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 | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 171 | 136 | 178 | 188 | 134 | 291 | 151 | 239 | 258 |
N.S. |
1 | 1.09 | 0.87 | 1.13 | 1.20 | 0.85 | 1.85 | 0.96 | 1.52 | 1.64 |
time (sec) |
N/A | 0.459 | 1.643 | 0.476 | 0.033 | 0.079 | 0.171 | 0.148 | 0.166 | 16.232 |
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 | 81 | 86 | 92 | 77 | 98 | 71 | 170 | 78 | 135 | 84 |
N.S. |
1 | 1.06 | 1.14 | 0.95 | 1.21 | 0.88 | 2.10 | 0.96 | 1.67 | 1.04 |
time (sec) |
N/A | 0.269 | 0.568 | 1.208 | 0.033 | 0.074 | 0.115 | 0.113 | 0.178 | 16.885 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 53 | 30 | 29 | 28 | 39 | 29 | 28 | 29 |
N.S. |
1 | 1.00 | 1.83 | 1.03 | 1.00 | 0.97 | 1.34 | 1.00 | 0.97 | 1.00 |
time (sec) |
N/A | 0.155 | 0.026 | 0.332 | 0.030 | 0.071 | 0.075 | 0.112 | 0.160 | 16.716 |
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 | 25 | 25 | 50 | 36 | 54 | 60 | 95 | 41 | 35 | 26 |
N.S. |
1 | 1.00 | 2.00 | 1.44 | 2.16 | 2.40 | 3.80 | 1.64 | 1.40 | 1.04 |
time (sec) |
N/A | 0.192 | 1.127 | 0.456 | 0.027 | 0.078 | 0.775 | 0.127 | 0.156 | 16.412 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 229 | 88 | 137 | 162 | 0 | 110 | 177 | 91 |
N.S. |
1 | 1.00 | 3.05 | 1.17 | 1.83 | 2.16 | 0.00 | 1.47 | 2.36 | 1.21 |
time (sec) |
N/A | 0.318 | 4.842 | 0.666 | 0.037 | 0.082 | 0.000 | 0.142 | 0.170 | 16.383 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 138 | 350 | 176 | 265 | 438 | 0 | 229 | 511 | 186 |
N.S. |
1 | 1.03 | 2.61 | 1.31 | 1.98 | 3.27 | 0.00 | 1.71 | 3.81 | 1.39 |
time (sec) |
N/A | 0.505 | 7.037 | 1.044 | 0.044 | 0.089 | 0.000 | 0.128 | 0.180 | 17.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 218 | 494 | 253 | 382 | 796 | 0 | 347 | 764 | 301 |
N.S. |
1 | 1.05 | 2.39 | 1.22 | 1.85 | 3.85 | 0.00 | 1.68 | 3.69 | 1.45 |
time (sec) |
N/A | 0.825 | 7.841 | 1.486 | 0.058 | 0.112 | 0.000 | 0.170 | 0.200 | 18.906 |
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 | 157 | 170 | 135 | 177 | 191 | 127 | 291 | 151 | 239 | 292 |
N.S. |
1 | 1.08 | 0.86 | 1.13 | 1.22 | 0.81 | 1.85 | 0.96 | 1.52 | 1.86 |
time (sec) |
N/A | 0.481 | 1.379 | 0.437 | 0.075 | 0.075 | 0.179 | 0.126 | 0.171 | 17.249 |
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 | 81 | 86 | 92 | 80 | 99 | 72 | 170 | 79 | 135 | 127 |
N.S. |
1 | 1.06 | 1.14 | 0.99 | 1.22 | 0.89 | 2.10 | 0.98 | 1.67 | 1.57 |
time (sec) |
N/A | 0.264 | 0.451 | 1.197 | 0.030 | 0.074 | 0.121 | 0.133 | 0.164 | 17.803 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 53 | 30 | 29 | 27 | 39 | 29 | 27 | 29 |
N.S. |
1 | 1.00 | 1.83 | 1.03 | 1.00 | 0.93 | 1.34 | 1.00 | 0.93 | 1.00 |
time (sec) |
N/A | 0.162 | 0.048 | 0.325 | 0.028 | 0.077 | 0.084 | 0.101 | 0.163 | 16.316 |
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 | 33 | 33 | 93 | 43 | 66 | 54 | 107 | 79 | 50 | 33 |
N.S. |
1 | 1.00 | 2.82 | 1.30 | 2.00 | 1.64 | 3.24 | 2.39 | 1.52 | 1.00 |
time (sec) |
N/A | 0.202 | 0.125 | 0.564 | 0.030 | 0.078 | 1.045 | 0.140 | 0.182 | 15.948 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 162 | 122 | 185 | 148 | 0 | 187 | 231 | 126 |
N.S. |
1 | 1.00 | 1.95 | 1.47 | 2.23 | 1.78 | 0.00 | 2.25 | 2.78 | 1.52 |
time (sec) |
N/A | 0.324 | 0.443 | 0.923 | 0.037 | 0.085 | 0.000 | 0.131 | 0.181 | 16.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 146 | 255 | 264 | 493 | 420 | 0 | 458 | 1972 | 360 |
