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 | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 133 | 148 | 127 | 205 | 248 | 1165 | 212 | 111 |
N.S. |
1 | 1.00 | 1.10 | 1.22 | 1.05 | 1.69 | 2.05 | 9.63 | 1.75 | 0.92 |
time (sec) |
N/A | 0.260 | 0.109 | 0.931 | 0.041 | 0.080 | 0.981 | 0.129 | 0.221 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 133 | 147 | 778 | 165 | 248 | 778 | 168 | 111 |
N.S. |
1 | 1.00 | 1.10 | 1.21 | 6.43 | 1.36 | 2.05 | 6.43 | 1.39 | 0.92 |
time (sec) |
N/A | 0.249 | 0.111 | 0.921 | 0.045 | 0.087 | 0.974 | 0.120 | 0.217 | 0.037 |
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 | 121 | 121 | 133 | 169 | 136 | 178 | 226 | 187 | 169 | 129 |
N.S. |
1 | 1.00 | 1.10 | 1.40 | 1.12 | 1.47 | 1.87 | 1.55 | 1.40 | 1.07 |
time (sec) |
N/A | 0.263 | 0.098 | 0.934 | 0.042 | 0.081 | 1.875 | 0.142 | 0.199 | 0.042 |
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 | 121 | 121 | 133 | 170 | 136 | 194 | 226 | 187 | 178 | 131 |
N.S. |
1 | 1.00 | 1.10 | 1.40 | 1.12 | 1.60 | 1.87 | 1.55 | 1.47 | 1.08 |
time (sec) |
N/A | 0.256 | 0.099 | 0.937 | 0.037 | 0.086 | 1.843 | 0.150 | 0.196 | 5.248 |
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 | 121 | 121 | 133 | 143 | 142 | 208 | 216 | 186 | 189 | 170 |
N.S. |
1 | 1.00 | 1.10 | 1.18 | 1.17 | 1.72 | 1.79 | 1.54 | 1.56 | 1.40 |
time (sec) |
N/A | 0.253 | 0.112 | 0.965 | 0.046 | 0.089 | 1.962 | 0.153 | 0.238 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 133 | 138 | 142 | 210 | 1394 | 186 | 189 | 159 |
N.S. |
1 | 1.00 | 1.10 | 1.14 | 1.17 | 1.74 | 11.52 | 1.54 | 1.56 | 1.31 |
time (sec) |
N/A | 0.256 | 0.120 | 1.010 | 0.037 | 0.086 | 0.737 | 0.157 | 0.210 | 5.230 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 133 | 132 | 138 | 238 | 1731 | 176 | 211 | 147 |
N.S. |
1 | 1.00 | 1.10 | 1.09 | 1.14 | 1.97 | 14.31 | 1.45 | 1.74 | 1.21 |
time (sec) |
N/A | 0.253 | 0.104 | 0.986 | 0.038 | 0.088 | 1.014 | 0.142 | 0.205 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 133 | 130 | 138 | 252 | 1975 | 176 | 222 | 147 |
N.S. |
1 | 1.00 | 1.10 | 1.07 | 1.14 | 2.08 | 16.32 | 1.45 | 1.83 | 1.21 |
time (sec) |
N/A | 0.254 | 0.106 | 0.939 | 0.034 | 0.087 | 1.491 | 0.147 | 0.198 | 5.318 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 199 | 254 | 340 | 0 | 1079 | 0 | 733 | 892 | 240 |
N.S. |
1 | 1.12 | 1.44 | 1.92 | 0.00 | 6.10 | 0.00 | 4.14 | 5.04 | 1.36 |
time (sec) |
N/A | 0.421 | 0.460 | 5.174 | 0.000 | 0.097 | 0.000 | 0.189 | 0.200 | 0.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 170 | 217 | 296 | 0 | 1005 | 0 | 531 | 573 | 168 |
N.S. |
1 | 1.14 | 1.46 | 1.99 | 0.00 | 6.74 | 0.00 | 3.56 | 3.85 | 1.13 |
time (sec) |
N/A | 0.363 | 0.512 | 1.517 | 0.000 | 0.096 | 0.000 | 0.171 | 0.205 | 5.435 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 168 | 215 | 297 | 0 | 629 | 0 | 531 | 540 | 167 |
N.S. |
1 | 1.14 | 1.46 | 2.02 | 0.00 | 4.28 | 0.00 | 3.61 | 3.67 | 1.14 |
time (sec) |
N/A | 0.343 | 0.409 | 1.448 | 0.000 | 0.093 | 0.000 | 0.169 | 0.220 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 139 | 214 | 257 | 0 | 472 | 0 | 354 | 260 | 97 |
N.S. |
1 | 1.15 | 1.77 | 2.12 | 0.00 | 3.90 | 0.00 | 2.93 | 2.15 | 0.80 |
time (sec) |
N/A | 0.300 | 0.276 | 1.535 | 0.000 | 0.091 | 0.000 | 0.125 | 0.188 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 137 | 192 | 253 | 0 | 200 | 0 | 354 | 245 | 97 |
