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 | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 133 | 111 | 77 | 292 | 70 | 0 | 113 | 106 |
N.S. |
1 | 1.03 | 0.86 | 0.60 | 2.26 | 0.54 | 0.00 | 0.88 | 0.82 |
time (sec) |
N/A | 0.574 | 1.728 | 0.955 | 0.284 | 0.261 | 0.000 | 0.388 | 16.396 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 102 | 173 | 65 | 227 | 83 | 0 | 101 | 98 |
N.S. |
1 | 0.94 | 1.60 | 0.60 | 2.10 | 0.77 | 0.00 | 0.94 | 0.91 |
time (sec) |
N/A | 0.602 | 0.614 | 0.909 | 0.290 | 0.283 | 0.000 | 0.363 | 14.959 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 101 | 177 | 66 | 164 | 99 | 0 | 96 | 115 |
N.S. |
1 | 1.04 | 1.82 | 0.68 | 1.69 | 1.02 | 0.00 | 0.99 | 1.19 |
time (sec) |
N/A | 0.593 | 0.491 | 1.064 | 0.290 | 0.271 | 0.000 | 0.352 | 13.317 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 0 | 137 | 58 | 90 | 95 | 0 | 73 | 84 |
N.S. |
1 | 0.00 | 1.54 | 0.65 | 1.01 | 1.07 | 0.00 | 0.82 | 0.94 |
time (sec) |
N/A | 0.000 | 1.003 | 0.575 | 0.220 | 0.268 | 0.000 | 0.360 | 13.481 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 0 | 175 | 60 | 92 | 146 | 0 | 73 | 105 |
N.S. |
1 | 0.00 | 1.70 | 0.58 | 0.89 | 1.42 | 0.00 | 0.71 | 1.02 |
time (sec) |
N/A | 0.000 | 1.354 | 0.806 | 0.203 | 0.255 | 0.000 | 0.398 | 13.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 0 | 223 | 110 | 174 | 191 | 0 | 134 | 201 |
N.S. |
1 | 0.00 | 1.76 | 0.87 | 1.37 | 1.50 | 0.00 | 1.06 | 1.58 |
time (sec) |
N/A | 0.000 | 1.405 | 0.899 | 0.201 | 0.257 | 0.000 | 0.428 | 13.935 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 145 | 0 | 265 | 136 | 214 | 214 | 0 | 163 | 249 |
N.S. |
1 | 0.00 | 1.83 | 0.94 | 1.48 | 1.48 | 0.00 | 1.12 | 1.72 |
time (sec) |
N/A | 0.000 | 3.100 | 1.111 | 0.200 | 0.259 | 0.000 | 0.404 | 14.481 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 157 | 151 | 106 | 210 | 0 | 649 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.68 | 1.34 | 0.00 | 4.13 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.746 | 0.518 | 10.939 | 0.000 | 0.360 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 154 | 149 | 170 | 154 | 0 | 603 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 1.10 | 1.00 | 0.00 | 3.92 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.739 | 0.622 | 10.279 | 0.000 | 0.366 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 97 | 69 | 142 | 0 | 555 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.66 | 1.37 | 0.00 | 5.34 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.582 | 0.279 | 8.324 | 0.000 | 0.375 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 97 | 226 | 115 | 0 | 550 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 2.19 | 1.12 | 0.00 | 5.34 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.607 | 0.951 | 7.324 | 0.000 | 0.194 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-1) | C | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 150 | 143 | 201 | 0 | 670 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.92 | 1.30 | 0.00 | 4.32 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.786 | 0.567 | 10.071 | 0.000 | 0.198 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 160 | 156 | 120 | 164 | 0 | 705 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.75 | 1.02 | 0.00 | 4.41 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.772 | 0.569 | 11.421 | 0.000 | 0.200 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 194 | 194 | 205 | 265 | 0 | 769 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.06 | 1.37 | 0.00 | 3.