Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 136 | 138 | 103 | 146 | 220 | 221 | 348 | 326 | 0 |
N.S. |
1 | 1.03 | 1.05 | 0.78 | 1.11 | 1.67 | 1.67 | 2.64 | 2.47 | 0.00 |
time (sec) |
N/A | 0.857 | 0.849 | 0.253 | 0.040 | 0.129 | 3.909 | 0.150 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 181 | 162 | 130 | 179 | 304 | 342 | 637 | 379 | 0 |
N.S. |
1 | 1.06 | 0.95 | 0.76 | 1.05 | 1.79 | 2.01 | 3.75 | 2.23 | 0.00 |
time (sec) |
N/A | 0.969 | 1.207 | 0.246 | 0.051 | 0.105 | 5.758 | 0.172 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 223 | 194 | 173 | 226 | 360 | 694 | 672 | 453 | 0 |
N.S. |
1 | 1.07 | 0.93 | 0.83 | 1.09 | 1.73 | 3.34 | 3.23 | 2.18 | 0.00 |
time (sec) |
N/A | 1.204 | 1.466 | 0.355 | 0.041 | 0.126 | 7.200 | 0.145 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 266 | 214 | 204 | 275 | 451 | 1044 | 918 | 505 | 0 |
N.S. |
1 | 1.07 | 0.86 | 0.82 | 1.11 | 1.82 | 4.21 | 3.70 | 2.04 | 0.00 |
time (sec) |
N/A | 1.252 | 1.653 | 0.345 | 0.043 | 0.156 | 13.229 | 0.165 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 310 | 444 | 254 | 284 | 362 | 610 | 367 | 319 | 32 | 0 |
N.S. |
1 | 1.43 | 0.82 | 0.92 | 1.17 | 1.97 | 1.18 | 1.03 | 0.10 | 0.00 |
time (sec) |
N/A | 2.385 | 1.754 | 0.395 | 0.047 | 0.101 | 0.562 | 0.154 | 200.027 | 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 | 248 | 328 | 203 | 224 | 281 | 463 | 313 | 252 | 411 | 0 |
N.S. |
1 | 1.32 | 0.82 | 0.90 | 1.13 | 1.87 | 1.26 | 1.02 | 1.66 | 0.00 |
time (sec) |
N/A | 1.443 | 1.033 | 0.263 | 0.037 | 0.131 | 0.551 | 0.193 | 0.585 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 243 | 166 | 166 | 230 | 383 | 265 | 201 | 29 | 0 |
N.S. |
1 | 1.18 | 0.81 | 0.81 | 1.12 | 1.86 | 1.29 | 0.98 | 0.14 | 0.00 |
time (sec) |
N/A | 0.882 | 0.700 | 0.267 | 0.041 | 0.094 | 0.503 | 0.199 | 200.023 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 191 | 159 | 257 | 199 | 717 | 425 | 0 | 292 | 0 |
N.S. |
1 | 1.09 | 0.91 | 1.47 | 1.14 | 4.10 | 2.43 | 0.00 | 1.67 | 0.00 |
time (sec) |
N/A | 1.399 | 0.708 | 0.227 | 0.042 | 0.849 | 5.283 | 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 | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 174 | 147 | 209 | 186 | 675 | 371 | 168 | 494 | 0 |
N.S. |
1 | 1.09 | 0.92 | 1.31 | 1.17 | 4.25 | 2.33 | 1.06 | 3.11 | 0.00 |
time (sec) |
N/A | 1.259 | 0.665 | 0.303 | 0.044 | 1.805 | 2.566 | 0.191 | 0.190 | 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 | 162 | 179 | 182 | 166 | 198 | 695 | 313 | 273 | 410 | 0 |
N.S. |
1 | 1.10 | 1.12 | 1.02 | 1.22 | 4.29 | 1.93 | 1.69 | 2.53 | 0.00 |
time (sec) |
N/A | 1.348 | 1.092 | 0.254 | 0.045 | 0.383 | 4.311 | 0.197 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 198 | 162 | 167 | 221 | 762 | 338 | 478 | 509 | 0 |
N.S. |
1 | 1.06 | 0.87 | 0.90 | 1.19 | 4.10 | 1.82 | 2.57 | 2.74 | 0.00 |
