Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 153 | 147 | 261 | 0 | 0 | 0 | 0 | 207 | 0 |
N.S. |
1 | 1.17 | 1.12 | 1.99 | 0.00 | 0.00 | 0.00 | 0.00 | 1.58 | 0.00 |
time (sec) |
N/A | 1.019 | 0.436 | 1.249 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 80 | 87 | 163 | 119 | 165 | 0 | 0 | 147 | 0 |
N.S. |
1 | 0.93 | 1.01 | 1.90 | 1.38 | 1.92 | 0.00 | 0.00 | 1.71 | 0.00 |
time (sec) |
N/A | 0.563 | 0.231 | 1.102 | 0.130 | 0.141 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 78 | 168 | 0 | 0 | 0 | 0 | 183 | 0 |
N.S. |
1 | 1.00 | 0.98 | 2.10 | 0.00 | 0.00 | 0.00 | 0.00 | 2.29 | 0.00 |
time (sec) |
N/A | 0.546 | 0.363 | 0.891 | 0.000 | 0.000 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 52 | 103 | 0 | 127 | 0 | 0 | 125 | 0 |
N.S. |
1 | 1.00 | 1.16 | 2.29 | 0.00 | 2.82 | 0.00 | 0.00 | 2.78 | 0.00 |
time (sec) |
N/A | 0.374 | 0.183 | 0.923 | 0.000 | 0.145 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 66 | 110 | 58 | 0 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.00 | 1.29 | 2.16 | 1.14 | 0.00 | 0.00 | 0.00 | 2.57 | 0.00 |
time (sec) |
N/A | 0.296 | 0.040 | 0.879 | 0.039 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 96 | 143 | 155 | 0 | 0 | 0 | 0 | 206 | 0 |
N.S. |
1 | 1.02 | 1.52 | 1.65 | 0.00 | 0.00 | 0.00 | 0.00 | 2.19 | 0.00 |
time (sec) |
N/A | 0.663 | 0.368 | 1.195 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 88 | 102 | 244 | 119 | 0 | 0 | 0 | 162 | 0 |
N.S. |
1 | 0.97 | 1.12 | 2.68 | 1.31 | 0.00 | 0.00 | 0.00 | 1.78 | 0.00 |
time (sec) |
N/A | 0.375 | 0.231 | 1.187 | 0.039 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 160 | 269 | 224 | 0 | 0 | 0 | 0 | 253 | 0 |
N.S. |
1 | 0.99 | 1.66 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.56 | 0.00 |
time (sec) |
N/A | 0.984 | 2.732 | 1.184 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 142 | 168 | 604 | 0 | 0 | 0 | 0 | 190 | 0 |
N.S. |
1 | 0.95 | 1.13 | 4.05 | 0.00 | 0.00 | 0.00 | 0.00 | 1.28 | 0.00 |
time (sec) |
N/A | 0.475 | 0.276 | 1.217 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 251 | 202 | 970 | 0 | 0 | 0 | 0 | 370 | 0 |
N.S. |
1 | 1.31 | 1.05 | 5.05 | 0.00 | 0.00 | 0.00 | 0.00 | 1.93 | 0.00 |
time (sec) |
N/A | 1.119 | 0.532 | 1.165 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 139 | 132 | 237 | 0 | 218 | 0 | 0 | 281 | 0 |
N.S. |
1 | 0.95 | 0.90 | 1.62 | 0.00 | 1.49 | 0.00 | 0.00 | 1.92 | 0.00 |
time (sec) |
N/A | 0.543 | 0.291 | 1.092 | 0.000 | 0.138 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 166 | 166 | 897 | 0 | 0 | 0 | 0 | 330 | 0 |
N.S. |
1 | 1.19 | 1.19 | 6.45 | 0.00 | 0.00 | 0.00 | 0.00 | 2.37 | 0.00 |
time (sec) |
N/A | 0.955 | 0.441 | 0.987 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 104 | 93 | 157 | 138 | 187 | 0 | 0 | 262 | 0 |
N.S. |
1 | 0.99 | 0.89 | 1.50 | 1.31 | 1.78 | 0.00 | 0.00 | 2.50 | 0.00 |
time (sec) |
N/A | 0.581 | 0.251 | 1.102 | 0.123 | 0.125 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 74 | 88 | 729 | 137 | 0 | 0 | 0 | 266 | 0 |
N.S. |
1 | 0.92 | 1.10 | 9.11 | 1.71 | 0.00 | 0.00 | 0.00 | 3.32 | 0.00 |
time (sec) |
N/A | 0.475 | 0.229 | 1.108 | 0.042 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 74 | 72 | 121 | 0 | 165 | 0 | 0 | 237 | 0 |
N.S. |
1 | 0.99 | 0.96 | 1.61 | 0.00 | 2.20 | 0.00 | 0.00 | 3.16 | 0.00 |
time (sec) |
N/A | 0.416 | 0.201 | 1.104 | 0.000 | 0.129 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 113 | 100 | 619 | 126 | 0 | 0 | 0 | 274 | 0 |
N.S. |
1 | 1.05 | 0.93 | 5.73 | 1.17 | 0.00 | 0.00 | 0.00 | 2.54 | 0.00 |
time (sec) |
N/A | 0.427 | 0.068 | 0.914 | 0.040 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 169 | 209 | 208 | 0 | 0 | 0 | 0 | 391 | 0 |
N.S. |
1 | 1.14 | 1.41 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | 2.64 | 0.00 |
time (sec) |
N/A | 0.930 | 0.660 | 1.218 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 140 | 125 | 778 | 0 | 0 | 0 | 0 | 305 | 0 |
N.S. |