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.703 | 17.639 | 19.127 | 0.000 | 0.374 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 192 | 192 | 204 | 201 | 0 | 721 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.06 | 1.05 | 0.00 | 3.76 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.659 | 27.023 | 13.577 | 0.000 | 0.375 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 168 | 220 | 0 | 677 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.22 | 1.59 | 0.00 | 4.91 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.559 | 11.755 | 14.067 | 0.000 | 0.387 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 164 | 163 | 0 | 660 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.18 | 1.17 | 0.00 | 4.75 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.587 | 19.808 | 11.951 | 0.000 | 0.192 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-1) | C | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 224 | 224 | 135 | 238 | 0 | 790 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.60 | 1.06 | 0.00 | 3.53 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.719 | 19.948 | 17.572 | 0.000 | 0.205 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-1) | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 234 | 234 | 169 | 301 | 0 | 849 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.72 | 1.29 | 0.00 | 3.63 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.701 | 18.127 | 17.500 | 0.000 | 0.211 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 142 | 122 | 128 | 0 | 126 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.88 | 0.92 | 0.00 | 0.91 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.848 | 1.735 | 5.149 | 0.000 | 0.094 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 106 | 193 | 173 | 0 | 111 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.86 | 1.66 | 0.00 | 1.07 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.674 | 3.189 | 5.362 | 0.000 | 0.100 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 104 | 69 | 112 | 0 | 88 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.68 | 1.10 | 0.00 | 0.86 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.682 | 1.261 | 3.802 | 0.000 | 0.092 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 103 | 210 | 149 | 0 | 123 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 2.21 | 1.57 | 0.00 | 1.29 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.693 | 4.750 | 4.590 | 0.000 | 0.093 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 109 | 77 | 121 | 0 | 108 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.76 | 1.20 | 0.00 | 1.07 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.744 | 1.132 | 4.429 | 0.000 | 0.084 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-1) | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 135 | 141 | 124 | 187 | 0 | 163 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.92 | 1.39 | 0.00 | 1.21 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.851 | 1.518 | 5.841 | 0.000 | 0.093 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-1) | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 135 | 145 | 91 | 136 | 0 | 215 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.67 | 1.01 | 0.00 | 1.59 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.860 | 1.738 | 4.814 | 0.000 | 0.114 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 162 | 168 | 94 | 145 | 0 | 125 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.58 | 0.90 | 0.00 | 0.77 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.849 | 2.539 | 6.867 | 0.000 | 0.094 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 187 | 198 | 446 | 173 | 0 | 171 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 2.39 | 0.93 | 0.00 | 0.91 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.890 | 7.280 | 7.114 | 0.000 | 0.099 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 189 | 200 | 119 | 153 | 0 | 140 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.63 | 0.81 | 0.00 | 0.74 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.864 | 2.836 | 5.378 | 0.000 | 0.101 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 188 | 202 | 234 | 205 | 0 | 179 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 