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 | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 62 | 62 | 65 | 0 | 453 | 0 | 40 | 40 | 0 |
N.S. |
1 | 0.42 | 0.42 | 0.44 | 0.00 | 3.06 | 0.00 | 0.27 | 0.27 | 0.00 |
time (sec) |
N/A | 0.732 | 0.044 | 0.115 | 0.000 | 0.115 | 0.000 | 0.113 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 72 | 72 | 73 | 0 | 482 | 0 | 49 | 48 | 0 |
N.S. |
1 | 0.39 | 0.39 | 0.39 | 0.00 | 2.58 | 0.00 | 0.26 | 0.26 | 0.00 |
time (sec) |
N/A | 0.753 | 0.047 | 0.115 | 0.000 | 0.138 | 0.000 | 0.137 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 102 | 87 | 108 | 0 | 0 | 0 | 86 | 82 | 0 |
N.S. |
1 | 0.39 | 0.33 | 0.41 | 0.00 | 0.00 | 0.00 | 0.33 | 0.31 | 0.00 |
time (sec) |
N/A | 0.837 | 0.083 | 0.119 | 0.000 | 0.000 | 0.000 | 0.117 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 91 | 77 | 99 | 0 | 0 | 0 | 74 | 73 | 0 |
N.S. |
1 | 0.42 | 0.35 | 0.45 | 0.00 | 0.00 | 0.00 | 0.34 | 0.33 | 0.00 |
time (sec) |
N/A | 0.821 | 0.075 | 0.118 | 0.000 | 0.000 | 0.000 | 0.121 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 81 | 71 | 91 | 0 | 0 | 0 | 54 | 64 | 0 |
N.S. |
1 | 0.46 | 0.40 | 0.52 | 0.00 | 0.00 | 0.00 | 0.31 | 0.36 | 0.00 |
time (sec) |
N/A | 0.806 | 0.058 | 0.116 | 0.000 | 0.000 | 0.000 | 0.137 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 76 | 76 | 79 | 0 | 0 | 0 | 46 | 57 | 0 |
N.S. |
1 | 0.55 | 0.55 | 0.57 | 0.00 | 0.00 | 0.00 | 0.33 | 0.41 | 0.00 |
time (sec) |
N/A | 0.796 | 0.050 | 0.117 | 0.000 | 0.000 | 0.000 | 0.117 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 60 | 60 | 77 | 0 | 348 | 0 | 46 | 55 | 0 |
N.S. |
1 | 0.66 | 0.66 | 0.85 | 0.00 | 3.82 | 0.00 | 0.51 | 0.60 | 0.00 |
time (sec) |
N/A | 0.686 | 0.042 | 0.115 | 0.000 | 0.102 | 0.000 | 0.125 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 60 | 60 | 77 | 0 | 343 | 0 | 0 | 55 | 0 |
N.S. |
1 | 0.66 | 0.66 | 0.85 | 0.00 | 3.77 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.584 | 0.035 | 0.112 | 0.000 | 0.110 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 69 | 65 | 86 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 0.42 | 0.39 | 0.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.767 | 0.059 | 0.118 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 79 | 76 | 111 | 0 | 0 | 0 | 0 | 90 | 0 |
N.S. |
1 | 0.38 | 0.37 | 0.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.791 | 0.068 | 0.119 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 96 | 91 | 131 | 0 | 0 | 0 | 0 | 106 | 0 |
N.S. |
1 | 0.38 | 0.36 | 0.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.830 | 0.082 | 0.117 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 106 | 99 | 140 | 0 | 0 | 0 | 0 | 115 | 0 |
N.S. |
1 | 0.36 | 0.33 | 0.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.849 | 0.091 | 0.119 | 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 | A | A | F | F | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 312 | 121 | 97 | 179 | 0 | 0 | 0 | 118 | 155 | 0 |
N.S. |
1 | 0.39 | 0.31 | 0.57 | 0.00 | 0.00 | 0.00 | 0.38 | 0.50 | 0.00 |
time (sec) |
N/A | 0.876 | 0.141 | 0.119 | 0.000 | 0.000 | 0.000 | 0.155 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 109 | 87 | 171 | 0 | 0 | 0 | 0 | 147 | 0 |
N.S. |
