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 | B | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 81 | 57 | 130 | 118 | 103 | 0 | 122 | 103 | 84 |
N.S. |
1 | 1.17 | 0.83 | 1.88 | 1.71 | 1.49 | 0.00 | 1.77 | 1.49 | 1.22 |
time (sec) |
N/A | 0.469 | 0.175 | 0.102 | 0.115 | 0.088 | 0.000 | 0.155 | 0.151 | 0.032 |
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 | 107 | 141 | 69 | 173 | 140 | 96 | 0 | 59 | 158 | 114 |
N.S. |
1 | 1.32 | 0.64 | 1.62 | 1.31 | 0.90 | 0.00 | 0.55 | 1.48 | 1.07 |
time (sec) |
N/A | 0.575 | 0.210 | 0.122 | 0.034 | 0.098 | 0.000 | 0.142 | 0.157 | 0.039 |
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 | 140 | 173 | 78 | 207 | 161 | 135 | 0 | 59 | 221 | 141 |
N.S. |
1 | 1.24 | 0.56 | 1.48 | 1.15 | 0.96 | 0.00 | 0.42 | 1.58 | 1.01 |
time (sec) |
N/A | 0.621 | 0.471 | 0.155 | 0.033 | 0.089 | 0.000 | 0.148 | 0.168 | 0.025 |
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 | 173 | 245 | 101 | 281 | 199 | 179 | 0 | 0 | 337 | 183 |
N.S. |
1 | 1.42 | 0.58 | 1.62 | 1.15 | 1.03 | 0.00 | 0.00 | 1.95 | 1.06 |
time (sec) |
N/A | 0.704 | 0.639 | 0.174 | 0.029 | 0.091 | 0.000 | 0.000 | 0.185 | 13.128 |
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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 314 | 117 | 355 | 231 | 275 | 0 | 0 | 420 | 224 |
N.S. |
1 | 1.52 | 0.57 | 1.72 | 1.12 | 1.33 | 0.00 | 0.00 | 2.04 | 1.09 |
time (sec) |
N/A | 0.836 | 0.738 | 0.192 | 0.036 | 0.098 | 0.000 | 0.000 | 0.276 | 13.127 |
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 | 321 | 101 | 94 | 112 | 0 | 96 | 0 | 132 | 69 | 0 |
N.S. |
1 | 0.31 | 0.29 | 0.35 | 0.00 | 0.30 | 0.00 | 0.41 | 0.21 | 0.00 |
time (sec) |
N/A | 0.700 | 0.103 | 0.079 | 0.000 | 0.082 | 0.000 | 0.141 | 0.169 | 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 | 236 | 78 | 73 | 96 | 0 | 74 | 0 | 106 | 53 | 0 |
N.S. |
1 | 0.33 | 0.31 | 0.41 | 0.00 | 0.31 | 0.00 | 0.45 | 0.22 | 0.00 |
time (sec) |
N/A | 0.671 | 0.074 | 0.071 | 0.000 | 0.076 | 0.000 | 0.139 | 0.152 | 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 | 146 | 62 | 62 | 80 | 0 | 42 | 0 | 70 | 35 | 0 |
N.S. |
1 | 0.42 | 0.42 | 0.55 | 0.00 | 0.29 | 0.00 | 0.48 | 0.24 | 0.00 |
time (sec) |
N/A | 0.642 | 0.052 | 0.069 | 0.000 | 0.091 | 0.000 | 0.134 | 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 | 67 | 39 | 38 | 50 | 0 | 17 | 0 | 40 | 12 | 0 |
N.S. |
1 | 0.58 | 0.57 | 0.75 | 0.00 | 0.25 | 0.00 | 0.60 | 0.18 | 0.00 |
time (sec) |
N/A | 0.578 | 0.035 | 0.063 | 0.000 | 0.089 | 0.000 | 0.132 | 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 | 72 | 51 | 43 | 57 | 0 | 24 | 0 | 0 | 19 | 0 |
N.S. |
1 | 0.71 | 0.60 | 0.79 | 0.00 | 0.33 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.620 | 0.033 | 0.067 | 0.000 | 0.087 | 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 | 173 | 84 | 71 | 102 | 0 | 68 | 0 | 0 | 64 | 0 |
N.S. |
1 | 0.49 | 0.41 | 0.59 | 0.00 | 0.39 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.672 | 0.081 | 0.076 | 0.000 | 0.116 | 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 | 263 | 113 | 97 | 175 | 0 | 137 | 0 | 0 | 147 | 0 |
N.S. |
1 | 0.43 | 0.37 | 0.67 | 0.00 | 0.52 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.741 | 0.136 | 0.082 | 0.000 | 0.120 | 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 | 359 | 142 | 119 | 247 | 0 | 205 | 0 | 0 | 234 | 0 |