1.24 | 1.09 | 0.00 | 0.95 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.876 | 6.265 | 5.924 | 0.000 | 0.099 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-1) | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 190 | 204 | 82 | 148 | 0 | 165 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.43 | 0.78 | 0.00 | 0.87 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.866 | 1.967 | 5.886 | 0.000 | 0.091 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-1) | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 224 | 235 | 163 | 213 | 0 | 222 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.73 | 0.95 | 0.00 | 0.99 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.983 | 1.991 | 6.276 | 0.000 | 0.093 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-1) | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 224 | 235 | 113 | 160 | 0 | 236 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.50 | 0.71 | 0.00 | 1.05 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.948 | 1.648 | 6.726 | 0.000 | 0.095 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 247 | 247 | 160 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.661 | 0.687 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 195 | 195 | 127 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.577 | 0.423 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 97 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.486 | 0.127 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 383 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 3.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.551 | 16.385 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 207 | 216 | 612 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 2.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.875 | 4.799 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 236 | 245 | 995 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 4.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.924 | 6.094 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 106 | 168 | 1243 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.58 | 11.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.701 | 9.562 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 107 | 169 | 433 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.58 | 4.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.617 | 2.373 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 115 | 178 | 277 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.55 | 2.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.612 | 2.849 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 120 | 180 | 484 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.50 | 4.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.661 | 2.319 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 130 | 197 | 276 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.52 | 2.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.589 | 2.063 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 180 | 173 | 116 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.359 | 0.842 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 123 | 127 | 84 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.302 | 0.378 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 83 | 84 | 67 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.276 | 0.119 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 42 | 0 | 0 | 0 | 0 | 0 | 64 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.52 |
time (sec) |