N.S. |
1 | 1.03 | 1.80 | 1.86 | 3.47 | 2.96 | 0.00 | 3.23 | 13.89 | 2.54 |
time (sec) |
N/A | 0.530 | 1.811 | 2.023 | 0.053 | 0.094 | 0.000 | 0.164 | 0.189 | 20.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 226 | 632 | 398 | 963 | 729 | 0 | 957 | 4415 | 730 |
N.S. |
1 | 1.05 | 2.94 | 1.85 | 4.48 | 3.39 | 0.00 | 4.45 | 20.53 | 3.40 |
time (sec) |
N/A | 0.850 | 1.614 | 4.092 | 0.083 | 0.109 | 0.000 | 0.159 | 0.240 | 20.626 |
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 | 157 | 169 | 136 | 176 | 188 | 126 | 291 | 151 | 239 | 292 |
N.S. |
1 | 1.08 | 0.87 | 1.12 | 1.20 | 0.80 | 1.85 | 0.96 | 1.52 | 1.86 |
time (sec) |
N/A | 0.468 | 1.565 | 0.551 | 0.033 | 0.076 | 0.170 | 0.148 | 0.165 | 16.167 |
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 | 81 | 86 | 92 | 80 | 98 | 70 | 170 | 79 | 135 | 128 |
N.S. |
1 | 1.06 | 1.14 | 0.99 | 1.21 | 0.86 | 2.10 | 0.98 | 1.67 | 1.58 |
time (sec) |
N/A | 0.261 | 0.526 | 1.303 | 0.031 | 0.076 | 0.118 | 0.113 | 0.170 | 16.495 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 53 | 30 | 29 | 26 | 39 | 29 | 26 | 29 |
N.S. |
1 | 1.00 | 1.83 | 1.03 | 1.00 | 0.90 | 1.34 | 1.00 | 0.90 | 1.00 |
time (sec) |
N/A | 0.161 | 0.027 | 0.336 | 0.031 | 0.074 | 0.072 | 0.134 | 0.167 | 15.551 |
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 | 33 | 33 | 96 | 47 | 62 | 57 | 109 | 79 | 54 | 32 |
N.S. |
1 | 1.00 | 2.91 | 1.42 | 1.88 | 1.73 | 3.30 | 2.39 | 1.64 | 0.97 |
time (sec) |
N/A | 0.197 | 0.358 | 0.583 | 0.030 | 0.081 | 1.039 | 0.127 | 0.167 | 16.517 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 166 | 130 | 182 | 154 | 0 | 189 | 241 | 126 |
N.S. |
1 | 1.00 | 2.00 | 1.57 | 2.19 | 1.86 | 0.00 | 2.28 | 2.90 | 1.52 |
time (sec) |
N/A | 0.312 | 0.769 | 0.957 | 0.039 | 0.082 | 0.000 | 0.130 | 0.183 | 16.447 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 147 | 261 | 275 | 491 | 423 | 0 | 458 | 2068 | 361 |
N.S. |
1 | 1.04 | 1.84 | 1.94 | 3.46 | 2.98 | 0.00 | 3.23 | 14.56 | 2.54 |
time (sec) |
N/A | 0.538 | 2.210 | 2.048 | 0.063 | 0.092 | 0.000 | 0.145 | 0.182 | 20.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 225 | 636 | 410 | 959 | 735 | 0 | 957 | 4604 | 731 |
N.S. |
1 | 1.05 | 2.96 | 1.91 | 4.46 | 3.42 | 0.00 | 4.45 | 21.41 | 3.40 |
time (sec) |
N/A | 0.814 | 1.882 | 4.122 | 0.087 | 0.109 | 0.000 | 0.171 | 0.249 | 21.314 |
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 | 260 | 284 | 237 | 293 | 330 | 255 | 682 | 286 | 600 | 376 |
N.S. |
1 | 1.09 | 0.91 | 1.13 | 1.27 | 0.98 | 2.62 | 1.10 | 2.31 | 1.45 |
time (sec) |
N/A | 0.852 | 1.952 | 15.322 | 0.034 | 0.090 | 0.284 | 0.159 | 0.165 | 16.852 |
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 | 170 | 180 | 144 | 177 | 189 | 147 | 294 | 167 | 242 | 333 |
N.S. |
1 | 1.06 | 0.85 | 1.04 | 1.11 | 0.86 | 1.73 | 0.98 | 1.42 | 1.96 |
time (sec) |
N/A | 0.487 | 1.362 | 0.432 | 0.036 | 0.079 | 0.162 | 0.130 | 0.168 | 16.682 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 89 | 77 | 88 | 100 | 73 | 162 | 81 | 134 | 125 |
N.S. |
1 | 0.98 | 0.85 | 0.97 | 1.10 | 0.80 | 1.78 | 0.89 | 1.47 | 1.37 |
time (sec) |
N/A | 0.261 | 0.479 | 1.135 | 0.030 | 0.072 | 0.118 | 0.110 | 0.193 | 16.732 |
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 | 27 | 27 | 49 | 28 | 27 | 26 | 34 | 27 | 26 | 40 |
