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 | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 24 | 0 | 31 | 0 | 0 | 40 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.00 | 1.07 | 0.00 | 0.00 | 1.38 | 0.79 |
time (sec) |
N/A | 0.135 | 0.017 | 0.134 | 0.000 | 0.091 | 0.000 | 0.000 | 0.269 | 0.243 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 37 | 32 | 0 | 52 | 0 | 0 | 66 | 52 |
N.S. |
1 | 1.00 | 0.63 | 0.54 | 0.00 | 0.88 | 0.00 | 0.00 | 1.12 | 0.88 |
time (sec) |
N/A | 0.146 | 0.055 | 0.137 | 0.000 | 0.083 | 0.000 | 0.000 | 0.299 | 0.297 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 96 | 48 | 43 | 0 | 74 | 0 | 0 | 92 | 81 |
N.S. |
1 | 1.09 | 0.55 | 0.49 | 0.00 | 0.84 | 0.00 | 0.00 | 1.05 | 0.92 |
time (sec) |
N/A | 0.162 | 0.072 | 0.195 | 0.000 | 0.098 | 0.000 | 0.000 | 0.382 | 0.309 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 133 | 59 | 54 | 0 | 96 | 0 | 0 | 118 | 110 |
N.S. |
1 | 1.14 | 0.50 | 0.46 | 0.00 | 0.82 | 0.00 | 0.00 | 1.01 | 0.94 |
time (sec) |
N/A | 0.180 | 0.106 | 0.135 | 0.000 | 0.086 | 0.000 | 0.000 | 0.407 | 0.325 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 338 | 66 | 66 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 0.20 | 0.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.153 | 0.015 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 65 | 65 | 0 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.21 | 0.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.150 | 0.013 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 281 | 320 | 65 | 0 | 0 | 0 | 107 | 0 | 18 | 0 |
N.S. |
1 | 1.14 | 0.23 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.261 | 0.016 | 0.000 | 0.000 | 0.000 | 1.713 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 312 | 70 | 70 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 0.22 | 0.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.171 | 0.014 | 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 | C | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 340 | 70 | 70 | 0 | 0 | 0 | 0 | 0 | 66 | 0 |
N.S. |
1 | 0.21 | 0.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.173 | 0.014 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 175 | 173 | 0 | 0 | 227 | 0 | 0 | 122 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 1.30 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.209 | 0.258 | 0.000 | 0.000 | 0.087 | 0.000 | 0.000 | 0.560 | 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 | 136 | 143 | 221 | 0 | 0 | 209 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.05 | 1.62 | 0.00 | 0.00 | 1.54 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.211 | 0.625 | 0.000 | 0.000 | 0.087 | 0.000 | 0.000 | 0.422 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 143 | 0 | 0 | 192 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.29 | 0.00 | 0.00 | 1.73 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.175 | 0.163 | 0.000 | 0.000 | 0.080 | 0.000 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 24 | 0 | 32 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.00 | 1.10 | 0.00 | 0.00 | 1.41 | 0.00 |
time (sec) |
N/A | 0.142 | 0.017 | 0.126 | 0.000 | 0.086 | 0.000 | 0.000 | 0.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 49 | 30 | 0 | 42 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.51 | 0.00 | 0.71 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.150 | 0.058 | 0.132 | 0.000 | 0.065 | 0.000 | 0.000 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 94 | 46 | 41 | 0 | 74 | 0 | 0 | 92 | 0 |
N.S. |
1 | 1.07 | 0.52 | 0.47 | 0.00 | 0.84 | 0.00 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 0.165 | 0.074 | 0.138 | 0.000 | 0.077 | 0.000 | 0.000 | 0.349 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 133 | 59 | 54 | 0 | 86 | 0 | 0 | 93 | 0 |
N.S. |
1 | 1.14 | 0.50 | 0.46 | 0.00 | 0.74 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.184 | 0.092 | 0.136 | 0.000 | 0.092 | 0.000 | 0.000 | 0.373 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 677 | 66 | 66 | 0 | 0 | 0 | 0 | 0 | 76 | 0 |
N.S. |
1 | 0.10 | 0.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.159 | 0.014 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.446 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 648 | 65 | 65 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 0.10 | 0.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.160 | 0.014 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 656 | 65 | 65 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 0.10 | 0.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.156 | 0.015 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 652 | 735 | 70 | 0 | 0 | 0 | 104 | 0 | 47 | 0 |
N.S. |