N.S. |
1 | 1.15 | 1.61 | 2.13 | 0.00 | 1.68 | 0.00 | 2.97 | 2.06 | 0.82 |
time (sec) |
N/A | 0.302 | 0.232 | 1.426 | 0.000 | 0.084 | 0.000 | 0.131 | 0.205 | 5.392 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 110 | 151 | 228 | 0 | 237 | 0 | 393 | 203 | 83 |
N.S. |
1 | 1.07 | 1.47 | 2.21 | 0.00 | 2.30 | 0.00 | 3.82 | 1.97 | 0.81 |
time (sec) |
N/A | 0.262 | 0.203 | 1.638 | 0.000 | 0.093 | 0.000 | 0.139 | 0.204 | 5.400 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 110 | 153 | 228 | 0 | 407 | 0 | 393 | 195 | 161 |
N.S. |
1 | 1.07 | 1.49 | 2.21 | 0.00 | 3.95 | 0.00 | 3.82 | 1.89 | 1.56 |
time (sec) |
N/A | 0.269 | 0.209 | 1.380 | 0.000 | 0.131 | 0.000 | 0.124 | 0.201 | 5.333 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 151 | 193 | 274 | 0 | 900 | 0 | 497 | 305 | 153 |
N.S. |
1 | 1.15 | 1.47 | 2.09 | 0.00 | 6.87 | 0.00 | 3.79 | 2.33 | 1.17 |
time (sec) |
N/A | 0.315 | 0.254 | 1.423 | 0.000 | 0.092 | 0.000 | 0.153 | 0.228 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 153 | 242 | 274 | 0 | 1116 | 0 | 497 | 604 | 1345 |
N.S. |
1 | 1.15 | 1.82 | 2.06 | 0.00 | 8.39 | 0.00 | 3.74 | 4.54 | 10.11 |
time (sec) |
N/A | 0.327 | 0.362 | 1.462 | 0.000 | 0.096 | 0.000 | 0.146 | 0.189 | 5.715 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 196 | 219 | 301 | 0 | 1880 | 0 | 605 | 1021 | 230 |
N.S. |
1 | 1.22 | 1.36 | 1.87 | 0.00 | 11.68 | 0.00 | 3.76 | 6.34 | 1.43 |
time (sec) |
N/A | 0.378 | 0.424 | 1.508 | 0.000 | 0.115 | 0.000 | 0.159 | 0.194 | 5.352 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 234 | 351 | 407 | 0 | 1293 | 0 | 876 | 2640 | 1060 |
N.S. |
1 | 1.10 | 1.66 | 1.92 | 0.00 | 6.10 | 0.00 | 4.13 | 12.45 | 5.00 |
time (sec) |
N/A | 0.450 | 1.387 | 1.713 | 0.000 | 0.172 | 0.000 | 0.155 | 0.212 | 5.358 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 205 | 290 | 344 | 0 | 1211 | 0 | 646 | 1750 | 249 |
N.S. |
1 | 1.12 | 1.58 | 1.88 | 0.00 | 6.62 | 0.00 | 3.53 | 9.56 | 1.36 |
time (sec) |
N/A | 0.402 | 0.959 | 1.661 | 0.000 | 0.106 | 0.000 | 0.149 | 0.218 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 203 | 296 | 353 | 0 | 816 | 0 | 646 | 1696 | 834 |
N.S. |
1 | 1.12 | 1.64 | 1.95 | 0.00 | 4.51 | 0.00 | 3.57 | 9.37 | 4.61 |
time (sec) |
N/A | 0.393 | 0.951 | 1.674 | 0.000 | 0.123 | 0.000 | 0.141 | 0.228 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 174 | 254 | 302 | 0 | 659 | 0 | 441 | 843 | 165 |
N.S. |
1 | 1.13 | 1.65 | 1.96 | 0.00 | 4.28 | 0.00 | 2.86 | 5.47 | 1.07 |
time (sec) |
N/A | 0.340 | 0.834 | 1.628 | 0.000 | 0.114 | 0.000 | 0.163 | 0.213 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 172 | 256 | 302 | 0 | 361 | 0 | 441 | 810 | 597 |
N.S. |
1 | 1.13 | 1.68 | 1.99 | 0.00 | 2.38 | 0.00 | 2.90 | 5.33 | 3.93 |
time (sec) |
N/A | 0.345 | 0.876 | 2.240 | 0.000 | 0.095 | 0.000 | 0.133 | 0.207 | 5.360 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 142 | 230 | 277 | 0 | 376 | 0 | 439 | 841 | 131 |
N.S. |
1 | 1.07 | 1.73 | 2.08 | 0.00 | 2.83 | 0.00 | 3.30 | 6.32 | 0.98 |
time (sec) |
N/A | 0.300 | 0.797 | 1.352 | 0.000 | 0.096 | 0.000 | 0.149 | 0.218 | 5.267 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 142 | 230 | 277 | 0 | 516 | 0 | 438 | 807 | 225 |
N.S. |