1 | 0.93 | 0.83 | 5.19 | 0.00 | 0.00 | 0.00 | 0.00 | 2.03 | 0.00 |
time (sec) |
N/A | 0.476 | 0.361 | 1.204 | 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 | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 256 | 331 | 314 | 0 | 0 | 0 | 0 | 434 | 0 |
N.S. |
1 | 1.15 | 1.49 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.95 | 0.00 |
time (sec) |
N/A | 1.405 | 3.875 | 1.258 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 188 | 239 | 1155 | 236 | 0 | 0 | 0 | 330 | 0 |
N.S. |
1 | 0.91 | 1.16 | 5.61 | 1.15 | 0.00 | 0.00 | 0.00 | 1.60 | 0.00 |
time (sec) |
N/A | 0.646 | 0.358 | 1.186 | 0.050 | 0.000 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 94 | 63 | 74 | 83 | 83 | 82 | 0 | 22 | 0 |
N.S. |
1 | 1.09 | 0.73 | 0.86 | 0.97 | 0.97 | 0.95 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.752 | 0.035 | 1.373 | 0.035 | 0.087 | 0.438 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 73 | 48 | 82 | 59 | 55 | 65 | 0 | 22 | 0 |
N.S. |
1 | 1.04 | 0.69 | 1.17 | 0.84 | 0.79 | 0.93 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.615 | 0.031 | 1.449 | 0.042 | 0.088 | 0.355 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 42 | 40 | 55 | 62 | 42 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.82 | 1.12 | 1.27 | 0.86 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.511 | 0.047 | 0.926 | 0.035 | 0.096 | 0.317 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 47 | 26 | 38 | 24 | 38 | 24 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.68 | 0.93 | 1.36 | 0.86 | 1.36 | 0.86 | 0.00 |
time (sec) |
N/A | 0.372 | 0.035 | 0.793 | 0.027 | 0.088 | 0.228 | 0.117 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 11 | 23 | 10 | 23 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 1.77 | 0.77 | 1.77 | 0.85 | 0.85 |
time (sec) |
N/A | 0.295 | 0.006 | 0.240 | 0.025 | 0.085 | 0.194 | 0.109 | 0.195 | 3.005 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 46 | 57 | 89 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.35 | 1.68 | 2.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.486 | 0.098 | 0.935 | 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 | A | B | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 56 | 25 | 39 | 0 | 71 | 22 | 0 |
N.S. |
1 | 1.00 | 1.07 | 2.07 | 0.93 | 1.44 | 0.00 | 2.63 | 0.81 | 0.00 |
time (sec) |
N/A | 0.287 | 0.044 | 1.093 | 0.035 | 0.095 | 0.000 | 0.134 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 84 | 126 | 150 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.05 | 1.58 | 1.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.517 | 0.539 | 1.347 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 124 | 120 | 173 | 134 | 158 | 0 | 0 | 84 | 0 |
N.S. |
1 | 0.71 | 0.69 | 0.99 | 0.77 | 0.90 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.382 | 0.123 | 1.455 | 0.040 | 0.105 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 158 | 129 | 338 | 0 | 0 | 0 | 0 | 85 | 0 |
N.S. |
1 | 0.87 | 0.71 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.610 | 0.590 | 0.535 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 80 | 92 | 147 | 73 | 127 | 0 | 0 | 62 | 0 |
N.S. |
1 | 0.76 | 0.88 | 1.40 | 0.70 | 1.21 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.300 | 0.107 | 0.615 | 0.038 | 0.091 | 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(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 120 | 256 | 0 | 0 | 0 | 0 | 60 | 0 |
N.S. |
1 | 1.00 | 1.08 | 2.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.362 | 0.302 | 0.572 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 135 | 168 | 331 | 0 | 0 | 0 | 0 | 75 | 0 |
N.S. |
1 | 0.76 | 0.95 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.667 | 0.373 | 0.831 | 0.000 | 0.000 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 129 | 251 | 0 | 0 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.00 | 1.23 | 2.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.415 | 0.316 | 0.898 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 150 | 223 | 334 | 0 | 0 | 0 | 0 | 96 | 0 |
