Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 121 | 90 | 258 | 0 | 524 | 0 | 0 | 168 | 0 |
N.S. |
1 | 0.70 | 0.52 | 1.48 | 0.00 | 3.01 | 0.00 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.619 | 0.072 | 0.195 | 0.000 | 0.216 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 160 | 121 | 290 | 0 | 594 | 0 | 0 | 338 | 0 |
N.S. |
1 | 0.74 | 0.56 | 1.35 | 0.00 | 2.76 | 0.00 | 0.00 | 1.57 | 0.00 |
time (sec) |
N/A | 0.683 | 0.096 | 0.202 | 0.000 | 0.235 | 0.000 | 0.000 | 0.161 | 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 | 164 | 174 | 147 | 121 | 0 | 337 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.06 | 0.90 | 0.74 | 0.00 | 2.05 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.877 | 0.925 | 0.069 | 0.000 | 0.138 | 0.000 | 0.000 | 0.145 | 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 | 124 | 129 | 148 | 104 | 0 | 317 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.04 | 1.19 | 0.84 | 0.00 | 2.56 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.701 | 1.442 | 0.068 | 0.000 | 0.123 | 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 | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 82 | 66 | 87 | 0 | 295 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.05 | 0.85 | 1.12 | 0.00 | 3.78 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.530 | 0.046 | 0.056 | 0.000 | 0.114 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 78 | 132 | 88 | 0 | 275 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.03 | 1.74 | 1.16 | 0.00 | 3.62 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.640 | 0.646 | 0.075 | 0.000 | 0.110 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 45 | 39 | 0 | 58 | 0 | 0 | 42 | 47 |
N.S. |
1 | 1.00 | 1.22 | 1.05 | 0.00 | 1.57 | 0.00 | 0.00 | 1.14 | 1.27 |
time (sec) |
N/A | 0.528 | 0.215 | 0.062 | 0.000 | 0.103 | 0.000 | 0.000 | 0.151 | 13.674 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 58 | 45 | 0 | 68 | 0 | 0 | 63 | 53 |
N.S. |
1 | 1.00 | 0.75 | 0.58 | 0.00 | 0.88 | 0.00 | 0.00 | 0.82 | 0.69 |
time (sec) |
N/A | 0.585 | 0.259 | 0.070 | 0.000 | 0.079 | 0.000 | 0.000 | 0.151 | 13.747 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 122 | 66 | 53 | 0 | 77 | 0 | 0 | 81 | 100 |
N.S. |
1 | 1.08 | 0.58 | 0.47 | 0.00 | 0.68 | 0.00 | 0.00 | 0.72 | 0.88 |
time (sec) |
N/A | 0.711 | 0.249 | 0.063 | 0.000 | 0.094 | 0.000 | 0.000 | 0.151 | 13.685 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 175 | 74 | 61 | 0 | 84 | 0 | 0 | 99 | 108 |
N.S. |
1 | 1.15 | 0.49 | 0.40 | 0.00 | 0.55 | 0.00 | 0.00 | 0.65 | 0.71 |
time (sec) |
N/A | 1.091 | 0.297 | 0.066 | 0.000 | 0.079 | 0.000 | 0.000 | 0.154 | 13.710 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 157 | 50 | 127 | 0 | 188 | 0 | 142 | 85 | 0 |
N.S. |
1 | 1.21 | 0.38 | 0.98 | 0.00 | 1.45 | 0.00 | 1.09 | 0.65 | 0.00 |
time (sec) |
N/A | 1.198 | 0.050 | 0.139 | 0.000 | 0.114 | 0.000 | 0.137 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 124 | 50 | 119 | 0 | 172 | 0 | 127 | 67 | 0 |
N.S. |
1 | 1.18 | 0.48 | 1.13 | 0.00 | 1.64 | 0.00 | 1.21 | 0.64 | 0.00 |
time (sec) |
