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 | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 115 | 82 | 87 | 0 | 153 | 0 | 250 | 69 | 0 |
N.S. |
1 | 1.14 | 0.81 | 0.86 | 0.00 | 1.51 | 0.00 | 2.48 | 0.68 | 0.00 |
time (sec) |
N/A | 0.914 | 0.178 | 0.233 | 0.000 | 0.106 | 0.000 | 0.140 | 0.159 | 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 | 130 | 150 | 95 | 95 | 0 | 169 | 0 | 324 | 90 | 0 |
N.S. |
1 | 1.15 | 0.73 | 0.73 | 0.00 | 1.30 | 0.00 | 2.49 | 0.69 | 0.00 |
time (sec) |
N/A | 0.992 | 0.222 | 0.279 | 0.000 | 0.115 | 0.000 | 0.131 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 87 | 86 | 92 | 0 | 58 | 0 | 100 | 54 | 0 |
N.S. |
1 | 0.38 | 0.38 | 0.41 | 0.00 | 0.26 | 0.00 | 0.44 | 0.24 | 0.00 |
time (sec) |
N/A | 0.873 | 0.071 | 0.148 | 0.000 | 0.097 | 0.000 | 0.121 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 75 | 74 | 83 | 0 | 49 | 0 | 84 | 46 | 0 |
N.S. |
1 | 0.40 | 0.40 | 0.45 | 0.00 | 0.26 | 0.00 | 0.45 | 0.25 | 0.00 |
time (sec) |
N/A | 0.842 | 0.053 | 0.148 | 0.000 | 0.086 | 0.000 | 0.117 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 69 | 65 | 76 | 0 | 42 | 0 | 72 | 38 | 0 |
N.S. |
1 | 0.46 | 0.43 | 0.50 | 0.00 | 0.28 | 0.00 | 0.48 | 0.25 | 0.00 |
time (sec) |
N/A | 0.776 | 0.048 | 0.152 | 0.000 | 0.090 | 0.000 | 0.130 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 59 | 58 | 67 | 0 | 33 | 0 | 56 | 30 | 0 |
N.S. |
1 | 0.53 | 0.52 | 0.60 | 0.00 | 0.29 | 0.00 | 0.50 | 0.27 | 0.00 |
time (sec) |
N/A | 0.647 | 0.019 | 0.145 | 0.000 | 0.080 | 0.000 | 0.115 | 0.169 | 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 | 112 | 50 | 50 | 61 | 0 | 26 | 0 | 41 | 24 | 0 |
N.S. |
1 | 0.45 | 0.45 | 0.54 | 0.00 | 0.23 | 0.00 | 0.37 | 0.21 | 0.00 |
time (sec) |
N/A | 0.686 | 0.034 | 0.151 | 0.000 | 0.087 | 0.000 | 0.122 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 56 | 54 | 64 | 0 | 33 | 0 | 46 | 31 | 0 |
N.S. |
1 | 0.49 | 0.47 | 0.56 | 0.00 | 0.29 | 0.00 | 0.40 | 0.27 | 0.00 |
time (sec) |
N/A | 0.804 | 0.046 | 0.147 | 0.000 | 0.089 | 0.000 | 0.136 | 0.445 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 68 | 63 | 77 | 0 | 88 | 0 | 64 | 34 | 0 |
N.S. |
1 | 0.45 | 0.41 | 0.51 | 0.00 | 0.58 | 0.00 | 0.42 | 0.22 | 0.00 |
time (sec) |
N/A | 0.828 | 0.054 | 0.151 | 0.000 | 0.123 | 0.000 | 0.141 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 78 | 75 | 85 | 0 | 98 | 0 | 78 | 56 | 0 |
N.S. |
1 | 0.40 | 0.39 | 0.44 | 0.00 | 0.51 | 0.00 | 0.40 | 0.29 | 0.00 |
time (sec) |
N/A | 0.825 | 0.066 | 0.152 | 0.000 | 0.092 | 0.000 | 0.117 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 83 | 79 | 93 | 0 | 104 | 0 | 92 | 64 | 0 |
N.S. |
1 | 0.37 | 0.35 | 0.41 | 0.00 | 0.46 | 0.00 | 0.41 | 0.28 | 0.00 |
time (sec) |
N/A | 0.820 | 0.059 | 0.190 | 0.000 | 0.086 | 0.000 | 0.130 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 86 | 74 | 0 | 0 | 0 | 0 | 0 | 437 | 0 |
N.S. |
1 | 0.63 | 0.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.21 | 0.00 |
time (sec) |
N/A | 0.854 | 0.067 | 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 | C | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 173 | 129 | 0 | 0 | 0 | 0 | 0 | 55 | 0 |
N.S. |