1 | 1.07 | 1.73 | 2.08 | 0.00 | 3.88 | 0.00 | 3.29 | 6.07 | 1.69 |
time (sec) |
N/A | 0.297 | 0.670 | 1.321 | 0.000 | 0.100 | 0.000 | 0.132 | 0.226 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 162 | 223 | 294 | 0 | 980 | 0 | 504 | 872 | 179 |
N.S. |
1 | 1.12 | 1.54 | 2.03 | 0.00 | 6.76 | 0.00 | 3.48 | 6.01 | 1.23 |
time (sec) |
N/A | 0.312 | 0.485 | 1.316 | 0.000 | 0.102 | 0.000 | 0.189 | 0.209 | 5.252 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 162 | 218 | 292 | 0 | 1083 | 0 | 507 | 847 | 183 |
N.S. |
1 | 1.12 | 1.50 | 2.01 | 0.00 | 7.47 | 0.00 | 3.50 | 5.84 | 1.26 |
time (sec) |
N/A | 0.321 | 0.754 | 1.280 | 0.000 | 0.098 | 0.000 | 0.142 | 0.189 | 5.275 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 205 | 260 | 323 | 0 | 1884 | 0 | 650 | 1012 | 264 |
N.S. |
1 | 1.18 | 1.49 | 1.86 | 0.00 | 10.83 | 0.00 | 3.74 | 5.82 | 1.52 |
time (sec) |
N/A | 0.376 | 0.845 | 1.314 | 0.000 | 0.106 | 0.000 | 0.162 | 0.220 | 5.367 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 207 | 268 | 318 | 0 | 2171 | 0 | 646 | 1651 | 2280 |
N.S. |
1 | 1.18 | 1.52 | 1.81 | 0.00 | 12.34 | 0.00 | 3.67 | 9.38 | 12.95 |
time (sec) |
N/A | 0.381 | 0.994 | 1.355 | 0.000 | 0.115 | 0.000 | 0.133 | 0.227 | 5.331 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 250 | 298 | 350 | 0 | 3285 | 0 | 779 | 2451 | 336 |
N.S. |
1 | 1.22 | 1.45 | 1.71 | 0.00 | 16.02 | 0.00 | 3.80 | 11.96 | 1.64 |
time (sec) |
N/A | 0.451 | 1.078 | 1.449 | 0.000 | 0.128 | 0.000 | 0.151 | 0.209 | 5.731 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 244 | 343 | 432 | 0 | 1426 | 0 | 753 | 3296 | 364 |
N.S. |
1 | 1.09 | 1.53 | 1.93 | 0.00 | 6.37 | 0.00 | 3.36 | 14.71 | 1.62 |
time (sec) |
N/A | 0.448 | 1.964 | 1.653 | 0.000 | 0.118 | 0.000 | 0.211 | 0.238 | 0.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 242 | 353 | 432 | 0 | 1029 | 0 | 753 | 3221 | 966 |
N.S. |
1 | 1.08 | 1.58 | 1.93 | 0.00 | 4.59 | 0.00 | 3.36 | 14.38 | 4.31 |
time (sec) |
N/A | 0.449 | 2.223 | 1.596 | 0.000 | 0.107 | 0.000 | 0.194 | 0.218 | 5.237 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 213 | 292 | 361 | 0 | 853 | 0 | 521 | 1789 | 264 |
N.S. |
1 | 1.09 | 1.50 | 1.85 | 0.00 | 4.37 | 0.00 | 2.67 | 9.17 | 1.35 |
time (sec) |
N/A | 0.402 | 1.980 | 1.536 | 0.000 | 0.108 | 0.000 | 0.188 | 0.216 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 211 | 298 | 359 | 0 | 552 | 0 | 521 | 1735 | 720 |
N.S. |
1 | 1.09 | 1.54 | 1.86 | 0.00 | 2.86 | 0.00 | 2.70 | 8.99 | 3.73 |
time (sec) |
N/A | 0.404 | 1.851 | 1.525 | 0.000 | 0.103 | 0.000 | 0.159 | 0.264 | 5.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 181 | 257 | 305 | 0 | 543 | 0 | 510 | 1815 | 215 |
N.S. |
1 | 1.05 | 1.49 | 1.77 | 0.00 | 3.16 | 0.00 | 2.97 | 10.55 | 1.25 |
time (sec) |
N/A | 0.353 | 1.496 | 1.431 | 0.000 | 0.170 | 0.000 | 0.168 | 0.236 | 5.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 181 | 263 | 305 | 0 | 696 | 0 | 510 | 1761 | 309 |
N.S. |
1 | 1.05 | 1.53 | 1.77 | 0.00 | 4.05 | 0.00 | 2.97 | 10.24 | 1.80 |
time (sec) |
N/A | 0.353 | 1.411 | 1.476 | 0.000 | 0.106 | 0.000 | 0.151 | 0.261 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 201 | 267 | 324 | 0 | 1296 | 0 | 567 | 1866 | 251 |
N.S. |
1 | 1.12 | 1.48 | 1.80 | 0.00 | 7.20 | 0.00 | 3.15 | 10.37 | 1.39 |
time (sec) |
