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 | B | F | F | F(-2) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 1071 | 0 | 0 | 0 | 0 | 0 | 84 | 0 |
N.S. |
1 | 1.00 | 12.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.383 | 5.933 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 342 | 0 | 0 | 0 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.00 | 3.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.464 | 5.409 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 342 | 0 | 0 | 0 | 0 | 0 | 91 | 0 |
N.S. |
1 | 1.00 | 3.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.478 | 9.838 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.474 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 687 | 0 | 243 | 0 | 0 | 0 | 0 | 0 | 83 | 0 |
N.S. |
1 | 0.00 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.000 | 4.053 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.422 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 95 | 1290 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.01 | 13.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.382 | 22.691 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.041 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 230 | 73 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.17 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.640 | 0.038 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.344 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 253 | 216 | 0 | 0 | 0 | 0 | 0 | 80 | 0 |
N.S. |
1 | 1.18 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 6.760 | 8.594 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.446 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 402 | 0 | 0 | 0 | 0 | 0 | 80 | 0 |
N.S. |
1 | 1.00 | 4.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.374 | 4.397 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 401 | 0 | 0 | 0 | 0 | 0 | 80 | 0 |
N.S. |
1 | 1.00 | 4.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.370 | 4.490 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 94 | 94 | 96 | 96 | 104 | 97 | 101 | 87 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.02 | 1.02 | 1.11 | 1.03 | 1.07 | 0.93 |
time (sec) |
N/A | 0.426 | 0.021 | 1.273 | 0.030 | 0.072 | 0.034 | 0.127 | 0.242 | 0.465 |
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 | 70 | 70 | 70 | 72 | 70 | 70 | 80 | 74 | 77 | 66 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.00 | 1.00 | 1.14 | 1.06 | 1.10 | 0.94 |
time (sec) |
N/A | 0.374 | 0.013 | 0.776 | 0.034 | 0.063 | 0.029 | 0.120 | 0.204 | 0.435 |
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 | 50 | 50 | 50 | 49 | 48 | 48 | 51 | 50 | 53 | 48 |
N.S. |
1 | 1.00 | 1.00 | 0.98 | 0.96 | 0.96 | 1.02 | 1.00 | 1.06 | 0.96 |
time (sec) |
N/A | 0.334 | 0.008 | 0.796 | 0.031 | 0.063 | 0.027 | 0.116 | 0.202 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 25 | 24 | 24 | 26 | 26 | 29 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.86 | 0.86 | 0.93 | 0.93 | 1.04 | 0.89 |
time (sec) |
N/A | 0.276 | 0.008 | 0.427 | 0.025 | 0.065 | 0.024 | 0.119 | 0.234 | 0.432 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 131 | 128 | 42 | 128 | 369 | 71 | 133 | 159 | 123 |
N.S. |
1 | 0.91 | 0.89 | 0.29 | 0.89 | 2.56 | 0.49 | 0.92 | 1.10 | 0.85 |
time (sec) |
N/A | 0.504 | 0.072 | 0.845 | 0.110 | 0.088 | 0.239 | 0.130 | 0.224 | 0.663 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 158 | 145 | 65 | 158 | 537 | 97 | 160 | 349 | 143 |
N.S. |
1 | 0.93 | 0.86 | 0.38 | 0.93 | 3.18 | 0.57 | 0.95 | 2.07 | 0.85 |
time (sec) |