N/A | 0.229 | 0.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 14.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 92 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.245 | 0.506 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 112 | 123 | 179 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.305 | 1.068 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 240 | 245 | 492 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 2.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.429 | 3.891 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 230 | 317 | 7069 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.38 | 30.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.809 | 21.752 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 95 | 121 | 4297 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.27 | 45.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.690 | 17.343 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 142 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.475 | 1.509 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 349 | 441 | 350 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.26 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.692 | 4.574 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 382 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 3.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.521 | 16.603 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 214 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.521 | 3.044 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 212 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.507 | 3.532 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 105 | 133 | 212 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.27 | 2.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.516 | 4.385 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 124 | 113 | 87 | 91 | 93 | 0 | 317 | 89 |
N.S. |
1 | 1.04 | 0.95 | 0.73 | 0.76 | 0.78 | 0.00 | 2.66 | 0.75 |
time (sec) |
N/A | 0.376 | 0.146 | 1.855 | 0.205 | 0.293 | 0.000 | 0.339 | 14.350 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 93 | 83 | 67 | 69 | 71 | 0 | 248 | 67 |
N.S. |
1 | 1.07 | 0.95 | 0.77 | 0.79 | 0.82 | 0.00 | 2.85 | 0.77 |
time (sec) |
N/A | 0.352 | 0.067 | 1.576 | 0.196 | 0.276 | 0.000 | 0.326 | 13.937 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 64 | 57 | 47 | 47 | 49 | 0 | 66 | 45 |
N.S. |
1 | 1.10 | 0.98 | 0.81 | 0.81 | 0.84 | 0.00 | 1.14 | 0.78 |
time (sec) |
N/A | 0.333 | 0.037 | 1.639 | 0.198 | 0.273 | 0.000 | 0.314 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 25 | 37 | 26 | 23 | 25 | 0 | 32 | 23 |
N.S. |
1 | 0.96 | 1.42 | 1.00 | 0.88 | 0.96 | 0.00 | 1.23 | 0.88 |
time (sec) |
N/A | 0.267 | 0.025 | 0.782 | 0.189 | 0.277 | 0.000 | 0.295 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 65 | 33 | 45 | 51 | 0 | 61 | 63 |
N.S. |
1 | 1.00 | 2.50 | 1.27 | 1.73 | 1.96 | 0.00 | 2.35 | 2.42 |
time (sec) |
N/A | 0.377 | 0.019 | 0.567 | 0.196 | 0.280 | 0.000 | 0.281 | 0.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 64 | 62 | 120 | 61 | 71 | 123 | 0 | 169 | 76 |
N.S. |
1 | 0.97 | 1.88 | 0.95 | 1.11 | 1.92 | 0.00 | 2.64 | 1.19 |
time (sec) |
N/A | 0.514 | 0.015 | 1.155 | 0.199 | 0.290 | 0.000 | 0.297 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 101 | 176 | 83 | 110 | 201 | 0 | 266 | 117 |
N.S. |
1 | 1.01 | 1.76 | 0.83 | 1.10 | 2.01 | 0.00 | 2.66 | 1.17 |
time (sec) |
N/A | 0.635 | 0.020 | 1.296 | 0.237 | 0.264 | 0.000 | 0.318 | 13.909 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 139 | 232 | 103 | 143 | 284 | 0 | 357 | 148 |
N.S. |
1 | 0.99 | 1.66 | 0.74 | 1.02 | 2.03 | 0.00 | 2.55 | 1.06 |
time (sec) |
N/A | 0.772 | 0.053 | 1.245 | 0.210 | 0.271 | 0.000 | 0.310 | 13.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 125 | 118 | 96 | 106 | 102 | 0 | 228 | 332 |
N.S. |
1 | 0.98 | 0.93 | 0.76 | 0.83 | 0.80 | 0.00 | 1.80 | 2.61 |
time (sec) |
N/A | 0.612 | 0.465 | 1.887 | 0.217 | 0.283 | 0.000 | 0.323 | 15.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 87 | 86 | 76 | 81 | 79 | 0 | 172 | 267 |
N.S. |
1 | 0.98 | 0.97 | 0.85 | 0.91 | 0.89 | 0.00 | 1.93 | 3.00 |
