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 | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 134 | 197 | 92 | 187 | 183 | 0 | 147 | 119 | 124 |
N.S. |
1 | 1.07 | 1.58 | 0.74 | 1.50 | 1.46 | 0.00 | 1.18 | 0.95 | 0.99 |
time (sec) |
N/A | 0.912 | 1.801 | 0.247 | 0.038 | 0.089 | 0.000 | 0.166 | 0.189 | 11.724 |
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 | 102 | 104 | 63 | 56 | 115 | 93 | 0 | 75 | 66 | 66 |
N.S. |
1 | 1.02 | 0.62 | 0.55 | 1.13 | 0.91 | 0.00 | 0.74 | 0.65 | 0.65 |
time (sec) |
N/A | 0.578 | 1.130 | 0.214 | 0.035 | 0.089 | 0.000 | 0.182 | 0.176 | 11.335 |
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 | 102 | 99 | 135 | 56 | 115 | 93 | 0 | 75 | 66 | 66 |
N.S. |
1 | 0.97 | 1.32 | 0.55 | 1.13 | 0.91 | 0.00 | 0.74 | 0.65 | 0.65 |
time (sec) |
N/A | 0.486 | 0.875 | 0.199 | 0.039 | 0.073 | 0.000 | 0.150 | 0.179 | 11.551 |
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 | 108 | 118 | 241 | 69 | 160 | 138 | 0 | 121 | 94 | 133 |
N.S. |
1 | 1.09 | 2.23 | 0.64 | 1.48 | 1.28 | 0.00 | 1.12 | 0.87 | 1.23 |
time (sec) |
N/A | 0.678 | 0.920 | 0.212 | 0.108 | 0.075 | 0.000 | 0.167 | 0.205 | 11.748 |
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 | 136 | 152 | 365 | 89 | 231 | 173 | 0 | 157 | 174 | 155 |
N.S. |
1 | 1.12 | 2.68 | 0.65 | 1.70 | 1.27 | 0.00 | 1.15 | 1.28 | 1.14 |
time (sec) |
N/A | 0.980 | 2.315 | 0.364 | 0.109 | 0.088 | 0.000 | 0.147 | 0.176 | 11.777 |
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 | 187 | 194 | 435 | 107 | 322 | 190 | 0 | 200 | 247 | 204 |
N.S. |
1 | 1.04 | 2.33 | 0.57 | 1.72 | 1.02 | 0.00 | 1.07 | 1.32 | 1.09 |
time (sec) |
N/A | 1.170 | 2.278 | 0.485 | 0.110 | 0.087 | 0.000 | 0.177 | 0.178 | 11.273 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 216 | 491 | 125 | 412 | 205 | 0 | 228 | 268 | 237 |
N.S. |
1 | 0.99 | 2.25 | 0.57 | 1.89 | 0.94 | 0.00 | 1.05 | 1.23 | 1.09 |
time (sec) |
N/A | 1.240 | 2.694 | 0.519 | 0.115 | 0.085 | 0.000 | 0.153 | 0.180 | 11.145 |
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 | 238 | 253 | 880 | 196 | 419 | 358 | 0 | 267 | 469 | 272 |
N.S. |
1 | 1.06 | 3.70 | 0.82 | 1.76 | 1.50 | 0.00 | 1.12 | 1.97 | 1.14 |
time (sec) |
N/A | 1.810 | 8.374 | 0.580 | 0.045 | 0.090 | 0.000 | 0.217 | 0.179 | 10.986 |
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 | 194 | 219 | 593 | 160 | 326 | 317 | 0 | 220 | 324 | 237 |
N.S. |
1 | 1.13 | 3.06 | 0.82 | 1.68 | 1.63 | 0.00 | 1.13 | 1.67 | 1.22 |
time (sec) |
N/A | 1.543 | 6.798 | 0.457 | 0.039 | 0.091 | 0.000 | 0.205 | 0.205 | 11.491 |
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 | 163 | 182 | 239 | 112 | 228 | 236 | 0 | 181 | 147 | 198 |
N.S. |
1 | 1.12 | 1.47 | 0.69 | 1.40 | 1.45 | 0.00 | 1.11 | 0.90 | 1.21 |
time (sec) |
N/A | 1.236 | 2.343 | 0.295 | 0.041 | 0.090 | 0.000 | 0.201 | 0.176 | 12.197 |
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 | 146 | 138 | 109 | 84 | 175 | 125 | 0 | 117 | 108 | 85 |
N.S. |
1 | 0.95 | 0.75 | 0.58 | 1.20 | 0.86 | 0.00 | 0.80 | 0.74 | 0.58 |
time (sec) |
N/A | 0.733 | 1.538 | 0.256 | 0.038 | 0.076 | 0.000 | 0.179 | 0.181 | 11.362 |
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 | 137 | 163 | 80 | 174 | 124 | 0 | 117 | 108 | 84 |
N.S. |