1 | 1.01 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.988 | 0.307 | 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 | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 60 | 56 | 61 | 54 | 74 | 0 | 0 | 32 | 93 |
N.S. |
1 | 0.73 | 0.68 | 0.74 | 0.66 | 0.90 | 0.00 | 0.00 | 0.39 | 1.13 |
time (sec) |
N/A | 0.811 | 0.065 | 0.204 | 0.045 | 0.082 | 0.000 | 0.000 | 0.150 | 13.546 |
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 | 83 | 62 | 60 | 63 | 57 | 75 | 0 | 0 | 30 | 94 |
N.S. |
1 | 0.75 | 0.72 | 0.76 | 0.69 | 0.90 | 0.00 | 0.00 | 0.36 | 1.13 |
time (sec) |
N/A | 0.820 | 0.052 | 0.155 | 0.044 | 0.091 | 0.000 | 0.000 | 0.151 | 13.287 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 173 | 110 | 0 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.01 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.966 | 0.331 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 85 | 75 | 0 | 0 | 0 | 0 | 0 | 91 | 0 |
N.S. |
1 | 0.62 | 0.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.841 | 0.073 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 280 | 0 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.00 | 2.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.799 | 3.055 | 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(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 101 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.788 | 0.869 | 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 | 111 | 111 | 81 | 0 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.756 | 0.339 | 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 | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 43 | 49 | 0 | 80 | 0 | 0 | 54 | 78 |
N.S. |
1 | 1.00 | 0.93 | 1.07 | 0.00 | 1.74 | 0.00 | 0.00 | 1.17 | 1.70 |
time (sec) |
N/A | 0.413 | 0.332 | 0.149 | 0.000 | 0.084 | 0.000 | 0.000 | 0.153 | 13.352 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 110 | 84 | 0 | 165 | 0 | 0 | 70 | 173 |
N.S. |
1 | 1.00 | 1.08 | 0.82 | 0.00 | 1.62 | 0.00 | 0.00 | 0.69 | 1.70 |
time (sec) |
N/A | 0.710 | 0.800 | 0.152 | 0.000 | 0.141 | 0.000 | 0.000 | 0.154 | 13.387 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 163 | 299 | 140 | 0 | 291 | 0 | 0 | 92 | 289 |
N.S. |
1 | 0.98 | 1.80 | 0.84 | 0.00 | 1.75 | 0.00 | 0.00 | 0.55 | 1.74 |
time (sec) |
N/A | 1.043 | 2.234 | 0.152 | 0.000 | 0.130 | 0.000 | 0.000 | 0.167 | 13.476 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 224 | 260 | 218 | 0 | 453 | 0 | 0 | 108 | 441 |
N.S. |
1 | 0.94 | 1.09 | 0.91 | 0.00 | 1.90 | 0.00 | 0.00 | 0.45 | 1.85 |
time (sec) |
N/A | 1.397 | 1.946 | 0.161 | 0.000 | 0.153 | 0.000 | 0.000 | 0.161 | 13.616 |
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 | 356 | 275 | 133 | 0 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.77 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 1.090 | 0.919 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 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 | 164 | 164 | 127 | 0 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 1.170 | 0.666 | 0.000 | 0.000 | 0.000 | 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 | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 43 | 49 | 0 | 82 | 0 | 0 | 55 | 81 |