time (sec) |
N/A | 0.498 | 0.174 | 1.726 | 0.201 | 0.283 | 0.000 | 0.300 | 14.541 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 49 | 54 | 55 | 59 | 55 | 0 | 114 | 83 |
N.S. |
1 | 0.96 | 1.06 | 1.08 | 1.16 | 1.08 | 0.00 | 2.24 | 1.63 |
time (sec) |
N/A | 0.391 | 0.122 | 1.217 | 0.199 | 0.284 | 0.000 | 0.289 | 13.933 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 35 | 41 | 42 | 50 | 63 | 0 | 77 | 60 |
N.S. |
1 | 0.95 | 1.11 | 1.14 | 1.35 | 1.70 | 0.00 | 2.08 | 1.62 |
time (sec) |
N/A | 0.426 | 0.079 | 1.191 | 0.197 | 0.281 | 0.000 | 0.303 | 14.566 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 60 | 69 | 63 | 76 | 125 | 0 | 133 | 101 |
N.S. |
1 | 0.87 | 1.00 | 0.91 | 1.10 | 1.81 | 0.00 | 1.93 | 1.46 |
time (sec) |
N/A | 0.475 | 0.038 | 0.967 | 0.206 | 0.285 | 0.000 | 0.315 | 14.849 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 84 | 91 | 83 | 96 | 174 | 0 | 194 | 142 |
N.S. |
1 | 0.83 | 0.90 | 0.82 | 0.95 | 1.72 | 0.00 | 1.92 | 1.41 |
time (sec) |
N/A | 0.485 | 0.045 | 1.056 | 0.206 | 0.277 | 0.000 | 0.314 | 14.363 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 128 | 112 | 120 | 105 | 125 | 0 | 418 | 104 |
N.S. |
1 | 1.03 | 0.90 | 0.97 | 0.85 | 1.01 | 0.00 | 3.37 | 0.84 |
time (sec) |
N/A | 0.462 | 2.221 | 1.802 | 0.206 | 0.292 | 0.000 | 0.389 | 13.948 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 82 | 72 | 90 | 71 | 92 | 0 | 100 | 69 |
N.S. |
1 | 1.02 | 0.90 | 1.12 | 0.89 | 1.15 | 0.00 | 1.25 | 0.86 |
time (sec) |
N/A | 0.409 | 0.678 | 1.799 | 0.199 | 0.285 | 0.000 | 0.357 | 14.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 41 | 37 | 40 | 40 | 50 | 0 | 50 | 40 |
N.S. |
1 | 0.98 | 0.88 | 0.95 | 0.95 | 1.19 | 0.00 | 1.19 | 0.95 |
time (sec) |
N/A | 0.332 | 0.107 | 0.538 | 0.203 | 0.294 | 0.000 | 0.314 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 89 | 91 | 66 | 73 | 97 | 0 | 124 | 62 |
N.S. |
1 | 1.20 | 1.23 | 0.89 | 0.99 | 1.31 | 0.00 | 1.68 | 0.84 |
time (sec) |
N/A | 0.435 | 0.833 | 0.511 | 0.193 | 0.265 | 0.000 | 0.310 | 14.601 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 148 | 329 | 116 | 119 | 205 | 0 | 314 | 120 |
N.S. |
1 | 1.30 | 2.89 | 1.02 | 1.04 | 1.80 | 0.00 | 2.75 | 1.05 |
time (sec) |
N/A | 0.578 | 1.385 | 0.942 | 0.201 | 0.295 | 0.000 | 0.326 | 0.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 175 | 188 | 193 | 163 | 173 | 176 | 0 | 379 | 231 |
N.S. |
1 | 1.07 | 1.10 | 0.93 | 0.99 | 1.01 | 0.00 | 2.17 | 1.32 |
time (sec) |
N/A | 0.901 | 2.140 | 2.136 | 0.289 | 0.291 | 0.000 | 0.378 | 16.744 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 178 | 199 | 157 | 133 | 125 | 142 | 0 | 285 | 207 |
N.S. |
1 | 1.12 | 0.88 | 0.75 | 0.70 | 0.80 | 0.00 | 1.60 | 1.16 |
time (sec) |
N/A | 1.429 | 1.457 | 1.801 | 0.287 | 0.289 | 0.000 | 0.372 | 14.822 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 121 | 77 | 80 | 108 | 0 | 159 | 143 |
N.S. |
1 | 1.00 | 1.57 | 1.00 | 1.04 | 1.40 | 0.00 | 2.06 | 1.86 |
time (sec) |
N/A | 0.384 | 0.975 | 1.385 | 0.291 | 0.282 | 0.000 | 0.334 | 14.663 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 54 | 138 | 76 | 73 | 104 | 0 | 167 | 108 |
N.S. |
1 | 0.92 | 2.34 | 1.29 | 1.24 | 1.76 | 0.00 | 2.83 | 1.83 |
time (sec) |
N/A | 0.761 | 1.143 | 0.995 | 0.201 | 0.267 | 0.000 | 0.333 | 14.577 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 87 | 259 | 116 | 112 | 178 | 0 | 226 | 182 |
N.S. |
1 | 0.87 | 2.59 | 1.16 | 1.12 | 1.78 | 0.00 | 2.26 | 1.82 |
time (sec) |
N/A | 0.694 | 1.283 | 1.667 | 0.203 | 0.274 | 0.000 | 0.337 | 14.683 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 143 | 122 | 368 | 154 | 143 | 241 | 0 | 326 | 248 |
N.S. |
1 | 0.85 | 2.57 | 1.08 | 1.00 | 1.69 | 0.00 | 2.28 | 1.73 |
time (sec) |
N/A | 0.781 | 1.439 | 1.763 | 0.208 | 0.277 | 0.000 | 0.361 | 14.213 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 170 | 169 | 154 | 174 | 142 | 175 | 0 | 695 | 143 |