N/A | 0.369 | 1.887 | 1.503 | 0.000 | 0.114 | 0.000 | 0.163 | 0.213 | 0.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 201 | 261 | 324 | 0 | 1345 | 0 | 567 | 1810 | 255 |
N.S. |
1 | 1.12 | 1.45 | 1.80 | 0.00 | 7.47 | 0.00 | 3.15 | 10.06 | 1.42 |
time (sec) |
N/A | 0.367 | 1.620 | 1.356 | 0.000 | 0.109 | 0.000 | 0.161 | 0.251 | 5.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 220 | 266 | 340 | 0 | 1980 | 0 | 645 | 1942 | 320 |
N.S. |
1 | 1.13 | 1.37 | 1.75 | 0.00 | 10.21 | 0.00 | 3.32 | 10.01 | 1.65 |
time (sec) |
N/A | 0.385 | 1.165 | 1.384 | 0.000 | 0.118 | 0.000 | 0.189 | 0.228 | 5.353 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 220 | 272 | 340 | 0 | 1991 | 0 | 645 | 1892 | 317 |
N.S. |
1 | 1.13 | 1.40 | 1.75 | 0.00 | 10.26 | 0.00 | 3.32 | 9.75 | 1.63 |
time (sec) |
N/A | 0.389 | 0.997 | 1.290 | 0.000 | 0.118 | 0.000 | 0.153 | 0.198 | 5.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 263 | 300 | 355 | 0 | 3252 | 0 | 813 | 2160 | 421 |
N.S. |
1 | 1.17 | 1.33 | 1.58 | 0.00 | 14.45 | 0.00 | 3.61 | 9.60 | 1.87 |
time (sec) |
N/A | 0.442 | 1.488 | 1.368 | 0.000 | 0.128 | 0.000 | 0.159 | 0.275 | 5.503 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 265 | 306 | 355 | 0 | 3517 | 0 | 813 | 3095 | 3227 |
N.S. |
1 | 1.17 | 1.35 | 1.56 | 0.00 | 15.49 | 0.00 | 3.58 | 13.63 | 14.22 |
time (sec) |
N/A | 0.450 | 1.648 | 1.429 | 0.000 | 0.136 | 0.000 | 0.160 | 0.295 | 5.974 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 308 | 355 | 382 | 0 | 4956 | 0 | 958 | 4318 | 543 |
N.S. |
1 | 1.19 | 1.38 | 1.48 | 0.00 | 19.21 | 0.00 | 3.71 | 16.74 | 2.10 |
time (sec) |
N/A | 0.533 | 2.031 | 1.543 | 0.000 | 0.173 | 0.000 | 0.188 | 0.364 | 5.649 |
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 | 141 | 212 | 112 | 118 | 150 | 112 | 0 | 138 | 149 | 75 |
N.S. |
1 | 1.50 | 0.79 | 0.84 | 1.06 | 0.79 | 0.00 | 0.98 | 1.06 | 0.53 |
time (sec) |
N/A | 0.442 | 0.269 | 2.398 | 0.111 | 0.079 | 0.000 | 0.148 | 0.220 | 5.362 |
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 | 128 | 188 | 101 | 109 | 141 | 105 | 0 | 129 | 138 | 66 |
N.S. |
1 | 1.47 | 0.79 | 0.85 | 1.10 | 0.82 | 0.00 | 1.01 | 1.08 | 0.52 |
time (sec) |
N/A | 0.397 | 0.202 | 1.549 | 0.112 | 0.084 | 0.000 | 0.154 | 0.217 | 0.057 |
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 | 127 | 196 | 100 | 109 | 141 | 101 | 0 | 129 | 129 | 66 |
N.S. |
1 | 1.54 | 0.79 | 0.86 | 1.11 | 0.80 | 0.00 | 1.02 | 1.02 | 0.52 |
time (sec) |
N/A | 0.388 | 0.181 | 1.398 | 0.115 | 0.081 | 0.000 | 0.153 | 0.204 | 0.050 |
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 | 116 | 174 | 78 | 99 | 132 | 97 | 0 | 120 | 106 | 57 |
N.S. |
1 | 1.50 | 0.67 | 0.85 | 1.14 | 0.84 | 0.00 | 1.03 | 0.91 | 0.49 |
time (sec) |
N/A | 0.360 | 0.173 | 1.399 | 0.114 | 0.079 | 0.000 | 0.143 | 0.201 | 0.052 |
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 | 115 | 184 | 76 | 99 | 132 | 96 | 0 | 120 | 106 | 57 |
N.S. |
1 | 1.60 | 0.66 | 0.86 | 1.15 | 0.83 | 0.00 | 1.04 | 0.92 | 0.50 |
time (sec) |
N/A | 0.364 | 0.172 | 1.286 | 0.113 | 0.084 | 0.000 | 0.135 | 0.189 | 5.284 |
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 | 136 | 190 | 103 | 109 | 141 | 134 | 0 | 129 | 155 | 66 |
N.S. |
1 | 1.40 | 0.76 | 0.80 | 1.04 | 0.99 | 0.00 | 0.95 | 1.14 | 0.49 |
time (sec) |
N/A | 0.376 | 0.290 | 1.281 | 0.126 | 0.088 | 0.000 | 0.153 | 0.227 | 5.227 |