N/A | 0.514 | 0.076 | 0.883 | 0.110 | 0.088 | 0.331 | 0.129 | 0.230 | 0.286 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 183 | 175 | 84 | 192 | 743 | 133 | 180 | 560 | 173 |
N.S. |
1 | 0.93 | 0.89 | 0.43 | 0.97 | 3.77 | 0.68 | 0.91 | 2.84 | 0.88 |
time (sec) |
N/A | 0.567 | 0.109 | 0.836 | 0.112 | 0.092 | 0.434 | 0.134 | 0.217 | 0.716 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 122 | 122 | 123 | 124 | 124 | 139 | 132 | 135 | 116 |
N.S. |
1 | 1.00 | 1.00 | 1.01 | 1.02 | 1.02 | 1.14 | 1.08 | 1.11 | 0.95 |
time (sec) |
N/A | 0.483 | 0.015 | 0.759 | 0.034 | 0.066 | 0.038 | 0.116 | 0.246 | 0.068 |
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 | 82 | 82 | 82 | 86 | 82 | 82 | 90 | 91 | 94 | 75 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.00 | 1.00 | 1.10 | 1.11 | 1.15 | 0.91 |
time (sec) |
N/A | 0.398 | 0.010 | 0.753 | 0.032 | 0.086 | 0.030 | 0.123 | 0.229 | 0.050 |
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 | 50 | 50 | 50 | 49 | 48 | 48 | 51 | 50 | 53 | 48 |
N.S. |
1 | 1.00 | 1.00 | 0.98 | 0.96 | 0.96 | 1.02 | 1.00 | 1.06 | 0.96 |
time (sec) |
N/A | 0.323 | 0.008 | 0.679 | 0.033 | 0.067 | 0.025 | 0.124 | 0.222 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 173 | 167 | 78 | 189 | 505 | 156 | 211 | 279 | 152 |
N.S. |
1 | 1.00 | 0.97 | 0.45 | 1.09 | 2.92 | 0.90 | 1.22 | 1.61 | 0.88 |
time (sec) |
N/A | 0.530 | 0.069 | 0.888 | 0.112 | 0.092 | 0.370 | 0.126 | 0.214 | 0.292 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 203 | 210 | 99 | 226 | 771 | 189 | 233 | 575 | 191 |
N.S. |
1 | 1.00 | 1.03 | 0.49 | 1.11 | 3.80 | 0.93 | 1.15 | 2.83 | 0.94 |
time (sec) |
N/A | 0.693 | 0.163 | 0.885 | 0.109 | 0.093 | 0.634 | 0.131 | 0.299 | 0.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 253 | 221 | 217 | 131 | 267 | 1067 | 233 | 264 | 892 | 249 |
N.S. |
1 | 0.87 | 0.86 | 0.52 | 1.06 | 4.22 | 0.92 | 1.04 | 3.53 | 0.98 |
time (sec) |
N/A | 0.710 | 0.200 | 0.901 | 0.120 | 0.146 | 0.868 | 0.129 | 0.219 | 0.726 |
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 | 157 | 164 | 174 | 168 | 168 | 202 | 190 | 193 | 153 |
N.S. |
1 | 1.00 | 1.04 | 1.11 | 1.07 | 1.07 | 1.29 | 1.21 | 1.23 | 0.97 |
time (sec) |
N/A | 0.537 | 0.020 | 0.761 | 0.038 | 0.065 | 0.039 | 0.123 | 0.212 | 0.433 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 122 | 122 | 123 | 124 | 124 | 139 | 132 | 135 | 116 |
N.S. |
1 | 1.00 | 1.00 | 1.01 | 1.02 | 1.02 | 1.14 | 1.08 | 1.11 | 0.95 |
time (sec) |
N/A | 0.460 | 0.017 | 0.760 | 0.025 | 0.068 | 0.036 | 0.122 | 0.199 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 70 | 72 | 70 | 70 | 80 | 74 | 77 | 66 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.00 | 1.00 | 1.14 | 1.06 | 1.10 | 0.94 |
time (sec) |
N/A | 0.369 | 0.009 | 0.680 | 0.025 | 0.081 | 0.028 | 0.109 | 0.255 | 0.407 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 206 | 202 | 131 | 272 | 679 | 257 | 296 | 415 | 193 |
N.S. |
1 | 1.00 | 0.98 | 0.64 | 1.32 | 3.30 | 1.25 | 1.44 | 2.01 | 0.94 |
time (sec) |
N/A | 0.605 | 0.045 | 0.918 | 0.113 | 0.101 | 0.599 | 0.127 | 0.226 | 0.678 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 235 | 227 | 153 | 306 | 1029 | 291 | 319 | 816 | 239 |
N.S. |
1 | 1.00 | 0.97 | 0.65 | 1.30 | 4.38 | 1.24 | 1.36 | 3.47 | 1.02 |
time (sec) |
N/A | 0.721 | 0.132 | 0.917 | 0.110 | 0.098 | 1.804 | 0.130 | 0.256 | 0.717 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 287 | 291 | 179 | 347 | 1407 | 333 | 346 | 1238 | 313 |
N.S. |
1 | 1.00 | 1.01 | 0.62 | 1.21 | 4.90 | 1.16 | 1.21 | 4.31 | 1.09 |
time (sec) |