1 | 0.99 | 1.18 | 0.58 | 1.26 | 0.90 | 0.00 | 0.85 | 0.78 | 0.61 |
time (sec) |
N/A | 0.722 | 1.686 | 0.254 | 0.044 | 0.076 | 0.000 | 0.151 | 0.187 | 11.221 |
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 | 132 | 193 | 78 | 175 | 124 | 0 | 117 | 108 | 88 |
N.S. |
1 | 0.96 | 1.40 | 0.57 | 1.27 | 0.90 | 0.00 | 0.85 | 0.78 | 0.64 |
time (sec) |
N/A | 0.625 | 3.173 | 0.242 | 0.037 | 0.074 | 0.000 | 0.185 | 0.167 | 11.150 |
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 | 138 | 158 | 329 | 89 | 201 | 181 | 0 | 154 | 122 | 163 |
N.S. |
1 | 1.14 | 2.38 | 0.64 | 1.46 | 1.31 | 0.00 | 1.12 | 0.88 | 1.18 |
time (sec) |
N/A | 0.908 | 4.028 | 0.254 | 0.115 | 0.083 | 0.000 | 0.174 | 0.166 | 11.201 |
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 | 166 | 190 | 485 | 107 | 271 | 223 | 0 | 190 | 202 | 202 |
N.S. |
1 | 1.14 | 2.92 | 0.64 | 1.63 | 1.34 | 0.00 | 1.14 | 1.22 | 1.22 |
time (sec) |
N/A | 1.281 | 5.212 | 0.422 | 0.117 | 0.082 | 0.000 | 0.160 | 0.205 | 11.082 |
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 | 223 | 238 | 555 | 123 | 364 | 240 | 0 | 233 | 275 | 179 |
N.S. |
1 | 1.07 | 2.49 | 0.55 | 1.63 | 1.08 | 0.00 | 1.04 | 1.23 | 0.80 |
time (sec) |
N/A | 1.530 | 5.311 | 0.493 | 0.123 | 0.086 | 0.000 | 0.179 | 0.161 | 10.907 |
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 | 256 | 262 | 611 | 140 | 452 | 257 | 0 | 261 | 349 | 300 |
N.S. |
1 | 1.02 | 2.39 | 0.55 | 1.77 | 1.00 | 0.00 | 1.02 | 1.36 | 1.17 |
time (sec) |
N/A | 1.648 | 5.840 | 0.625 | 0.127 | 0.090 | 0.000 | 0.183 | 0.163 | 11.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 187 | 98 | 123 | 0 | 122 | 0 | 268 | 48 | 512 |
N.S. |
1 | 1.00 | 0.52 | 0.66 | 0.00 | 0.65 | 0.00 | 1.43 | 0.26 | 2.74 |
time (sec) |
N/A | 1.005 | 0.377 | 1.112 | 0.000 | 0.105 | 0.000 | 0.427 | 0.181 | 20.292 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 146 | 81 | 103 | 0 | 105 | 0 | 222 | 48 | 407 |
N.S. |
1 | 1.01 | 0.56 | 0.72 | 0.00 | 0.73 | 0.00 | 1.54 | 0.33 | 2.83 |
time (sec) |
N/A | 0.766 | 0.232 | 0.935 | 0.000 | 0.085 | 0.000 | 0.452 | 0.187 | 15.826 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 112 | 80 | 81 | 0 | 87 | 0 | 176 | 48 | 212 |
N.S. |
1 | 1.11 | 0.79 | 0.80 | 0.00 | 0.86 | 0.00 | 1.74 | 0.48 | 2.10 |
time (sec) |
N/A | 0.623 | 0.200 | 0.839 | 0.000 | 0.082 | 0.000 | 0.403 | 0.217 | 15.511 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 53 | 57 | 0 | 66 | 0 | 129 | 46 | 159 |
N.S. |
1 | 1.00 | 0.85 | 0.92 | 0.00 | 1.06 | 0.00 | 2.08 | 0.74 | 2.56 |
time (sec) |
N/A | 0.372 | 0.117 | 0.793 | 0.000 | 0.078 | 0.000 | 0.365 | 0.175 | 1.944 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 76 | 107 | 147 | 235 | 0 | 193 | 37 | 0 |
N.S. |
1 | 1.00 | 1.15 | 1.62 | 2.23 | 3.56 | 0.00 | 2.92 | 0.56 | 0.00 |
time (sec) |
N/A | 0.401 | 0.374 | 1.296 | 0.158 | 0.097 | 0.000 | 0.396 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 83 | 220 | 939 | 261 | 0 | 336 | 50 | 0 |
N.S. |
1 | 1.00 | 1.22 | 3.24 | 13.81 | 3.84 | 0.00 | 4.94 | 0.74 | 0.00 |
time (sec) |
N/A | 0.368 | 0.281 | 1.495 | 0.215 | 0.126 | 0.000 | 0.649 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 109 | 117 | 240 | 1851 | 308 | 0 | 630 | 54 | 0 |
N.S. |
1 | 0.93 | 1.00 | 2.05 | 15.82 | 2.63 | 0.00 | 5.38 | 0.46 | 0.00 |