N.S. |
1 | 1.00 | 0.93 | 1.07 | 0.00 | 1.78 | 0.00 | 0.00 | 1.20 | 1.76 |
time (sec) |
N/A | 0.475 | 0.454 | 0.153 | 0.000 | 0.084 | 0.000 | 0.000 | 0.155 | 13.316 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 43 | 49 | 0 | 80 | 0 | 0 | 54 | 78 |
N.S. |
1 | 1.00 | 0.93 | 1.07 | 0.00 | 1.74 | 0.00 | 0.00 | 1.17 | 1.70 |
time (sec) |
N/A | 0.415 | 0.044 | 0.266 | 0.000 | 0.113 | 0.000 | 0.000 | 0.147 | 0.001 |
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 | 277 | 224 | 127 | 0 | 0 | 0 | 0 | 0 | 55 | 0 |
N.S. |
1 | 0.81 | 0.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 1.080 | 1.564 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 460 | 362 | 201 | 0 | 0 | 0 | 0 | 0 | 73 | 0 |
N.S. |
1 | 0.79 | 0.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 1.357 | 2.514 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 330 | 239 | 110 | 93 | 0 | 175 | 0 | 0 | 73 | 175 |
N.S. |
1 | 0.72 | 0.33 | 0.28 | 0.00 | 0.53 | 0.00 | 0.00 | 0.22 | 0.53 |
time (sec) |
N/A | 1.044 | 1.088 | 0.160 | 0.000 | 0.085 | 0.000 | 0.000 | 0.165 | 13.298 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 108 | 109 | 96 | 0 | 180 | 0 | 0 | 73 | 175 |
N.S. |
1 | 1.06 | 1.07 | 0.94 | 0.00 | 1.76 | 0.00 | 0.00 | 0.72 | 1.72 |
time (sec) |
N/A | 0.817 | 1.122 | 0.162 | 0.000 | 0.087 | 0.000 | 0.000 | 0.156 | 13.822 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 103 | 108 | 86 | 0 | 171 | 0 | 0 | 71 | 176 |
N.S. |
1 | 1.06 | 1.11 | 0.89 | 0.00 | 1.76 | 0.00 | 0.00 | 0.73 | 1.81 |
time (sec) |
N/A | 0.741 | 0.804 | 0.161 | 0.000 | 0.089 | 0.000 | 0.000 | 0.155 | 13.446 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 110 | 84 | 0 | 165 | 0 | 0 | 70 | 173 |
N.S. |
1 | 1.00 | 1.08 | 0.82 | 0.00 | 1.62 | 0.00 | 0.00 | 0.69 | 1.70 |
time (sec) |
N/A | 0.665 | 0.194 | 0.145 | 0.000 | 0.085 | 0.000 | 0.000 | 0.154 | 0.001 |
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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 944 | 624 | 220 | 0 | 0 | 0 | 0 | 0 | 72 | 0 |
N.S. |
1 | 0.66 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.694 | 2.214 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 127 | 83 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.713 | 0.215 | 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 | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 36 | 38 | 34 | 42 | 0 | 0 | 38 | 59 |
N.S. |
1 | 1.00 | 0.71 | 0.75 | 0.67 | 0.82 | 0.00 | 0.00 | 0.75 | 1.16 |
time (sec) |
N/A | 0.631 | 0.098 | 0.994 | 0.039 | 0.093 | 0.000 | 0.000 | 0.139 | 13.383 |
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 | 52 | 52 | 36 | 40 | 36 | 44 | 0 | 0 | 40 | 59 |
N.S. |
1 | 1.00 | 0.69 | 0.77 | 0.69 | 0.85 | 0.00 | 0.00 | 0.77 | 1.13 |
time (sec) |
N/A | 0.631 | 0.076 | 0.522 | 0.056 | 0.080 | 0.000 | 0.000 | 0.150 | 13.198 |
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 | 63 | 63 | 72 | 0 | 0 | 0 | 0 | 0 | 720 | 0 |
N.S. |
1 | 1.00 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 11.43 | 0.00 |
time (sec) |
N/A | 0.553 | 0.029 | 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 | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 67 | 0 | 0 | 0 | 648 | 0 | 194 | 0 |
