 | 0 | 254 | 0 | 0 | 122 | 0 |
N.S. |
1 | 1.03 | 0.42 | 0.00 | 0.00 | 1.09 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.583 | 0.045 | 0.000 | 0.000 | 0.129 | 0.000 | 0.000 | 0.705 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 302 | 73 | 0 | 0 | 208 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.18 | 0.29 | 0.00 | 0.00 | 0.82 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.713 | 0.052 | 0.000 | 0.000 | 0.081 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 270 | 57 | 0 | 0 | 195 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.25 | 0.26 | 0.00 | 0.00 | 0.90 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.658 | 0.028 | 0.000 | 0.000 | 0.080 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 237 | 34 | 0 | 0 | 195 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.21 | 0.17 | 0.00 | 0.00 | 0.99 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.587 | 0.027 | 0.000 | 0.000 | 0.090 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 311 | 437 | 90 | 0 | 0 | 339 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.41 | 0.29 | 0.00 | 0.00 | 1.09 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.835 | 0.037 | 0.000 | 0.000 | 0.090 | 0.000 | 0.000 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 258 | 64 | 0 | 0 | 211 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.30 | 0.32 | 0.00 | 0.00 | 1.06 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.538 | 0.018 | 0.000 | 0.000 | 0.118 | 0.000 | 0.000 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 294 | 72 | 0 | 0 | 234 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.29 | 0.32 | 0.00 | 0.00 | 1.03 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.578 | 0.022 | 0.000 | 0.000 | 0.142 | 0.000 | 0.000 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 265 | 328 | 81 | 0 | 0 | 243 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.24 | 0.31 | 0.00 | 0.00 | 0.92 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.635 | 0.026 | 0.000 | 0.000 | 0.122 | 0.000 | 0.000 | 0.384 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 186 | 73 | 0 | 0 | 117 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.05 | 0.41 | 0.00 | 0.00 | 0.66 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.426 | 0.044 | 0.000 | 0.000 | 0.130 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 156 | 54 | 0 | 0 | 116 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.11 | 0.39 | 0.00 | 0.00 | 0.83 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.375 | 0.028 | 0.000 | 0.000 | 0.130 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 123 | 34 | 0 | 0 | 104 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.06 | 0.29 | 0.00 | 0.00 | 0.90 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.325 | 0.032 | 0.000 | 0.000 | 0.075 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 175 | 90 | 0 | 0 | 145 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.07 | 0.55 | 0.00 | 0.00 | 0.89 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.398 | 0.038 | 0.000 | 0.000 | 0.119 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 113 | 59 | 0 | 0 | 120 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.02 | 0.53 | 0.00 | 0.00 | 1.08 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.361 | 0.018 | 0.000 | 0.000 | 0.129 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 149 | 69 | 0 | 0 | 138 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.05 | 0.49 | 0.00 | 0.00 | 0.97 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.374 | 0.023 | 0.000 | 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 | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 571 | 734 | 83 | 0 | 0 | 435 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.29 | 0.15 | 0.00 | 0.00 | 0.76 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.399 | 0.055 | 0.000 | 0.000 | 0.152 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 523 | 697 | 63 | 0 | 0 | 428 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.33 | 0.12 | 0.00 | 0.00 | 0.82 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.266 | 0.028 | 0.000 | 0.000 | 0.144 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 504 | 656 | 41 | 0 | 0 | 383 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.30 | 0.08 | 0.00 | 0.00 | 0.76 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.202 | 0.035 | 0.000 | 0.000 | 0.106 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 630 | 918 | 97 | 0 | 0 | 509 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.46 | 0.15 | 0.00 | 0.00 | 0.81 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.780 | 0.047 | 0.000 | 0.000 | 0.084 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 259 | 331 | 71 | 0 | 0 | 345 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.28 | 0.27 | 0.00 | 0.00 | 1.33 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.674 | 0.022 | 0.000 | 0.000 | 0.093 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 295 | 370 | 84 | 0 | 0 | 381 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.25 | 0.28 | 0.00 | 0.00 | 1.29 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.717 | 0.027 | 0.000 | 0.000 | 0.088 | 0.000 | 0.000 | 200.022 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 114 | 94 | 748 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.76 | 6.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.456 | 0.052 | 0.679 | 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 | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 58 | 417 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.16 | 8.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.350 | 0.030 | 0.331 | 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 | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 29 | 175 | 0 | 0 | 126 | 0 | 122 | 0 |
N.S. |
1 | 1.00 | 0.74 | 4.49 | 0.00 | 0.00 | 3.23 | 0.00 | 3.13 | 0.00 |
time (sec) |
N/A | 0.303 | 0.011 | 0.177 | 0.000 | 0.000 | 1.660 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 29 | 158 | 0 | 0 | 133 | 0 | 55 | 0 |
N.S. |
1 | 1.00 | 0.74 | 4.05 | 0.00 | 0.00 | 3.41 | 0.00 | 1.41 | 0.00 |
time (sec) |
N/A | 0.306 | 0.013 | 0.193 | 0.000 | 0.000 | 2.364 | 0.000 | 0.178 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 58 | 428 | 0 | 0 | 0 | 0 | 411 | 0 |
N.S. |
1 | 1.00 | 1.16 | 8.56 | 0.00 | 0.00 | 0.00 | 0.00 | 8.22 | 0.00 |
time (sec) |
N/A | 0.350 | 0.026 | 0.474 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 115 | 94 | 1196 | 0 | 0 | 0 | 0 | 838 | 0 |
N.S. |
1 | 0.93 | 0.76 | 9.65 | 0.00 | 0.00 | 0.00 | 0.00 | 6.76 | 0.00 |
time (sec) |
N/A | 0.458 | 0.047 | 1.326 | 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 | C | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 161 | 113 | 146 | 0 | 0 | 0 | 0 | 167 | 0 |
N.S. |
1 | 1.36 | 0.96 | 1.24 | 0.00 | 0.00 | 0.00 | 0.00 | 1.42 | 0.00 |
time (sec) |
N/A | 0.858 | 0.096 | 0.111 | 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 | C | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 85 | 71 | 0 | 0 | 94 | 0 | 41 | 0 |
N.S. |
1 | 1.00 | 1.08 | 0.90 | 0.00 | 0.00 | 1.19 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.376 | 0.055 | 0.091 | 0.000 | 0.000 | 1.504 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 85 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.361 | 0.054 | 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 | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 161 | 113 | 0 | 0 | 0 | 0 | 0 | 93 | 0 |
N.S. |
1 | 1.36 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.864 | 0.094 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 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(-2) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 0 | 0 | 0 | 0 | 0 | 0 | 1098 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 30.50 | 0.00 |
time (sec) |
N/A | 0.321 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.454 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 0 | 0 | 0 | 0 | 0 | 0 | 128 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.56 | 0.00 |
time (sec) |
N/A | 0.311 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.753 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 0 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.311 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.375 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 0 | 0 | 0 | 0 | 0 | 0 | 127 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.53 | 0.00 |
time (sec) |
N/A | 0.316 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.549 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 0 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.312 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.026 | 0.000 |