N.S. |
1 | 0.75 | 1.11 | 1.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.892 | 2.120 | 0.920 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 80 | 117 | 137 | 133 | 217 | 0 | 0 | 75 | 0 |
N.S. |
1 | 0.75 | 1.10 | 1.29 | 1.25 | 2.05 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.535 | 0.288 | 0.936 | 0.051 | 0.124 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 135 | 130 | 201 | 145 | 199 | 0 | 0 | 130 | 0 |
N.S. |
1 | 0.62 | 0.60 | 0.93 | 0.67 | 0.92 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.671 | 0.170 | 1.069 | 0.041 | 0.101 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 245 | 251 | 799 | 0 | 0 | 0 | 0 | 132 | 0 |
N.S. |
1 | 0.96 | 0.99 | 3.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 1.275 | 0.568 | 0.606 | 0.000 | 0.000 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 91 | 102 | 176 | 85 | 167 | 0 | 0 | 108 | 0 |
N.S. |
1 | 0.62 | 0.70 | 1.21 | 0.58 | 1.14 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.307 | 0.127 | 1.491 | 0.039 | 0.098 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 196 | 200 | 496 | 0 | 0 | 0 | 0 | 108 | 0 |
N.S. |
1 | 1.11 | 1.13 | 2.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.587 | 0.543 | 0.652 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 210 | 248 | 428 | 0 | 0 | 0 | 0 | 122 | 0 |
N.S. |
1 | 0.84 | 0.99 | 1.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 1.075 | 0.556 | 0.841 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 189 | 200 | 230 | 0 | 0 | 0 | 0 | 114 | 0 |
N.S. |
1 | 1.07 | 1.13 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.633 | 0.732 | 0.862 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 218 | 352 | 289 | 0 | 0 | 0 | 0 | 146 | 0 |
N.S. |
1 | 0.81 | 1.30 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 1.047 | 3.027 | 0.994 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 188 | 217 | 257 | 0 | 0 | 0 | 0 | 120 | 0 |
N.S. |
1 | 1.02 | 1.18 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.913 | 0.572 | 0.979 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 145 | 140 | 217 | 156 | 263 | 0 | 0 | 177 | 0 |
N.S. |
1 | 0.55 | 0.53 | 0.82 | 0.59 | 0.99 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.647 | 0.216 | 0.983 | 0.043 | 0.102 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 337 | 344 | 388 | 1165 | 0 | 0 | 0 | 0 | 179 | 0 |
N.S. |
1 | 1.02 | 1.15 | 3.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 1.661 | 0.790 | 0.635 | 0.000 | 0.000 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 100 | 112 | 192 | 96 | 225 | 0 | 0 | 155 | 0 |
N.S. |
1 | 0.52 | 0.58 | 0.99 | 0.50 | 1.17 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.309 | 0.144 | 0.935 | 0.040 | 0.109 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 267 | 317 | 801 | 0 | 0 | 0 | 0 | 155 | 0 |
N.S. |
1 | 1.06 | 1.26 | 3.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.780 | 0.521 | 0.720 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 333 | 297 | 339 | 540 | 0 | 0 | 0 | 0 | 170 | 0 |
N.S. |
1 | 0.89 | 1.02 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 1.409 | 0.627 | 0.956 | 0.000 | 0.000 | 0.000 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 289 | 270 | 285 | 0 | 0 | 0 | 0 | 162 | 0 |
N.S. |
1 | 0.99 | 0.92 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 1.038 | 1.158 | 1.050 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 355 | 306 | 424 | 339 | 0 | 0 | 0 | 0 | 194 | 0 |
N.S. |
1 | 0.86 | 1.19 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 2.262 | 5.805 | 1.060 | 0.000 | 0.000 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 285 | 286 | 322 | 0 | 0 | 0 | 0 | 176 | 0 |
N.S. |
1 | 1.07 | 1.08 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 1.032 | 0.882 | 0.964 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 226 | 119 | 172 | 174 | 161 | 0 | 0 | 89 | 0 |