N.S. |
1 | 1.00 | 1.24 | 0.00 | 0.00 | 0.00 | 12.00 | 0.00 | 3.59 | 0.00 |
time (sec) |
N/A | 0.537 | 0.022 | 0.000 | 0.000 | 0.000 | 13.403 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 0 | 0 | 0 | 24 | 0 | 110 | 43 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 | 2.39 | 0.93 |
time (sec) |
N/A | 0.269 | 0.105 | 0.000 | 0.000 | 0.000 | 0.493 | 0.000 | 0.156 | 13.727 |
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 | 65 | 55 | 73 | 0 | 0 | 0 | 648 | 0 | 196 | 0 |
N.S. |
1 | 0.85 | 1.12 | 0.00 | 0.00 | 0.00 | 9.97 | 0.00 | 3.02 | 0.00 |
time (sec) |
N/A | 0.540 | 0.034 | 0.000 | 0.000 | 0.000 | 11.362 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 64 | 74 | 0 | 0 | 0 | 0 | 0 | 712 | 0 |
N.S. |
1 | 0.97 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 10.79 | 0.00 |
time (sec) |
N/A | 0.559 | 0.036 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 118 | 122 | 0 | 0 | 0 | 0 | 0 | 88 | 0 |
N.S. |
1 | 1.39 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.690 | 0.305 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 118 | 122 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 2.07 | 2.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.674 | 0.327 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 118 | 118 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.39 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.713 | 0.319 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 118 | 119 | 0 | 0 | 0 | 0 | 0 | 86 | 0 |
N.S. |
1 | 1.39 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 0.707 | 0.352 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 336 | 120 | 188 | 380 | 201 | 0 | 461 | 243 | 332 |
N.S. |
1 | 1.98 | 0.71 | 1.11 | 2.24 | 1.18 | 0.00 | 2.71 | 1.43 | 1.95 |
time (sec) |
N/A | 0.870 | 0.401 | 0.119 | 0.116 | 0.093 | 0.000 | 0.151 | 0.209 | 13.497 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 262 | 104 | 172 | 302 | 179 | 0 | 355 | 203 | 258 |
N.S. |
1 | 1.91 | 0.76 | 1.26 | 2.20 | 1.31 | 0.00 | 2.59 | 1.48 | 1.88 |
time (sec) |
N/A | 0.781 | 0.336 | 0.106 | 0.115 | 0.087 | 0.000 | 0.162 | 0.178 | 13.318 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 188 | 94 | 156 | 223 | 157 | 0 | 249 | 155 | 183 |
N.S. |
1 | 1.81 | 0.90 | 1.50 | 2.14 | 1.51 | 0.00 | 2.39 | 1.49 | 1.76 |
time (sec) |
N/A | 0.671 | 0.229 | 0.105 | 0.114 | 0.110 | 0.000 | 0.145 | 0.160 | 13.623 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 113 | 53 | 127 | 117 | 104 | 0 | 130 | 103 | 84 |
N.S. |
1 | 1.98 | 0.93 | 2.23 | 2.05 | 1.82 | 0.00 | 2.28 | 1.81 | 1.47 |
time (sec) |
N/A | 0.543 | 0.160 | 0.088 | 0.114 | 0.090 | 0.000 | 0.167 | 0.154 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 101 | 56 | 144 | 116 | 93 | 0 | 0 | 70 | 62 |
N.S. |
1 | 1.46 | 0.81 | 2.09 | 1.68 | 1.35 | 0.00 | 0.00 | 1.01 | 0.90 |
time (sec) |
N/A | 0.516 | 0.191 | 0.132 | 0.029 | 0.107 | 0.000 | 0.000 | 0.161 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 170 | 83 | 218 | 160 | 134 | 0 | 0 | 156 | 128 |
N.S. |
1 | 1.63 | 0.80 | 2.10 | 1.54 | 1.29 | 0.00 | 0.00 | 1.50 | 1.23 |
time (sec) |