1 | 1.13 | 0.11 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.529 | 0.015 | 0.000 | 0.000 | 0.000 | 2.771 | 0.000 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 689 | 70 | 70 | 0 | 0 | 0 | 0 | 0 | 92 | 0 |
N.S. |
1 | 0.10 | 0.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.157 | 0.015 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.371 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 131 | 70 | 104 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 0.91 | 0.49 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.184 | 0.028 | 0.231 | 0.000 | 0.000 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 92 | 70 | 94 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 0.87 | 0.66 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.160 | 0.020 | 0.162 | 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 | C | F | F | F | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 57 | 70 | 0 | 0 | 0 | 102 | 0 | 23 | 0 |
N.S. |
1 | 0.80 | 0.99 | 0.00 | 0.00 | 0.00 | 1.44 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.144 | 0.018 | 0.000 | 0.000 | 0.000 | 1.747 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 68 | 94 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.00 | 0.87 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.154 | 0.019 | 0.173 | 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 | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 70 | 105 | 0 | 0 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.151 | 0.020 | 0.181 | 0.000 | 0.000 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 123 | 70 | 113 | 0 | 0 | 0 | 0 | 88 | 0 |
N.S. |
1 | 1.07 | 0.61 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.174 | 0.022 | 0.192 | 0.000 | 0.000 | 0.000 | 0.000 | 0.253 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 164 | 70 | 114 | 0 | 0 | 0 | 0 | 108 | 0 |
N.S. |
1 | 1.11 | 0.47 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.189 | 0.024 | 0.185 | 0.000 | 0.000 | 0.000 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 236 | 70 | 477 | 0 | 194 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.27 | 0.38 | 2.56 | 0.00 | 1.04 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.304 | 0.339 | 1.283 | 0.000 | 0.079 | 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(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 207 | 68 | 0 | 0 | 221 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.26 | 0.41 | 0.00 | 0.00 | 1.35 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.283 | 1.081 | 0.000 | 0.000 | 0.084 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 27 | 0 | 31 | 0 | 0 | 45 | 38 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.00 | 0.94 | 0.00 | 0.00 | 1.36 | 1.15 |
time (sec) |
N/A | 0.128 | 4.669 | 0.138 | 0.000 | 0.074 | 0.000 | 0.000 | 0.187 | 0.412 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 45 | 32 | 0 | 44 | 0 | 0 | 65 | 46 |
N.S. |
1 | 1.00 | 0.67 | 0.48 | 0.00 | 0.66 | 0.00 | 0.00 | 0.97 | 0.69 |
time (sec) |
N/A | 0.144 | 5.841 | 0.151 | 0.000 | 0.091 | 0.000 | 0.000 | 0.187 | 0.403 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 108 | 52 | 38 | 0 | 57 | 0 | 0 | 84 | 51 |
N.S. |
1 | 1.08 | 0.52 | 0.38 | 0.00 | 0.57 | 0.00 | 0.00 | 0.84 | 0.51 |
time (sec) |
N/A | 0.158 | 6.681 | 0.155 | 0.000 | 0.088 | 0.000 | 0.000 | 0.213 | 0.453 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 149 | 57 | 43 | 0 | 68 | 0 | 0 | 104 | 57 |
N.S. |
1 | 1.12 | 0.43 | 0.32 | 0.00 | 0.51 | 0.00 | 0.00 | 0.78 | 0.43 |
time (sec) |
N/A | 0.175 | 10.097 | 0.160 | 0.000 | 0.090 | 0.000 | 0.000 | 0.223 | 0.481 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 236 | 70 | 466 | 0 | 198 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.27 | 0.38 | 2.51 | 0.00 | 1.06 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.308 | 0.381 | 1.171 | 0.000 | 0.092 | 0.000 | 0.000 | 0.174 | 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 | 164 | 207 | 70 | 0 | 0 | 221 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.26 | 0.43 | 0.00 | 0.00 | 1.35 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.293 | 0.869 | 0.000 | 0.000 | 0.096 | 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(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 27 | 0 | 31 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.00 | 1.00 | 0.00 | 0.00 | 1.45 | 0.00 |
time (sec) |
N/A | 0.130 | 2.300 | 0.141 | 0.000 | 0.068 | 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 | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 45 | 32 | 0 | 44 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.00 | 0.67 | 0.48 | 0.00 | 0.66 | 0.00 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.146 | 5.781 | 0.148 | 0.000 | 0.078 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 108 | 52 | 38 | 0 | 57 | 0 | 0 | 84 | 0 |
N.S. |