N/A | 1.167 | 0.048 | 0.137 | 0.000 | 0.109 | 0.000 | 0.138 | 0.143 | 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 | 80 | 91 | 77 | 111 | 0 | 156 | 0 | 112 | 49 | 0 |
N.S. |
1 | 1.14 | 0.96 | 1.39 | 0.00 | 1.95 | 0.00 | 1.40 | 0.61 | 0.00 |
time (sec) |
N/A | 0.925 | 0.092 | 0.139 | 0.000 | 0.089 | 0.000 | 0.153 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 58 | 50 | 98 | 0 | 133 | 0 | 96 | 33 | 0 |
N.S. |
1 | 1.16 | 1.00 | 1.96 | 0.00 | 2.66 | 0.00 | 1.92 | 0.66 | 0.00 |
time (sec) |
N/A | 0.683 | 0.027 | 0.129 | 0.000 | 0.091 | 0.000 | 0.141 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | B | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 58 | 47 | 98 | 0 | 120 | 95 | 0 | 41 | 0 |
N.S. |
1 | 1.23 | 1.00 | 2.09 | 0.00 | 2.55 | 2.02 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 1.097 | 0.038 | 0.141 | 0.000 | 0.104 | 4.009 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 55 | 28 | 25 | 0 | 28 | 0 | 121 | 44 | 24 |
N.S. |
1 | 1.31 | 0.67 | 0.60 | 0.00 | 0.67 | 0.00 | 2.88 | 1.05 | 0.57 |
time (sec) |
N/A | 1.105 | 0.046 | 0.133 | 0.000 | 0.078 | 0.000 | 0.156 | 0.157 | 13.649 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 78 | 36 | 33 | 0 | 36 | 0 | 164 | 62 | 32 |
N.S. |
1 | 1.13 | 0.52 | 0.48 | 0.00 | 0.52 | 0.00 | 2.38 | 0.90 | 0.46 |
time (sec) |
N/A | 1.168 | 0.052 | 0.138 | 0.000 | 0.084 | 0.000 | 0.190 | 0.152 | 13.649 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 105 | 44 | 41 | 0 | 44 | 0 | 203 | 81 | 77 |
N.S. |
1 | 1.09 | 0.46 | 0.43 | 0.00 | 0.46 | 0.00 | 2.11 | 0.84 | 0.80 |
time (sec) |
N/A | 1.283 | 0.066 | 0.139 | 0.000 | 0.103 | 0.000 | 0.244 | 0.155 | 13.586 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 130 | 52 | 49 | 0 | 52 | 0 | 243 | 99 | 98 |
N.S. |
1 | 1.07 | 0.43 | 0.40 | 0.00 | 0.43 | 0.00 | 2.01 | 0.82 | 0.81 |
time (sec) |
N/A | 1.209 | 0.079 | 0.136 | 0.000 | 0.083 | 0.000 | 0.287 | 0.156 | 13.705 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 188 | 252 | 224 | 0 | 568 | 0 | 0 | 169 | 0 |
N.S. |
1 | 0.72 | 0.97 | 0.86 | 0.00 | 2.18 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.861 | 1.561 | 0.171 | 0.000 | 0.159 | 0.000 | 0.000 | 0.151 | 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 | 220 | 160 | 244 | 202 | 0 | 552 | 0 | 0 | 151 | 0 |
N.S. |
1 | 0.73 | 1.11 | 0.92 | 0.00 | 2.51 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.836 | 1.139 | 0.161 | 0.000 | 0.168 | 0.000 | 0.000 | 0.151 | 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 | 180 | 132 | 236 | 180 | 0 | 536 | 0 | 0 | 133 | 0 |
N.S. |
1 | 0.73 | 1.31 | 1.00 | 0.00 | 2.98 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.696 | 1.731 | 0.159 | 0.000 | 0.194 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 104 | 95 | 160 | 0 | 512 | 0 | 0 | 117 | 0 |
N.S. |
1 | 0.77 | 0.70 | 1.19 | 0.00 | 3.79 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.592 | 0.089 | 0.151 | 0.000 | 0.165 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 100 | 218 | 161 | 0 | 490 | 0 | 0 | 131 | 0 |
N.S. |
1 | 0.78 | 1.69 | 1.25 | 0.00 | 3.80 | 0.00 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.708 | 1.059 | 0.163 | 0.000 | 0.161 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 138 | 155 | 140 | 0 | 353 | 0 | 0 | 152 | 0 |