N.S. |
1 | 0.99 | 0.91 | 1.02 | 0.84 | 1.03 | 0.00 | 4.09 | 0.84 |
time (sec) |
N/A | 0.543 | 1.390 | 2.446 | 0.199 | 0.284 | 0.000 | 0.435 | 13.583 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 103 | 102 | 116 | 98 | 123 | 0 | 128 | 99 |
N.S. |
1 | 0.89 | 0.88 | 1.00 | 0.84 | 1.06 | 0.00 | 1.10 | 0.85 |
time (sec) |
N/A | 0.404 | 0.860 | 2.534 | 0.202 | 0.292 | 0.000 | 0.398 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 64 | 61 | 56 | 57 | 57 | 67 | 0 | 66 | 57 |
N.S. |
1 | 0.95 | 0.88 | 0.89 | 0.89 | 1.05 | 0.00 | 1.03 | 0.89 |
time (sec) |
N/A | 0.350 | 0.154 | 0.823 | 0.205 | 0.269 | 0.000 | 0.346 | 13.584 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 118 | 89 | 92 | 112 | 139 | 0 | 250 | 85 |
N.S. |
1 | 1.16 | 0.87 | 0.90 | 1.10 | 1.36 | 0.00 | 2.45 | 0.83 |
time (sec) |
N/A | 0.527 | 0.957 | 0.651 | 0.198 | 0.274 | 0.000 | 0.344 | 0.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 162 | 188 | 669 | 162 | 171 | 290 | 0 | 482 | 159 |
N.S. |
1 | 1.16 | 4.13 | 1.00 | 1.06 | 1.79 | 0.00 | 2.98 | 0.98 |
time (sec) |
N/A | 0.719 | 7.220 | 1.311 | 0.195 | 0.285 | 0.000 | 0.379 | 13.956 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 299 | 299 | 818 | 234 | 242 | 241 | 0 | 563 | 373 |
N.S. |
1 | 1.00 | 2.74 | 0.78 | 0.81 | 0.81 | 0.00 | 1.88 | 1.25 |
time (sec) |
N/A | 0.698 | 7.091 | 2.570 | 0.287 | 0.302 | 0.000 | 0.438 | 14.780 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 236 | 260 | 696 | 194 | 183 | 196 | 0 | 431 | 281 |
N.S. |
1 | 1.10 | 2.95 | 0.82 | 0.78 | 0.83 | 0.00 | 1.83 | 1.19 |
time (sec) |
N/A | 1.836 | 6.749 | 2.285 | 0.291 | 0.301 | 0.000 | 0.388 | 14.697 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 138 | 131 | 327 | 128 | 129 | 151 | 0 | 346 | 202 |
N.S. |
1 | 0.95 | 2.37 | 0.93 | 0.93 | 1.09 | 0.00 | 2.51 | 1.46 |
time (sec) |
N/A | 1.226 | 1.203 | 1.856 | 0.290 | 0.284 | 0.000 | 0.359 | 13.879 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 121 | 406 | 129 | 139 | 151 | 0 | 225 | 181 |
N.S. |
1 | 0.91 | 3.05 | 0.97 | 1.05 | 1.14 | 0.00 | 1.69 | 1.36 |
time (sec) |
N/A | 0.717 | 2.442 | 1.049 | 0.208 | 0.279 | 0.000 | 0.352 | 14.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 205 | 205 | 610 | 187 | 190 | 260 | 0 | 361 | 260 |
N.S. |
1 | 1.00 | 2.98 | 0.91 | 0.93 | 1.27 | 0.00 | 1.76 | 1.27 |
time (sec) |
N/A | 0.762 | 1.438 | 1.600 | 0.200 | 0.272 | 0.000 | 0.379 | 13.855 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 279 | 279 | 812 | 243 | 230 | 354 | 0 | 498 | 363 |
N.S. |
1 | 1.00 | 2.91 | 0.87 | 0.82 | 1.27 | 0.00 | 1.78 | 1.30 |
time (sec) |
N/A | 0.872 | 2.156 | 1.872 | 0.204 | 0.273 | 0.000 | 0.418 | 13.684 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 223 | 202 | 282 | 275 | 224 | 222 | 0 | 1559 | 249 |
N.S. |
1 | 0.91 | 1.26 | 1.23 | 1.00 | 1.00 | 0.00 | 6.99 | 1.12 |
time (sec) |
N/A | 0.514 | 1.809 | 1.355 | 0.197 | 0.284 | 0.000 | 0.361 | 0.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 152 | 137 | 172 | 160 | 141 | 140 | 0 | 867 | 151 |
N.S. |
1 | 0.90 | 1.13 | 1.05 | 0.93 | 0.92 | 0.00 | 5.70 | 0.99 |
time (sec) |
N/A | 0.452 | 0.311 | 0.834 | 0.198 | 0.280 | 0.000 | 0.326 | 13.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 80 | 89 | 82 | 80 | 78 | 0 | 102 | 79 |
N.S. |
1 | 0.90 | 1.00 | 0.92 | 0.90 | 0.88 | 0.00 | 1.15 | 0.89 |
time (sec) |
N/A | 0.399 | 0.098 | 0.775 | 0.194 | 0.288 | 0.000 | 0.326 | 13.510 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 31 | 30 | 48 | 33 | 31 | 0 | 38 | 30 |
N.S. |
1 | 0.91 | 0.88 | 1.41 | 0.97 | 0.91 | 0.00 | 1.12 | 0.88 |
time (sec) |
N/A | 0.322 | 0.018 | 0.471 | 0.198 | 0.274 | 0.000 | 0.300 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 76 | 63 | 57 | 64 | 64 | 0 | 100 | 68 |
N.S. |
1 | 1.03 | 0.85 | 0.77 | 0.86 | 0.86 | 0.00 | 1.35 | 0.92 |
time (sec) |
N/A | 0.375 | 0.225 | 0.722 | 0.198 | 0.282 | 0.000 | 0.328 | 13.674 |