1 | 0.41 | 0.32 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.843 | 0.121 | 0.118 | 0.000 | 0.000 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 105 | 87 | 155 | 0 | 0 | 0 | 0 | 139 | 0 |
N.S. |
1 | 0.45 | 0.38 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.847 | 0.105 | 0.118 | 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 | A | A | F | A | F | F(-2) | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 89 | 85 | 155 | 0 | 461 | 0 | 0 | 139 | 0 |
N.S. |
1 | 0.48 | 0.46 | 0.84 | 0.00 | 2.51 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.819 | 0.068 | 0.118 | 0.000 | 0.168 | 0.000 | 0.000 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 89 | 84 | 150 | 0 | 457 | 0 | 0 | 134 | 0 |
N.S. |
1 | 0.48 | 0.46 | 0.82 | 0.00 | 2.48 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.821 | 0.069 | 0.119 | 0.000 | 0.179 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 74 | 60 | 150 | 0 | 459 | 0 | 0 | 134 | 0 |
N.S. |
1 | 0.54 | 0.44 | 1.09 | 0.00 | 3.35 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.704 | 0.068 | 0.118 | 0.000 | 0.177 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 89 | 85 | 155 | 0 | 455 | 0 | 0 | 139 | 0 |
N.S. |
1 | 0.48 | 0.46 | 0.84 | 0.00 | 2.47 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.625 | 0.053 | 0.115 | 0.000 | 0.163 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 92 | 86 | 182 | 0 | 0 | 0 | 0 | 166 | 0 |
N.S. |
1 | 0.37 | 0.34 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.840 | 0.080 | 0.118 | 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 | A | A | F | F | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 295 | 104 | 97 | 211 | 0 | 0 | 0 | 0 | 195 | 0 |
N.S. |
1 | 0.35 | 0.33 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.847 | 0.094 | 0.118 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 345 | 122 | 115 | 231 | 0 | 0 | 0 | 0 | 215 | 0 |
N.S. |
1 | 0.35 | 0.33 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.879 | 0.136 | 0.118 | 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 | A | A | F | A | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 118 | 103 | 227 | 0 | 567 | 0 | 0 | 226 | 0 |
N.S. |
1 | 0.43 | 0.37 | 0.82 | 0.00 | 2.05 | 0.00 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 0.740 | 0.091 | 0.121 | 0.000 | 0.159 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 78 | 82 | 227 | 0 | 0 | 316 | 0 | 152 | 0 |
N.S. |
1 | 0.98 | 1.02 | 2.84 | 0.00 | 0.00 | 3.95 | 0.00 | 1.90 | 0.00 |
time (sec) |
N/A | 0.496 | 0.042 | 0.129 | 0.000 | 0.000 | 6.292 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 72 | 143 | 0 | 0 | 204 | 0 | 98 | 0 |
N.S. |
1 | 1.00 | 0.95 | 1.88 | 0.00 | 0.00 | 2.68 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.470 | 0.045 | 0.104 | 0.000 | 0.000 | 3.456 | 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 | 80 | 78 | 82 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 0.98 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.492 | 0.034 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 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 | 80 | 78 | 82 | 0 | 0 | 0 | 0 | 0 | 76 | 0 |
N.S. |