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 | 136 | 200 | 104 | 109 | 141 | 158 | 0 | 129 | 310 | 66 |
N.S. |
1 | 1.47 | 0.76 | 0.80 | 1.04 | 1.16 | 0.00 | 0.95 | 2.28 | 0.49 |
time (sec) |
N/A | 0.378 | 0.244 | 1.336 | 0.131 | 0.083 | 0.000 | 0.117 | 0.206 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 159 | 151 | 193 | 0 | 473 | 1149 | 257 | 434 | 1144 |
N.S. |
1 | 0.96 | 0.92 | 1.17 | 0.00 | 2.87 | 6.96 | 1.56 | 2.63 | 6.93 |
time (sec) |
N/A | 0.305 | 1.675 | 1.082 | 0.000 | 0.104 | 0.693 | 0.165 | 0.218 | 6.252 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 80 | 41 | 0 | 91 | 216 | 58 | 76 | 89 |
N.S. |
1 | 1.00 | 1.36 | 0.69 | 0.00 | 1.54 | 3.66 | 0.98 | 1.29 | 1.51 |
time (sec) |
N/A | 0.201 | 0.885 | 0.870 | 0.000 | 0.082 | 0.105 | 0.111 | 0.203 | 5.384 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 120 | 101 | 114 | 0 | 309 | 379 | 153 | 255 | 335 |
N.S. |
1 | 0.98 | 0.82 | 0.93 | 0.00 | 2.51 | 3.08 | 1.24 | 2.07 | 2.72 |
time (sec) |
N/A | 0.256 | 0.860 | 0.937 | 0.000 | 0.094 | 0.570 | 0.162 | 0.227 | 5.591 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 18 | 16 | 15 | 28 | 65 | 15 | 24 | 15 |
N.S. |
1 | 1.00 | 0.95 | 0.84 | 0.79 | 1.47 | 3.42 | 0.79 | 1.26 | 0.79 |
time (sec) |
N/A | 0.151 | 0.030 | 0.814 | 0.036 | 0.079 | 0.070 | 0.135 | 0.218 | 5.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 96 | 78 | 0 | 193 | 0 | 97 | 148 | 0 |
N.S. |
1 | 1.00 | 1.16 | 0.94 | 0.00 | 2.33 | 0.00 | 1.17 | 1.78 | 0.00 |
time (sec) |
N/A | 0.243 | 0.438 | 1.048 | 0.000 | 0.107 | 0.000 | 0.131 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 292 | 182 | 0 | 189 | 0 | 215 | 124 | 0 |
N.S. |
1 | 1.00 | 3.89 | 2.43 | 0.00 | 2.52 | 0.00 | 2.87 | 1.65 | 0.00 |
time (sec) |
N/A | 0.206 | 0.973 | 1.062 | 0.000 | 0.115 | 0.000 | 0.148 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 103 | 89 | 0 | 371 | 0 | 246 | 494 | 0 |
N.S. |
1 | 1.00 | 1.13 | 0.98 | 0.00 | 4.08 | 0.00 | 2.70 | 5.43 | 0.00 |
time (sec) |
N/A | 0.227 | 10.210 | 1.020 | 0.000 | 0.135 | 0.000 | 0.185 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 38 | 38 | 0 | 98 | 0 | 199 | 173 | 111 |
N.S. |
1 | 1.00 | 0.97 | 0.97 | 0.00 | 2.51 | 0.00 | 5.10 | 4.44 | 2.85 |
time (sec) |
N/A | 0.173 | 10.086 | 1.224 | 0.000 | 0.252 | 0.000 | 0.172 | 0.204 | 5.531 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 132 | 62 | 135 | 0 | 721 | 0 | 0 | 994 | 0 |
N.S. |
1 | 0.99 | 0.47 | 1.02 | 0.00 | 5.42 | 0.00 | 0.00 | 7.47 | 0.00 |
time (sec) |
N/A | 0.283 | 10.039 | 1.029 | 0.000 | 0.512 | 0.000 | 0.000 | 0.655 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 62 | 70 | 0 | 274 | 0 | 417 | 427 | 589 |
N.S. |
1 | 1.00 | 0.78 | 0.89 | 0.00 | 3.47 | 0.00 | 5.28 | 5.41 | 7.46 |
time (sec) |
N/A | 0.220 | 10.033 | 1.467 | 0.000 | 1.150 | 0.000 | 0.447 | 0.197 | 5.743 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 183 | 62 | 157 | 0 | 1213 | 0 | 1336 | 1607 | 0 |
N.S. |
1 | 1.05 | 0.35 | 0.90 | 0.00 | 6.93 | 0.00 | 7.63 | 9.18 | 0.00 |
time (sec) |
N/A | 0.338 | 10.034 | 1.040 | 0.000 | 1.971 | 0.000 | 0.478 | 2.594 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 92 | 79 | 0 | 251 | 656 | 128 | 237 | 241 |
N.S. |
1 | 1.00 | 0.94 | 0.81 | 0.00 | 2.56 | 6.69 | 1.31 | 2.42 | 2.46 |
time (sec) |