N.S. |
1 | 1.05 | 0.55 | 0.80 | 0.81 | 0.75 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.705 | 0.157 | 1.268 | 0.043 | 0.104 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 200 | 151 | 519 | 0 | 0 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.04 | 0.79 | 2.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.652 | 0.623 | 0.679 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 145 | 93 | 155 | 117 | 132 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.02 | 0.65 | 1.09 | 0.82 | 0.93 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.460 | 0.133 | 1.051 | 0.038 | 0.101 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 121 | 273 | 0 | 0 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.00 | 1.02 | 2.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.406 | 0.618 | 0.632 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 74 | 127 | 55 | 96 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.00 | 1.16 | 1.98 | 0.86 | 1.50 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.252 | 0.147 | 0.729 | 0.041 | 0.095 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 76 | 77 | 28 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 1.62 | 1.64 | 0.60 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.220 | 0.034 | 0.369 | 0.036 | 0.000 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 79 | 129 | 233 | 0 | 0 | 0 | 0 | 67 | 0 |
N.S. |
1 | 0.65 | 1.06 | 1.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.686 | 0.286 | 0.871 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 77 | 169 | 101 | 132 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 1.22 | 2.68 | 1.60 | 2.10 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.464 | 0.177 | 0.860 | 0.041 | 0.146 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 153 | 229 | 333 | 0 | 0 | 0 | 0 | 100 | 0 |
N.S. |
1 | 0.75 | 1.13 | 1.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.956 | 2.054 | 0.885 | 0.000 | 0.000 | 0.000 | 0.000 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 139 | 131 | 166 | 121 | 222 | 0 | 0 | 79 | 0 |
N.S. |
1 | 0.99 | 0.93 | 1.18 | 0.86 | 1.57 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.633 | 0.209 | 0.939 | 0.037 | 0.144 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 154 | 174 | 238 | 0 | 197 | 0 | 0 | 169 | 0 |
N.S. |
1 | 0.73 | 0.82 | 1.12 | 0.00 | 0.93 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.511 | 0.355 | 1.041 | 0.000 | 0.161 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 222 | 161 | 274 | 0 | 0 | 0 | 0 | 207 | 0 |
N.S. |
1 | 1.08 | 0.78 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.763 | 0.491 | 1.010 | 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 | A | C | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 105 | 130 | 176 | 119 | 166 | 0 | 0 | 147 | 0 |
N.S. |
1 | 0.77 | 0.96 | 1.29 | 0.88 | 1.22 | 0.00 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.386 | 0.315 | 0.939 | 0.122 | 0.150 | 0.000 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 146 | 232 | 0 | 0 | 0 | 0 | 183 | 0 |
N.S. |
1 | 1.00 | 1.12 | 1.78 | 0.00 | 0.00 | 0.00 | 0.00 | 1.41 | 0.00 |
time (sec) |
N/A | 0.464 | 0.287 | 0.904 | 0.000 | 0.000 | 0.000 | 0.000 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 86 | 125 | 0 | 128 | 0 | 0 | 125 | 0 |
N.S. |
1 | 1.00 | 1.23 | 1.79 | 0.00 | 1.83 | 0.00 | 0.00 | 1.79 | 0.00 |
time (sec) |
N/A | 0.272 | 0.245 | 0.814 | 0.000 | 0.124 | 0.000 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 100 | 143 | 58 | 0 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.00 | 1.32 | 1.88 | 0.76 | 0.00 | 0.00 | 0.00 | 1.72 | 0.00 |
time (sec) |
N/A | 0.247 | 0.076 | 0.773 | 0.043 | 0.000 | 0.000 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 146 | 231 | 271 | 0 | 0 | 0 | 0 | 206 | 0 |
N.S. |