time (sec) |
N/A | 0.554 | 0.267 | 1.641 | 0.303 | 0.114 | 0.000 | 0.614 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 150 | 70 | 259 | 2981 | 346 | 0 | 889 | 54 | 0 |
N.S. |
1 | 0.94 | 0.44 | 1.62 | 18.63 | 2.16 | 0.00 | 5.56 | 0.34 | 0.00 |
time (sec) |
N/A | 0.731 | 0.136 | 1.559 | 0.435 | 0.118 | 0.000 | 0.663 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 191 | 70 | 279 | 8561 | 380 | 0 | 1080 | 54 | 0 |
N.S. |
1 | 0.94 | 0.34 | 1.37 | 42.17 | 1.87 | 0.00 | 5.32 | 0.27 | 0.00 |
time (sec) |
N/A | 0.929 | 0.128 | 1.645 | 0.608 | 0.138 | 0.000 | 0.713 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 197 | 100 | 124 | 0 | 127 | 0 | 258 | 93 | 596 |
N.S. |
1 | 1.04 | 0.53 | 0.66 | 0.00 | 0.67 | 0.00 | 1.37 | 0.49 | 3.15 |
time (sec) |
N/A | 1.110 | 0.456 | 1.778 | 0.000 | 0.085 | 0.000 | 0.651 | 0.200 | 20.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 146 | 82 | 104 | 0 | 108 | 0 | 215 | 93 | 479 |
N.S. |
1 | 1.06 | 0.59 | 0.75 | 0.00 | 0.78 | 0.00 | 1.56 | 0.67 | 3.47 |
time (sec) |
N/A | 0.792 | 0.248 | 1.535 | 0.000 | 0.082 | 0.000 | 0.551 | 0.197 | 16.771 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 99 | 70 | 82 | 0 | 89 | 0 | 170 | 91 | 213 |
N.S. |
1 | 0.98 | 0.69 | 0.81 | 0.00 | 0.88 | 0.00 | 1.68 | 0.90 | 2.11 |
time (sec) |
N/A | 0.507 | 0.211 | 1.481 | 0.000 | 0.080 | 0.000 | 0.511 | 0.221 | 15.503 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 108 | 102 | 141 | 998 | 314 | 0 | 263 | 80 | 0 |
N.S. |
1 | 1.03 | 0.97 | 1.34 | 9.50 | 2.99 | 0.00 | 2.50 | 0.76 | 0.00 |
time (sec) |
N/A | 0.608 | 0.574 | 2.089 | 0.203 | 0.103 | 0.000 | 0.521 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 92 | 232 | 1801 | 292 | 0 | 406 | 105 | 0 |
N.S. |
1 | 1.00 | 0.89 | 2.25 | 17.49 | 2.83 | 0.00 | 3.94 | 1.02 | 0.00 |
time (sec) |
N/A | 0.593 | 0.385 | 3.522 | 0.299 | 0.113 | 0.000 | 0.731 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 118 | 119 | 241 | 0 | 320 | 0 | 639 | 113 | 0 |
N.S. |
1 | 0.99 | 1.00 | 2.03 | 0.00 | 2.69 | 0.00 | 5.37 | 0.95 | 0.00 |
time (sec) |
N/A | 0.666 | 0.349 | 1.946 | 0.000 | 0.114 | 0.000 | 0.692 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 160 | 137 | 260 | 0 | 360 | 0 | 897 | 113 | 0 |
N.S. |
1 | 0.98 | 0.84 | 1.59 | 0.00 | 2.20 | 0.00 | 5.47 | 0.69 | 0.00 |
time (sec) |
N/A | 0.859 | 0.641 | 1.915 | 0.000 | 0.121 | 0.000 | 0.725 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 201 | 154 | 280 | 0 | 396 | 0 | 1088 | 113 | 0 |
N.S. |
1 | 0.96 | 0.74 | 1.34 | 0.00 | 1.89 | 0.00 | 5.21 | 0.54 | 0.00 |
time (sec) |
N/A | 1.079 | 0.853 | 1.977 | 0.000 | 0.140 | 0.000 | 0.844 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 237 | 249 | 117 | 146 | 0 | 157 | 0 | 306 | 141 | 856 |
N.S. |
1 | 1.05 | 0.49 | 0.62 | 0.00 | 0.66 | 0.00 | 1.29 | 0.59 | 3.61 |
time (sec) |
N/A | 1.513 | 4.351 | 237.899 | 0.000 | 0.101 | 0.000 | 0.816 | 0.218 | 21.912 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 180 | 96 | 126 | 0 | 136 | 0 | 261 | 141 | 723 |
N.S. |
1 | 1.03 | 0.55 | 0.72 | 0.00 | 0.78 | 0.00 | 1.49 | 0.81 | 4.13 |
time (sec) |
N/A | 0.939 | 0.798 | 88.739 | 0.000 | 0.086 | 0.000 | 0.778 | 0.213 | 21.808 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 133 | 89 | 106 | 0 | 115 | 0 | 216 | 139 | 590 |