1 | 0.98 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.496 | 0.038 | 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 | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 78 | 82 | 0 | 0 | 0 | 0 | 0 | 116 | 0 |
N.S. |
1 | 0.98 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.45 | 0.00 |
time (sec) |
N/A | 0.497 | 0.038 | 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 | A | A | A | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 70 | 99 | 82 | 285 | 1760 | 460 | 336 | 374 |
N.S. |
1 | 1.00 | 0.85 | 1.21 | 1.00 | 3.48 | 21.46 | 5.61 | 4.10 | 4.56 |
time (sec) |
N/A | 0.545 | 0.055 | 0.125 | 0.029 | 0.144 | 0.461 | 0.142 | 0.153 | 24.791 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 54 | 65 | 54 | 128 | 585 | 197 | 138 | 160 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 1.00 | 2.37 | 10.83 | 3.65 | 2.56 | 2.96 |
time (sec) |
N/A | 0.508 | 0.107 | 0.047 | 0.031 | 0.123 | 0.348 | 0.139 | 0.156 | 24.599 |
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 | 24 | 24 | 20 | 26 | 24 | 29 | 82 | 41 | 25 | 26 |
N.S. |
1 | 1.00 | 0.83 | 1.08 | 1.00 | 1.21 | 3.42 | 1.71 | 1.04 | 1.08 |
time (sec) |
N/A | 0.436 | 0.018 | 0.028 | 0.030 | 0.066 | 0.189 | 0.129 | 0.147 | 24.770 |
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 | 22 | 22 | 22 | 100 | 0 | 0 | 44 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.00 | 4.55 | 0.00 | 0.00 | 2.00 | 0.00 | 1.50 | 0.00 |
time (sec) |
N/A | 0.418 | 0.013 | 0.125 | 0.000 | 0.000 | 1.339 | 0.000 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 67 | 177 | 0 | 0 | 673 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 0.96 | 2.53 | 0.00 | 0.00 | 9.61 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.498 | 0.041 | 0.553 | 0.000 | 0.000 | 3.344 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 67 | 224 | 0 | 0 | 2173 | 0 | 46 | 0 |
N.S. |
1 | 1.00 | 0.96 | 3.20 | 0.00 | 0.00 | 31.04 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.506 | 0.039 | 3.426 | 0.000 | 0.000 | 5.443 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 274 | 115 | 102 | 376 | 144 | 476 | 0 | 0 | 341 | 468 |
N.S. |
1 | 0.42 | 0.37 | 1.37 | 0.53 | 1.74 | 0.00 | 0.00 | 1.24 | 1.71 |
time (sec) |
N/A | 0.839 | 0.093 | 0.127 | 0.050 | 0.103 | 0.000 | 0.000 | 0.158 | 24.713 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 85 | 84 | 179 | 80 | 211 | 0 | 0 | 141 | 228 |
N.S. |
1 | 0.49 | 0.48 | 1.03 | 0.46 | 1.21 | 0.00 | 0.00 | 0.81 | 1.31 |
time (sec) |
N/A | 0.789 | 0.086 | 0.123 | 0.045 | 0.123 | 0.000 | 0.000 | 0.156 | 23.936 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 54 | 49 | 51 | 30 | 80 | 0 | 0 | 27 | 51 |
N.S. |
1 | 0.66 | 0.60 | 0.62 | 0.37 | 0.98 | 0.00 | 0.00 | 0.33 | 0.62 |
time (sec) |
N/A | 0.700 | 0.036 | 0.119 | 0.044 | 0.122 | 0.000 | 0.000 | 0.150 | 23.759 |
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 | 51 | 51 | 51 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.691 | 0.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 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 | 134 | 103 | 107 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 0.77 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.774 | 0.046 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 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 | 134 | 103 | 107 | 0 | 0 | 0 | 0 | 0 | 51 | 0 |