N.S. |
1 | 0.40 | 0.33 | 0.69 | 0.00 | 0.57 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.798 | 0.201 | 0.091 | 0.000 | 0.102 | 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 | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 182 | 150 | 250 | 0 | 425 | 1059 | 561 | 184 | 0 |
N.S. |
1 | 0.96 | 0.79 | 1.32 | 0.00 | 2.24 | 5.57 | 2.95 | 0.97 | 0.00 |
time (sec) |
N/A | 0.950 | 0.265 | 0.315 | 0.000 | 0.138 | 19.383 | 0.277 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 147 | 134 | 234 | 0 | 381 | 500 | 416 | 148 | 0 |
N.S. |
1 | 0.94 | 0.86 | 1.50 | 0.00 | 2.44 | 3.21 | 2.67 | 0.95 | 0.00 |
time (sec) |
N/A | 0.900 | 0.207 | 0.289 | 0.000 | 0.136 | 10.636 | 0.222 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 112 | 115 | 202 | 0 | 304 | 376 | 266 | 102 | 0 |
N.S. |
1 | 0.92 | 0.94 | 1.66 | 0.00 | 2.49 | 3.08 | 2.18 | 0.84 | 0.00 |
time (sec) |
N/A | 0.804 | 0.186 | 0.250 | 0.000 | 0.114 | 7.214 | 0.190 | 0.160 | 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 | 88 | 72 | 80 | 197 | 0 | 252 | 0 | 0 | 51 | 0 |
N.S. |
1 | 0.82 | 0.91 | 2.24 | 0.00 | 2.86 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.705 | 0.141 | 0.211 | 0.000 | 0.129 | 0.000 | 0.000 | 0.152 | 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 | 78 | 93 | 68 | 160 | 0 | 216 | 0 | 0 | 85 | 0 |
N.S. |
1 | 1.19 | 0.87 | 2.05 | 0.00 | 2.77 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.664 | 0.168 | 0.233 | 0.000 | 0.122 | 0.000 | 0.000 | 0.155 | 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 | 118 | 126 | 95 | 214 | 0 | 280 | 0 | 0 | 142 | 0 |
N.S. |
1 | 1.07 | 0.81 | 1.81 | 0.00 | 2.37 | 0.00 | 0.00 | 1.20 | 0.00 |
time (sec) |
N/A | 0.902 | 0.154 | 0.178 | 0.000 | 0.110 | 0.000 | 0.000 | 0.159 | 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 | 152 | 158 | 105 | 298 | 0 | 352 | 0 | 0 | 217 | 0 |
N.S. |
1 | 1.04 | 0.69 | 1.96 | 0.00 | 2.32 | 0.00 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 1.125 | 0.169 | 0.188 | 0.000 | 0.132 | 0.000 | 0.000 | 0.165 | 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 | 187 | 190 | 133 | 382 | 0 | 496 | 0 | 0 | 370 | 0 |
N.S. |
1 | 1.02 | 0.71 | 2.04 | 0.00 | 2.65 | 0.00 | 0.00 | 1.98 | 0.00 |
time (sec) |
N/A | 1.343 | 0.218 | 0.207 | 0.000 | 0.177 | 0.000 | 0.000 | 0.187 | 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 | 322 | 102 | 95 | 112 | 0 | 96 | 0 | 132 | 69 | 0 |
N.S. |
1 | 0.32 | 0.30 | 0.35 | 0.00 | 0.30 | 0.00 | 0.41 | 0.21 | 0.00 |
time (sec) |
N/A | 0.711 | 0.090 | 0.082 | 0.000 | 0.095 | 0.000 | 0.147 | 0.153 | 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 | 324 | 102 | 97 | 112 | 0 | 96 | 0 | 133 | 69 | 0 |
N.S. |
1 | 0.31 | 0.30 | 0.35 | 0.00 | 0.30 | 0.00 | 0.41 | 0.21 | 0.00 |
time (sec) |
N/A | 0.691 | 0.079 | 0.079 | 0.000 | 0.108 | 0.000 | 0.150 | 0.170 | 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 | 234 | 80 | 78 | 96 | 0 | 72 | 0 | 107 | 53 | 0 |
N.S. |
1 | 0.34 | 0.33 | 0.41 | 0.00 | 0.31 | 0.00 | 0.46 | 0.23 | 0.00 |
time (sec) |
N/A | 0.683 | 0.071 | 0.076 | 0.000 | 0.087 | 0.000 | 0.147 | 0.155 | 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 | 148 | 60 | 57 | 69 | 0 | 44 | 0 | 71 | 35 | 0 |
N.S. |
1 | 0.41 | 0.39 | 0.47 | 0.00 | 0.30 | 0.00 | 0.48 | 0.24 | 0.00 |