N/A | 0.242 | 2.383 | 0.882 | 0.000 | 0.106 | 0.244 | 0.365 | 0.209 | 5.731 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 204 | 221 | 294 | 0 | 677 | 3067 | 389 | 663 | 0 |
N.S. |
1 | 0.99 | 1.07 | 1.42 | 0.00 | 3.27 | 14.82 | 1.88 | 3.20 | 0.00 |
time (sec) |
N/A | 0.360 | 2.513 | 1.044 | 0.000 | 0.118 | 0.786 | 0.383 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 44 | 41 | 0 | 149 | 371 | 58 | 131 | 58 |
N.S. |
1 | 1.00 | 0.75 | 0.69 | 0.00 | 2.53 | 6.29 | 0.98 | 2.22 | 0.98 |
time (sec) |
N/A | 0.202 | 1.601 | 0.881 | 0.000 | 0.093 | 0.176 | 0.346 | 0.206 | 5.646 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 165 | 153 | 193 | 0 | 473 | 1042 | 257 | 434 | 0 |
N.S. |
1 | 1.00 | 0.93 | 1.17 | 0.00 | 2.87 | 6.32 | 1.56 | 2.63 | 0.00 |
time (sec) |
N/A | 0.304 | 1.681 | 0.949 | 0.000 | 0.113 | 0.638 | 0.415 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 18 | 16 | 15 | 55 | 146 | 15 | 51 | 15 |
N.S. |
1 | 1.00 | 0.95 | 0.84 | 0.79 | 2.89 | 7.68 | 0.79 | 2.68 | 0.79 |
time (sec) |
N/A | 0.157 | 0.026 | 0.806 | 0.029 | 0.089 | 0.123 | 0.382 | 0.204 | 5.655 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 120 | 124 | 119 | 0 | 257 | 0 | 149 | 342 | 0 |
N.S. |
1 | 1.04 | 1.08 | 1.03 | 0.00 | 2.23 | 0.00 | 1.30 | 2.97 | 0.00 |
time (sec) |
N/A | 0.277 | 1.012 | 1.020 | 0.000 | 0.127 | 0.000 | 0.369 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 118 | 244 | 179 | 0 | 281 | 0 | 440 | 296 | 0 |
N.S. |
1 | 1.04 | 2.16 | 1.58 | 0.00 | 2.49 | 0.00 | 3.89 | 2.62 | 0.00 |
time (sec) |
N/A | 0.250 | 1.520 | 1.087 | 0.000 | 0.141 | 0.000 | 0.532 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 120 | 62 | 114 | 0 | 331 | 0 | 378 | 501 | 0 |
N.S. |
1 | 1.04 | 0.54 | 0.99 | 0.00 | 2.88 | 0.00 | 3.29 | 4.36 | 0.00 |
time (sec) |
N/A | 0.282 | 10.041 | 1.056 | 0.000 | 0.188 | 0.000 | 0.382 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 112 | 95 | 311 | 0 | 345 | 0 | 431 | 291 | 0 |
N.S. |
1 | 1.05 | 0.89 | 2.91 | 0.00 | 3.22 | 0.00 | 4.03 | 2.72 | 0.00 |
time (sec) |
N/A | 0.254 | 10.068 | 1.184 | 0.000 | 0.313 | 0.000 | 0.437 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 128 | 162 | 124 | 0 | 615 | 0 | 0 | 932 | 0 |
N.S. |
1 | 1.04 | 1.32 | 1.01 | 0.00 | 5.00 | 0.00 | 0.00 | 7.58 | 0.00 |
time (sec) |
N/A | 0.271 | 10.212 | 1.011 | 0.000 | 0.503 | 0.000 | 0.000 | 0.692 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 38 | 38 | 0 | 183 | 0 | 588 | 310 | 1156 |
N.S. |
1 | 1.00 | 0.97 | 0.97 | 0.00 | 4.69 | 0.00 | 15.08 | 7.95 | 29.64 |
time (sec) |
N/A | 0.167 | 10.150 | 1.456 | 0.000 | 1.080 | 0.000 | 0.495 | 0.279 | 5.763 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 169 | 62 | 157 | 0 | 1057 | 0 | 1312 | 1512 | 0 |
N.S. |
1 | 1.02 | 0.38 | 0.95 | 0.00 | 6.41 | 0.00 | 7.95 | 9.16 | 0.00 |
time (sec) |
N/A | 0.328 | 10.034 | 1.049 | 0.000 | 2.006 | 0.000 | 0.514 | 3.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 62 | 70 | 0 | 398 | 0 | 997 | 642 | 1814 |
N.S. |
1 | 1.00 | 0.78 | 0.89 | 0.00 | 5.04 | 0.00 | 12.62 | 8.13 | 22.96 |
time (sec) |
N/A | 0.223 | 10.038 | 1.963 | 0.000 | 5.343 | 0.000 | 0.531 | 0.256 | 6.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 220 | 62 | 194 | 0 | 1639 | 0 | 2225 | 2202 | 0 |
N.S. |
1 | 1.06 | 0.30 | 0.94 | 0.00 | 7.92 | 0.00 | 10.75 | 10.64 | 0.00 |