N/A | 0.856 | 0.188 | 0.915 | 0.118 | 0.116 | 4.035 | 0.142 | 0.213 | 0.762 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 252 | 253 | 201 | 364 | 873 | 371 | 391 | 568 | 250 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 1.44 | 3.46 | 1.47 | 1.55 | 2.25 | 0.99 |
time (sec) |
N/A | 0.708 | 0.111 | 1.026 | 0.116 | 0.096 | 0.727 | 0.138 | 0.240 | 0.709 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 208 | 203 | 131 | 273 | 700 | 257 | 296 | 415 | 192 |
N.S. |
1 | 1.00 | 0.98 | 0.63 | 1.31 | 3.37 | 1.24 | 1.42 | 2.00 | 0.92 |
time (sec) |
N/A | 0.592 | 0.065 | 0.894 | 0.110 | 0.151 | 0.593 | 0.136 | 0.220 | 0.680 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 173 | 167 | 78 | 190 | 507 | 156 | 211 | 279 | 152 |
N.S. |
1 | 1.00 | 0.97 | 0.45 | 1.10 | 2.93 | 0.90 | 1.22 | 1.61 | 0.88 |
time (sec) |
N/A | 0.496 | 0.079 | 0.894 | 0.110 | 0.090 | 0.373 | 0.125 | 0.226 | 0.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 130 | 129 | 42 | 128 | 390 | 71 | 133 | 159 | 123 |
N.S. |
1 | 0.90 | 0.89 | 0.29 | 0.88 | 2.69 | 0.49 | 0.92 | 1.10 | 0.85 |
time (sec) |
N/A | 0.482 | 0.050 | 0.804 | 0.110 | 0.097 | 0.234 | 0.128 | 0.226 | 0.631 |
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 | 288 | 248 | 224 | 207 | 293 | 254 | 447 | 278 | 188 | 1364 |
N.S. |
1 | 0.86 | 0.78 | 0.72 | 1.02 | 0.88 | 1.55 | 0.97 | 0.65 | 4.74 |
time (sec) |
N/A | 0.694 | 0.082 | 1.112 | 0.109 | 0.133 | 56.982 | 0.137 | 0.242 | 8.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 346 | 307 | 336 | 246 | 489 | 432 | 0 | 443 | 672 | 2589 |
N.S. |
1 | 0.89 | 0.97 | 0.71 | 1.41 | 1.25 | 0.00 | 1.28 | 1.94 | 7.48 |
time (sec) |
N/A | 0.857 | 0.187 | 1.166 | 0.111 | 3.886 | 0.000 | 0.139 | 0.266 | 18.728 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 320 | 320 | 313 | 304 | 509 | 1619 | 546 | 529 | 1349 | 416 |
N.S. |
1 | 1.00 | 0.98 | 0.95 | 1.59 | 5.06 | 1.71 | 1.65 | 4.22 | 1.30 |
time (sec) |
N/A | 0.878 | 0.211 | 0.908 | 0.118 | 0.109 | 5.540 | 0.131 | 0.204 | 0.433 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 267 | 260 | 218 | 397 | 1316 | 405 | 412 | 1074 | 302 |
N.S. |
1 | 1.00 | 0.97 | 0.82 | 1.49 | 4.93 | 1.52 | 1.54 | 4.02 | 1.13 |
time (sec) |
N/A | 0.753 | 0.167 | 0.916 | 0.110 | 0.102 | 2.258 | 0.127 | 0.212 | 0.794 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 234 | 227 | 153 | 306 | 1027 | 291 | 319 | 816 | 240 |
N.S. |
1 | 1.00 | 0.97 | 0.65 | 1.31 | 4.39 | 1.24 | 1.36 | 3.49 | 1.03 |
time (sec) |
N/A | 0.693 | 0.115 | 0.913 | 0.114 | 0.097 | 1.032 | 0.130 | 0.242 | 0.765 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 203 | 205 | 101 | 220 | 768 | 189 | 227 | 575 | 191 |
N.S. |
1 | 1.00 | 1.01 | 0.50 | 1.08 | 3.78 | 0.93 | 1.12 | 2.83 | 0.94 |
time (sec) |
N/A | 0.690 | 0.166 | 0.888 | 0.112 | 0.093 | 0.806 | 0.132 | 0.215 | 0.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 158 | 145 | 65 | 158 | 537 | 97 | 160 | 349 | 143 |
N.S. |
1 | 0.93 | 0.86 | 0.38 | 0.93 | 3.18 | 0.57 | 0.95 | 2.07 | 0.85 |
time (sec) |
N/A | 0.513 | 0.069 | 0.790 | 0.109 | 0.089 | 0.385 | 0.130 | 0.214 | 0.703 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 346 | 306 | 337 | 247 | 489 | 440 | 0 | 443 | 672 | 2492 |
N.S. |
1 | 0.88 | 0.97 | 0.71 | 1.41 | 1.27 | 0.00 | 1.28 | 1.94 | 7.20 |
time (sec) |
N/A | 0.834 | 0.192 | 1.148 | 0.122 | 3.862 | 0.000 | 0.143 | 0.233 | 17.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 419 | 373 | 381 | 285 | 784 | 897 | 0 | 664 | 1648 | 3637 |
N.S. |
1 | 0.89 | 0.91 | 0.68 | 1.87 | 2.14 | 0.00 | 1.58 | 3.93 | 8.68 |
time (sec) |
N/A | 1.092 | 0.513 | 1.227 | 0.129 | 47.358 | 0.000 | 0.140 | 0.280 | 25.744 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 324 | 322 | 161 | 377 | 0 | 118 | 131 | 0 | 195 | 0 |