N.S. |
1 | 0.96 | 0.64 | 0.77 | 0.00 | 0.83 | 0.00 | 1.57 | 1.01 | 4.28 |
time (sec) |
N/A | 0.645 | 0.392 | 27.710 | 0.000 | 0.079 | 0.000 | 0.742 | 0.225 | 16.894 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 150 | 128 | 169 | 1396 | 378 | 0 | 309 | 128 | 0 |
N.S. |
1 | 1.06 | 0.90 | 1.19 | 9.83 | 2.66 | 0.00 | 2.18 | 0.90 | 0.00 |
time (sec) |
N/A | 0.835 | 0.875 | 7.739 | 0.207 | 0.103 | 0.000 | 0.750 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 147 | 117 | 247 | 2780 | 386 | 0 | 480 | 165 | 0 |
N.S. |
1 | 1.03 | 0.82 | 1.73 | 19.44 | 2.70 | 0.00 | 3.36 | 1.15 | 0.00 |
time (sec) |
N/A | 0.902 | 3.436 | 23.498 | 0.324 | 0.123 | 0.000 | 0.812 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 151 | 155 | 323 | 0 | 348 | 0 | 709 | 177 | 0 |
N.S. |
1 | 0.98 | 1.01 | 2.10 | 0.00 | 2.26 | 0.00 | 4.60 | 1.15 | 0.00 |
time (sec) |
N/A | 0.946 | 0.841 | 76.776 | 0.000 | 0.113 | 0.000 | 0.926 | 0.328 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 169 | 117 | 262 | 0 | 380 | 0 | 905 | 177 | 0 |
N.S. |
1 | 1.03 | 0.71 | 1.60 | 0.00 | 2.32 | 0.00 | 5.52 | 1.08 | 0.00 |
time (sec) |
N/A | 0.974 | 0.725 | 244.391 | 0.000 | 0.120 | 0.000 | 0.961 | 0.358 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 212 | 137 | 282 | 0 | 420 | 0 | 1096 | 177 | 0 |
N.S. |
1 | 1.01 | 0.66 | 1.35 | 0.00 | 2.01 | 0.00 | 5.24 | 0.85 | 0.00 |
time (sec) |
N/A | 1.245 | 1.051 | 0.760 | 0.000 | 0.169 | 0.000 | 1.126 | 0.341 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 253 | 140 | 302 | 0 | 460 | 0 | 1377 | 177 | 0 |
N.S. |
1 | 1.00 | 0.55 | 1.19 | 0.00 | 1.81 | 0.00 | 5.42 | 0.70 | 0.00 |
time (sec) |
N/A | 1.471 | 0.727 | 1.733 | 0.000 | 0.155 | 0.000 | 1.099 | 0.357 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 226 | 140 | 251 | 0 | 432 | 0 | 252 | 71 | 0 |
N.S. |
1 | 1.12 | 0.69 | 1.24 | 0.00 | 2.14 | 0.00 | 1.25 | 0.35 | 0.00 |
time (sec) |
N/A | 1.343 | 0.378 | 1.358 | 0.000 | 0.115 | 0.000 | 0.676 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 174 | 123 | 224 | 0 | 397 | 0 | 229 | 71 | 0 |
N.S. |
1 | 1.09 | 0.77 | 1.41 | 0.00 | 2.50 | 0.00 | 1.44 | 0.45 | 0.00 |
time (sec) |
N/A | 0.958 | 0.267 | 1.161 | 0.000 | 0.113 | 0.000 | 0.659 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 125 | 106 | 200 | 0 | 352 | 0 | 165 | 71 | 0 |
N.S. |
1 | 1.06 | 0.90 | 1.69 | 0.00 | 2.98 | 0.00 | 1.40 | 0.60 | 0.00 |
time (sec) |
N/A | 0.627 | 0.200 | 1.092 | 0.000 | 0.115 | 0.000 | 0.537 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 88 | 157 | 0 | 287 | 0 | 131 | 69 | 0 |
N.S. |
1 | 1.00 | 1.13 | 2.01 | 0.00 | 3.68 | 0.00 | 1.68 | 0.88 | 0.00 |
time (sec) |
N/A | 0.378 | 0.122 | 0.901 | 0.000 | 0.106 | 0.000 | 0.444 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 92 | 170 | 699 | 307 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.00 | 1.01 | 1.87 | 7.68 | 3.37 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.439 | 0.460 | 0.935 | 0.378 | 0.506 | 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 | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 128 | 115 | 359 | 0 | 458 | 0 | 365 | 73 | 0 |
N.S. |
1 | 1.08 | 0.97 | 3.02 | 0.00 | 3.85 | 0.00 | 3.07 | 0.61 | 0.00 |
time (sec) |