N.S. |
1 | 1.10 | 1.24 | 1.12 | 0.00 | 2.82 | 0.00 | 0.00 | 1.22 | 0.00 |
time (sec) |
N/A | 0.744 | 0.425 | 0.166 | 0.000 | 0.125 | 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(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 177 | 162 | 165 | 0 | 381 | 0 | 0 | 171 | 0 |
N.S. |
1 | 1.04 | 0.95 | 0.97 | 0.00 | 2.24 | 0.00 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 0.781 | 0.525 | 0.163 | 0.000 | 0.147 | 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(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 221 | 170 | 187 | 0 | 397 | 0 | 0 | 189 | 0 |
N.S. |
1 | 1.06 | 0.81 | 0.89 | 0.00 | 1.90 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.928 | 0.535 | 0.167 | 0.000 | 0.133 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 276 | 178 | 206 | 0 | 413 | 0 | 0 | 207 | 0 |
N.S. |
1 | 1.12 | 0.72 | 0.84 | 0.00 | 1.68 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 1.308 | 0.585 | 0.171 | 0.000 | 0.127 | 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(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 177 | 147 | 133 | 0 | 337 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.08 | 0.90 | 0.81 | 0.00 | 2.05 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.895 | 0.947 | 0.102 | 0.000 | 0.158 | 0.000 | 0.000 | 0.152 | 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 | 124 | 132 | 139 | 116 | 0 | 321 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.06 | 1.12 | 0.94 | 0.00 | 2.59 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.722 | 1.996 | 0.099 | 0.000 | 0.163 | 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 | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 87 | 65 | 101 | 0 | 297 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.10 | 0.82 | 1.28 | 0.00 | 3.76 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.542 | 0.047 | 0.073 | 0.000 | 0.120 | 0.000 | 0.000 | 0.142 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 83 | 132 | 100 | 0 | 275 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.09 | 1.74 | 1.32 | 0.00 | 3.62 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.671 | 0.741 | 0.086 | 0.000 | 0.152 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 78 | 46 | 52 | 0 | 59 | 0 | 0 | 44 | 54 |
N.S. |
1 | 1.11 | 0.66 | 0.74 | 0.00 | 0.84 | 0.00 | 0.00 | 0.63 | 0.77 |
time (sec) |
N/A | 0.609 | 0.251 | 0.085 | 0.000 | 0.117 | 0.000 | 0.000 | 0.156 | 13.606 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 120 | 58 | 60 | 0 | 69 | 0 | 0 | 62 | 62 |
N.S. |
1 | 1.06 | 0.51 | 0.53 | 0.00 | 0.61 | 0.00 | 0.00 | 0.55 | 0.55 |
time (sec) |
N/A | 0.655 | 0.288 | 0.084 | 0.000 | 0.107 | 0.000 | 0.000 | 0.153 | 13.688 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 169 | 66 | 68 | 0 | 77 | 0 | 0 | 81 | 100 |
N.S. |
1 | 1.11 | 0.43 | 0.45 | 0.00 | 0.51 | 0.00 | 0.00 | 0.53 | 0.66 |
time (sec) |
N/A | 0.811 | 0.268 | 0.092 | 0.000 | 0.128 | 0.000 | 0.000 | 0.149 | 13.687 |
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 | 172 | 207 | 116 | 197 | 0 | 288 | 0 | 0 | 159 | 0 |