N.S. |
1 | 0.99 | 0.50 | 1.16 | 0.00 | 0.36 | 0.40 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.646 | 7.540 | 1.533 | 0.000 | 0.095 | 1.532 | 0.000 | 0.260 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 264 | 75 | 325 | 0 | 66 | 82 | 0 | 98 | 0 |
N.S. |
1 | 0.99 | 0.28 | 1.21 | 0.00 | 0.25 | 0.31 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.502 | 4.394 | 0.891 | 0.000 | 0.076 | 1.082 | 0.000 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 161 | 723 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 2.73 | 12.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.302 | 10.030 | 1.111 | 0.000 | 0.000 | 0.000 | 0.000 | 0.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 232 | 753 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 3.93 | 12.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.301 | 10.263 | 1.261 | 0.000 | 0.000 | 0.000 | 0.000 | 0.670 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 297 | 161 | 339 | 0 | 82 | 126 | 0 | 134 | 0 |
N.S. |
1 | 1.04 | 0.56 | 1.19 | 0.00 | 0.29 | 0.44 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.572 | 12.798 | 1.556 | 0.000 | 0.074 | 1.520 | 0.000 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 239 | 74 | 309 | 0 | 41 | 78 | 0 | 66 | 0 |
N.S. |
1 | 1.00 | 0.31 | 1.29 | 0.00 | 0.17 | 0.33 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.440 | 10.033 | 0.865 | 0.000 | 0.075 | 0.943 | 0.000 | 0.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 207 | 46 | 283 | 0 | 14 | 36 | 0 | 20 | 37 |
N.S. |
1 | 1.00 | 0.22 | 1.37 | 0.00 | 0.07 | 0.17 | 0.00 | 0.10 | 0.18 |
time (sec) |
N/A | 0.381 | 0.003 | 0.724 | 0.000 | 0.093 | 0.442 | 0.000 | 0.218 | 0.825 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 773 | 59 | 161 | 429 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 0.08 | 0.21 | 0.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.310 | 10.056 | 1.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 335 | 769 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.00 | 5.68 | 13.03 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.311 | 10.285 | 1.235 | 0.000 | 0.000 | 0.000 | 0.000 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 420 | 836 | 0 | 0 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.00 | 7.12 | 14.17 | 0.00 | 0.00 | 0.00 | 0.00 | 1.41 | 0.00 |
time (sec) |
N/A | 0.298 | 10.529 | 1.684 | 0.000 | 0.000 | 0.000 | 0.000 | 1.687 | 0.000 |
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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 290 | 310 | 161 | 398 | 0 | 141 | 0 | 0 | 306 | 0 |
N.S. |
1 | 1.07 | 0.56 | 1.37 | 0.00 | 0.49 | 0.00 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.614 | 13.277 | 2.083 | 0.000 | 0.092 | 0.000 | 0.000 | 0.323 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 251 | 73 | 336 | 0 | 82 | 78 | 0 | 176 | 0 |
N.S. |
1 | 1.00 | 0.29 | 1.34 | 0.00 | 0.33 | 0.31 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.435 | 10.035 | 0.847 | 0.000 | 0.086 | 3.177 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 232 | 55 | 306 | 0 | 51 | 36 | 0 | 31 | 37 |
N.S. |
1 | 1.00 | 0.24 | 1.32 | 0.00 | 0.22 | 0.16 | 0.00 | 0.13 | 0.16 |
time (sec) |
N/A | 0.403 | 0.009 | 0.746 | 0.000 | 0.076 | 0.544 | 0.000 | 0.255 | 0.617 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 330 | 753 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.00 | 5.32 | 12.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.310 | 10.198 | 1.045 | 0.000 | 0.000 | 0.000 | 0.000 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 380 | 830 | 0 | 0 | 0 | 0 | 100 | 0 |