N/A | 0.626 | 0.458 | 0.161 | 0.033 | 0.092 | 0.000 | 0.000 | 0.153 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 232 | 99 | 292 | 194 | 178 | 0 | 0 | 239 | 171 |
N.S. |
1 | 1.69 | 0.72 | 2.13 | 1.42 | 1.30 | 0.00 | 0.00 | 1.74 | 1.25 |
time (sec) |
N/A | 0.725 | 0.614 | 0.174 | 0.030 | 0.086 | 0.000 | 0.000 | 0.180 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 307 | 115 | 366 | 230 | 274 | 0 | 0 | 322 | 210 |
N.S. |
1 | 1.81 | 0.68 | 2.15 | 1.35 | 1.61 | 0.00 | 0.00 | 1.89 | 1.24 |
time (sec) |
N/A | 0.853 | 0.717 | 0.198 | 0.034 | 0.112 | 0.000 | 0.000 | 0.256 | 13.219 |
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 | 127 | 99 | 127 | 88 | 114 | 122 | 124 | 115 | 91 | 89 |
N.S. |
1 | 0.78 | 1.00 | 0.69 | 0.90 | 0.96 | 0.98 | 0.91 | 0.72 | 0.70 |
time (sec) |
N/A | 0.829 | 0.063 | 0.299 | 0.029 | 0.070 | 0.364 | 0.121 | 0.152 | 13.157 |
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 | 90 | 73 | 90 | 64 | 81 | 89 | 88 | 82 | 67 | 65 |
N.S. |
1 | 0.81 | 1.00 | 0.71 | 0.90 | 0.99 | 0.98 | 0.91 | 0.74 | 0.72 |
time (sec) |
N/A | 0.783 | 0.037 | 0.257 | 0.027 | 0.110 | 0.237 | 0.134 | 0.158 | 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 | 76 | 60 | 76 | 55 | 70 | 78 | 76 | 71 | 59 | 56 |
N.S. |
1 | 0.79 | 1.00 | 0.72 | 0.92 | 1.03 | 1.00 | 0.93 | 0.78 | 0.74 |
time (sec) |
N/A | 0.762 | 0.033 | 0.217 | 0.032 | 0.064 | 0.184 | 0.124 | 0.145 | 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 | 39 | 35 | 39 | 31 | 35 | 43 | 39 | 36 | 35 | 32 |
N.S. |
1 | 0.90 | 1.00 | 0.79 | 0.90 | 1.10 | 1.00 | 0.92 | 0.90 | 0.82 |
time (sec) |
N/A | 0.709 | 0.024 | 0.204 | 0.026 | 0.069 | 0.088 | 0.120 | 0.154 | 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 | 21 | 21 | 21 | 22 | 21 | 26 | 20 | 22 | 23 | 23 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.00 | 1.24 | 0.95 | 1.05 | 1.10 | 1.10 |
time (sec) |
N/A | 0.611 | 0.019 | 0.168 | 0.029 | 0.071 | 0.049 | 0.140 | 0.150 | 0.025 |
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 | 36 | 37 | 28 | 36 | 35 | 40 | 36 | 36 | 44 | 33 |
N.S. |
1 | 1.03 | 0.78 | 1.00 | 0.97 | 1.11 | 1.00 | 1.00 | 1.22 | 0.92 |
time (sec) |
N/A | 0.734 | 0.038 | 0.145 | 0.032 | 0.077 | 0.071 | 0.135 | 0.154 | 13.161 |
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 | 75 | 72 | 75 | 60 | 69 | 93 | 73 | 57 | 105 | 68 |
N.S. |
1 | 0.96 | 1.00 | 0.80 | 0.92 | 1.24 | 0.97 | 0.76 | 1.40 | 0.91 |
time (sec) |
N/A | 0.799 | 0.059 | 0.162 | 0.029 | 0.082 | 0.200 | 0.114 | 0.152 | 0.056 |
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 | 110 | 99 | 82 | 84 | 97 | 137 | 102 | 80 | 153 | 94 |
N.S. |
1 | 0.90 | 0.75 | 0.76 | 0.88 | 1.25 | 0.93 | 0.73 | 1.39 | 0.85 |
time (sec) |
N/A | 0.848 | 0.093 | 0.169 | 0.028 | 0.098 | 0.344 | 0.118 | 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 | 145 | 130 | 98 | 108 | 145 | 233 | 156 | 96 | 277 | 142 |
N.S. |
1 | 0.90 | 0.68 | 0.74 | 1.00 | 1.61 | 1.08 | 0.66 | 1.91 | 0.98 |
time (sec) |
N/A | 0.929 | 0.130 | 0.173 | 0.039 | 0.080 | 0.476 | 0.117 | 0.160 | 13.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 336 | 126 | 180 | 380 | 201 | 0 | 461 | 243 | 332 |
N.S. |
1 | 1.87 | 0.70 | 1.00 | 2.11 | 1.12 | 0.00 | 2.56 | 1.35 | 1.84 |