N.S. |
1 | 1.20 | 0.67 | 1.15 | 0.00 | 1.67 | 0.00 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 1.336 | 0.168 | 0.168 | 0.000 | 0.126 | 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 | 147 | 174 | 108 | 189 | 0 | 276 | 0 | 0 | 141 | 0 |
N.S. |
1 | 1.18 | 0.73 | 1.29 | 0.00 | 1.88 | 0.00 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 1.344 | 0.129 | 0.165 | 0.000 | 0.112 | 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 | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 141 | 100 | 181 | 0 | 256 | 0 | 0 | 123 | 0 |
N.S. |
1 | 1.16 | 0.82 | 1.48 | 0.00 | 2.10 | 0.00 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 1.062 | 0.111 | 0.168 | 0.000 | 0.155 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 108 | 92 | 168 | 0 | 236 | 0 | 0 | 107 | 0 |
N.S. |
1 | 1.17 | 1.00 | 1.83 | 0.00 | 2.57 | 0.00 | 0.00 | 1.16 | 0.00 |
time (sec) |
N/A | 0.799 | 0.030 | 0.150 | 0.000 | 0.115 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | B | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 104 | 86 | 165 | 0 | 220 | 141 | 0 | 120 | 0 |
N.S. |
1 | 1.21 | 1.00 | 1.92 | 0.00 | 2.56 | 1.64 | 0.00 | 1.40 | 0.00 |
time (sec) |
N/A | 1.202 | 0.050 | 0.164 | 0.000 | 0.096 | 4.350 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 86 | 69 | 142 | 0 | 169 | 0 | 0 | 135 | 0 |
N.S. |
1 | 1.05 | 0.84 | 1.73 | 0.00 | 2.06 | 0.00 | 0.00 | 1.65 | 0.00 |
time (sec) |
N/A | 1.156 | 0.073 | 0.168 | 0.000 | 0.116 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 79 | 152 | 0 | 189 | 0 | 278 | 155 | 0 |
N.S. |
1 | 1.00 | 0.70 | 1.35 | 0.00 | 1.67 | 0.00 | 2.46 | 1.37 | 0.00 |
time (sec) |
N/A | 1.237 | 0.102 | 0.165 | 0.000 | 0.092 | 0.000 | 0.304 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 117 | 87 | 160 | 0 | 209 | 0 | 356 | 173 | 0 |
N.S. |
1 | 1.04 | 0.77 | 1.42 | 0.00 | 1.85 | 0.00 | 3.15 | 1.53 | 0.00 |
time (sec) |
N/A | 1.264 | 0.167 | 0.172 | 0.000 | 0.102 | 0.000 | 0.291 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 167 | 95 | 168 | 0 | 221 | 0 | 434 | 191 | 0 |
N.S. |
1 | 1.02 | 0.58 | 1.03 | 0.00 | 1.36 | 0.00 | 2.66 | 1.17 | 0.00 |
time (sec) |
N/A | 1.289 | 0.163 | 0.175 | 0.000 | 0.088 | 0.000 | 0.374 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 172 | 167 | 197 | 0 | 353 | 0 | 0 | 95 | 0 |
N.S. |
1 | 0.70 | 0.68 | 0.81 | 0.00 | 1.45 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.787 | 1.214 | 0.105 | 0.000 | 0.135 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 144 | 159 | 180 | 0 | 337 | 0 | 0 | 83 | 0 |
N.S. |
1 | 0.71 | 0.79 | 0.89 | 0.00 | 1.67 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.740 | 1.071 | 0.105 | 0.000 | 0.135 | 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 | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 116 | 151 | 163 | 0 | 321 | 0 | 0 | 71 | 0 |
N.S. |
1 | 0.72 | 0.94 | 1.01 | 0.00 | 1.99 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.644 | 2.075 | 0.098 | 0.000 | 0.163 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 92 | 67 | 146 | 0 | 299 | 0 | 0 | 59 | 0 |
N.S. |