1 | 0.74 | 1.17 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.700 | 0.625 | 1.048 | 0.000 | 0.000 | 0.000 | 0.000 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 113 | 163 | 239 | 119 | 0 | 0 | 0 | 162 | 0 |
N.S. |
1 | 0.80 | 1.16 | 1.70 | 0.84 | 0.00 | 0.00 | 0.00 | 1.15 | 0.00 |
time (sec) |
N/A | 0.524 | 0.557 | 0.951 | 0.043 | 0.000 | 0.000 | 0.000 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 235 | 369 | 342 | 0 | 0 | 0 | 0 | 253 | 0 |
N.S. |
1 | 0.82 | 1.29 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 1.839 | 5.616 | 1.016 | 0.000 | 0.000 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 167 | 216 | 968 | 0 | 0 | 0 | 0 | 190 | 0 |
N.S. |
1 | 0.75 | 0.96 | 4.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.605 | 0.296 | 0.982 | 0.000 | 0.000 | 0.000 | 0.000 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 281 | 345 | 222 | 410 | 0 | 0 | 0 | 0 | 370 | 0 |
N.S. |
1 | 1.23 | 0.79 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 1.32 | 0.00 |
time (sec) |
N/A | 1.203 | 0.854 | 1.209 | 0.000 | 0.000 | 0.000 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 164 | 177 | 400 | 0 | 219 | 0 | 0 | 281 | 0 |
N.S. |
1 | 0.78 | 0.84 | 1.90 | 0.00 | 1.04 | 0.00 | 0.00 | 1.34 | 0.00 |
time (sec) |
N/A | 0.464 | 0.379 | 0.987 | 0.000 | 0.146 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 241 | 191 | 345 | 0 | 0 | 0 | 0 | 330 | 0 |
N.S. |
1 | 1.19 | 0.94 | 1.70 | 0.00 | 0.00 | 0.00 | 0.00 | 1.63 | 0.00 |
time (sec) |
N/A | 0.818 | 0.533 | 1.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 129 | 136 | 263 | 138 | 188 | 0 | 0 | 262 | 0 |
N.S. |
1 | 0.90 | 0.94 | 1.83 | 0.96 | 1.31 | 0.00 | 0.00 | 1.82 | 0.00 |
time (sec) |
N/A | 0.392 | 0.327 | 0.890 | 0.119 | 0.142 | 0.000 | 0.000 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 99 | 118 | 413 | 137 | 0 | 0 | 0 | 266 | 0 |
N.S. |
1 | 0.83 | 0.99 | 3.47 | 1.15 | 0.00 | 0.00 | 0.00 | 2.24 | 0.00 |
time (sec) |
N/A | 0.356 | 0.250 | 1.013 | 0.051 | 0.000 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 99 | 103 | 198 | 0 | 166 | 0 | 0 | 237 | 0 |
N.S. |
1 | 0.87 | 0.90 | 1.74 | 0.00 | 1.46 | 0.00 | 0.00 | 2.08 | 0.00 |
time (sec) |
N/A | 0.417 | 0.261 | 0.872 | 0.000 | 0.146 | 0.000 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 152 | 143 | 425 | 126 | 0 | 0 | 0 | 274 | 0 |
N.S. |
1 | 1.03 | 0.97 | 2.89 | 0.86 | 0.00 | 0.00 | 0.00 | 1.86 | 0.00 |
time (sec) |
N/A | 0.677 | 0.090 | 0.848 | 0.048 | 0.000 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 244 | 247 | 364 | 0 | 0 | 0 | 0 | 391 | 0 |
N.S. |
1 | 0.92 | 0.93 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 | 1.47 | 0.00 |
time (sec) |
N/A | 1.777 | 0.896 | 1.025 | 0.000 | 0.000 | 0.000 | 0.000 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 165 | 227 | 1257 | 0 | 0 | 0 | 0 | 305 | 0 |
N.S. |
1 | 0.77 | 1.06 | 5.87 | 0.00 | 0.00 | 0.00 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.486 | 0.299 | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 361 | 356 | 409 | 406 | 0 | 0 | 0 | 0 | 434 | 0 |
N.S. |
1 | 0.99 | 1.13 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 1.20 | 0.00 |
time (sec) |
N/A | 1.625 | 4.919 | 1.050 | 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 | A | A | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 295 | 213 | 267 | 372 | 236 | 0 | 0 | 0 | 330 | 0 |
N.S. |
1 | 0.72 | 0.91 | 1.26 | 0.80 | 0.00 | 0.00 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.651 | 0.329 | 1.019 | 0.054 | 0.000 | 0.000 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 94 | 63 | 74 | 83 | 83 | 82 | 0 | 22 | 0 |
N.S. |
1 | 1.09 | 0.73 | 0.86 | 0.97 | 0.97 | 0.95 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.482 | 0.024 | 0.657 | 0.035 | 0.095 | 1.199 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 73 | 48 | 82 | 59 | 55 | 65 | 0 | 22 | 0 |
N.S. |