1 | 1.08 | 0.52 | 0.38 | 0.00 | 0.57 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.162 | 7.843 | 0.157 | 0.000 | 0.107 | 0.000 | 0.000 | 0.223 | 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 | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 115 | 70 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.03 | 0.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.180 | 0.022 | 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 | C | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 70 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.160 | 0.016 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | B | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 68 | 0 | 0 | 0 | 100 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 1.58 | 0.00 | 0.00 | 0.00 | 2.33 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.138 | 0.016 | 0.000 | 0.000 | 0.000 | 2.246 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 70 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.158 | 0.017 | 0.000 | 0.000 | 0.000 | 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 | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 123 | 70 | 0 | 0 | 0 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.07 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.176 | 0.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 126 | 70 | 96 | 0 | 0 | 0 | 0 | 70 | 0 |
N.S. |
1 | 0.92 | 0.51 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.183 | 0.022 | 0.184 | 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 | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 90 | 70 | 88 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.87 | 0.68 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.166 | 0.024 | 0.161 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 70 | 94 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.154 | 0.019 | 0.167 | 0.000 | 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 | C | F | F | B | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 68 | 91 | 0 | 0 | 97 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 1.48 | 1.98 | 0.00 | 0.00 | 2.11 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.141 | 0.018 | 0.212 | 0.000 | 0.000 | 4.571 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 70 | 107 | 0 | 0 | 0 | 0 | 89 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.155 | 0.025 | 0.193 | 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 | C | C | F(-2) | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 123 | 70 | 113 | 0 | 0 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.07 | 0.61 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.173 | 0.020 | 0.205 | 0.000 | 0.000 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 270 | 70 | 480 | 0 | 233 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.24 | 0.32 | 2.21 | 0.00 | 1.07 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.334 | 1.052 | 1.089 | 0.000 | 0.082 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 239 | 70 | 476 | 0 | 296 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.23 | 0.36 | 2.44 | 0.00 | 1.52 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.317 | 0.668 | 1.006 | 0.000 | 0.094 | 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 | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 36 | 27 | 0 | 31 | 0 | 0 | 43 | 27 |
N.S. |
1 | 1.00 | 1.16 | 0.87 | 0.00 | 1.00 | 0.00 | 0.00 | 1.39 | 0.87 |
time (sec) |
N/A | 0.133 | 0.021 | 0.141 | 0.000 | 0.071 | 0.000 | 0.000 | 0.181 | 0.281 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 67 | 38 | 32 | 0 | 36 | 0 | 0 | 44 | 40 |
N.S. |
1 | 1.03 | 0.58 | 0.49 | 0.00 | 0.55 | 0.00 | 0.00 | 0.68 | 0.62 |
time (sec) |
N/A | 0.148 | 2.404 | 0.139 | 0.000 | 0.080 | 0.000 | 0.000 | 0.198 | 0.375 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 108 | 50 | 38 | 0 | 56 | 0 | 0 | 85 | 46 |
N.S. |
1 | 1.10 | 0.51 | 0.39 | 0.00 | 0.57 | 0.00 | 0.00 | 0.87 | 0.47 |
time (sec) |
N/A | 0.164 | 6.159 | 0.168 | 0.000 | 0.072 | 0.000 | 0.000 | 0.216 | 0.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 274 | 70 | 468 | 0 | 235 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.24 | 0.32 | 2.12 | 0.00 | 1.06 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.337 | 0.973 | 1.086 | 0.000 | 0.108 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 241 | 70 | 456 | 0 | 298 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.22 | 0.36 | 2.31 | 0.00 | 1.51 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.320 | 0.966 | 1.052 | 0.000 | 0.090 | 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(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 27 | 0 | 31 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.00 | 0.94 | 0.00 | 0.00 | 1.30 | 0.00 |
time (sec) |