1 | 0.80 | 0.58 | 1.27 | 0.00 | 2.60 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.560 | 0.064 | 0.086 | 0.000 | 0.114 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 90 | 131 | 151 | 0 | 277 | 0 | 0 | 65 | 0 |
N.S. |
1 | 0.83 | 1.20 | 1.39 | 0.00 | 2.54 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.695 | 1.127 | 0.101 | 0.000 | 0.113 | 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 | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 115 | 58 | 60 | 0 | 59 | 0 | 0 | 59 | 54 |
N.S. |
1 | 1.06 | 0.53 | 0.55 | 0.00 | 0.54 | 0.00 | 0.00 | 0.54 | 0.50 |
time (sec) |
N/A | 0.689 | 0.266 | 0.105 | 0.000 | 0.091 | 0.000 | 0.000 | 0.144 | 13.629 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 157 | 70 | 68 | 0 | 69 | 0 | 0 | 71 | 62 |
N.S. |
1 | 1.05 | 0.47 | 0.45 | 0.00 | 0.46 | 0.00 | 0.00 | 0.47 | 0.41 |
time (sec) |
N/A | 0.722 | 0.280 | 0.105 | 0.000 | 0.088 | 0.000 | 0.000 | 0.149 | 13.653 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 205 | 78 | 76 | 0 | 77 | 0 | 0 | 83 | 100 |
N.S. |
1 | 1.09 | 0.41 | 0.40 | 0.00 | 0.41 | 0.00 | 0.00 | 0.44 | 0.53 |
time (sec) |
N/A | 0.873 | 0.279 | 0.107 | 0.000 | 0.094 | 0.000 | 0.000 | 0.151 | 13.787 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 253 | 86 | 84 | 0 | 85 | 0 | 0 | 95 | 108 |
N.S. |
1 | 1.11 | 0.38 | 0.37 | 0.00 | 0.37 | 0.00 | 0.00 | 0.42 | 0.47 |
time (sec) |
N/A | 1.245 | 0.350 | 0.110 | 0.000 | 0.095 | 0.000 | 0.000 | 0.149 | 13.727 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 0 | 61 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 0.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.000 | 0.041 | 0.000 | 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 | F | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 0 | 95 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 0.00 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.000 | 0.069 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 187 | 155 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.01 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.577 | 0.452 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 97 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.489 | 0.491 | 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(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 163 | 113 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.98 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.568 | 0.086 | 0.000 | 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 | F(-1) | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 111 | 0 | 0 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.715 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F(-1) | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 111 | 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.681 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F(-1) | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 111 | 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.690 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F(-1) | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 111 | 0 | 0 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.749 