N.S. |
1 | 1.00 | 6.13 | 13.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.61 | 0.00 |
time (sec) |
N/A | 0.302 | 10.529 | 1.303 | 0.000 | 0.000 | 0.000 | 0.000 | 1.981 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 323 | 0 | 0 | 0 | 0 | 0 | 393 | 0 |
N.S. |
1 | 1.00 | 3.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.57 | 0.00 |
time (sec) |
N/A | 0.359 | 4.210 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.729 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 374 | 0 | 0 | 0 | 0 | 0 | 226 | 0 |
N.S. |
1 | 1.00 | 4.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.69 | 0.00 |
time (sec) |
N/A | 0.351 | 3.317 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.523 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 171 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 2.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.351 | 1.810 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 170 | 0 | 0 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.00 | 2.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.362 | 1.844 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 419 | 0 | 0 | 0 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.00 | 4.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.358 | 3.482 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 432 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 4.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.354 | 5.813 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.061 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 369 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 4.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.350 | 5.155 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.400 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 256 | 0 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.00 | 2.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.346 | 3.234 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.669 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 419 | 0 | 0 | 0 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.00 | 4.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.347 | 3.507 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 483 | 0 | 0 | 0 | 0 | 0 | 108 | 0 |
N.S. |
1 | 1.00 | 5.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.21 | 0.00 |
time (sec) |
N/A | 0.352 | 5.418 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.853 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 114 | 156 | 144 | 322 | 399 | 80 | 0 | 45 | 0 |
N.S. |
1 | 1.02 | 1.39 | 1.29 | 2.88 | 3.56 | 0.71 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.323 | 0.398 | 1.202 | 0.117 | 0.114 | 2.113 | 0.000 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 92 | 140 | 118 | 244 | 363 | 76 | 0 | 32 | 0 |
N.S. |
1 | 1.01 | 1.54 | 1.30 | 2.68 | 3.99 | 0.84 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.296 | 0.332 | 1.157 | 0.111 | 0.122 | 1.470 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 142 | 114 | 130 | 372 | 70 | 0 | 70 | 0 |
N.S. |
1 | 1.00 | 1.67 | 1.34 | 1.53 | 4.38 | 0.82 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 0.293 | 0.329 | 0.905 | 0.110 | 0.090 | 3.227 | 0.000 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 47 | 28 | 25 | 50 | 44 | 190 | 0 | 110 | 27 |
N.S. |
1 | 1.31 | 0.78 | 0.69 | 1.39 | 1.22 | 5.28 | 0.00 | 3.06 | 0.75 |
time (sec) |