N.S. |
1 | 0.77 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.791 | 0.049 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.151 | 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 | 136 | 110 | 114 | 0 | 0 | 0 | 391 | 0 | 68 | 0 |
N.S. |
1 | 0.81 | 0.84 | 0.00 | 0.00 | 0.00 | 2.88 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.694 | 0.047 | 0.000 | 0.000 | 0.000 | 44.965 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 91 | 77 | 47 | 0 | 0 | 258 | 0 | 190 | 0 |
N.S. |
1 | 1.07 | 0.91 | 0.55 | 0.00 | 0.00 | 3.04 | 0.00 | 2.24 | 0.00 |
time (sec) |
N/A | 0.569 | 0.079 | 0.130 | 0.000 | 0.000 | 10.395 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 91 | 76 | 47 | 0 | 0 | 257 | 0 | 190 | 0 |
N.S. |
1 | 1.08 | 0.90 | 0.56 | 0.00 | 0.00 | 3.06 | 0.00 | 2.26 | 0.00 |
time (sec) |
N/A | 0.545 | 0.059 | 0.120 | 0.000 | 0.000 | 9.948 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 60 | 47 | 0 | 0 | 243 | 0 | 100 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.81 | 0.00 | 0.00 | 4.19 | 0.00 | 1.72 | 0.00 |
time (sec) |
N/A | 0.439 | 0.030 | 0.122 | 0.000 | 0.000 | 6.095 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | B | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 59 | 59 | 44 | 0 | 0 | 236 | 0 | 90 | 0 |
N.S. |
1 | 1.13 | 1.13 | 0.85 | 0.00 | 0.00 | 4.54 | 0.00 | 1.73 | 0.00 |
time (sec) |
N/A | 0.386 | 0.021 | 0.117 | 0.000 | 0.000 | 6.987 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 74 | 90 | 0 | 0 | 286 | 0 | 62 | 0 |
N.S. |
1 | 1.00 | 1.03 | 1.25 | 0.00 | 0.00 | 3.97 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.491 | 0.036 | 0.131 | 0.000 | 0.000 | 10.056 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 77 | 93 | 0 | 0 | 284 | 0 | 65 | 0 |
N.S. |
1 | 1.00 | 1.03 | 1.24 | 0.00 | 0.00 | 3.79 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.501 | 0.033 | 0.125 | 0.000 | 0.000 | 7.767 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 80 | 112 | 0 | 0 | 292 | 0 | 65 | 0 |
N.S. |
1 | 1.00 | 1.03 | 1.44 | 0.00 | 0.00 | 3.74 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.497 | 0.026 | 0.136 | 0.000 | 0.000 | 11.885 | 0.000 | 0.156 | 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 | 134 | 119 | 105 | 0 | 0 | 0 | 272 | 0 | 202 | 0 |
N.S. |
1 | 0.89 | 0.78 | 0.00 | 0.00 | 0.00 | 2.03 | 0.00 | 1.51 | 0.00 |
time (sec) |
N/A | 0.773 | 0.112 | 0.000 | 0.000 | 0.000 | 11.196 | 0.000 | 0.183 | 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 | 133 | 119 | 104 | 0 | 0 | 0 | 270 | 0 | 202 | 0 |
N.S. |
1 | 0.89 | 0.78 | 0.00 | 0.00 | 0.00 | 2.03 | 0.00 | 1.52 | 0.00 |
time (sec) |
N/A | 0.765 | 0.117 | 0.000 | 0.000 | 0.000 | 8.698 | 0.000 | 0.160 | 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 | 96 | 86 | 88 | 0 | 0 | 0 | 311 | 0 | 105 | 0 |
N.S. |
1 | 0.90 | 0.92 | 0.00 | 0.00 | 0.00 | 3.24 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.637 | 0.048 | 0.000 | 0.000 | 0.000 | 7.399 | 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 | 90 | 86 | 86 | 0 | 0 | 0 | 306 | 0 | 95 | 0 |
N.S. |
1 | 0.96 | 0.96 | 0.00 | 0.00 | 0.00 | 3.40 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.540 | 0.028 | 0.000 | 0.000 | 0.000 | 6.827 | 0.000 | 0.156 | 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 | 110 | 100 | 102 | 0 | 0 | 0 | 299 | 0 | 64 | 0 |