time (sec) |
N/A | 0.878 | 0.359 | 0.122 | 0.118 | 0.122 | 0.000 | 0.158 | 0.205 | 0.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 263 | 110 | 173 | 302 | 179 | 0 | 355 | 203 | 258 |
N.S. |
1 | 1.79 | 0.75 | 1.18 | 2.05 | 1.22 | 0.00 | 2.41 | 1.38 | 1.76 |
time (sec) |
N/A | 0.806 | 0.328 | 0.110 | 0.115 | 0.105 | 0.000 | 0.150 | 0.182 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 187 | 94 | 157 | 223 | 156 | 0 | 248 | 163 | 183 |
N.S. |
1 | 1.67 | 0.84 | 1.40 | 1.99 | 1.39 | 0.00 | 2.21 | 1.46 | 1.63 |
time (sec) |
N/A | 0.675 | 0.259 | 0.093 | 0.114 | 0.093 | 0.000 | 0.146 | 0.158 | 13.231 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 79 | 57 | 129 | 118 | 106 | 0 | 130 | 101 | 84 |
N.S. |
1 | 1.16 | 0.84 | 1.90 | 1.74 | 1.56 | 0.00 | 1.91 | 1.49 | 1.24 |
time (sec) |
N/A | 0.480 | 0.173 | 0.108 | 0.113 | 0.086 | 0.000 | 0.143 | 0.162 | 13.193 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 140 | 69 | 185 | 133 | 128 | 0 | 0 | 130 | 100 |
N.S. |
1 | 1.33 | 0.66 | 1.76 | 1.27 | 1.22 | 0.00 | 0.00 | 1.24 | 0.95 |
time (sec) |
N/A | 0.568 | 0.217 | 0.128 | 0.029 | 0.137 | 0.000 | 0.000 | 0.155 | 13.492 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 173 | 78 | 225 | 153 | 170 | 0 | 63 | 199 | 121 |
N.S. |
1 | 1.25 | 0.57 | 1.63 | 1.11 | 1.23 | 0.00 | 0.46 | 1.44 | 0.88 |
time (sec) |
N/A | 0.609 | 0.520 | 0.154 | 0.034 | 0.095 | 0.000 | 0.172 | 0.155 | 13.156 |
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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 244 | 101 | 299 | 192 | 204 | 0 | 0 | 282 | 160 |
N.S. |
1 | 1.43 | 0.59 | 1.75 | 1.12 | 1.19 | 0.00 | 0.00 | 1.65 | 0.94 |
time (sec) |
N/A | 0.744 | 0.936 | 0.171 | 0.035 | 0.108 | 0.000 | 0.000 | 0.167 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 313 | 117 | 373 | 226 | 248 | 0 | 0 | 475 | 203 |
N.S. |
1 | 1.53 | 0.57 | 1.83 | 1.11 | 1.22 | 0.00 | 0.00 | 2.33 | 1.00 |
time (sec) |
N/A | 0.838 | 0.772 | 0.190 | 0.035 | 0.093 | 0.000 | 0.000 | 0.247 | 13.754 |
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 | 116 | 93 | 116 | 80 | 103 | 111 | 112 | 184 | 83 | 81 |
N.S. |
1 | 0.80 | 1.00 | 0.69 | 0.89 | 0.96 | 0.97 | 1.59 | 0.72 | 0.70 |
time (sec) |
N/A | 0.814 | 0.061 | 0.340 | 0.032 | 0.070 | 0.359 | 0.123 | 0.160 | 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 | 100 | 78 | 100 | 71 | 92 | 100 | 100 | 160 | 75 | 72 |
N.S. |
1 | 0.78 | 1.00 | 0.71 | 0.92 | 1.00 | 1.00 | 1.60 | 0.75 | 0.72 |
time (sec) |
N/A | 0.788 | 0.038 | 0.276 | 0.026 | 0.085 | 0.258 | 0.131 | 0.145 | 13.343 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 53 | 63 | 47 | 59 | 67 | 65 | 136 | 51 | 48 |
N.S. |
1 | 0.84 | 1.00 | 0.75 | 0.94 | 1.06 | 1.03 | 2.16 | 0.81 | 0.76 |
time (sec) |
N/A | 0.760 | 0.032 | 0.223 | 0.040 | 0.079 | 0.164 | 0.123 | 0.146 | 13.324 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 41 | 51 | 40 | 46 | 56 | 53 | 112 | 43 | 43 |
N.S. |
1 | 0.80 | 1.00 | 0.78 | 0.90 | 1.10 | 1.04 | 2.20 | 0.84 | 0.84 |
time (sec) |
N/A | 0.710 | 0.025 | 0.204 | 0.031 | 0.067 | 0.112 | 0.125 | 0.148 | 13.306 |