N/A | 0.264 | 0.232 | 0.803 | 0.032 | 0.098 | 22.568 | 0.000 | 0.297 | 0.590 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 60 | 40 | 37 | 85 | 69 | 709 | 0 | 150 | 44 |
N.S. |
1 | 1.09 | 0.73 | 0.67 | 1.55 | 1.25 | 12.89 | 0.00 | 2.73 | 0.80 |
time (sec) |
N/A | 0.286 | 0.299 | 0.827 | 0.034 | 0.078 | 115.245 | 0.000 | 0.287 | 0.609 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 87 | 51 | 48 | 119 | 91 | 0 | 0 | 190 | 58 |
N.S. |
1 | 1.18 | 0.69 | 0.65 | 1.61 | 1.23 | 0.00 | 0.00 | 2.57 | 0.78 |
time (sec) |
N/A | 0.309 | 0.592 | 0.830 | 0.035 | 0.082 | 0.000 | 0.000 | 0.322 | 0.874 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 114 | 62 | 59 | 153 | 113 | 0 | 0 | 230 | 73 |
N.S. |
1 | 1.23 | 0.67 | 0.63 | 1.65 | 1.22 | 0.00 | 0.00 | 2.47 | 0.78 |
time (sec) |
N/A | 0.349 | 0.529 | 0.851 | 0.032 | 0.088 | 0.000 | 0.000 | 0.337 | 0.718 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 464 | 559 | 232 | 0 | 0 | 0 | 0 | 0 | 95 | 0 |
N.S. |
1 | 1.20 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 1.273 | 10.246 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.311 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 464 | 537 | 217 | 0 | 0 | 0 | 0 | 0 | 77 | 0 |
N.S. |
1 | 1.16 | 0.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 1.166 | 10.117 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 398 | 409 | 428 | 0 | 0 | 644 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.03 | 1.08 | 0.00 | 0.00 | 1.62 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.778 | 2.757 | 0.000 | 0.000 | 16.029 | 0.000 | 0.000 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 452 | 464 | 153 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.03 | 0.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.923 | 10.050 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 473 | 541 | 213 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.14 | 0.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.170 | 10.099 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 492 | 569 | 240 | 0 | 0 | 0 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.16 | 0.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 1.312 | 10.138 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 144 | 167 | 164 | 552 | 421 | 126 | 0 | 65 | 0 |
N.S. |
1 | 1.07 | 1.25 | 1.22 | 4.12 | 3.14 | 0.94 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.407 | 0.556 | 1.338 | 0.129 | 0.129 | 5.649 | 0.000 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 122 | 165 | 144 | 436 | 399 | 121 | 0 | 54 | 0 |
N.S. |
1 | 1.06 | 1.43 | 1.25 | 3.79 | 3.47 | 1.05 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.371 | 0.578 | 1.330 | 0.119 | 0.135 | 3.081 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 114 | 154 | 132 | 296 | 412 | 0 | 0 | 111 | 0 |
N.S. |
1 | 1.08 | 1.45 | 1.25 | 2.79 | 3.89 | 0.00 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 0.364 | 0.485 | 1.590 | 0.119 | 0.160 | 0.000 | 0.000 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 116 | 137 | 117 | 180 | 521 | 0 | 0 | 171 | 0 |
N.S. |
1 | 1.18 | 1.40 | 1.19 | 1.84 | 5.32 | 0.00 | 0.00 | 1.74 | 0.00 |
time (sec) |
N/A | 0.372 | 0.380 | 1.030 | 0.122 | 0.141 | 0.000 | 0.000 | 0.313 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 81 | 40 | 37 | 105 | 67 | 0 | 0 | 231 | 44 |
N.S. |
1 | 1.53 | 0.75 | 0.70 | 1.98 | 1.26 | 0.00 | 0.00 | 4.36 | 0.83 |
time (sec) |
N/A | 0.318 | 0.337 | 0.967 | 0.040 | 0.121 | 0.000 | 0.000 | 0.307 | 0.643 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 118 | 51 | 48 | 155 | 91 | 0 | 0 | 291 | 56 |
N.S. |
1 | 1.64 | 0.71 | 0.67 | 2.15 | 1.26 | 0.00 | 0.00 | 4.04 | 0.78 |