N.S. |
1 | 0.91 | 0.93 | 0.00 | 0.00 | 0.00 | 2.72 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.730 | 0.057 | 0.000 | 0.000 | 0.000 | 10.680 | 0.000 | 0.177 | 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 | 113 | 103 | 105 | 0 | 0 | 0 | 298 | 0 | 67 | 0 |
N.S. |
1 | 0.91 | 0.93 | 0.00 | 0.00 | 0.00 | 2.64 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.702 | 0.061 | 0.000 | 0.000 | 0.000 | 10.026 | 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 | 116 | 106 | 108 | 0 | 0 | 0 | 306 | 0 | 67 | 0 |
N.S. |
1 | 0.91 | 0.93 | 0.00 | 0.00 | 0.00 | 2.64 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.704 | 0.045 | 0.000 | 0.000 | 0.000 | 12.101 | 0.000 | 0.165 | 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 | 29 | 28 | 22 | 21 | 23 | 23 | 24 | 23 | 20 | 20 |
N.S. |
1 | 0.97 | 0.76 | 0.72 | 0.79 | 0.79 | 0.83 | 0.79 | 0.69 | 0.69 |
time (sec) |
N/A | 0.406 | 0.026 | 0.102 | 0.027 | 0.079 | 0.031 | 0.135 | 0.147 | 23.540 |
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 | 29 | 28 | 22 | 21 | 23 | 23 | 26 | 23 | 20 | 20 |
N.S. |
1 | 0.97 | 0.76 | 0.72 | 0.79 | 0.79 | 0.90 | 0.79 | 0.69 | 0.69 |
time (sec) |
N/A | 0.405 | 0.024 | 0.102 | 0.028 | 0.093 | 0.036 | 0.117 | 0.151 | 0.035 |
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 | 29 | 28 | 22 | 21 | 23 | 23 | 24 | 23 | 20 | 20 |
N.S. |
1 | 0.97 | 0.76 | 0.72 | 0.79 | 0.79 | 0.83 | 0.79 | 0.69 | 0.69 |
time (sec) |
N/A | 0.403 | 0.021 | 0.100 | 0.033 | 0.089 | 0.034 | 0.141 | 0.155 | 0.034 |
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 | 29 | 28 | 22 | 21 | 23 | 23 | 26 | 23 | 20 | 20 |
N.S. |
1 | 0.97 | 0.76 | 0.72 | 0.79 | 0.79 | 0.90 | 0.79 | 0.69 | 0.69 |
time (sec) |
N/A | 0.388 | 0.020 | 0.099 | 0.035 | 0.093 | 0.034 | 0.140 | 0.152 | 0.034 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 19 | 14 | 19 | 19 | 19 | 19 | 17 | 17 |
N.S. |
1 | 1.00 | 1.27 | 0.93 | 1.27 | 1.27 | 1.27 | 1.27 | 1.13 | 1.13 |
time (sec) |
N/A | 0.320 | 0.017 | 0.097 | 0.026 | 0.097 | 0.033 | 0.136 | 0.145 | 0.032 |
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 | 21 | 19 | 19 | 18 | 19 | 19 | 20 | 20 | 19 | 19 |
N.S. |
1 | 0.90 | 0.90 | 0.86 | 0.90 | 0.90 | 0.95 | 0.95 | 0.90 | 0.90 |
time (sec) |
N/A | 0.381 | 0.023 | 0.104 | 0.029 | 0.099 | 0.064 | 0.124 | 0.166 | 0.032 |
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 | 19 | 18 | 18 | 19 | 19 | 23 | 17 | 20 | 20 | 20 |
N.S. |
1 | 0.95 | 0.95 | 1.00 | 1.00 | 1.21 | 0.89 | 1.05 | 1.05 | 1.05 |
time (sec) |
N/A | 0.394 | 0.019 | 0.102 | 0.026 | 0.107 | 0.072 | 0.118 | 0.153 | 0.036 |
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 | 23 | 22 | 22 | 21 | 20 | 25 | 22 | 21 | 22 | 22 |
N.S. |
1 | 0.96 | 0.96 | 0.91 | 0.87 | 1.09 | 0.96 | 0.91 | 0.96 | 0.96 |
time (sec) |
N/A | 0.402 | 0.022 | 0.109 | 0.030 | 0.069 | 0.068 | 0.115 | 0.151 | 0.047 |
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 | 15 | 15 | 15 | 21 | 21 | 21 | 24 | 21 | 20 | 21 |
N.S. |
1 | 1.00 | 1.00 | 1.40 | 1.40 | 1.40 | 1.60 | 1.40 | 1.33 | 1.40 |
time (sec) |
N/A | 0.358 | 0.014 | 0.109 | 0.031 | 0.061 | 0.088 | 0.138 | 0.149 | 0.040 |