N.S. |
1 | 1.00 | 1.81 | 1.04 | 1.00 | 0.96 | 1.26 | 1.00 | 0.96 | 1.48 |
time (sec) |
N/A | 0.165 | 0.006 | 0.321 | 0.029 | 0.070 | 0.071 | 0.109 | 0.181 | 15.273 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 67 | 57 | 61 | 0 | 434 | 3179 | 89 | 80 | 75 |
N.S. |
1 | 1.10 | 0.93 | 1.00 | 0.00 | 7.11 | 52.11 | 1.46 | 1.31 | 1.23 |
time (sec) |
N/A | 0.237 | 0.157 | 0.403 | 0.000 | 0.114 | 88.316 | 0.128 | 0.181 | 16.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 127 | 116 | 203 | 0 | 819 | 0 | 214 | 485 | 195 |
N.S. |
1 | 1.05 | 0.96 | 1.68 | 0.00 | 6.77 | 0.00 | 1.77 | 4.01 | 1.61 |
time (sec) |
N/A | 0.374 | 0.332 | 0.690 | 0.000 | 0.134 | 0.000 | 0.117 | 0.185 | 15.626 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 223 | 200 | 611 | 0 | 1947 | 0 | 856 | 5132 | 700 |
N.S. |
1 | 1.13 | 1.02 | 3.10 | 0.00 | 9.88 | 0.00 | 4.35 | 26.05 | 3.55 |
time (sec) |
N/A | 0.617 | 0.741 | 1.508 | 0.000 | 0.172 | 0.000 | 0.157 | 0.232 | 18.905 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F(-2) | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 338 | 606 | 1655 | 0 | 4069 | 0 | 2558 | 22 | 1946 |
N.S. |
1 | 1.16 | 2.08 | 5.67 | 0.00 | 13.93 | 0.00 | 8.76 | 0.08 | 6.66 |
time (sec) |
N/A | 1.082 | 1.623 | 4.469 | 0.000 | 0.295 | 0.000 | 0.247 | 200.027 | 17.746 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 193 | 399 | 701 | 0 | 168 | 0 | 0 | 374 | 0 |
N.S. |
1 | 1.04 | 2.16 | 3.79 | 0.00 | 0.91 | 0.00 | 0.00 | 2.02 | 0.00 |
time (sec) |
N/A | 1.029 | 4.750 | 0.822 | 0.000 | 0.092 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 142 | 349 | 686 | 0 | 147 | 0 | 0 | 230 | 0 |
N.S. |
1 | 1.02 | 2.51 | 4.94 | 0.00 | 1.06 | 0.00 | 0.00 | 1.65 | 0.00 |
time (sec) |
N/A | 0.706 | 2.545 | 0.500 | 0.000 | 0.083 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 326 | 461 | 0 | 108 | 0 | 0 | 123 | 0 |
N.S. |
1 | 1.00 | 7.24 | 10.24 | 0.00 | 2.40 | 0.00 | 0.00 | 2.73 | 0.00 |
time (sec) |
N/A | 0.248 | 1.903 | 1.161 | 0.000 | 0.082 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 128 | 152 | 0 | 54 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 2.84 | 3.38 | 0.00 | 1.20 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.252 | 0.289 | 0.598 | 0.000 | 0.079 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 390 | 425 | 0 | 238 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.00 | 4.15 | 4.52 | 0.00 | 2.53 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.379 | 4.398 | 0.474 | 0.000 | 0.088 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 193 | 430 | 586 | 0 | 363 | 0 | 0 | 128 | 0 |
N.S. |
1 | 1.03 | 2.30 | 3.13 | 0.00 | 1.94 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.993 | 2.386 | 0.514 | 0.000 | 0.100 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 244 | 436 | 649 | 0 | 485 | 0 | 0 | 198 | 0 |
N.S. |
1 | 1.05 | 1.87 | 2.79 | 0.00 | 2.08 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 1.241 | 2.839 | 0.525 | 0.000 | 0.095 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 347 | 359 | 3767 | 2260 | 0 | 1589 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.03 | 10.86 | 6.51 | 0.00 | 4.58 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.694 | 6.530 | 1.082 | 0.000 | 0.131 | 0.000 | 0.000 | 200.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 284 | 2190 | 1490 | 0 | 1481 | 0 | 0 | 1198 | 0 |