time (sec) |
N/A | 0.635 | 0.054 | 0.075 | 0.000 | 0.091 | 0.000 | 0.134 | 0.146 | 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 | 109 | 50 | 51 | 65 | 0 | 27 | 0 | 63 | 22 | 0 |
N.S. |
1 | 0.46 | 0.47 | 0.60 | 0.00 | 0.25 | 0.00 | 0.58 | 0.20 | 0.00 |
time (sec) |
N/A | 0.620 | 0.042 | 0.069 | 0.000 | 0.142 | 0.000 | 0.135 | 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 | 115 | 62 | 57 | 85 | 0 | 49 | 0 | 0 | 46 | 0 |
N.S. |
1 | 0.54 | 0.50 | 0.74 | 0.00 | 0.43 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.638 | 0.071 | 0.082 | 0.000 | 0.110 | 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(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 84 | 64 | 102 | 0 | 81 | 0 | 0 | 75 | 0 |
N.S. |
1 | 0.49 | 0.37 | 0.60 | 0.00 | 0.47 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.701 | 0.097 | 0.072 | 0.000 | 0.107 | 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 | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 114 | 96 | 175 | 0 | 138 | 0 | 0 | 147 | 0 |
N.S. |
1 | 0.43 | 0.36 | 0.66 | 0.00 | 0.52 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.744 | 0.129 | 0.092 | 0.000 | 0.108 | 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 | 360 | 145 | 116 | 247 | 0 | 207 | 0 | 0 | 235 | 0 |
N.S. |
1 | 0.40 | 0.32 | 0.69 | 0.00 | 0.58 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.799 | 0.204 | 0.089 | 0.000 | 0.142 | 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 | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 322 | 100 | 95 | 112 | 0 | 96 | 0 | 156 | 79 | 0 |
N.S. |
1 | 0.31 | 0.30 | 0.35 | 0.00 | 0.30 | 0.00 | 0.48 | 0.25 | 0.00 |
time (sec) |
N/A | 0.702 | 0.080 | 0.076 | 0.000 | 0.113 | 0.000 | 0.116 | 0.153 | 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 | 238 | 80 | 75 | 96 | 0 | 74 | 0 | 118 | 63 | 0 |
N.S. |
1 | 0.34 | 0.32 | 0.40 | 0.00 | 0.31 | 0.00 | 0.50 | 0.26 | 0.00 |
time (sec) |
N/A | 0.683 | 0.068 | 0.075 | 0.000 | 0.097 | 0.000 | 0.123 | 0.162 | 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 | 147 | 59 | 63 | 80 | 0 | 44 | 0 | 72 | 45 | 0 |
N.S. |
1 | 0.40 | 0.43 | 0.54 | 0.00 | 0.30 | 0.00 | 0.49 | 0.31 | 0.00 |
time (sec) |
N/A | 0.618 | 0.050 | 0.069 | 0.000 | 0.100 | 0.000 | 0.133 | 0.159 | 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 | 68 | 41 | 39 | 52 | 0 | 19 | 0 | 36 | 17 | 0 |
N.S. |
1 | 0.60 | 0.57 | 0.76 | 0.00 | 0.28 | 0.00 | 0.53 | 0.25 | 0.00 |
time (sec) |
N/A | 0.594 | 0.038 | 0.057 | 0.000 | 0.085 | 0.000 | 0.116 | 0.152 | 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 | 72 | 48 | 43 | 59 | 0 | 26 | 0 | 0 | 21 | 0 |
N.S. |
1 | 0.67 | 0.60 | 0.82 | 0.00 | 0.36 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.619 | 0.035 | 0.057 | 0.000 | 0.092 | 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(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 85 | 70 | 103 | 0 | 66 | 0 | 0 | 63 | 0 |
N.S. |
1 | 0.49 | 0.41 | 0.60 | 0.00 | 0.38 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.684 | 0.080 | 0.072 | 0.000 | 0.120 | 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 | 263 | 110 | 95 | 175 | 0 | 135 | 0 | 0 | 146 | 0 |
N.S. |
1 | 0.42 | 0.36 | 0.67 | 0.00 | 0.51 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.743 | 0.175 | 0.085 | 0.000 | 0.112 | 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 | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 358 | 143 | 119 | 247 | 0 | 201 | 0 | 0 | 233 | 0 |