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 110 | 0 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.638 | 0.000 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 67 | 0 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.568 | 0.034 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 93 | 0 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.619 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.145 | 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 | 57 | 69 | 46 | 0 | 0 | 0 | 269 | 0 | 89 | 0 |
N.S. |
1 | 1.21 | 0.81 | 0.00 | 0.00 | 0.00 | 4.72 | 0.00 | 1.56 | 0.00 |
time (sec) |
N/A | 0.597 | 0.031 | 0.000 | 0.000 | 0.000 | 5.101 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 90 | 0 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.580 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 88 | 0 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.594 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 124 | 87 | 0 | 0 | 0 | 0 | 0 | 218 | 0 |
N.S. |
1 | 1.09 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.91 | 0.00 |
time (sec) |
N/A | 0.698 | 0.060 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 74 | 47 | 85 | 113 | 113 | 119 | 113 | 84 | 113 |
N.S. |
1 | 0.88 | 0.56 | 1.01 | 1.35 | 1.35 | 1.42 | 1.35 | 1.00 | 1.35 |
time (sec) |
N/A | 0.637 | 0.047 | 0.188 | 0.029 | 0.078 | 0.043 | 0.114 | 0.144 | 13.123 |
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 | 62 | 39 | 61 | 82 | 82 | 87 | 82 | 60 | 82 |
N.S. |
1 | 0.90 | 0.57 | 0.88 | 1.19 | 1.19 | 1.26 | 1.19 | 0.87 | 1.19 |
time (sec) |
N/A | 0.587 | 0.036 | 0.167 | 0.032 | 0.078 | 0.041 | 0.113 | 0.143 | 0.023 |
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 | 48 | 31 | 53 | 70 | 70 | 70 | 70 | 52 | 70 |
N.S. |
1 | 0.92 | 0.60 | 1.02 | 1.35 | 1.35 | 1.35 | 1.35 | 1.00 | 1.35 |
time (sec) |
N/A | 0.553 | 0.029 | 0.163 | 0.029 | 0.088 | 0.033 | 0.109 | 0.142 | 0.021 |
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 | 34 | 23 | 29 | 38 | 38 | 36 | 38 | 28 | 38 |
N.S. |
1 | 0.97 | 0.66 | 0.83 | 1.09 | 1.09 | 1.03 | 1.09 | 0.80 | 1.09 |
time (sec) |
N/A | 0.523 | 0.022 | 0.152 | 0.035 | 0.079 | 0.031 | 0.137 | 0.157 | 0.027 |
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 | 20 | 14 | 21 | 21 | 20 | 21 | 18 | 17 |
N.S. |
1 | 1.00 | 1.33 | 0.93 | 1.40 | 1.40 | 1.33 | 1.40 | 1.20 | 1.13 |
time (sec) |
N/A | 0.429 | 0.018 | 0.119 | 0.027 | 0.061 | 0.022 | 0.135 | 0.146 | 0.019 |
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 | 16 | 16 | 18 | 13 | 13 | 13 | 10 | 14 | 12 | 14 |
N.S. |
1 | 1.00 | 1.12 | 0.81 | 0.81 | 0.81 | 0.62 | 0.88 | 0.75 | 0.88 |
time (sec) |
N/A | 0.467 | 0.064 | 0.136 | 0.024 | 0.086 | 0.060 | 0.114 | 0.151 | 13.057 |
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 | 47 | 35 | 51 | 63 | 76 | 54 | 51 | 93 | 46 |
N.S. |
1 | 0.92 | 0.69 | 1.00 | 1.24 | 1.49 | 1.06 | 1.00 | 1.82 | 0.90 |
time (sec) |
N/A | 0.553 | 0.036 | 0.202 | 0.029 | 0.083 | 0.149 | 0.108 | 0.142 | 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 | 86 | 76 | 63 | 76 | 91 | 121 | 85 | 74 | 145 | 73 |
N.S. |