1 | 1.04 | 0.69 | 1.17 | 0.84 | 0.79 | 0.93 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.416 | 0.019 | 0.597 | 0.034 | 0.097 | 0.982 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 42 | 40 | 55 | 62 | 42 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.82 | 1.12 | 1.27 | 0.86 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.426 | 0.013 | 0.597 | 0.046 | 0.093 | 0.687 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 47 | 26 | 38 | 24 | 38 | 24 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.68 | 0.93 | 1.36 | 0.86 | 1.36 | 0.86 | 0.00 |
time (sec) |
N/A | 0.360 | 0.008 | 0.564 | 0.035 | 0.102 | 0.573 | 0.116 | 0.260 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 11 | 23 | 10 | 23 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 1.77 | 0.77 | 1.77 | 0.85 | 0.85 |
time (sec) |
N/A | 0.315 | 0.001 | 0.224 | 0.035 | 0.086 | 0.664 | 0.120 | 0.225 | 2.889 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 46 | 57 | 89 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.35 | 1.68 | 2.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.592 | 0.081 | 0.551 | 0.000 | 0.000 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 56 | 25 | 39 | 0 | 71 | 22 | 0 |
N.S. |
1 | 1.00 | 1.07 | 2.07 | 0.93 | 1.44 | 0.00 | 2.63 | 0.81 | 0.00 |
time (sec) |
N/A | 0.338 | 0.011 | 1.070 | 0.031 | 0.110 | 0.000 | 0.136 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 84 | 126 | 150 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.05 | 1.58 | 1.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.635 | 0.113 | 1.272 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 2540 | 119 | 23 | 174 | 29 | 24 | 0 | 158 | 25 |
N.S. |
1 | 101.60 | 4.76 | 0.92 | 6.96 | 1.16 | 0.96 | 0.00 | 6.32 | 1.00 |
time (sec) |
N/A | 2.793 | 0.188 | 1.815 | 0.171 | 0.098 | 24.498 | 0.000 | 0.494 | 3.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | B | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 198 | 23 | 25 | 29 | 24 | 25 | 111 | 25 |
N.S. |
1 | 1.00 | 7.92 | 0.92 | 1.00 | 1.16 | 0.96 | 1.00 | 4.44 | 1.00 |
time (sec) |
N/A | 1.054 | 4.743 | 0.352 | 0.135 | 0.098 | 12.845 | 0.154 | 0.496 | 2.950 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 836 | 92 | 21 | 107 | 25 | 22 | 0 | 123 | 23 |
N.S. |
1 | 36.35 | 4.00 | 0.91 | 4.65 | 1.09 | 0.96 | 0.00 | 5.35 | 1.00 |
time (sec) |
N/A | 0.846 | 0.169 | 0.234 | 0.116 | 0.096 | 5.967 | 0.000 | 0.346 | 2.944 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 27 | 23 | 120 | 25 | 22 | 0 | 97 | 25 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 4.80 | 1.00 | 0.88 | 0.00 | 3.88 | 1.00 |
time (sec) |
N/A | 1.389 | 4.238 | 0.707 | 0.733 | 0.097 | 11.271 | 0.000 | 0.308 | 3.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | B | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 211 | 23 | 25 | 25 | 24 | 0 | 108 | 25 |
N.S. |
1 | 1.00 | 8.44 | 0.92 | 1.00 | 1.00 | 0.96 | 0.00 | 4.32 | 1.00 |
time (sec) |
N/A | 0.896 | 5.524 | 0.740 | 0.117 | 0.103 | 6.391 | 0.000 | 0.388 | 3.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 313 | 320 | 257 | 0 | 0 | 0 | 0 | 0 | 611 | 0 |
N.S. |
1 | 1.02 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.95 | 0.00 |
time (sec) |
N/A | 1.985 | 0.310 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 215 | 188 | 0 | 0 | 0 | 0 | 0 | 346 | 0 |
N.S. |
1 | 0.99 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.59 | 0.00 |
time (sec) |
N/A | 0.528 | 0.013 | 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 | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 126 | 118 | 0 | 0 | 0 | 0 | 0 | 152 | 0 |
N.S. |
1 | 0.98 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 0.347 | 0.033 | 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 | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 26 | 26 | 36 | 26 | 47 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 1.50 | 1.08 | 1.96 | 1.08 |
time (sec) |
N/A | 0.249 | 3.048 | 1.309 | 0.120 | 0.100 | 2.230 | 0.123 | 0.203 | 3.102 |