N.S. |
1 | 0.40 | 0.33 | 0.69 | 0.00 | 0.56 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.818 | 0.198 | 0.080 | 0.000 | 0.118 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 182 | 150 | 250 | 0 | 425 | 1059 | 561 | 184 | 0 |
N.S. |
1 | 0.96 | 0.79 | 1.32 | 0.00 | 2.24 | 5.57 | 2.95 | 0.97 | 0.00 |
time (sec) |
N/A | 0.950 | 0.265 | 0.326 | 0.000 | 0.136 | 19.478 | 0.271 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 147 | 134 | 234 | 0 | 381 | 500 | 416 | 148 | 0 |
N.S. |
1 | 0.94 | 0.86 | 1.50 | 0.00 | 2.44 | 3.21 | 2.67 | 0.95 | 0.00 |
time (sec) |
N/A | 0.915 | 0.205 | 0.286 | 0.000 | 0.101 | 10.179 | 0.241 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 110 | 115 | 202 | 0 | 303 | 376 | 266 | 102 | 0 |
N.S. |
1 | 0.92 | 0.96 | 1.68 | 0.00 | 2.52 | 3.13 | 2.22 | 0.85 | 0.00 |
time (sec) |
N/A | 0.817 | 0.182 | 0.244 | 0.000 | 0.109 | 7.048 | 0.183 | 0.153 | 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 | 88 | 72 | 80 | 196 | 0 | 252 | 0 | 0 | 51 | 0 |
N.S. |
1 | 0.82 | 0.91 | 2.23 | 0.00 | 2.86 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.745 | 0.131 | 0.213 | 0.000 | 0.113 | 0.000 | 0.000 | 0.146 | 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 | 80 | 93 | 68 | 154 | 0 | 212 | 0 | 0 | 85 | 0 |
N.S. |
1 | 1.16 | 0.85 | 1.92 | 0.00 | 2.65 | 0.00 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.679 | 0.184 | 0.239 | 0.000 | 0.112 | 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 | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 127 | 95 | 202 | 0 | 279 | 0 | 0 | 142 | 0 |
N.S. |
1 | 1.06 | 0.79 | 1.68 | 0.00 | 2.32 | 0.00 | 0.00 | 1.18 | 0.00 |
time (sec) |
N/A | 0.937 | 0.145 | 0.180 | 0.000 | 0.120 | 0.000 | 0.000 | 0.144 | 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 | 154 | 159 | 105 | 286 | 0 | 351 | 0 | 0 | 217 | 0 |
N.S. |
1 | 1.03 | 0.68 | 1.86 | 0.00 | 2.28 | 0.00 | 0.00 | 1.41 | 0.00 |
time (sec) |
N/A | 1.136 | 0.164 | 0.296 | 0.000 | 0.123 | 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 | 189 | 191 | 131 | 370 | 0 | 495 | 0 | 0 | 370 | 0 |
N.S. |
1 | 1.01 | 0.69 | 1.96 | 0.00 | 2.62 | 0.00 | 0.00 | 1.96 | 0.00 |
time (sec) |
N/A | 1.420 | 0.209 | 0.207 | 0.000 | 0.186 | 0.000 | 0.000 | 0.178 | 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 | 322 | 100 | 95 | 112 | 0 | 96 | 0 | 157 | 79 | 0 |
N.S. |
1 | 0.31 | 0.30 | 0.35 | 0.00 | 0.30 | 0.00 | 0.49 | 0.25 | 0.00 |
time (sec) |
N/A | 0.787 | 0.092 | 0.085 | 0.000 | 0.106 | 0.000 | 0.125 | 0.167 | 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 | 324 | 103 | 97 | 112 | 0 | 96 | 0 | 157 | 79 | 0 |
N.S. |
1 | 0.32 | 0.30 | 0.35 | 0.00 | 0.30 | 0.00 | 0.48 | 0.24 | 0.00 |
time (sec) |
N/A | 0.713 | 0.083 | 0.082 | 0.000 | 0.089 | 0.000 | 0.126 | 0.160 | 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 | 235 | 77 | 79 | 96 | 0 | 74 | 0 | 118 | 63 | 0 |
N.S. |
1 | 0.33 | 0.34 | 0.41 | 0.00 | 0.31 | 0.00 | 0.50 | 0.27 | 0.00 |
time (sec) |
N/A | 0.680 | 0.079 | 0.082 | 0.000 | 0.099 | 0.000 | 0.116 | 0.159 | 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 | 148 | 62 | 57 | 69 | 0 | 42 | 0 | 73 | 37 | 0 |
N.S. |
1 | 0.42 | 0.39 | 0.47 | 0.00 | 0.28 | 0.00 | 0.49 | 0.25 | 0.00 |