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 | 38 | 38 | 0 | 0 | 0 | 0 | 0 | 0 | 12 | 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 | 0.319 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
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 | 38 | 38 | 0 | 0 | 0 | 0 | 0 | 0 | 12 | 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 | 0.310 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 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 | 0.69 | 0.00 |
time (sec) |
N/A | 0.308 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.266 | 0.000 |
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 | 40 | 40 | 0 | 0 | 0 | 0 | 0 | 0 | 15 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.320 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 177 | 210 | 0 | 0 | 0 | 0 | 0 | 15 | 0 |
N.S. |
1 | 0.86 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.511 | 0.246 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 165 | 116 | 0 | 0 | 0 | 0 | 0 | 15 | 0 |
N.S. |
1 | 1.04 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.470 | 0.070 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 105 | 0 | 0 | 0 | 0 | 0 | 13 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.371 | 0.037 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 53 | 0 | 0 | 0 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.305 | 0.048 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 125 | 106 | 0 | 0 | 0 | 0 | 0 | 15 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.408 | 0.032 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 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 | 79 | 79 | 82 | 0 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.342 | 0.022 | 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 | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 120 | 114 | 0 | 0 | 0 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.397 | 0.042 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 174 | 119 | 0 | 0 | 0 | 0 | 0 | 138 | 0 |
N.S. |
1 | 1.02 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.463 | 0.077 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 315 | 284 | 217 | 197 | 749 | 177 | 1222 | 206 | 27 | 0 |
N.S. |
1 | 0.90 | 0.69 | 0.63 | 2.38 | 0.56 | 3.88 | 0.65 | 0.09 | 0.00 |
time (sec) |
N/A | 0.780 | 1.112 | 0.852 | 0.043 | 0.105 | 1.865 | 0.149 | 200.017 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 208 | 176 | 150 | 529 | 139 | 857 | 156 | 361 | 0 |
N.S. |
1 | 0.87 | 0.74 | 0.63 | 2.22 | 0.58 | 3.60 | 0.66 | 1.52 | 0.00 |
time (sec) |
N/A | 0.608 | 0.501 | 0.510 | 0.041 | 0.116 | 1.581 | 0.145 | 2.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 180 | 135 | 113 | 351 | 106 | 585 | 114 | 228 | 0 |
N.S. |
1 | 1.05 | 0.79 | 0.66 | 2.05 | 0.62 | 3.42 | 0.67 | 1.33 | 0.00 |
time (sec) |
N/A | 0.535 | 0.197 | 0.445 | 0.040 | 0.119 | 1.348 | 0.128 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 121 | 108 | 87 | 209 | 79 | 362 | 76 | 124 | 0 |
N.S. |
1 | 1.10 | 0.98 | 0.79 | 1.90 | 0.72 | 3.29 | 0.69 | 1.13 | 0.00 |
time (sec) |
N/A | 0.445 | 0.161 | 0.310 | 0.034 | 0.116 | 0.915 | 0.129 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 65 | 28 | 69 | 62 | 60 | 36 | 52 | 49 | 97 |
N.S. |
1 | 1.25 | 0.54 | 1.33 | 1.19 | 1.15 | 0.69 | 1.00 | 0.94 | 1.87 |
time (sec) |
N/A | 0.354 | 0.025 | 0.225 | 0.028 | 0.108 | 0.801 | 0.132 | 0.161 | 23.840 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 111 | 142 | 107 | 233 | 144 | 0 | 113 | 152 | 118 |
N.S. |
1 | 1.25 | 1.60 | 1.20 | 2.62 | 1.62 | 0.00 | 1.27 | 1.71 | 1.33 |
time (sec) |
N/A | 0.478 | 0.114 | 0.221 | 0.034 | 0.091 | 0.000 | 0.180 | 0.150 | 23.887 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 120 | 93 | 239 | 224 | 0 | 145 | 198 | 218 |
N.S. |
1 | 1.00 | 0.92 | 0.72 | 1.84 | 1.72 | 0.00 | 1.12 | 1.52 | 1.68 |
time (sec) |
N/A | 0.420 | 0.096 | 0.661 | 0.037 | 0.089 | 0.000 | 0.162 | 0.187 | 24.478 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 198 | 154 | 187 | 424 | 452 | 0 | 471 | 510 | 0 |
N.S. |
1 | 0.99 | 0.77 | 0.93 | 2.11 | 2.25 | 0.00 | 2.34 | 2.54 | 0.00 |
time (sec) |
N/A | 0.509 | 0.188 | 0.355 | 0.038 | 0.083 | 0.000 | 0.164 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 294 | 234 | 281 | 644 | 690 | 0 | 884 | 852 | 0 |