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 | 48 | 40 | 32 | 31 | 40 | 40 | 41 | 40 | 30 | 40 |
N.S. |
1 | 0.83 | 0.67 | 0.65 | 0.83 | 0.83 | 0.85 | 0.83 | 0.62 | 0.83 |
time (sec) |
N/A | 0.453 | 0.031 | 0.139 | 0.033 | 0.070 | 0.031 | 0.124 | 0.162 | 0.060 |
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 | 48 | 40 | 40 | 31 | 40 | 40 | 44 | 40 | 30 | 40 |
N.S. |
1 | 0.83 | 0.83 | 0.65 | 0.83 | 0.83 | 0.92 | 0.83 | 0.62 | 0.83 |
time (sec) |
N/A | 0.468 | 0.028 | 0.129 | 0.026 | 0.068 | 0.043 | 0.135 | 0.148 | 0.048 |
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 | 48 | 40 | 32 | 31 | 40 | 40 | 41 | 40 | 30 | 40 |
N.S. |
1 | 0.83 | 0.67 | 0.65 | 0.83 | 0.83 | 0.85 | 0.83 | 0.62 | 0.83 |
time (sec) |
N/A | 0.464 | 0.027 | 0.134 | 0.026 | 0.060 | 0.033 | 0.131 | 0.153 | 0.048 |
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 | 48 | 40 | 32 | 31 | 40 | 40 | 44 | 40 | 30 | 40 |
N.S. |
1 | 0.83 | 0.67 | 0.65 | 0.83 | 0.83 | 0.92 | 0.83 | 0.62 | 0.83 |
time (sec) |
N/A | 0.428 | 0.025 | 0.131 | 0.033 | 0.078 | 0.029 | 0.116 | 0.143 | 0.048 |
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 | 35 | 33 | 23 | 28 | 36 | 36 | 36 | 36 | 28 | 36 |
N.S. |
1 | 0.94 | 0.66 | 0.80 | 1.03 | 1.03 | 1.03 | 1.03 | 0.80 | 1.03 |
time (sec) |
N/A | 0.386 | 0.020 | 0.132 | 0.033 | 0.067 | 0.043 | 0.128 | 0.155 | 0.049 |
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 | 40 | 31 | 34 | 28 | 36 | 36 | 39 | 37 | 30 | 36 |
N.S. |
1 | 0.78 | 0.85 | 0.70 | 0.90 | 0.90 | 0.98 | 0.92 | 0.75 | 0.90 |
time (sec) |
N/A | 0.430 | 0.025 | 0.121 | 0.028 | 0.110 | 0.061 | 0.125 | 0.160 | 0.043 |
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 | 41 | 33 | 36 | 32 | 39 | 41 | 36 | 40 | 32 | 39 |
N.S. |
1 | 0.80 | 0.88 | 0.78 | 0.95 | 1.00 | 0.88 | 0.98 | 0.78 | 0.95 |
time (sec) |
N/A | 0.443 | 0.020 | 0.125 | 0.031 | 0.101 | 0.081 | 0.116 | 0.147 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 30 | 37 | 37 | 39 | 37 | 30 | 29 |
N.S. |
1 | 1.00 | 1.00 | 1.76 | 2.18 | 2.18 | 2.29 | 2.18 | 1.76 | 1.71 |
time (sec) |
N/A | 0.395 | 0.021 | 0.131 | 0.037 | 0.099 | 0.086 | 0.136 | 0.146 | 0.044 |
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 | 39 | 31 | 38 | 30 | 36 | 40 | 37 | 37 | 32 | 32 |
N.S. |
1 | 0.79 | 0.97 | 0.77 | 0.92 | 1.03 | 0.95 | 0.95 | 0.82 | 0.82 |
time (sec) |
N/A | 0.437 | 0.020 | 0.129 | 0.030 | 0.098 | 0.100 | 0.114 | 0.170 | 0.043 |
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 | 43 | 35 | 35 | 32 | 40 | 42 | 41 | 41 | 32 | 32 |
N.S. |
1 | 0.81 | 0.81 | 0.74 | 0.93 | 0.98 | 0.95 | 0.95 | 0.74 | 0.74 |
time (sec) |
N/A | 0.444 | 0.023 | 0.132 | 0.031 | 0.088 | 0.133 | 0.118 | 0.152 | 0.055 |
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 | 42 | 34 | 23 | 31 | 40 | 40 | 42 | 40 | 30 | 40 |
N.S. |
1 | 0.81 | 0.55 | 0.74 | 0.95 | 0.95 | 1.00 | 0.95 | 0.71 | 0.95 |
time (sec) |
N/A | 0.463 | 0.014 | 0.132 | 0.033 | 0.101 | 0.170 | 0.133 | 0.154 | 0.037 |
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 | 87 | 70 | 70 | 55 | 73 | 73 | 76 | 73 | 54 | 73 |
N.S. |
1 | 0.80 | 0.80 | 0.63 | 0.84 | 0.84 | 0.87 | 0.84 | 0.62 | 0.84 |
time (sec) |
N/A | 0.507 | 0.043 | 0.142 | 0.032 | 0.105 | 0.034 | 0.121 | 0.148 | 23.596 |