N.S. |
1 | 1.00 | 7.74 | 5.27 | 0.00 | 5.23 | 0.00 | 0.00 | 4.23 | 0.00 |
time (sec) |
N/A | 1.090 | 6.315 | 0.729 | 0.000 | 0.113 | 0.000 | 0.000 | 18.843 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 1408 | 691 | 0 | 1369 | 0 | 0 | 182 | 0 |
N.S. |
1 | 1.00 | 13.04 | 6.40 | 0.00 | 12.68 | 0.00 | 0.00 | 1.69 | 0.00 |
time (sec) |
N/A | 0.365 | 6.269 | 2.055 | 0.000 | 0.105 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 285 | 295 | 0 | 509 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 2.64 | 2.73 | 0.00 | 4.71 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.380 | 0.544 | 0.728 | 0.000 | 0.087 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 186 | 1540 | 2639 | 0 | 1695 | 0 | 0 | 88 | 0 |
N.S. |
1 | 1.00 | 8.28 | 14.19 | 0.00 | 9.11 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.551 | 6.382 | 0.989 | 0.000 | 0.116 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 382 | 397 | 2408 | 3636 | 0 | 2741 | 0 | 0 | 161 | 0 |
N.S. |
1 | 1.04 | 6.30 | 9.52 | 0.00 | 7.18 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 1.541 | 6.428 | 1.715 | 0.000 | 0.189 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 490 | 526 | 4116 | 5022 | 0 | 4863 | 0 | 0 | 261 | 0 |
N.S. |
1 | 1.07 | 8.40 | 10.25 | 0.00 | 9.92 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 2.307 | 6.559 | 3.760 | 0.000 | 0.435 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 142 | 130 | 74 | 0 | 101 | 0 | 0 | 374 | 0 |
N.S. |
1 | 1.02 | 0.94 | 0.53 | 0.00 | 0.73 | 0.00 | 0.00 | 2.69 | 0.00 |
time (sec) |
N/A | 0.419 | 6.085 | 0.556 | 0.000 | 0.072 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 104 | 60 | 0 | 81 | 0 | 75207 | 230 | 0 |
N.S. |
1 | 1.00 | 1.12 | 0.65 | 0.00 | 0.87 | 0.00 | 808.68 | 2.47 | 0.00 |
time (sec) |
N/A | 0.295 | 1.648 | 0.339 | 0.000 | 0.076 | 0.000 | 1.337 | 0.206 | 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 | 44 | 44 | 75 | 50 | 0 | 61 | 0 | 0 | 123 | 39 |
N.S. |
1 | 1.00 | 1.70 | 1.14 | 0.00 | 1.39 | 0.00 | 0.00 | 2.80 | 0.89 |
time (sec) |
N/A | 0.190 | 0.029 | 0.363 | 0.000 | 0.069 | 0.000 | 0.000 | 0.210 | 0.336 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 101 | 77 | 0 | 134 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 2.10 | 1.60 | 0.00 | 2.79 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.273 | 0.133 | 0.909 | 0.000 | 0.078 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 154 | 117 | 0 | 268 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.00 | 1.60 | 1.22 | 0.00 | 2.79 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.374 | 0.278 | 0.357 | 0.000 | 0.082 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 147 | 180 | 190 | 0 | 341 | 0 | 0 | 128 | 0 |
N.S. |
1 | 1.04 | 1.27 | 1.34 | 0.00 | 2.40 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.519 | 0.467 | 0.365 | 0.000 | 0.088 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 193 | 151 | 86 | 0 | 121 | 0 | 0 | 555 | 0 |
N.S. |
1 | 1.04 | 0.82 | 0.46 | 0.00 | 0.65 | 0.00 | 0.00 | 3.00 | 0.00 |
time (sec) |
N/A | 0.576 | 7.342 | 0.572 | 0.000 | 0.069 | 0.000 | 0.000 | 0.318 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 142 | 127 | 74 | 0 | 101 | 0 | 0 | 374 | 0 |
N.S. |