time (sec) |
N/A | 0.386 | 10.041 | 1.089 | 0.000 | 9.787 | 0.000 | 0.618 | 10.037 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 130 | 110 | 133 | 0 | 676 | 0 | 1387 | 1083 | 3111 |
N.S. |
1 | 1.10 | 0.93 | 1.13 | 0.00 | 5.73 | 0.00 | 11.75 | 9.18 | 26.36 |
time (sec) |
N/A | 0.269 | 10.061 | 2.860 | 0.000 | 15.046 | 0.000 | 0.749 | 0.383 | 7.739 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 92 | 79 | 0 | 338 | 913 | 128 | 334 | 128 |
N.S. |
1 | 1.00 | 0.94 | 0.81 | 0.00 | 3.45 | 9.32 | 1.31 | 3.41 | 1.31 |
time (sec) |
N/A | 0.242 | 3.723 | 1.112 | 0.000 | 0.136 | 0.397 | 0.372 | 0.280 | 6.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 249 | 315 | 427 | 0 | 923 | 8670 | 545 | 942 | 0 |
N.S. |
1 | 1.00 | 1.27 | 1.71 | 0.00 | 3.71 | 34.82 | 2.19 | 3.78 | 0.00 |
time (sec) |
N/A | 0.413 | 4.311 | 1.179 | 0.000 | 0.136 | 0.905 | 0.409 | 0.407 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 44 | 41 | 0 | 215 | 559 | 58 | 200 | 58 |
N.S. |
1 | 1.00 | 0.75 | 0.69 | 0.00 | 3.64 | 9.47 | 0.98 | 3.39 | 0.98 |
time (sec) |
N/A | 0.194 | 2.335 | 0.907 | 0.000 | 0.107 | 0.290 | 0.369 | 0.228 | 6.373 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 210 | 223 | 294 | 0 | 675 | 2958 | 387 | 663 | 0 |
N.S. |
1 | 1.01 | 1.08 | 1.42 | 0.00 | 3.26 | 14.29 | 1.87 | 3.20 | 0.00 |
time (sec) |
N/A | 0.359 | 2.534 | 0.993 | 0.000 | 0.115 | 0.712 | 0.346 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 18 | 16 | 15 | 94 | 260 | 15 | 92 | 15 |
N.S. |
1 | 1.00 | 0.95 | 0.84 | 0.79 | 4.95 | 13.68 | 0.79 | 4.84 | 0.79 |
time (sec) |
N/A | 0.151 | 0.025 | 0.823 | 0.033 | 0.094 | 0.202 | 0.369 | 0.227 | 5.763 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 157 | 172 | 158 | 0 | 383 | 0 | 237 | 591 | 0 |
N.S. |
1 | 1.05 | 1.15 | 1.06 | 0.00 | 2.57 | 0.00 | 1.59 | 3.97 | 0.00 |
time (sec) |
N/A | 0.320 | 1.450 | 1.055 | 0.000 | 0.156 | 0.000 | 0.407 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 161 | 295 | 262 | 0 | 427 | 0 | 814 | 527 | 0 |
N.S. |
1 | 1.05 | 1.93 | 1.71 | 0.00 | 2.79 | 0.00 | 5.32 | 3.44 | 0.00 |
time (sec) |
N/A | 0.281 | 2.372 | 1.126 | 0.000 | 0.190 | 0.000 | 0.663 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 157 | 62 | 174 | 0 | 491 | 0 | 510 | 1030 | 0 |
N.S. |
1 | 1.07 | 0.42 | 1.18 | 0.00 | 3.34 | 0.00 | 3.47 | 7.01 | 0.00 |
time (sec) |
N/A | 0.313 | 10.042 | 1.157 | 0.000 | 0.275 | 0.000 | 0.401 | 0.503 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 155 | 331 | 329 | 0 | 529 | 0 | 612 | 675 | 0 |
N.S. |
1 | 1.07 | 2.28 | 2.27 | 0.00 | 3.65 | 0.00 | 4.22 | 4.66 | 0.00 |
time (sec) |
N/A | 0.286 | 2.896 | 1.478 | 0.000 | 0.470 | 0.000 | 0.494 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 157 | 62 | 175 | 0 | 535 | 0 | 692 | 916 | 0 |
N.S. |
1 | 1.07 | 0.42 | 1.19 | 0.00 | 3.64 | 0.00 | 4.71 | 6.23 | 0.00 |
time (sec) |
N/A | 0.311 | 10.043 | 1.635 | 0.000 | 0.751 | 0.000 | 0.788 | 1.127 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 149 | 97 | 440 | 0 | 549 | 0 | 1013 | 579 | 0 |
N.S. |
1 | 1.07 | 0.70 | 3.17 | 0.00 | 3.95 | 0.00 | 7.29 | 4.17 | 0.00 |
time (sec) |
N/A | 0.287 | 10.083 | 2.737 | 0.000 | 1.330 | 0.000 | 0.679 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 165 | 233 | 167 | 0 | 907 | 0 | 1249 | 1421 | 0 |
N.S. |