N/A | 0.130 | 1.708 | 0.141 | 0.000 | 0.092 | 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 | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 38 | 32 | 0 | 36 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 0.58 | 0.49 | 0.00 | 0.55 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.148 | 2.229 | 0.133 | 0.000 | 0.072 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 106 | 50 | 38 | 0 | 56 | 0 | 0 | 85 | 0 |
N.S. |
1 | 1.06 | 0.50 | 0.38 | 0.00 | 0.56 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.159 | 6.126 | 0.170 | 0.000 | 0.079 | 0.000 | 0.000 | 0.215 | 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 | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 151 | 70 | 0 | 0 | 0 | 0 | 0 | 109 | 0 |
N.S. |
1 | 1.09 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.193 | 0.026 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 114 | 70 | 0 | 0 | 0 | 0 | 0 | 72 | 0 |
N.S. |
1 | 1.01 | 0.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.169 | 0.021 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 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 | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 70 | 0 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.154 | 0.018 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 68 | 0 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.155 | 0.018 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 103 | 70 | 0 | 0 | 0 | 95 | 0 | 43 | 0 |
N.S. |
1 | 1.27 | 0.86 | 0.00 | 0.00 | 0.00 | 1.17 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.165 | 0.018 | 0.000 | 0.000 | 0.000 | 15.678 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 143 | 70 | 0 | 0 | 0 | 0 | 0 | 89 | 0 |
N.S. |
1 | 1.25 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.186 | 0.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 184 | 70 | 0 | 0 | 0 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.25 | 0.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.204 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 128 | 70 | 101 | 0 | 0 | 0 | 0 | 99 | 0 |
N.S. |
1 | 0.90 | 0.49 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.183 | 0.024 | 0.187 | 0.000 | 0.000 | 0.000 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 116 | 70 | 107 | 0 | 0 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.01 | 0.61 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.169 | 0.018 | 0.177 | 0.000 | 0.000 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 70 | 105 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.154 | 0.019 | 0.166 | 0.000 | 0.000 | 0.000 | 0.000 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 119 | 68 | 107 | 0 | 0 | 0 | 0 | 86 | 0 |
N.S. |
1 | 1.45 | 0.83 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 0.176 | 0.019 | 0.191 | 0.000 | 0.000 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 103 | 70 | 0 | 0 | 0 | 95 | 0 | 50 | 0 |
N.S. |
1 | 1.27 | 0.86 | 0.00 | 0.00 | 0.00 | 1.17 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.169 | 0.020 | 0.000 | 0.000 | 0.000 | 69.519 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 143 | 70 | 124 | 0 | 0 | 0 | 0 | 130 | 0 |
N.S. |
1 | 1.25 | 0.61 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.194 | 0.021 | 0.220 | 0.000 | 0.000 | 0.000 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 184 | 70 | 130 | 0 | 0 | 0 | 0 | 150 | 0 |
N.S. |
1 | 1.25 | 0.48 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.207 | 0.023 | 0.224 | 0.000 | 0.000 | 0.000 | 0.000 | 0.260 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 272 | 70 | 493 | 0 | 343 | 0 | 0 | 97 | 0 |
N.S. |
1 | 1.19 | 0.31 | 2.16 | 0.00 | 1.50 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.326 | 2.431 | 1.108 | 0.000 | 0.089 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 27 | 0 | 42 | 0 | 0 | 48 | 38 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.00 | 1.27 | 0.00 | 0.00 | 1.45 | 1.15 |
time (sec) |
N/A | 0.129 | 0.989 | 0.159 | 0.000 | 0.084 | 0.000 | 0.000 | 0.200 | 0.260 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 45 | 32 | 0 | 44 | 0 | 0 | 64 | 38 |
N.S. |
1 | 1.00 | 0.67 | 0.48 | 0.00 | 0.66 | 0.00 | 0.00 | 0.96 | 0.57 |
time (sec) |
N/A | 0.146 | 2.333 | 0.150 | 0.000 | 0.080 | 0.000 | 0.000 | 0.212 | 0.382 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 108 | 50 | 38 | 0 | 56 | 0 | 0 | 82 | 45 |
N.S. |
1 | 1.08 | 0.50 | 0.38 | 0.00 | 0.56 | 0.00 | 0.00 | 0.82 | 0.45 |
time (sec) |
N/A | 0.160 | 5.178 | 0.219 | 0.000 | 0.087 | 0.000 | 0.000 | 0.214 | 0.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 149 | 57 | 43 | 0 | 54 | 0 | 0 | 64 | 56 |
N.S. |
1 | 1.12 | 0.43 | 0.32 | 0.00 | 0.41 | 0.00 | 0.00 | 0.48 | 0.42 |
time (sec) |