1 | 1.02 | 0.91 | 0.53 | 0.00 | 0.73 | 0.00 | 0.00 | 2.69 | 0.00 |
time (sec) |
N/A | 0.419 | 5.752 | 0.413 | 0.000 | 0.073 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 103 | 60 | 0 | 80 | 0 | 74679 | 230 | 0 |
N.S. |
1 | 1.00 | 1.11 | 0.65 | 0.00 | 0.86 | 0.00 | 803.00 | 2.47 | 0.00 |
time (sec) |
N/A | 0.299 | 3.639 | 0.353 | 0.000 | 0.068 | 0.000 | 1.270 | 0.219 | 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 | 44 | 44 | 75 | 50 | 0 | 59 | 0 | 0 | 123 | 39 |
N.S. |
1 | 1.00 | 1.70 | 1.14 | 0.00 | 1.34 | 0.00 | 0.00 | 2.80 | 0.89 |
time (sec) |
N/A | 0.193 | 0.031 | 0.349 | 0.000 | 0.067 | 0.000 | 0.000 | 0.196 | 0.455 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 99 | 77 | 0 | 52 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 2.02 | 1.57 | 0.00 | 1.06 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.249 | 0.139 | 0.943 | 0.000 | 0.080 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 152 | 118 | 0 | 187 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.00 | 1.58 | 1.23 | 0.00 | 1.95 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.367 | 0.281 | 0.367 | 0.000 | 0.080 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 147 | 178 | 190 | 0 | 257 | 0 | 0 | 128 | 0 |
N.S. |
1 | 1.04 | 1.25 | 1.34 | 0.00 | 1.81 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.511 | 0.439 | 0.362 | 0.000 | 0.080 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 272 | 5490 | 306 | 0 | 268 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.05 | 21.28 | 1.19 | 0.00 | 1.04 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.777 | 36.351 | 0.913 | 0.000 | 0.090 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 199 | 5377 | 200 | 0 | 189 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.05 | 28.30 | 1.05 | 0.00 | 0.99 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.552 | 17.696 | 0.737 | 0.000 | 0.102 | 0.000 | 0.000 | 200.035 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 5279 | 126 | 0 | 125 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 41.90 | 1.00 | 0.00 | 0.99 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.379 | 17.486 | 0.667 | 0.000 | 0.081 | 0.000 | 0.000 | 200.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 565 | 113 | 0 | 80 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 10.27 | 2.05 | 0.00 | 1.45 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.234 | 16.105 | 0.683 | 0.000 | 0.075 | 0.000 | 0.000 | 200.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 63264 | 172 | 0 | 349 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 718.91 | 1.95 | 0.00 | 3.97 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.356 | 54.388 | 1.887 | 0.000 | 0.244 | 0.000 | 0.000 | 200.018 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F(-1) | B | F(-2) | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 160 | 0 | 350 | 0 | 622 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 0.00 | 2.19 | 0.00 | 3.89 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.539 | 0.000 | 0.732 | 0.000 | 0.252 | 0.000 | 0.000 | 200.