N/A | 0.685 | 0.177 | 1.687 | 0.000 | 0.662 | 0.000 | 0.703 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 177 | 135 | 385 | 0 | 506 | 0 | 621 | 77 | 0 |
N.S. |
1 | 1.07 | 0.82 | 2.33 | 0.00 | 3.07 | 0.00 | 3.76 | 0.47 | 0.00 |
time (sec) |
N/A | 0.999 | 0.270 | 1.819 | 0.000 | 1.197 | 0.000 | 0.844 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 230 | 150 | 404 | 0 | 539 | 0 | 818 | 77 | 0 |
N.S. |
1 | 1.12 | 0.73 | 1.96 | 0.00 | 2.62 | 0.00 | 3.97 | 0.37 | 0.00 |
time (sec) |
N/A | 1.371 | 0.461 | 1.700 | 0.000 | 1.175 | 0.000 | 0.884 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 232 | 160 | 276 | 0 | 504 | 0 | 277 | 91 | 0 |
N.S. |
1 | 1.07 | 0.74 | 1.28 | 0.00 | 2.33 | 0.00 | 1.28 | 0.42 | 0.00 |
time (sec) |
N/A | 1.347 | 1.631 | 1.956 | 0.000 | 0.115 | 0.000 | 0.807 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 180 | 141 | 250 | 0 | 459 | 0 | 247 | 91 | 0 |
N.S. |
1 | 1.05 | 0.82 | 1.46 | 0.00 | 2.68 | 0.00 | 1.44 | 0.53 | 0.00 |
time (sec) |
N/A | 1.003 | 0.936 | 1.767 | 0.000 | 0.114 | 0.000 | 0.970 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 121 | 125 | 220 | 0 | 386 | 0 | 187 | 91 | 0 |
N.S. |
1 | 1.03 | 1.06 | 1.86 | 0.00 | 3.27 | 0.00 | 1.58 | 0.77 | 0.00 |
time (sec) |
N/A | 0.637 | 0.517 | 1.609 | 0.000 | 0.110 | 0.000 | 0.743 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 127 | 194 | 0 | 367 | 0 | 133 | 89 | 0 |
N.S. |
1 | 1.00 | 1.46 | 2.23 | 0.00 | 4.22 | 0.00 | 1.53 | 1.02 | 0.00 |
time (sec) |
N/A | 0.403 | 0.573 | 1.581 | 0.000 | 0.115 | 0.000 | 0.551 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 133 | 230 | 245 | 0 | 548 | 0 | 0 | 81 | 0 |
N.S. |
1 | 1.05 | 1.81 | 1.93 | 0.00 | 4.31 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.630 | 2.335 | 1.606 | 0.000 | 1.600 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 178 | 169 | 435 | 0 | 609 | 0 | 418 | 93 | 0 |
N.S. |
1 | 1.05 | 0.99 | 2.56 | 0.00 | 3.58 | 0.00 | 2.46 | 0.55 | 0.00 |
time (sec) |
N/A | 1.017 | 0.725 | 2.038 | 0.000 | 2.075 | 0.000 | 0.805 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 232 | 395 | 454 | 0 | 644 | 0 | 638 | 97 | 0 |
N.S. |
1 | 1.05 | 1.79 | 2.05 | 0.00 | 2.91 | 0.00 | 2.89 | 0.44 | 0.00 |
time (sec) |
N/A | 1.457 | 1.604 | 2.144 | 0.000 | 3.038 | 0.000 | 1.013 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 289 | 499 | 474 | 0 | 675 | 0 | 816 | 97 | 0 |
N.S. |
1 | 1.08 | 1.86 | 1.77 | 0.00 | 2.52 | 0.00 | 3.04 | 0.36 | 0.00 |
time (sec) |
N/A | 1.818 | 6.117 | 2.051 | 0.000 | 3.032 | 0.000 | 1.158 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 232 | 161 | 300 | 0 | 557 | 0 | 276 | 111 | 0 |
N.S. |
1 | 1.07 | 0.75 | 1.39 | 0.00 | 2.58 | 0.00 | 1.28 | 0.51 | 0.00 |
time (sec) |
N/A | 1.403 | 1.853 | 2.003 | 0.000 | 0.120 | 0.000 | 0.772 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F | A | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 178 | 628 | 267 | 0 | 484 | 0 | 258 | 111 | 0 |
N.S. |
1 | 1.05 | 3.72 | 1.58 | 0.00 | 2.86 | 0.00 | 1.53 | 0.66 | 0.00 |
time (sec) |
N/A | 1.000 | 11.032 | 1.757 | 0.000 | 0.118 | 0.000 | 0.854 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 132 | 131 | 276 | 0 | 475 | 0 | 170 | 111 | 0 |
N.S. |
1 | 1.05 | 1.04 | 2.19 | 0.00 | 3.77 | 0.00 | 1.35 | 0.88 | 0.00 |