time (sec) |
N/A | 0.388 | 0.469 | 0.960 | 0.035 | 0.124 | 0.000 | 0.000 | 0.317 | 0.664 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 116 | 62 | 59 | 206 | 113 | 0 | 0 | 351 | 71 |
N.S. |
1 | 1.27 | 0.68 | 0.65 | 2.26 | 1.24 | 0.00 | 0.00 | 3.86 | 0.78 |
time (sec) |
N/A | 0.396 | 0.622 | 0.959 | 0.034 | 0.105 | 0.000 | 0.000 | 0.370 | 0.659 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 143 | 73 | 70 | 257 | 135 | 0 | 0 | 411 | 86 |
N.S. |
1 | 1.30 | 0.66 | 0.64 | 2.34 | 1.23 | 0.00 | 0.00 | 3.74 | 0.78 |
time (sec) |
N/A | 0.430 | 1.015 | 0.981 | 0.050 | 0.131 | 0.000 | 0.000 | 0.438 | 0.675 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 99 | 97 | 0 | 0 | 0 | 168 | 0 | 85 | 0 |
N.S. |
1 | 1.11 | 1.09 | 0.00 | 0.00 | 0.00 | 1.89 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.363 | 7.512 | 0.000 | 0.000 | 0.000 | 2.182 | 0.000 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 93 | 85 | 0 | 0 | 0 | 126 | 0 | 65 | 0 |
N.S. |
1 | 1.04 | 0.96 | 0.00 | 0.00 | 0.00 | 1.42 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.357 | 5.749 | 0.000 | 0.000 | 0.000 | 1.453 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 93 | 75 | 0 | 0 | 0 | 121 | 0 | 54 | 0 |
N.S. |
1 | 1.04 | 0.84 | 0.00 | 0.00 | 0.00 | 1.36 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.385 | 10.034 | 0.000 | 0.000 | 0.000 | 1.512 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 74 | 62 | 0 | 0 | 0 | 0 | 0 | 111 | 0 |
N.S. |
1 | 0.90 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.35 | 0.00 |
time (sec) |
N/A | 0.343 | 10.036 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 74 | 70 | 0 | 0 | 0 | 0 | 0 | 171 | 0 |
N.S. |
1 | 0.91 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.11 | 0.00 |
time (sec) |
N/A | 0.317 | 10.052 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 77 | 85 | 0 | 0 | 0 | 0 | 0 | 231 | 0 |
N.S. |
1 | 0.90 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.69 | 0.00 |
time (sec) |
N/A | 0.308 | 10.055 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 98 | 95 | 0 | 0 | 0 | 0 | 0 | 291 | 0 |
N.S. |
1 | 1.14 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.38 | 0.00 |
time (sec) |
N/A | 0.353 | 10.130 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 139 | 179 | 0 | 0 | 0 | 131 | 0 | 173 | 0 |
N.S. |
1 | 1.09 | 1.40 | 0.00 | 0.00 | 0.00 | 1.02 | 0.00 | 1.35 | 0.00 |
time (sec) |
N/A | 0.438 | 8.096 | 0.000 | 0.000 | 0.000 | 1.795 | 0.000 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 72 | 0 | 0 | 0 | 82 | 0 | 82 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.323 | 5.552 | 0.000 | 0.000 | 0.000 | 1.092 | 0.000 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 160 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 2.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.308 | 10.134 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 232 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 3.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.302 | 10.261 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.527 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 165 | 223 | 166 | 436 | 554 | 126 | 0 | 54 | 0 |
N.S. |
1 | 0.96 | 1.30 | 0.97 | 2.53 | 3.22 | 0.73 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.458 | 0.777 | 1.474 | 0.116 | 0.139 | 3.549 | 0.000 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 107 | 163 | 225 | 244 | 362 | 78 | 0 | 31 | 0 |
N.S. |
1 | 0.96 | 1.47 | 2.03 | 2.20 | 3.26 | 0.70 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.334 | 0.447 | 1.291 | 0.121 | 0.098 | 1.527 | 0.000 | 0.235 | 0.000 |