1 | 0.88 | 0.73 | 0.88 | 1.06 | 1.41 | 0.99 | 0.86 | 1.69 | 0.85 |
time (sec) |
N/A | 0.602 | 0.048 | 0.152 | 0.034 | 0.089 | 0.222 | 0.120 | 0.152 | 13.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 105 | 82 | 92 | 140 | 217 | 141 | 91 | 269 | 121 |
N.S. |
1 | 0.87 | 0.68 | 0.76 | 1.16 | 1.79 | 1.17 | 0.75 | 2.22 | 1.00 |
time (sec) |
N/A | 0.656 | 0.077 | 0.159 | 0.038 | 0.102 | 0.344 | 0.136 | 0.144 | 13.138 |
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 | 66 | 58 | 39 | 75 | 101 | 101 | 109 | 102 | 76 | 101 |
N.S. |
1 | 0.88 | 0.59 | 1.14 | 1.53 | 1.53 | 1.65 | 1.55 | 1.15 | 1.53 |
time (sec) |
N/A | 0.598 | 0.037 | 0.200 | 0.031 | 0.093 | 0.052 | 0.115 | 0.145 | 13.158 |
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 | 52 | 47 | 31 | 69 | 92 | 92 | 100 | 90 | 68 | 92 |
N.S. |
1 | 0.90 | 0.60 | 1.33 | 1.77 | 1.77 | 1.92 | 1.73 | 1.31 | 1.77 |
time (sec) |
N/A | 0.560 | 0.033 | 0.182 | 0.030 | 0.073 | 0.045 | 0.122 | 0.143 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 33 | 23 | 45 | 59 | 59 | 63 | 78 | 44 | 59 |
N.S. |
1 | 0.94 | 0.66 | 1.29 | 1.69 | 1.69 | 1.80 | 2.23 | 1.26 | 1.69 |
time (sec) |
N/A | 0.525 | 0.026 | 0.174 | 0.032 | 0.088 | 0.046 | 0.120 | 0.151 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 37 | 16 | 47 | 47 | 48 | 64 | 35 | 47 |
N.S. |
1 | 1.00 | 2.18 | 0.94 | 2.76 | 2.76 | 2.82 | 3.76 | 2.06 | 2.76 |
time (sec) |
N/A | 0.477 | 0.027 | 0.148 | 0.029 | 0.063 | 0.051 | 0.138 | 0.141 | 0.017 |
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 | 46 | 44 | 38 | 32 | 33 | 37 | 36 | 60 | 35 | 33 |
N.S. |
1 | 0.96 | 0.83 | 0.70 | 0.72 | 0.80 | 0.78 | 1.30 | 0.76 | 0.72 |
time (sec) |
N/A | 0.502 | 0.023 | 0.141 | 0.031 | 0.076 | 0.066 | 0.115 | 0.146 | 13.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 25 | 13 | 19 | 19 | 17 | 27 | 32 | 12 |
N.S. |
1 | 1.00 | 1.92 | 1.00 | 1.46 | 1.46 | 1.31 | 2.08 | 2.46 | 0.92 |
time (sec) |
N/A | 0.463 | 0.016 | 0.152 | 0.036 | 0.079 | 0.089 | 0.115 | 0.146 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 16 | 41 | 41 | 42 | 15 | 31 | 40 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 2.28 | 2.28 | 2.33 | 0.83 | 1.72 | 2.22 |
time (sec) |
N/A | 0.476 | 0.103 | 0.152 | 0.030 | 0.071 | 0.118 | 0.117 | 0.143 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 76 | 52 | 65 | 102 | 147 | 99 | 91 | 181 | 83 |
N.S. |
1 | 0.87 | 0.60 | 0.75 | 1.17 | 1.69 | 1.14 | 1.05 | 2.08 | 0.95 |
time (sec) |
N/A | 0.591 | 0.048 | 0.168 | 0.032 | 0.086 | 0.241 | 0.134 | 0.142 | 0.053 |
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 | 122 | 105 | 80 | 92 | 130 | 191 | 129 | 127 | 233 | 111 |
N.S. |
1 | 0.86 | 0.66 | 0.75 | 1.07 | 1.57 | 1.06 | 1.04 | 1.91 | 0.91 |
time (sec) |
N/A | 0.642 | 0.063 | 0.171 | 0.039 | 0.099 | 0.316 | 0.117 | 0.145 | 13.156 |
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 | 73 | 66 | 39 | 61 | 80 | 80 | 87 | 80 | 60 | 80 |
N.S. |
1 | 0.90 | 0.53 | 0.84 | 1.10 | 1.10 | 1.19 | 1.10 | 0.82 | 1.10 |
time (sec) |
N/A | 0.587 | 0.036 | 0.168 | 0.025 | 0.064 | 0.040 | 0.137 | 0.150 | 0.023 |
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 | 55 | 51 | 31 | 53 | 70 | 70 | 70 | 70 | 52 | 70 |