time (sec) |
N/A | 0.627 | 0.056 | 0.066 | 0.000 | 0.089 | 0.000 | 0.118 | 0.157 | 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 | 107 | 47 | 47 | 67 | 0 | 25 | 0 | 55 | 23 | 0 |
N.S. |
1 | 0.44 | 0.44 | 0.63 | 0.00 | 0.23 | 0.00 | 0.51 | 0.21 | 0.00 |
time (sec) |
N/A | 0.612 | 0.038 | 0.069 | 0.000 | 0.095 | 0.000 | 0.135 | 0.154 | 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 | 113 | 62 | 55 | 87 | 0 | 47 | 0 | 0 | 46 | 0 |
N.S. |
1 | 0.55 | 0.49 | 0.77 | 0.00 | 0.42 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.637 | 0.068 | 0.072 | 0.000 | 0.099 | 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(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 79 | 63 | 102 | 0 | 81 | 0 | 0 | 75 | 0 |
N.S. |
1 | 0.47 | 0.38 | 0.61 | 0.00 | 0.48 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.693 | 0.100 | 0.073 | 0.000 | 0.102 | 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 | 264 | 113 | 95 | 175 | 0 | 137 | 0 | 0 | 147 | 0 |
N.S. |
1 | 0.43 | 0.36 | 0.66 | 0.00 | 0.52 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.748 | 0.137 | 0.081 | 0.000 | 0.106 | 0.000 | 0.000 | 0.140 | 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 | 357 | 140 | 108 | 247 | 0 | 208 | 0 | 0 | 235 | 0 |
N.S. |
1 | 0.39 | 0.30 | 0.69 | 0.00 | 0.58 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.804 | 0.251 | 0.094 | 0.000 | 0.149 | 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 | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 49 | 45 | 47 | 0 | 24 | 0 | 0 | 16 | 46 |
N.S. |
1 | 0.64 | 0.59 | 0.62 | 0.00 | 0.32 | 0.00 | 0.00 | 0.21 | 0.61 |
time (sec) |
N/A | 0.826 | 0.034 | 0.063 | 0.000 | 0.104 | 0.000 | 0.000 | 0.139 | 13.338 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 43 | 46 | 0 | 21 | 0 | 0 | 13 | 45 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 0.00 | 0.49 | 0.00 | 0.00 | 0.30 | 1.05 |
time (sec) |
N/A | 0.683 | 0.034 | 0.062 | 0.000 | 0.102 | 0.000 | 0.000 | 0.140 | 13.253 |
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 | 67 | 39 | 38 | 50 | 0 | 17 | 0 | 40 | 12 | 0 |
N.S. |
1 | 0.58 | 0.57 | 0.75 | 0.00 | 0.25 | 0.00 | 0.60 | 0.18 | 0.00 |
time (sec) |
N/A | 0.590 | 0.020 | 0.052 | 0.000 | 0.106 | 0.000 | 0.133 | 0.136 | 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 | 70 | 43 | 41 | 50 | 0 | 21 | 0 | 32 | 16 | 0 |
N.S. |
1 | 0.61 | 0.59 | 0.71 | 0.00 | 0.30 | 0.00 | 0.46 | 0.23 | 0.00 |
time (sec) |
N/A | 0.821 | 0.030 | 0.079 | 0.000 | 0.088 | 0.000 | 0.130 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 47 | 0 | 21 | 0 | 30 | 16 | 63 |
N.S. |
1 | 1.00 | 1.00 | 1.02 | 0.00 | 0.46 | 0.00 | 0.65 | 0.35 | 1.37 |
time (sec) |
N/A | 0.780 | 0.031 | 0.072 | 0.000 | 0.090 | 0.000 | 0.139 | 0.142 | 13.247 |
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 | 155 | 176 | 101 | 142 | 0 | 238 | 0 | 139 | 105 | 0 |
N.S. |
1 | 1.14 | 0.65 | 0.92 | 0.00 | 1.54 | 0.00 | 0.90 | 0.68 | 0.00 |
time (sec) |
N/A | 1.117 | 0.169 | 0.237 | 0.000 | 0.168 | 0.000 | 0.133 | 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 | 130 | 149 | 93 | 134 | 0 | 222 | 0 | 128 | 87 | 0 |
N.S. |
1 | 1.15 | 0.72 | 1.03 | 0.00 | 1.71 | 0.00 | 0.98 | 0.67 | 0.00 |
time (sec) |