N.S. |
1 | 1.04 | 0.83 | 0.99 | 2.28 | 2.44 | 0.00 | 3.12 | 3.01 | 0.00 |
time (sec) |
N/A | 0.621 | 0.480 | 0.822 | 0.037 | 0.093 | 0.000 | 0.171 | 0.387 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 92 | 160 | 149 | 105 | 110 | 123 | 261 | 201 |
N.S. |
1 | 1.00 | 1.00 | 1.74 | 1.62 | 1.14 | 1.20 | 1.34 | 2.84 | 2.18 |
time (sec) |
N/A | 0.464 | 0.193 | 0.272 | 0.104 | 0.072 | 0.250 | 0.115 | 0.148 | 0.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 72 | 109 | 116 | 77 | 75 | 83 | 189 | 153 |
N.S. |
1 | 1.00 | 1.00 | 1.51 | 1.61 | 1.07 | 1.04 | 1.15 | 2.62 | 2.12 |
time (sec) |
N/A | 0.416 | 0.075 | 0.245 | 0.110 | 0.071 | 0.184 | 0.132 | 0.163 | 23.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 54 | 70 | 87 | 53 | 46 | 53 | 128 | 107 |
N.S. |
1 | 1.00 | 1.00 | 1.30 | 1.61 | 0.98 | 0.85 | 0.98 | 2.37 | 1.98 |
time (sec) |
N/A | 0.384 | 0.045 | 0.194 | 0.104 | 0.067 | 0.153 | 0.106 | 0.172 | 23.266 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 37 | 41 | 64 | 35 | 29 | 35 | 79 | 60 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.73 | 0.95 | 0.78 | 0.95 | 2.14 | 1.62 |
time (sec) |
N/A | 0.341 | 0.029 | 0.180 | 0.107 | 0.070 | 0.118 | 0.143 | 0.155 | 23.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 32 | 21 | 46 | 22 | 14 | 16 | 37 | 21 |
N.S. |
1 | 1.00 | 1.60 | 1.05 | 2.30 | 1.10 | 0.70 | 0.80 | 1.85 | 1.05 |
time (sec) |
N/A | 0.293 | 0.013 | 0.121 | 0.107 | 0.068 | 0.076 | 0.119 | 0.165 | 23.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 31 | 47 | 78 | 27 | 100 | 33 | 84 | 32 |
N.S. |
1 | 1.00 | 0.82 | 1.24 | 2.05 | 0.71 | 2.63 | 0.87 | 2.21 | 0.84 |
time (sec) |
N/A | 0.351 | 0.028 | 0.229 | 0.108 | 0.080 | 0.414 | 0.136 | 0.153 | 23.517 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 39 | 96 | 126 | 40 | 156 | 61 | 161 | 98 |
N.S. |
1 | 1.00 | 0.71 | 1.75 | 2.29 | 0.73 | 2.84 | 1.11 | 2.93 | 1.78 |
time (sec) |
N/A | 0.377 | 0.036 | 0.231 | 0.107 | 0.128 | 0.315 | 0.145 | 0.149 | 23.381 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 63 | 201 | 188 | 69 | 228 | 89 | 303 | 154 |
N.S. |
1 | 1.00 | 0.83 | 2.64 | 2.47 | 0.91 | 3.00 | 1.17 | 3.99 | 2.03 |
time (sec) |
N/A | 0.407 | 0.045 | 0.271 | 0.108 | 0.133 | 0.444 | 0.111 | 0.173 | 23.482 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 88 | 267 | 263 | 94 | 286 | 126 | 464 | 199 |
N.S. |
1 | 1.00 | 0.95 | 2.87 | 2.83 | 1.01 | 3.08 | 1.35 | 4.99 | 2.14 |
time (sec) |
N/A | 0.422 | 0.059 | 0.279 | 0.116 | 0.107 | 0.556 | 0.130 | 0.158 | 23.464 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 359 | 342 | 249 | 436 | 3081 | 264 | 0 | 334 | 29 | 0 |
N.S. |
1 | 0.95 | 0.69 | 1.21 | 8.58 | 0.74 | 0.00 | 0.93 | 0.08 | 0.00 |
time (sec) |
N/A | 0.877 | 0.681 | 2.319 | 0.084 | 0.147 | 0.000 | 0.157 | 200.015 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 282 | 264 | 201 | 342 | 2295 | 216 | 0 | 285 | 29 | 0 |
N.S. |
1 | 0.94 | 0.71 | 1.21 | 8.14 | 0.77 | 0.00 | 1.01 | 0.10 | 0.00 |
time (sec) |
N/A | 0.724 | 0.356 | 1.414 | 0.062 | 0.125 | 0.000 | 0.142 | 200.013 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 229 | 160 | 259 | 1608 | 174 | 0 | 243 | 770 | 0 |
N.S. |
1 | 1.01 | 0.70 | 1.14 | 7.08 | 0.77 | 0.00 | 1.07 | 3.39 | 0.00 |
time (sec) |
N/A | 0.632 | 0.294 | 1.323 | 0.052 | 0.139 | 0.000 | 0.162 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 171 | 132 | 186 | 1108 | 136 | 0 | 209 | 555 | 0 |
N.S. |
1 | 1.05 | 0.81 | 1.14 | 6.80 | 0.83 | 0.00 | 1.28 | 3.40 | 0.00 |
time (sec) |
N/A | 0.503 | 0.215 | 0.825 | 0.042 | 0.119 | 0.000 | 0.146 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 109 | 45 | 120 | 736 | 99 | 0 | 180 | 298 | 0 |
N.S. |
1 | 1.16 | 0.48 | 1.28 | 7.83 | 1.05 | 0.00 | 1.91 | 3.17 | 0.00 |
time (sec) |
N/A | 0.406 | 0.049 | 0.782 | 0.040 | 0.115 | 0.000 | 0.161 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 162 | 196 | 485 | 733 | 356 | 0 | 252 | 1336 | 0 |
N.S. |
1 | 1.21 | 1.46 | 3.62 | 5.47 | 2.66 | 0.00 | 1.88 | 9.97 | 0.00 |
time (sec) |
N/A | 0.573 | 1.230 | 0.516 | 0.042 | 0.130 | 0.000 | 0.248 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 185 | 145 | 174 | 992 | 389 | 0 | 0 | 1546 | 0 |
N.S. |
1 | 1.05 | 0.82 | 0.99 | 5.64 | 2.21 | 0.00 | 0.00 | 8.78 | 0.00 |
time (sec) |
N/A | 0.486 | 0.308 | 1.803 | 0.042 | 0.141 | 0.000 | 0.000 | 0.320 | 0.000 |