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 | 33 | 33 | 33 | 29 | 32 | 35 | 26 | 66 | 33 | 32 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.97 | 1.06 | 0.79 | 2.00 | 1.00 | 0.97 |
time (sec) |
N/A | 0.639 | 0.025 | 0.184 | 0.032 | 0.085 | 0.155 | 0.124 | 0.144 | 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 | 53 | 52 | 53 | 43 | 49 | 64 | 41 | 74 | 71 | 48 |
N.S. |
1 | 0.98 | 1.00 | 0.81 | 0.92 | 1.21 | 0.77 | 1.40 | 1.34 | 0.91 |
time (sec) |
N/A | 0.764 | 0.040 | 0.159 | 0.026 | 0.076 | 0.133 | 0.114 | 0.147 | 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 | 71 | 66 | 63 | 56 | 75 | 100 | 83 | 93 | 99 | 71 |
N.S. |
1 | 0.93 | 0.89 | 0.79 | 1.06 | 1.41 | 1.17 | 1.31 | 1.39 | 1.00 |
time (sec) |
N/A | 0.787 | 0.044 | 0.154 | 0.030 | 0.093 | 0.179 | 0.112 | 0.159 | 0.042 |
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 | 111 | 102 | 89 | 82 | 107 | 163 | 114 | 130 | 189 | 104 |
N.S. |
1 | 0.92 | 0.80 | 0.74 | 0.96 | 1.47 | 1.03 | 1.17 | 1.70 | 0.94 |
time (sec) |
N/A | 0.861 | 0.081 | 0.177 | 0.038 | 0.092 | 0.357 | 0.118 | 0.148 | 0.061 |
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 | 146 | 129 | 98 | 108 | 135 | 207 | 144 | 170 | 241 | 131 |
N.S. |
1 | 0.88 | 0.67 | 0.74 | 0.92 | 1.42 | 0.99 | 1.16 | 1.65 | 0.90 |
time (sec) |
N/A | 0.910 | 0.125 | 0.175 | 0.035 | 0.081 | 0.510 | 0.115 | 0.149 | 13.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 328 | 120 | 189 | 380 | 201 | 0 | 524 | 243 | 332 |
N.S. |
1 | 1.94 | 0.71 | 1.12 | 2.25 | 1.19 | 0.00 | 3.10 | 1.44 | 1.96 |
time (sec) |
N/A | 0.909 | 0.415 | 0.118 | 0.111 | 0.100 | 0.000 | 0.158 | 0.201 | 0.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 258 | 110 | 173 | 302 | 179 | 0 | 394 | 203 | 258 |
N.S. |
1 | 1.90 | 0.81 | 1.27 | 2.22 | 1.32 | 0.00 | 2.90 | 1.49 | 1.90 |
time (sec) |
N/A | 0.774 | 0.323 | 0.108 | 0.128 | 0.117 | 0.000 | 0.142 | 0.175 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 184 | 94 | 157 | 223 | 156 | 0 | 264 | 155 | 183 |
N.S. |
1 | 1.79 | 0.91 | 1.52 | 2.17 | 1.51 | 0.00 | 2.56 | 1.50 | 1.78 |
time (sec) |
N/A | 0.658 | 0.275 | 0.101 | 0.111 | 0.103 | 0.000 | 0.136 | 0.158 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 112 | 55 | 127 | 117 | 107 | 0 | 121 | 101 | 84 |
N.S. |
1 | 2.00 | 0.98 | 2.27 | 2.09 | 1.91 | 0.00 | 2.16 | 1.80 | 1.50 |
time (sec) |
N/A | 0.534 | 0.171 | 0.079 | 0.113 | 0.100 | 0.000 | 0.134 | 0.155 | 13.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 102 | 57 | 138 | 121 | 67 | 0 | 0 | 95 | 86 |
N.S. |
1 | 1.44 | 0.80 | 1.94 | 1.70 | 0.94 | 0.00 | 0.00 | 1.34 | 1.21 |
time (sec) |
N/A | 0.510 | 0.197 | 0.128 | 0.032 | 0.097 | 0.000 | 0.000 | 0.145 | 13.146 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 171 | 85 | 213 | 163 | 119 | 0 | 0 | 199 | 137 |
N.S. |
1 | 1.60 | 0.79 | 1.99 | 1.52 | 1.11 | 0.00 | 0.00 | 1.86 | 1.28 |
time (sec) |
N/A | 0.623 | 0.549 | 0.157 | 0.034 | 0.103 | 0.000 | 0.000 | 0.155 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 241 | 101 | 287 | 197 | 161 | 0 | 0 | 282 | 178 |
N.S. |
1 | 1.72 | 0.72 | 2.05 | 1.41 | 1.15 | 0.00 | 0.00 | 2.01 | 1.27 |
time (sec) |
N/A | 0.730 | 0.606 | 0.156 | 0.040 | 0.094 | 0.000 | 0.000 | 0.163 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 312 | 117 | 361 | 231 | 205 | 0 | 0 | 475 | 217 |