N/A | 1.073 | 0.207 | 0.240 | 0.000 | 0.112 | 0.000 | 0.132 | 0.145 | 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 | 99 | 112 | 84 | 124 | 0 | 204 | 0 | 116 | 68 | 0 |
N.S. |
1 | 1.13 | 0.85 | 1.25 | 0.00 | 2.06 | 0.00 | 1.17 | 0.69 | 0.00 |
time (sec) |
N/A | 1.016 | 0.174 | 0.228 | 0.000 | 0.136 | 0.000 | 0.129 | 0.140 | 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 | 78 | 91 | 77 | 114 | 0 | 188 | 0 | 106 | 50 | 0 |
N.S. |
1 | 1.17 | 0.99 | 1.46 | 0.00 | 2.41 | 0.00 | 1.36 | 0.64 | 0.00 |
time (sec) |
N/A | 0.822 | 0.081 | 0.217 | 0.000 | 0.110 | 0.000 | 0.132 | 0.138 | 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 | 88 | 72 | 80 | 196 | 0 | 252 | 0 | 0 | 51 | 0 |
N.S. |
1 | 0.82 | 0.91 | 2.23 | 0.00 | 2.86 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.717 | 0.045 | 0.217 | 0.000 | 0.101 | 0.000 | 0.000 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 76 | 82 | 145 | 0 | 238 | 0 | 127 | 60 | 0 |
N.S. |
1 | 0.96 | 1.04 | 1.84 | 0.00 | 3.01 | 0.00 | 1.61 | 0.76 | 0.00 |
time (sec) |
N/A | 0.950 | 0.220 | 0.239 | 0.000 | 0.110 | 0.000 | 0.176 | 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 | 79 | 97 | 78 | 142 | 0 | 162 | 0 | 194 | 58 | 0 |
N.S. |
1 | 1.23 | 0.99 | 1.80 | 0.00 | 2.05 | 0.00 | 2.46 | 0.73 | 0.00 |
time (sec) |
N/A | 0.965 | 0.143 | 0.248 | 0.000 | 0.111 | 0.000 | 0.154 | 0.140 | 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 | 103 | 119 | 86 | 151 | 0 | 186 | 0 | 231 | 84 | 0 |
N.S. |
1 | 1.16 | 0.83 | 1.47 | 0.00 | 1.81 | 0.00 | 2.24 | 0.82 | 0.00 |
time (sec) |
N/A | 1.056 | 0.156 | 0.264 | 0.000 | 0.117 | 0.000 | 0.165 | 0.149 | 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 | 133 | 151 | 94 | 159 | 0 | 202 | 0 | 316 | 152 | 0 |
N.S. |
1 | 1.14 | 0.71 | 1.20 | 0.00 | 1.52 | 0.00 | 2.38 | 1.14 | 0.00 |
time (sec) |
N/A | 1.112 | 0.152 | 0.247 | 0.000 | 0.111 | 0.000 | 0.177 | 0.153 | 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 | 158 | 173 | 102 | 167 | 0 | 218 | 0 | 362 | 122 | 0 |
N.S. |
1 | 1.09 | 0.65 | 1.06 | 0.00 | 1.38 | 0.00 | 2.29 | 0.77 | 0.00 |
time (sec) |
N/A | 1.168 | 0.172 | 0.247 | 0.000 | 0.118 | 0.000 | 0.248 | 0.148 | 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 | 74 | 71 | 89 | 0 | 48 | 0 | 141 | 43 | 0 |
N.S. |
1 | 0.40 | 0.38 | 0.48 | 0.00 | 0.26 | 0.00 | 0.76 | 0.23 | 0.00 |
time (sec) |
N/A | 0.934 | 0.065 | 0.097 | 0.000 | 0.103 | 0.000 | 0.131 | 0.144 | 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 | 152 | 68 | 63 | 82 | 0 | 41 | 0 | 107 | 36 | 0 |
N.S. |
1 | 0.45 | 0.41 | 0.54 | 0.00 | 0.27 | 0.00 | 0.70 | 0.24 | 0.00 |
time (sec) |
N/A | 0.888 | 0.049 | 0.076 | 0.000 | 0.099 | 0.000 | 0.126 | 0.145 | 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 | 113 | 58 | 56 | 73 | 0 | 32 | 0 | 89 | 27 | 0 |
N.S. |
1 | 0.51 | 0.50 | 0.65 | 0.00 | 0.28 | 0.00 | 0.79 | 0.24 | 0.00 |
time (sec) |
N/A | 0.786 | 0.037 | 0.092 | 0.000 | 0.082 | 0.000 | 0.154 | 0.140 | 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 | 109 | 50 | 51 | 65 | 0 | 27 | 0 | 63 | 22 | 0 |
N.S. |
1 | 0.46 | 0.47 | 0.60 | 0.00 | 0.25 | 0.00 | 0.58 | 0.20 | 0.00 |
time (sec) |
N/A | 0.644 | 0.021 | 0.069 | 0.000 | 0.102 | 0.000 | 0.136 | 0.142 | 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 | 108 | 55 | 51 | 66 | 0 | 32 | 0 | 44 | 27 | 0 |
N.S. |
1 | 0.51 | 0.47 | 0.61 | 0.00 | 0.30 | 0.00 | 0.41 | 0.25 | 0.00 |