time (sec) |
N/A | 0.653 | 1.105 | 1.734 | 0.000 | 0.118 | 0.000 | 0.915 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 124 | 206 | 325 | 0 | 475 | 0 | 170 | 109 | 0 |
N.S. |
1 | 0.98 | 1.63 | 2.58 | 0.00 | 3.77 | 0.00 | 1.35 | 0.87 | 0.00 |
time (sec) |
N/A | 0.542 | 1.082 | 1.654 | 0.000 | 0.116 | 0.000 | 0.728 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 176 | 343 | 376 | 0 | 670 | 0 | 0 | 101 | 0 |
N.S. |
1 | 1.07 | 2.09 | 2.29 | 0.00 | 4.09 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.918 | 7.381 | 1.665 | 0.000 | 3.418 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 223 | 208 | 504 | 0 | 739 | 0 | 464 | 113 | 0 |
N.S. |
1 | 1.08 | 1.00 | 2.43 | 0.00 | 3.57 | 0.00 | 2.24 | 0.55 | 0.00 |
time (sec) |
N/A | 1.355 | 3.488 | 2.133 | 0.000 | 4.419 | 0.000 | 1.117 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F(-1) | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 282 | 349 | 0 | 0 | 776 | 0 | 685 | 117 | 0 |
N.S. |
1 | 1.07 | 1.32 | 0.00 | 0.00 | 2.94 | 0.00 | 2.59 | 0.44 | 0.00 |
time (sec) |
N/A | 1.881 | 3.661 | 180.000 | 0.000 | 5.751 | 0.000 | 0.938 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | C | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 87 | 79 | 0 | 699 | 305 | 0 | 71 | 59 | 0 |
N.S. |
1 | 0.98 | 0.89 | 0.00 | 7.85 | 3.43 | 0.00 | 0.80 | 0.66 | 0.00 |
time (sec) |
N/A | 0.389 | 0.274 | 0.000 | 0.380 | 0.092 | 0.000 | 0.342 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 123 | 99 | 0 | 0 | 435 | 0 | 114 | 71 | 0 |
N.S. |
1 | 1.07 | 0.86 | 0.00 | 0.00 | 3.78 | 0.00 | 0.99 | 0.62 | 0.00 |
time (sec) |
N/A | 0.675 | 0.396 | 0.000 | 0.000 | 0.105 | 0.000 | 0.459 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 168 | 119 | 229 | 0 | 462 | 0 | 141 | 75 | 0 |
N.S. |
1 | 1.08 | 0.77 | 1.48 | 0.00 | 2.98 | 0.00 | 0.91 | 0.48 | 0.00 |
time (sec) |
N/A | 0.949 | 0.327 | 5.315 | 0.000 | 0.098 | 0.000 | 0.467 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 216 | 126 | 0 | 0 | 484 | 0 | 166 | 75 | 0 |
N.S. |
1 | 1.12 | 0.66 | 0.00 | 0.00 | 2.52 | 0.00 | 0.86 | 0.39 | 0.00 |
time (sec) |
N/A | 1.282 | 0.478 | 0.000 | 0.000 | 0.103 | 0.000 | 0.432 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 150 | 126 | 983 | 0 | 502 | 0 | 112 | 81 | 0 |
N.S. |
1 | 1.29 | 1.09 | 8.47 | 0.00 | 4.33 | 0.00 | 0.97 | 0.70 | 0.00 |
time (sec) |
N/A | 0.413 | 0.495 | 2.567 | 0.000 | 0.101 | 0.000 | 0.441 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 157 | 134 | 409 | 0 | 526 | 0 | 177 | 93 | 0 |
N.S. |
1 | 1.08 | 0.92 | 2.80 | 0.00 | 3.60 | 0.00 | 1.21 | 0.64 | 0.00 |
time (sec) |
N/A | 0.925 | 0.717 | 2.036 | 0.000 | 0.113 | 0.000 | 0.529 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 210 | 165 | 831 | 0 | 550 | 0 | 183 | 97 | 0 |
N.S. |
1 | 1.08 | 0.85 | 4.28 | 0.00 | 2.84 | 0.00 | 0.94 | 0.50 | 0.00 |
time (sec) |
N/A | 1.268 | 1.924 | 1.922 | 0.000 | 0.105 | 0.000 | 0.578 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 262 | 175 | 1264 | 0 | 572 | 0 | 208 | 97 | 0 |
N.S. |
1 | 1.11 | 0.74 | 5.36 | 0.00 | 2.42 | 0.00 | 0.88 | 0.41 | 0.00 |
time (sec) |
N/A | 1.634 | 2.185 | 2.446 | 0.000 | 0.111 | 0.000 | 0.616 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 210 | 149 | 796 | 0 | 590 | 0 | 138 | 102 | 0 |