N/A | 0.175 | 7.124 | 0.151 | 0.000 | 0.074 | 0.000 | 0.000 | 0.211 | 0.415 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 190 | 103 | 0 | 0 | 209 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.26 | 0.68 | 0.00 | 0.00 | 1.38 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.300 | 0.923 | 0.000 | 0.000 | 0.078 | 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 | 66 | 70 | 70 | 0 | 0 | 0 | 0 | 0 | 71 | 0 |
N.S. |
1 | 1.06 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.170 | 0.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.240 | 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 | 66 | 68 | 68 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.03 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.157 | 0.016 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.814 | 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 | 66 | 58 | 67 | 0 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.88 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.156 | 0.018 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.361 | 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 | 64 | 67 | 67 | 0 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.05 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.154 | 0.018 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.298 | 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 | 66 | 70 | 70 | 0 | 0 | 0 | 0 | 0 | 137 | 0 |
N.S. |
1 | 1.06 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.08 | 0.00 |
time (sec) |
N/A | 0.156 | 0.018 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.504 | 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 | 66 | 70 | 70 | 0 | 0 | 0 | 0 | 0 | 209 | 0 |
N.S. |
1 | 1.06 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.17 | 0.00 |
time (sec) |
N/A | 0.155 | 0.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.629 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 77 | 103 | 167 | 128 | 819 | 256 | 132 | 133 |
N.S. |
1 | 1.00 | 0.93 | 1.24 | 2.01 | 1.54 | 9.87 | 3.08 | 1.59 | 1.60 |
time (sec) |
N/A | 0.200 | 0.058 | 0.148 | 0.048 | 0.085 | 0.408 | 0.130 | 0.165 | 0.296 |
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 | 53 | 53 | 43 | 47 | 81 | 58 | 245 | 103 | 57 | 66 |
N.S. |
1 | 1.00 | 0.81 | 0.89 | 1.53 | 1.09 | 4.62 | 1.94 | 1.08 | 1.25 |
time (sec) |
N/A | 0.172 | 0.048 | 0.119 | 0.038 | 0.096 | 0.300 | 0.127 | 0.165 | 0.196 |
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 | 52 | 52 | 52 | 0 | 0 | 0 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.152 | 0.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 52 | 0 | 0 | 0 | 0 | 0 | 364 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 7.00 | 0.00 |
time (sec) |
N/A | 0.149 | 0.036 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 68 | 67 | 0 | 0 | 0 | 0 | 0 | 619 | 0 |
N.S. |
1 | 0.91 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 8.25 | 0.00 |
time (sec) |
N/A | 0.163 | 0.091 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 68 | 67 | 0 | 0 | 0 | 0 | 0 | 340 | 0 |
N.S. |
1 | 0.91 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.53 | 0.00 |
time (sec) |
N/A | 0.158 | 0.065 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 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 | 75 | 65 | 64 | 0 | 0 | 0 | 0 | 0 | 148 | 0 |
N.S. |
1 | 0.87 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.97 | 0.00 |
time (sec) |
N/A | 0.159 | 0.074 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 66 | 65 | 0 | 0 | 0 | 0 | 0 | 405 | 0 |
N.S. |
1 | 0.86 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.26 | 0.00 |
time (sec) |
N/A | 0.156 | 0.098 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 59 | 59 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.02 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.161 | 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 | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 41 | 53 | 0 | 0 | 0 | 124 | 0 | 102 | 0 |
N.S. |
1 | 0.75 | 0.96 | 0.00 | 0.00 | 0.00 | 2.25 | 0.00 | 1.85 | 0.00 |
time (sec) |
N/A | 0.150 | 0.068 | 0.000 | 0.000 | 0.000 | 1.957 | 0.000 | 0.161 | 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 | 67 | 57 | 72 | 0 | 0 | 0 | 146 | 0 | 143 | 0 |
N.S. |
1 | 0.85 | 1.07 | 0.00 | 0.00 | 0.00 | 2.18 | 0.00 | 2.13 | 0.00 |
time (sec) |
N/A | 0.160 | 0.038 | 0.000 | 0.000 | 0.000 | 2.510 | 0.000 | 0.164 | 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 | 20 | 20 | 20 | 0 | 0 | 0 | 39 | 0 | 103 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 1.95 | 0.00 | 5.15 | 0.00 |
time (sec) |
N/A | 0.128 | 0.055 | 0.000 | 0.000 | 0.000 | 2.094 | 0.000 | 0.162 | 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 | 32 | 32 | 32 | 0 | 0 | 0 | 37 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 1.16 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.137 | 0.044 | 0.000 | 0.000 | 0.000 | 5.034 | 0.000 | 0.162 | 0.000 |