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F(-1) | A | F(-2) | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 226 | 244 | 0 | 350 | 0 | 895 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.08 | 0.00 | 1.55 | 0.00 | 3.96 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.758 | 0.000 | 0.757 | 0.000 | 0.334 | 0.000 | 0.000 | 200.019 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 205 | 5238 | 204 | 0 | 192 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.05 | 26.72 | 1.04 | 0.00 | 0.98 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.573 | 39.108 | 0.847 | 0.000 | 0.085 | 0.000 | 0.000 | 200.020 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 5142 | 130 | 0 | 127 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 39.55 | 1.00 | 0.00 | 0.98 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.393 | 14.016 | 0.753 | 0.000 | 0.078 | 0.000 | 0.000 | 200.016 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 5053 | 117 | 0 | 80 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 88.65 | 2.05 | 0.00 | 1.40 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.231 | 17.604 | 0.724 | 0.000 | 0.078 | 0.000 | 0.000 | 200.017 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 61904 | 175 | 0 | 107 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 680.26 | 1.92 | 0.00 | 1.18 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.354 | 60.495 | 1.834 | 0.000 | 0.092 | 0.000 | 0.000 | 200.016 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F(-1) | B | F(-2) | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 164 | 0 | 364 | 0 | 424 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 0.00 | 2.22 | 0.00 | 2.59 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.536 | 0.000 | 0.763 | 0.000 | 0.125 | 0.000 | 0.000 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F(-1) | A | F(-2) | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 250 | 0 | 364 | 0 | 655 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.08 | 0.00 | 1.57 | 0.00 | 2.82 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.770 | 0.000 | 0.773 | 0.000 | 0.190 | 0.000 | 0.000 | 200.017 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 107 | 80 | 176 | 0 | 579 | 0 | 160 | 157 | 950 |
N.S. |
1 | 1.06 | 0.79 | 1.74 | 0.00 | 5.73 | 0.00 | 1.58 | 1.55 | 9.41 |
time (sec) |
N/A | 0.340 | 0.226 | 0.494 | 0.000 | 0.146 | 0.000 | 0.396 | 0.180 | 25.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 30 | 22 | 20 | 41 | 11 | 22 | 25 | 22 | 34 |
N.S. |
1 | 1.36 | 1.00 | 0.91 | 1.86 | 0.50 | 1.00 | 1.14 | 1.00 | 1.55 |
time (sec) |
N/A | 0.238 | 0.065 | 0.252 | 0.107 | 0.081 | 0.150 | 0.385 | 0.177 | 15.283 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 102 | 79 | 171 | 0 | 553 | 0 | 158 | 262 | 988 |
N.S. |
1 | 1.05 | 0.81 | 1.76 | 0.00 | 5.70 | 0.00 | 1.63 | 2.70 | 10.19 |
time (sec) |
N/A | 0.400 | 0.205 | 0.575 | 0.000 | 0.146 | 0.000 | 0.387 | 0.179 | 26.664 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 56 | 50 | 53 | 0 | 349 | 0 | 73 | 322 | 47 |
N.S. |
1 | 1.10 | 0.98 | 1.04 | 0.00 | 6.84 | 0.00 | 1.43 | 6.31 | 0.92 |
time (sec) |
N/A | 0.283 | 0.041 | 0.457 | 0.000 | 0.131 | 0.000 | 0.348 | 0.177 | 16.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 148 | 120 | 180 | 0 | 663 | 0 | 161 | 347 | 977 |
N.S. |
1 | 1.04 | 0.85 | 1.27 | 0.00 | 4.67 | 0.00 | 1.13 | 2.44 | 6.88 |
time (sec) |
N/A | 0.664 | 0.306 | 1.418 | 0.000 | 1.462 | 0.000 | 0.340 | 0.198 | 25.375 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 371 | 337 | 2490 | 50433 | 0 | 1504 | 0 | 0 | 391 | 0 |