N.S. |
1 | 1.38 | 0.98 | 5.24 | 0.00 | 3.88 | 0.00 | 0.91 | 0.67 | 0.00 |
time (sec) |
N/A | 0.438 | 1.280 | 2.514 | 0.000 | 0.102 | 0.000 | 0.653 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 199 | 189 | 454 | 0 | 612 | 0 | 183 | 114 | 0 |
N.S. |
1 | 1.08 | 1.03 | 2.47 | 0.00 | 3.33 | 0.00 | 0.99 | 0.62 | 0.00 |
time (sec) |
N/A | 1.215 | 1.577 | 2.121 | 0.000 | 0.112 | 0.000 | 0.627 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 252 | 187 | 921 | 0 | 634 | 0 | 224 | 118 | 0 |
N.S. |
1 | 1.07 | 0.79 | 3.90 | 0.00 | 2.69 | 0.00 | 0.95 | 0.50 | 0.00 |
time (sec) |
N/A | 1.647 | 2.010 | 1.990 | 0.000 | 0.119 | 0.000 | 0.667 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 305 | 199 | 1399 | 0 | 656 | 0 | 234 | 118 | 0 |
N.S. |
1 | 1.09 | 0.71 | 5.00 | 0.00 | 2.34 | 0.00 | 0.84 | 0.42 | 0.00 |
time (sec) |
N/A | 2.056 | 2.497 | 2.619 | 0.000 | 0.115 | 0.000 | 0.817 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 194 | 200 | 691 | 0 | 233 | 0 | 0 | 83 | 0 |
N.S. |
1 | 0.97 | 1.01 | 3.47 | 0.00 | 1.17 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.896 | 2.036 | 10.777 | 0.000 | 0.113 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 166 | 168 | 635 | 0 | 219 | 0 | 0 | 81 | 0 |
N.S. |
1 | 0.97 | 0.98 | 3.69 | 0.00 | 1.27 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.739 | 1.786 | 4.714 | 0.000 | 0.095 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 137 | 94 | 400 | 0 | 188 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.01 | 0.70 | 2.96 | 0.00 | 1.39 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.696 | 1.476 | 2.940 | 0.000 | 0.091 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 106 | 77 | 240 | 0 | 141 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.00 | 0.73 | 2.26 | 0.00 | 1.33 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.595 | 1.638 | 2.712 | 0.000 | 0.089 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 113 | 83 | 321 | 0 | 142 | 0 | 0 | 74 | 0 |
N.S. |
1 | 1.03 | 0.75 | 2.92 | 0.00 | 1.29 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.590 | 0.981 | 3.911 | 0.000 | 0.092 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 143 | 99 | 355 | 0 | 169 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.01 | 0.70 | 2.52 | 0.00 | 1.20 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.709 | 1.139 | 6.928 | 0.000 | 0.092 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 170 | 113 | 383 | 0 | 187 | 0 | 0 | 83 | 0 |
N.S. |
1 | 0.99 | 0.66 | 2.23 | 0.00 | 1.09 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.778 | 1.491 | 13.620 | 0.000 | 0.094 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 226 | 463 | 825 | 0 | 263 | 0 | 0 | 125 | 0 |
N.S. |
1 | 0.97 | 1.98 | 3.53 | 0.00 | 1.12 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 1.112 | 4.910 | 6.850 | 0.000 | 0.097 | 0.000 | 0.000 | 0.198 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 196 | 321 | 716 | 0 | 239 | 0 | 0 | 114 | 0 |
N.S. |
1 | 0.98 | 1.61 | 3.60 | 0.00 | 1.20 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 1.028 | 5.877 | 4.924 | 0.000 | 0.095 | 0.000 | 0.000 | 0.188 | 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 | 160 | 164 | 313 | 513 | 0 | 202 | 0 | 0 | 105 | 0 |