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 | 87 | 70 | 70 | 55 | 73 | 73 | 82 | 73 | 54 | 73 |
N.S. |
1 | 0.80 | 0.80 | 0.63 | 0.84 | 0.84 | 0.94 | 0.84 | 0.62 | 0.84 |
time (sec) |
N/A | 0.506 | 0.049 | 0.138 | 0.026 | 0.086 | 0.031 | 0.122 | 0.154 | 0.034 |
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 | 84 | 73 | 70 | 55 | 73 | 73 | 78 | 73 | 54 | 73 |
N.S. |
1 | 0.87 | 0.83 | 0.65 | 0.87 | 0.87 | 0.93 | 0.87 | 0.64 | 0.87 |
time (sec) |
N/A | 0.535 | 0.039 | 0.136 | 0.027 | 0.090 | 0.044 | 0.146 | 0.154 | 0.034 |
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 | 69 | 61 | 70 | 55 | 73 | 73 | 82 | 73 | 54 | 73 |
N.S. |
1 | 0.88 | 1.01 | 0.80 | 1.06 | 1.06 | 1.19 | 1.06 | 0.78 | 1.06 |
time (sec) |
N/A | 0.478 | 0.035 | 0.133 | 0.032 | 0.060 | 0.035 | 0.124 | 0.146 | 0.033 |
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 | 47 | 31 | 52 | 69 | 69 | 70 | 69 | 52 | 69 |
N.S. |
1 | 0.90 | 0.60 | 1.00 | 1.33 | 1.33 | 1.35 | 1.33 | 1.00 | 1.33 |
time (sec) |
N/A | 0.416 | 0.026 | 0.130 | 0.033 | 0.070 | 0.056 | 0.121 | 0.148 | 0.034 |
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 | 79 | 61 | 51 | 52 | 69 | 69 | 76 | 70 | 54 | 69 |
N.S. |
1 | 0.77 | 0.65 | 0.66 | 0.87 | 0.87 | 0.96 | 0.89 | 0.68 | 0.87 |
time (sec) |
N/A | 0.469 | 0.035 | 0.148 | 0.029 | 0.065 | 0.067 | 0.136 | 0.155 | 0.038 |
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 | 76 | 59 | 59 | 54 | 70 | 75 | 70 | 71 | 56 | 70 |
N.S. |
1 | 0.78 | 0.78 | 0.71 | 0.92 | 0.99 | 0.92 | 0.93 | 0.74 | 0.92 |
time (sec) |
N/A | 0.484 | 0.033 | 0.127 | 0.035 | 0.102 | 0.088 | 0.122 | 0.156 | 0.038 |
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 | 78 | 61 | 58 | 54 | 69 | 75 | 75 | 70 | 56 | 71 |
N.S. |
1 | 0.78 | 0.74 | 0.69 | 0.88 | 0.96 | 0.96 | 0.90 | 0.72 | 0.91 |
time (sec) |
N/A | 0.497 | 0.029 | 0.132 | 0.045 | 0.094 | 0.133 | 0.124 | 0.146 | 0.037 |
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 | 72 | 55 | 55 | 52 | 70 | 74 | 70 | 71 | 55 | 69 |
N.S. |
1 | 0.76 | 0.76 | 0.72 | 0.97 | 1.03 | 0.97 | 0.99 | 0.76 | 0.96 |
time (sec) |
N/A | 0.485 | 0.033 | 0.133 | 0.034 | 0.092 | 0.133 | 0.138 | 0.146 | 0.038 |
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 | 69 | 61 | 39 | 59 | 79 | 79 | 87 | 79 | 60 | 79 |
N.S. |
1 | 0.88 | 0.57 | 0.86 | 1.14 | 1.14 | 1.26 | 1.14 | 0.87 | 1.14 |
time (sec) |
N/A | 0.444 | 0.034 | 0.137 | 0.033 | 0.086 | 0.048 | 0.145 | 0.160 | 0.039 |
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 | 63 | 52 | 49 | 50 | 57 | 59 | 53 | 70 | 61 | 64 |
N.S. |
1 | 0.83 | 0.78 | 0.79 | 0.90 | 0.94 | 0.84 | 1.11 | 0.97 | 1.02 |
time (sec) |
N/A | 0.500 | 0.046 | 0.112 | 0.028 | 0.105 | 0.113 | 0.126 | 0.155 | 0.048 |
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 | 53 | 45 | 41 | 43 | 49 | 51 | 44 | 53 | 53 | 54 |
N.S. |
1 | 0.85 | 0.77 | 0.81 | 0.92 | 0.96 | 0.83 | 1.00 | 1.00 | 1.02 |
time (sec) |
N/A | 0.489 | 0.036 | 0.114 | 0.027 | 0.066 | 0.082 | 0.116 | 0.149 | 23.682 |
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 | 39 | 34 | 28 | 34 | 40 | 42 | 32 | 39 | 44 | 38 |
N.S. |
1 | 0.87 | 0.72 | 0.87 | 1.03 | 1.08 | 0.82 | 1.00 | 1.13 | 0.97 |
time (sec) |
N/A | 0.470 | 0.030 | 0.109 | 0.029 | 0.111 | 0.078 | 0.127 | 0.157 | 0.049 |