N.S. |
1 | 0.93 | 0.56 | 0.96 | 1.27 | 1.27 | 1.27 | 1.27 | 0.95 | 1.27 |
time (sec) |
N/A | 0.567 | 0.031 | 0.159 | 0.033 | 0.087 | 0.036 | 0.129 | 0.140 | 0.020 |
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 | 37 | 36 | 30 | 29 | 37 | 37 | 36 | 37 | 28 | 37 |
N.S. |
1 | 0.97 | 0.81 | 0.78 | 1.00 | 1.00 | 0.97 | 1.00 | 0.76 | 1.00 |
time (sec) |
N/A | 0.518 | 0.022 | 0.154 | 0.029 | 0.068 | 0.034 | 0.128 | 0.143 | 0.028 |
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 | 16 | 16 | 21 | 14 | 20 | 20 | 19 | 20 | 18 | 17 |
N.S. |
1 | 1.00 | 1.31 | 0.88 | 1.25 | 1.25 | 1.19 | 1.25 | 1.12 | 1.06 |
time (sec) |
N/A | 0.427 | 0.018 | 0.122 | 0.025 | 0.069 | 0.023 | 0.128 | 0.139 | 0.020 |
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 | 14 | 14 | 18 | 14 | 12 | 12 | 10 | 14 | 13 | 12 |
N.S. |
1 | 1.00 | 1.29 | 1.00 | 0.86 | 0.86 | 0.71 | 1.00 | 0.93 | 0.86 |
time (sec) |
N/A | 0.467 | 0.060 | 0.135 | 0.027 | 0.073 | 0.055 | 0.129 | 0.140 | 0.029 |
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 | 49 | 45 | 33 | 51 | 63 | 76 | 54 | 51 | 94 | 46 |
N.S. |
1 | 0.92 | 0.67 | 1.04 | 1.29 | 1.55 | 1.10 | 1.04 | 1.92 | 0.94 |
time (sec) |
N/A | 0.546 | 0.033 | 0.149 | 0.028 | 0.077 | 0.143 | 0.142 | 0.142 | 13.124 |
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 | 74 | 61 | 76 | 91 | 121 | 85 | 74 | 145 | 73 |
N.S. |
1 | 0.88 | 0.73 | 0.90 | 1.08 | 1.44 | 1.01 | 0.88 | 1.73 | 0.87 |
time (sec) |
N/A | 0.599 | 0.051 | 0.152 | 0.031 | 0.086 | 0.222 | 0.133 | 0.147 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 103 | 80 | 92 | 140 | 217 | 141 | 91 | 269 | 121 |
N.S. |
1 | 0.87 | 0.67 | 0.77 | 1.18 | 1.82 | 1.18 | 0.76 | 2.26 | 1.02 |
time (sec) |
N/A | 0.670 | 0.068 | 0.157 | 0.038 | 0.104 | 0.328 | 0.143 | 0.144 | 13.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 105 | 79 | 113 | 0 | 117 | 0 | 0 | 89 | 0 |
N.S. |
1 | 0.46 | 0.34 | 0.49 | 0.00 | 0.51 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.823 | 0.078 | 0.142 | 0.000 | 0.085 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 92 | 71 | 97 | 0 | 95 | 0 | 0 | 73 | 0 |
N.S. |
1 | 0.50 | 0.39 | 0.53 | 0.00 | 0.52 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.782 | 0.060 | 0.145 | 0.000 | 0.088 | 0.000 | 0.000 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 76 | 63 | 81 | 0 | 73 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.56 | 0.46 | 0.60 | 0.00 | 0.54 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.762 | 0.050 | 0.137 | 0.000 | 0.102 | 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 | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 66 | 53 | 63 | 0 | 43 | 0 | 0 | 39 | 0 |
N.S. |
1 | 0.71 | 0.57 | 0.68 | 0.00 | 0.46 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.736 | 0.038 | 0.138 | 0.000 | 0.080 | 0.000 | 0.000 | 0.149 | 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 | 46 | 46 | 41 | 44 | 0 | 22 | 0 | 36 | 22 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.96 | 0.00 | 0.48 | 0.00 | 0.78 | 0.48 | 0.00 |
time (sec) |
N/A | 0.614 | 0.024 | 0.135 | 0.000 | 0.094 | 0.000 | 0.109 | 0.154 | 0.000 |