time (sec) |
N/A | 0.869 | 0.048 | 0.081 | 0.000 | 0.116 | 0.000 | 0.159 | 0.143 | 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 | 147 | 67 | 61 | 82 | 0 | 85 | 0 | 56 | 40 | 0 |
N.S. |
1 | 0.46 | 0.41 | 0.56 | 0.00 | 0.58 | 0.00 | 0.38 | 0.27 | 0.00 |
time (sec) |
N/A | 0.881 | 0.067 | 0.076 | 0.000 | 0.085 | 0.000 | 0.146 | 0.149 | 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 | 188 | 77 | 73 | 90 | 0 | 93 | 0 | 68 | 48 | 0 |
N.S. |
1 | 0.41 | 0.39 | 0.48 | 0.00 | 0.49 | 0.00 | 0.36 | 0.26 | 0.00 |
time (sec) |
N/A | 0.878 | 0.072 | 0.090 | 0.000 | 0.098 | 0.000 | 0.170 | 0.141 | 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 | 222 | 83 | 77 | 98 | 0 | 101 | 0 | 76 | 56 | 0 |
N.S. |
1 | 0.37 | 0.35 | 0.44 | 0.00 | 0.45 | 0.00 | 0.34 | 0.25 | 0.00 |
time (sec) |
N/A | 0.888 | 0.076 | 0.071 | 0.000 | 0.091 | 0.000 | 0.156 | 0.147 | 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 | 264 | 95 | 91 | 106 | 0 | 109 | 0 | 88 | 64 | 0 |
N.S. |
1 | 0.36 | 0.34 | 0.40 | 0.00 | 0.41 | 0.00 | 0.33 | 0.24 | 0.00 |
time (sec) |
N/A | 0.912 | 0.075 | 0.098 | 0.000 | 0.119 | 0.000 | 0.149 | 0.138 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 50 | 45 | 47 | 0 | 24 | 0 | 53 | 25 | 46 |
N.S. |
1 | 0.66 | 0.59 | 0.62 | 0.00 | 0.32 | 0.00 | 0.70 | 0.33 | 0.61 |
time (sec) |
N/A | 0.831 | 0.040 | 0.084 | 0.000 | 0.102 | 0.000 | 0.120 | 0.144 | 13.745 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 44 | 46 | 0 | 21 | 0 | 50 | 20 | 45 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 0.00 | 0.48 | 0.00 | 1.14 | 0.45 | 1.02 |
time (sec) |
N/A | 0.679 | 0.031 | 0.064 | 0.000 | 0.080 | 0.000 | 0.117 | 0.155 | 13.743 |
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 | 68 | 41 | 39 | 52 | 0 | 19 | 0 | 36 | 17 | 0 |
N.S. |
1 | 0.60 | 0.57 | 0.76 | 0.00 | 0.28 | 0.00 | 0.53 | 0.25 | 0.00 |
time (sec) |
N/A | 0.593 | 0.023 | 0.051 | 0.000 | 0.084 | 0.000 | 0.119 | 0.144 | 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 | 69 | 45 | 40 | 50 | 0 | 21 | 0 | 37 | 22 | 0 |
N.S. |
1 | 0.65 | 0.58 | 0.72 | 0.00 | 0.30 | 0.00 | 0.54 | 0.32 | 0.00 |
time (sec) |
N/A | 0.824 | 0.033 | 0.063 | 0.000 | 0.092 | 0.000 | 0.138 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 46 | 47 | 0 | 21 | 0 | 49 | 23 | 63 |
N.S. |
1 | 1.00 | 0.98 | 1.00 | 0.00 | 0.45 | 0.00 | 1.04 | 0.49 | 1.34 |
time (sec) |
N/A | 0.796 | 0.034 | 0.064 | 0.000 | 0.076 | 0.000 | 0.122 | 0.151 | 13.684 |
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 | 155 | 177 | 101 | 142 | 0 | 238 | 0 | 139 | 105 | 0 |
N.S. |
1 | 1.14 | 0.65 | 0.92 | 0.00 | 1.54 | 0.00 | 0.90 | 0.68 | 0.00 |
time (sec) |
N/A | 1.147 | 0.182 | 0.248 | 0.000 | 0.093 | 0.000 | 0.154 | 0.141 | 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 | 130 | 149 | 93 | 134 | 0 | 222 | 0 | 128 | 87 | 0 |
N.S. |
1 | 1.15 | 0.72 | 1.03 | 0.00 | 1.71 | 0.00 | 0.98 | 0.67 | 0.00 |
time (sec) |
N/A | 1.102 | 0.202 | 0.248 | 0.000 | 0.096 | 0.000 | 0.134 | 0.152 | 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 | 101 | 116 | 84 | 125 | 0 | 204 | 0 | 117 | 68 | 0 |
N.S. |
1 | 1.15 | 0.83 | 1.24 | 0.00 | 2.02 | 0.00 | 1.16 | 0.67 | 0.00 |
time (sec) |
N/A | 0.965 | 0.178 | 0.218 | 0.000 | 0.102 | 0.000 | 0.144 | 0.155 | 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 | 78 | 92 | 100 | 114 | 0 | 188 | 0 | 106 | 50 | 0 |