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 | 30 | 28 | 23 | 28 | 31 | 30 | 24 | 30 | 36 | 27 |
N.S. |
1 | 0.93 | 0.77 | 0.93 | 1.03 | 1.00 | 0.80 | 1.00 | 1.20 | 0.90 |
time (sec) |
N/A | 0.423 | 0.023 | 0.105 | 0.027 | 0.095 | 0.073 | 0.150 | 0.158 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 18 | 14 | 15 | 15 | 12 | 15 | 13 | 13 |
N.S. |
1 | 1.00 | 1.20 | 0.93 | 1.00 | 1.00 | 0.80 | 1.00 | 0.87 | 0.87 |
time (sec) |
N/A | 0.335 | 0.054 | 0.103 | 0.031 | 0.089 | 0.060 | 0.119 | 0.156 | 23.568 |
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 | 31 | 24 | 24 | 25 | 30 | 35 | 19 | 32 | 41 | 22 |
N.S. |
1 | 0.77 | 0.77 | 0.81 | 0.97 | 1.13 | 0.61 | 1.03 | 1.32 | 0.71 |
time (sec) |
N/A | 0.450 | 0.027 | 0.112 | 0.031 | 0.096 | 0.100 | 0.122 | 0.149 | 23.563 |
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 | 43 | 35 | 35 | 35 | 42 | 57 | 31 | 45 | 64 | 34 |
N.S. |
1 | 0.81 | 0.81 | 0.81 | 0.98 | 1.33 | 0.72 | 1.05 | 1.49 | 0.79 |
time (sec) |
N/A | 0.470 | 0.037 | 0.112 | 0.034 | 0.117 | 0.125 | 0.128 | 0.144 | 0.068 |
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 | 60 | 49 | 52 | 47 | 56 | 75 | 46 | 56 | 77 | 47 |
N.S. |
1 | 0.82 | 0.87 | 0.78 | 0.93 | 1.25 | 0.77 | 0.93 | 1.28 | 0.78 |
time (sec) |
N/A | 0.489 | 0.056 | 0.115 | 0.031 | 0.072 | 0.159 | 0.113 | 0.160 | 0.074 |
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 | 71 | 57 | 71 | 55 | 64 | 83 | 54 | 64 | 85 | 55 |
N.S. |
1 | 0.80 | 1.00 | 0.77 | 0.90 | 1.17 | 0.76 | 0.90 | 1.20 | 0.77 |
time (sec) |
N/A | 0.500 | 0.044 | 0.113 | 0.032 | 0.069 | 0.162 | 0.118 | 0.155 | 23.571 |
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 | 79 | 68 | 68 | 58 | 75 | 95 | 71 | 61 | 102 | 77 |
N.S. |
1 | 0.86 | 0.86 | 0.73 | 0.95 | 1.20 | 0.90 | 0.77 | 1.29 | 0.97 |
time (sec) |
N/A | 0.531 | 0.051 | 0.122 | 0.030 | 0.072 | 0.234 | 0.153 | 0.150 | 0.101 |
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 | 70 | 62 | 53 | 52 | 66 | 79 | 63 | 52 | 97 | 65 |
N.S. |
1 | 0.89 | 0.76 | 0.74 | 0.94 | 1.13 | 0.90 | 0.74 | 1.39 | 0.93 |
time (sec) |
N/A | 0.538 | 0.043 | 0.125 | 0.039 | 0.075 | 0.183 | 0.146 | 0.147 | 0.202 |
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 | 51 | 46 | 35 | 52 | 66 | 78 | 61 | 52 | 94 | 49 |
N.S. |
1 | 0.90 | 0.69 | 1.02 | 1.29 | 1.53 | 1.20 | 1.02 | 1.84 | 0.96 |
time (sec) |
N/A | 0.500 | 0.035 | 0.118 | 0.032 | 0.072 | 0.150 | 0.134 | 0.163 | 0.066 |
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 | 51 | 46 | 34 | 47 | 59 | 77 | 53 | 47 | 93 | 42 |
N.S. |
1 | 0.90 | 0.67 | 0.92 | 1.16 | 1.51 | 1.04 | 0.92 | 1.82 | 0.82 |
time (sec) |
N/A | 0.507 | 0.032 | 0.122 | 0.039 | 0.104 | 0.147 | 0.117 | 0.156 | 23.576 |
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 | 51 | 46 | 35 | 51 | 63 | 76 | 56 | 51 | 94 | 47 |
N.S. |
1 | 0.90 | 0.69 | 1.00 | 1.24 | 1.49 | 1.10 | 1.00 | 1.84 | 0.92 |
time (sec) |
N/A | 0.400 | 0.025 | 0.119 | 0.033 | 0.106 | 0.226 | 0.135 | 0.167 | 0.064 |
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 | 64 | 52 | 48 | 42 | 60 | 89 | 58 | 50 | 114 | 60 |
N.S. |
1 | 0.81 | 0.75 | 0.66 | 0.94 | 1.39 | 0.91 | 0.78 | 1.78 | 0.94 |
time (sec) |
N/A | 0.495 | 0.048 | 0.131 | 0.028 | 0.111 | 0.285 | 0.125 | 0.156 | 23.592 |