1 | 1.06 | 1.50 | 1.08 | 0.00 | 5.85 | 0.00 | 8.06 | 9.17 | 0.00 |
time (sec) |
N/A | 0.312 | 10.338 | 3.668 | 0.000 | 2.174 | 0.000 | 0.563 | 3.096 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 38 | 38 | 0 | 270 | 0 | 1241 | 472 | 3088 |
N.S. |
1 | 1.00 | 0.97 | 0.97 | 0.00 | 6.92 | 0.00 | 31.82 | 12.10 | 79.18 |
time (sec) |
N/A | 0.168 | 10.034 | 7.243 | 0.000 | 5.366 | 0.000 | 0.698 | 0.345 | 8.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 206 | 62 | 241 | 0 | 1441 | 0 | 2227 | 2079 | 0 |
N.S. |
1 | 1.05 | 0.31 | 1.22 | 0.00 | 7.31 | 0.00 | 11.30 | 10.55 | 0.00 |
time (sec) |
N/A | 0.363 | 10.041 | 10.783 | 0.000 | 10.525 | 0.000 | 0.696 | 11.071 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 62 | 70 | 0 | 530 | 0 | 1843 | 882 | 5511 |
N.S. |
1 | 1.00 | 0.78 | 0.89 | 0.00 | 6.71 | 0.00 | 23.33 | 11.16 | 69.76 |
time (sec) |
N/A | 0.213 | 10.052 | 19.789 | 0.000 | 15.885 | 0.000 | 1.248 | 0.378 | 9.742 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 257 | 62 | 324 | 0 | 2107 | 0 | 3431 | 2847 | 0 |
N.S. |
1 | 1.08 | 0.26 | 1.36 | 0.00 | 8.82 | 0.00 | 14.36 | 11.91 | 0.00 |
time (sec) |
N/A | 0.443 | 10.046 | 33.774 | 0.000 | 24.665 | 0.000 | 1.166 | 30.549 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 130 | 110 | 133 | 0 | 851 | 0 | 2365 | 1401 | 9995 |
N.S. |
1 | 1.10 | 0.93 | 1.13 | 0.00 | 7.21 | 0.00 | 20.04 | 11.87 | 84.70 |
time (sec) |
N/A | 0.268 | 10.076 | 58.769 | 0.000 | 49.498 | 0.000 | 1.487 | 0.590 | 15.901 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 114 | 100 | 114 | 0 | 313 | 549 | 157 | 255 | 0 |
N.S. |
1 | 0.97 | 0.85 | 0.97 | 0.00 | 2.68 | 4.69 | 1.34 | 2.18 | 0.00 |
time (sec) |
N/A | 0.252 | 0.861 | 1.156 | 0.000 | 0.116 | 0.705 | 0.383 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 43 | 40 | 0 | 48 | 97 | 58 | 39 | 48 |
N.S. |
1 | 1.00 | 0.73 | 0.68 | 0.00 | 0.81 | 1.64 | 0.98 | 0.66 | 0.81 |
time (sec) |
N/A | 0.199 | 0.472 | 0.953 | 0.000 | 0.097 | 0.092 | 0.385 | 0.178 | 5.760 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 70 | 66 | 0 | 195 | 233 | 76 | 125 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.88 | 0.00 | 2.60 | 3.11 | 1.01 | 1.67 | 0.00 |
time (sec) |
N/A | 0.201 | 0.500 | 1.039 | 0.000 | 0.091 | 0.543 | 0.388 | 0.184 | 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 | 17 | 17 | 16 | 16 | 15 | 15 | 15 | 15 | 14 | 15 |
N.S. |
1 | 1.00 | 0.94 | 0.94 | 0.88 | 0.88 | 0.88 | 0.88 | 0.82 | 0.88 |
time (sec) |
N/A | 0.149 | 0.015 | 0.882 | 0.027 | 0.101 | 0.063 | 0.363 | 0.217 | 5.568 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 77 | 52 | 0 | 167 | 0 | 65 | 131 | 0 |
N.S. |
1 | 1.00 | 1.40 | 0.95 | 0.00 | 3.04 | 0.00 | 1.18 | 2.38 | 0.00 |
time (sec) |
N/A | 0.187 | 0.315 | 1.100 | 0.000 | 0.097 | 0.000 | 0.367 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 236 | 38 | 0 | 48 | 0 | 139 | 60 | 37 |
N.S. |
1 | 1.00 | 6.38 | 1.03 | 0.00 | 1.30 | 0.00 | 3.76 | 1.62 | 1.00 |
time (sec) |
N/A | 0.169 | 0.853 | 1.169 | 0.000 | 0.104 | 0.000 | 0.375 | 0.244 | 5.734 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 107 | 97 | 0 | 433 | 0 | 267 | 529 | 0 |
N.S. |
1 | 1.00 | 1.13 | 1.02 | 0.00 | 4.56 | 0.00 | 2.81 | 5.57 | 0.00 |
time (sec) |
N/A | 0.238 | 10.277 | 1.160 | 0.000 | 0.163 | 0.000 | 0.390 | 0.271 | 0.000 |