N.S. |
1 | 0.91 | 6.71 | 135.94 | 0.00 | 4.05 | 0.00 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 1.488 | 6.713 | 13.343 | 0.000 | 0.128 | 0.000 | 0.000 | 1.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 1580 | 2660 | 0 | 1367 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 13.39 | 22.54 | 0.00 | 11.58 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.515 | 6.412 | 10.128 | 0.000 | 0.118 | 0.000 | 0.000 | 0.662 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 339 | 1022 | 0 | 504 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.00 | 2.87 | 8.66 | 0.00 | 4.27 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.509 | 0.900 | 12.400 | 0.000 | 0.101 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 237 | 1732 | 40875 | 0 | 1724 | 0 | 0 | 101 | 0 |
N.S. |
1 | 0.99 | 7.22 | 170.31 | 0.00 | 7.18 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.758 | 6.648 | 8.367 | 0.000 | 0.150 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 492 | 443 | 2708 | 81611 | 0 | 2769 | 0 | 0 | 176 | 0 |
N.S. |
1 | 0.90 | 5.50 | 165.88 | 0.00 | 5.63 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 1.857 | 6.750 | 13.581 | 0.000 | 0.271 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 371 | 337 | 81485 | 50459 | 0 | 1498 | 0 | 0 | 124 | 0 |
N.S. |
1 | 0.91 | 219.64 | 136.01 | 0.00 | 4.04 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 1.382 | 35.456 | 13.022 | 0.000 | 0.132 | 0.000 | 0.000 | 64.862 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 54676 | 2660 | 0 | 1369 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 463.36 | 22.54 | 0.00 | 11.60 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.518 | 31.899 | 8.155 | 0.000 | 0.116 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 506 | 1018 | 0 | 509 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.00 | 4.29 | 8.63 | 0.00 | 4.31 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.510 | 15.335 | 12.678 | 0.000 | 0.099 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 237 | 54829 | 40867 | 0 | 1710 | 0 | 0 | 144 | 0 |
N.S. |
1 | 0.99 | 228.45 | 170.28 | 0.00 | 7.12 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.764 | 32.328 | 8.247 | 0.000 | 0.140 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 492 | 443 | 81703 | 81603 | 0 | 2752 | 0 | 0 | 249 | 0 |
N.S. |
1 | 0.90 | 166.06 | 165.86 | 0.00 | 5.59 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 1.927 | 32.615 | 14.247 | 0.000 | 0.213 | 0.000 | 0.000 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 103 | 80 | 176 | 0 | 555 | 0 | 158 | 262 | 965 |
N.S. |
1 | 1.05 | 0.82 | 1.80 | 0.00 | 5.66 | 0.00 | 1.61 | 2.67 | 9.85 |
time (sec) |
N/A | 0.379 | 0.255 | 0.542 | 0.000 | 0.130 | 0.000 | 0.295 | 0.161 | 27.705 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 56 | 50 | 53 | 0 | 349 | 0 | 73 | 67 | 47 |
N.S. |
1 | 1.10 | 0.98 | 1.04 | 0.00 | 6.84 | 0.00 | 1.43 | 1.31 | 0.92 |
time (sec) |
N/A | 0.285 | 0.039 | 0.404 | 0.000 | 0.114 | 0.000 | 0.335 | 0.152 | 15.470 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 120 | 104 | 123 | 0 | 669 | 0 | 142 | 262 | 531 |
N.S. |
1 | 1.00 | 0.87 | 1.02 | 0.00 | 5.58 | 0.00 | 1.18 | 2.18 | 4.42 |
time (sec) |
N/A | 0.636 | 5.228 | 0.823 | 0.000 | 1.448 | 0.000 | 0.311 | 0.150 | 22.346 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 17 | 51 | 10 | 14 | 24 | 0 | 22 | 9 | 9 |