N.S. |
1 | 1.02 | 1.96 | 3.21 | 0.00 | 1.26 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.883 | 3.393 | 4.001 | 0.000 | 0.094 | 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 | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 162 | 183 | 245 | 0 | 166 | 0 | 0 | 107 | 0 |
N.S. |
1 | 1.03 | 1.16 | 1.55 | 0.00 | 1.05 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.901 | 2.916 | 4.193 | 0.000 | 0.090 | 0.000 | 0.000 | 0.179 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 172 | 153 | 357 | 0 | 187 | 0 | 0 | 118 | 0 |
N.S. |
1 | 1.04 | 0.92 | 2.15 | 0.00 | 1.13 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.904 | 2.839 | 6.871 | 0.000 | 0.092 | 0.000 | 0.000 | 0.205 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 202 | 193 | 385 | 0 | 211 | 0 | 0 | 127 | 0 |
N.S. |
1 | 1.00 | 0.96 | 1.92 | 0.00 | 1.05 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 1.101 | 3.154 | 13.206 | 0.000 | 0.095 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 230 | 217 | 413 | 0 | 231 | 0 | 0 | 127 | 0 |
N.S. |
1 | 0.98 | 0.93 | 1.76 | 0.00 | 0.99 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 1.200 | 3.402 | 20.896 | 0.000 | 0.101 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 274 | 793 | 1153 | 0 | 283 | 0 | 0 | 167 | 0 |
N.S. |
1 | 0.99 | 2.86 | 4.16 | 0.00 | 1.02 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 1.475 | 8.385 | 13.346 | 0.000 | 0.100 | 0.000 | 0.000 | 0.220 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 246 | 465 | 904 | 0 | 263 | 0 | 0 | 156 | 0 |
N.S. |
1 | 1.01 | 1.91 | 3.70 | 0.00 | 1.08 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 1.388 | 5.147 | 7.016 | 0.000 | 0.106 | 0.000 | 0.000 | 0.202 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 215 | 244 | 916 | 0 | 243 | 0 | 0 | 147 | 0 |
N.S. |
1 | 1.02 | 1.16 | 4.34 | 0.00 | 1.15 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 1.254 | 3.126 | 5.793 | 0.000 | 0.105 | 0.000 | 0.000 | 0.209 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 201 | 202 | 654 | 0 | 215 | 0 | 0 | 147 | 0 |
N.S. |
1 | 1.01 | 1.02 | 3.29 | 0.00 | 1.08 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 1.226 | 2.710 | 5.287 | 0.000 | 0.098 | 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 | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 215 | 207 | 519 | 0 | 197 | 0 | 0 | 149 | 0 |
N.S. |
1 | 1.02 | 0.98 | 2.46 | 0.00 | 0.93 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 1.214 | 2.532 | 6.632 | 0.000 | 0.096 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 222 | 194 | 385 | 0 | 211 | 0 | 0 | 160 | 0 |
N.S. |
1 | 1.05 | 0.92 | 1.82 | 0.00 | 1.00 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 1.267 | 3.405 | 12.739 | 0.000 | 0.105 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 250 | 196 | 413 | 0 | 231 | 0 | 0 | 169 | 0 |
N.S. |
1 | 1.02 | 0.80 | 1.69 | 0.00 | 0.95 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 1.454 | 3.474 | 20.384 | 0.000 | 0.106 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 278 | 239 | 441 | 0 | 251 | 0 | 0 | 169 | 0 |
N.S. |
1 | 1.00 | 0.86 | 1.59 | 0.00 | 0.91 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 1.495 | 3.900 | 30.224 | 0.000 | 0.105 | 0.000 | 0.000 | 0.202 | 0.000 |