N.S. |
1 | 1.80 | 0.68 | 2.09 | 1.34 | 1.18 | 0.00 | 0.00 | 2.75 | 1.25 |
time (sec) |
N/A | 0.813 | 0.726 | 0.175 | 0.033 | 0.082 | 0.000 | 0.000 | 0.227 | 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 | 90 | 73 | 90 | 64 | 81 | 89 | 88 | 82 | 67 | 67 |
N.S. |
1 | 0.81 | 1.00 | 0.71 | 0.90 | 0.99 | 0.98 | 0.91 | 0.74 | 0.74 |
time (sec) |
N/A | 0.824 | 0.057 | 0.243 | 0.032 | 0.078 | 0.238 | 0.111 | 0.154 | 13.151 |
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 | 60 | 76 | 55 | 70 | 78 | 76 | 71 | 59 | 56 |
N.S. |
1 | 0.79 | 1.00 | 0.72 | 0.92 | 1.03 | 1.00 | 0.93 | 0.78 | 0.74 |
time (sec) |
N/A | 0.789 | 0.041 | 0.225 | 0.026 | 0.092 | 0.171 | 0.122 | 0.156 | 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 | 40 | 34 | 40 | 32 | 37 | 43 | 39 | 38 | 35 | 35 |
N.S. |
1 | 0.85 | 1.00 | 0.80 | 0.92 | 1.08 | 0.98 | 0.95 | 0.88 | 0.88 |
time (sec) |
N/A | 0.728 | 0.029 | 0.193 | 0.032 | 0.071 | 0.090 | 0.120 | 0.154 | 13.127 |
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 | 21 | 21 | 22 | 21 | 26 | 20 | 22 | 23 | 25 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.00 | 1.24 | 0.95 | 1.05 | 1.10 | 1.19 |
time (sec) |
N/A | 0.613 | 0.024 | 0.158 | 0.025 | 0.093 | 0.049 | 0.106 | 0.155 | 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 | 35 | 36 | 28 | 36 | 34 | 38 | 36 | 36 | 44 | 33 |
N.S. |
1 | 1.03 | 0.80 | 1.03 | 0.97 | 1.09 | 1.03 | 1.03 | 1.26 | 0.94 |
time (sec) |
N/A | 0.733 | 0.052 | 0.142 | 0.028 | 0.087 | 0.071 | 0.125 | 0.168 | 0.030 |
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 | 70 | 70 | 60 | 69 | 92 | 75 | 57 | 102 | 68 |
N.S. |
1 | 0.96 | 0.96 | 0.82 | 0.95 | 1.26 | 1.03 | 0.78 | 1.40 | 0.93 |
time (sec) |
N/A | 0.806 | 0.081 | 0.150 | 0.034 | 0.080 | 0.207 | 0.121 | 0.148 | 13.151 |
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 | 108 | 97 | 104 | 84 | 97 | 137 | 102 | 80 | 153 | 94 |
N.S. |
1 | 0.90 | 0.96 | 0.78 | 0.90 | 1.27 | 0.94 | 0.74 | 1.42 | 0.87 |
time (sec) |
N/A | 0.857 | 0.103 | 0.159 | 0.028 | 0.085 | 0.337 | 0.116 | 0.155 | 13.416 |
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 | 143 | 128 | 124 | 108 | 145 | 233 | 156 | 96 | 277 | 142 |
N.S. |
1 | 0.90 | 0.87 | 0.76 | 1.01 | 1.63 | 1.09 | 0.67 | 1.94 | 0.99 |
time (sec) |
N/A | 0.903 | 0.133 | 0.171 | 0.035 | 0.103 | 0.490 | 0.138 | 0.145 | 13.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 325 | 126 | 180 | 379 | 201 | 0 | 525 | 243 | 332 |
N.S. |
1 | 1.81 | 0.70 | 1.00 | 2.11 | 1.12 | 0.00 | 2.92 | 1.35 | 1.84 |
time (sec) |
N/A | 0.884 | 0.462 | 0.131 | 0.118 | 0.091 | 0.000 | 0.156 | 0.200 | 13.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 257 | 110 | 173 | 301 | 179 | 0 | 395 | 203 | 258 |
N.S. |
1 | 1.80 | 0.77 | 1.21 | 2.10 | 1.25 | 0.00 | 2.76 | 1.42 | 1.80 |
time (sec) |
N/A | 0.751 | 0.333 | 0.103 | 0.112 | 0.107 | 0.000 | 0.152 | 0.175 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 189 | 94 | 157 | 224 | 156 | 0 | 264 | 163 | 183 |
N.S. |
1 | 1.66 | 0.82 | 1.38 | 1.96 | 1.37 | 0.00 | 2.32 | 1.43 | 1.61 |
time (sec) |
N/A | 0.673 | 0.274 | 0.095 | 0.115 | 0.098 | 0.000 | 0.144 | 0.157 | 0.048 |