N.S. |
1 | 0.81 | 2.43 | 0.48 | 0.67 | 1.14 | 0.00 | 1.05 | 0.43 | 0.43 |
time (sec) |
N/A | 0.257 | 0.025 | 0.262 | 0.127 | 0.077 | 0.000 | 0.304 | 0.142 | 17.193 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 371 | 337 | 2490 | 21241 | 0 | 1511 | 0 | 0 | 31 | 0 |
N.S. |
1 | 0.91 | 6.71 | 57.25 | 0.00 | 4.07 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.463 | 6.671 | 14.135 | 0.000 | 0.139 | 0.000 | 0.000 | 200.016 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 1580 | 1862 | 0 | 1361 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 13.39 | 15.78 | 0.00 | 11.53 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.543 | 6.436 | 3.424 | 0.000 | 0.116 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 339 | 639 | 0 | 508 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.00 | 2.87 | 5.42 | 0.00 | 4.31 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.507 | 0.849 | 7.681 | 0.000 | 0.105 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 237 | 1732 | 12789 | 0 | 1711 | 0 | 0 | 101 | 0 |
N.S. |
1 | 0.99 | 7.22 | 53.29 | 0.00 | 7.13 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.771 | 6.648 | 2.468 | 0.000 | 0.137 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 492 | 443 | 2708 | 42265 | 0 | 2777 | 0 | 0 | 176 | 0 |
N.S. |
1 | 0.90 | 5.50 | 85.90 | 0.00 | 5.64 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 1.893 | 6.760 | 6.777 | 0.000 | 0.264 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 371 | 337 | 5904 | 21388 | 0 | 1496 | 0 | 0 | 31 | 0 |
N.S. |
1 | 0.91 | 15.91 | 57.65 | 0.00 | 4.03 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.429 | 24.539 | 1.479 | 0.000 | 0.132 | 0.000 | 0.000 | 200.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 5835 | 1851 | 0 | 1367 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 49.45 | 15.69 | 0.00 | 11.58 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.522 | 15.854 | 1.753 | 0.000 | 0.123 | 0.000 | 0.000 | 4.320 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 519 | 707 | 0 | 505 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.00 | 4.40 | 5.99 | 0.00 | 4.28 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.540 | 16.953 | 2.016 | 0.000 | 0.099 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 237 | 5959 | 12778 | 0 | 1710 | 0 | 0 | 144 | 0 |
N.S. |
1 | 0.99 | 24.83 | 53.24 | 0.00 | 7.12 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.798 | 16.579 | 1.452 | 0.000 | 0.131 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 492 | 443 | 6066 | 41817 | 0 | 2730 | 0 | 0 | 249 | 0 |
N.S. |
1 | 0.90 | 12.33 | 84.99 | 0.00 | 5.55 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 1.849 | 17.343 | 1.886 | 0.000 | 0.211 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1 | 1 | 1 | 2 | 1 | 1 | 10 | 1 | 13 | 1 |
N.S. |
1 | 1.00 | 1.00 | 2.00 | 1.00 | 1.00 | 10.00 | 1.00 | 13.00 | 1.00 |
time (sec) |
N/A | 0.163 | 0.000 | 0.156 | 0.119 | 0.050 | 0.189 | 0.289 | 0.155 | 15.827 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1 | 1 | 1 | 2 | 1 | 1 | 22 | 1 | 23 | 1 |
N.S. |
1 | 1.00 | 1.00 | 2.00 | 1.00 | 1.00 | 22.00 | 1.00 | 23.00 | 1.00 |
time (sec) |
N/A | 0.169 | 0.000 | 0.138 | 0.113 | 0.050 | 0.331 | 0.298 | 0.168 | 15.309 |