N.S. |
1 | 1.18 | 1.28 | 1.46 | 0.00 | 2.41 | 0.00 | 1.36 | 0.64 | 0.00 |
time (sec) |
N/A | 0.818 | 0.087 | 0.214 | 0.000 | 0.125 | 0.000 | 0.155 | 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 | 88 | 72 | 80 | 196 | 0 | 252 | 0 | 0 | 51 | 0 |
N.S. |
1 | 0.82 | 0.91 | 2.23 | 0.00 | 2.86 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.744 | 0.047 | 0.204 | 0.000 | 0.094 | 0.000 | 0.000 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 82 | 145 | 0 | 238 | 0 | 127 | 60 | 0 |
N.S. |
1 | 1.00 | 1.04 | 1.84 | 0.00 | 3.01 | 0.00 | 1.61 | 0.76 | 0.00 |
time (sec) |
N/A | 1.011 | 0.210 | 0.228 | 0.000 | 0.139 | 0.000 | 0.163 | 0.180 | 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 | 79 | 97 | 78 | 143 | 0 | 163 | 0 | 194 | 58 | 0 |
N.S. |
1 | 1.23 | 0.99 | 1.81 | 0.00 | 2.06 | 0.00 | 2.46 | 0.73 | 0.00 |
time (sec) |
N/A | 0.983 | 0.179 | 0.223 | 0.000 | 0.107 | 0.000 | 0.153 | 0.153 | 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 | 103 | 120 | 86 | 150 | 0 | 187 | 0 | 231 | 84 | 0 |
N.S. |
1 | 1.17 | 0.83 | 1.46 | 0.00 | 1.82 | 0.00 | 2.24 | 0.82 | 0.00 |
time (sec) |
N/A | 1.047 | 0.153 | 0.240 | 0.000 | 0.098 | 0.000 | 0.192 | 0.155 | 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 | 133 | 151 | 94 | 159 | 0 | 203 | 0 | 316 | 152 | 0 |
N.S. |
1 | 1.14 | 0.71 | 1.20 | 0.00 | 1.53 | 0.00 | 2.38 | 1.14 | 0.00 |
time (sec) |
N/A | 1.121 | 0.185 | 0.234 | 0.000 | 0.108 | 0.000 | 0.175 | 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 | 148 | 174 | 102 | 167 | 0 | 219 | 0 | 362 | 122 | 0 |
N.S. |
1 | 1.18 | 0.69 | 1.13 | 0.00 | 1.48 | 0.00 | 2.45 | 0.82 | 0.00 |
time (sec) |
N/A | 1.201 | 0.190 | 0.247 | 0.000 | 0.129 | 0.000 | 0.263 | 0.158 | 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 | 72 | 71 | 89 | 0 | 48 | 0 | 94 | 44 | 0 |
N.S. |
1 | 0.39 | 0.38 | 0.48 | 0.00 | 0.26 | 0.00 | 0.51 | 0.24 | 0.00 |
time (sec) |
N/A | 0.907 | 0.082 | 0.088 | 0.000 | 0.099 | 0.000 | 0.120 | 0.159 | 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 | 66 | 62 | 82 | 0 | 41 | 0 | 80 | 37 | 0 |
N.S. |
1 | 0.44 | 0.41 | 0.54 | 0.00 | 0.27 | 0.00 | 0.53 | 0.25 | 0.00 |
time (sec) |
N/A | 0.875 | 0.070 | 0.070 | 0.000 | 0.089 | 0.000 | 0.143 | 0.162 | 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 | 56 | 55 | 73 | 0 | 32 | 0 | 62 | 28 | 0 |
N.S. |
1 | 0.50 | 0.49 | 0.65 | 0.00 | 0.29 | 0.00 | 0.55 | 0.25 | 0.00 |
time (sec) |
N/A | 0.742 | 0.049 | 0.064 | 0.000 | 0.095 | 0.000 | 0.131 | 0.156 | 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 | 107 | 47 | 47 | 67 | 0 | 25 | 0 | 55 | 23 | 0 |
N.S. |
1 | 0.44 | 0.44 | 0.63 | 0.00 | 0.23 | 0.00 | 0.51 | 0.21 | 0.00 |
time (sec) |
N/A | 0.649 | 0.024 | 0.063 | 0.000 | 0.144 | 0.000 | 0.114 | 0.158 | 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 | 108 | 53 | 51 | 66 | 0 | 32 | 0 | 59 | 32 | 0 |
N.S. |
1 | 0.49 | 0.47 | 0.61 | 0.00 | 0.30 | 0.00 | 0.55 | 0.30 | 0.00 |
time (sec) |
N/A | 0.860 | 0.053 | 0.067 | 0.000 | 0.104 | 0.000 | 0.120 | 0.158 | 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 | 146 | 65 | 60 | 82 | 0 | 83 | 0 | 69 | 50 | 0 |
N.S. |
1 | 0.45 | 0.41 | 0.56 | 0.00 | 0.57 | 0.00 | 0.47 | 0.34 | 0.00 |
time (sec) |
N/A | 0.870 | 0.069 | 0.079 | 0.000 | 0.098 | 0.000 | 0.118 | 0.148 | 0.000 |