time (sec) |
N/A | 1.461 | 0.928 | 0.300 | 0.043 | 0.236 | 4.800 | 0.198 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 226 | 207 | 189 | 254 | 404 | 466 | 909 | 588 | 0 |
N.S. |
1 | 1.03 | 0.95 | 0.86 | 1.16 | 1.84 | 2.13 | 4.15 | 2.68 | 0.00 |
time (sec) |
N/A | 1.530 | 1.828 | 0.292 | 0.041 | 0.159 | 7.495 | 0.173 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 280 | 217 | 250 | 301 | 485 | 860 | 1071 | 661 | 0 |
N.S. |
1 | 1.05 | 0.81 | 0.94 | 1.13 | 1.82 | 3.22 | 4.01 | 2.48 | 0.00 |
time (sec) |
N/A | 1.768 | 1.849 | 0.410 | 0.041 | 0.172 | 8.621 | 0.175 | 0.390 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 328 | 343 | 295 | 309 | 383 | 627 | 1318 | 1480 | 792 | 0 |
N.S. |
1 | 1.05 | 0.90 | 0.94 | 1.17 | 1.91 | 4.02 | 4.51 | 2.41 | 0.00 |
time (sec) |
N/A | 1.948 | 2.353 | 0.409 | 0.047 | 0.260 | 16.749 | 0.162 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 326 | 370 | 275 | 372 | 558 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.13 | 0.84 | 1.14 | 1.71 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 2.732 | 1.556 | 0.285 | 0.179 | 0.000 | 0.000 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 273 | 226 | 288 | 404 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.11 | 0.92 | 1.18 | 1.65 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.782 | 1.686 | 0.232 | 0.113 | 0.000 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 193 | 171 | 236 | 299 | 0 | 0 | 0 | 3558 | 0 |
N.S. |
1 | 1.07 | 0.94 | 1.30 | 1.65 | 0.00 | 0.00 | 0.00 | 19.66 | 0.00 |
time (sec) |
N/A | 1.049 | 0.836 | 0.214 | 0.101 | 0.000 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 135 | 137 | 197 | 218 | 881 | 0 | 0 | 3317 | 0 |
N.S. |
1 | 1.04 | 1.05 | 1.52 | 1.68 | 6.78 | 0.00 | 0.00 | 25.52 | 0.00 |
time (sec) |
N/A | 0.592 | 0.556 | 0.193 | 0.083 | 120.084 | 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(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 182 | 168 | 202 | 0 | 0 | 0 | 0 | 435 | 0 |
N.S. |
1 | 1.36 | 1.25 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 3.25 | 0.00 |
time (sec) |
N/A | 0.886 | 0.804 | 0.184 | 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 | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 149 | 206 | 0 | 910 | 0 | 157 | 32 | 0 |
N.S. |
1 | 1.00 | 1.12 | 1.55 | 0.00 | 6.84 | 0.00 | 1.18 | 0.24 | 0.00 |
time (sec) |
N/A | 0.715 | 0.653 | 0.244 | 0.000 | 1.558 | 0.000 | 0.162 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 205 | 212 | 246 | 0 | 1301 | 0 | 300 | 746 | 0 |
N.S. |
1 | 1.10 | 1.13 | 1.32 | 0.00 | 6.96 | 0.00 | 1.60 | 3.99 | 0.00 |
time (sec) |
N/A | 0.871 | 1.174 | 0.260 | 0.000 | 3.979 | 0.000 | 0.158 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 281 | 260 | 305 | 0 | 1653 | 0 | 553 | 32 | 0 |
N.S. |
1 | 1.12 | 1.04 | 1.22 | 0.00 | 6.59 | 0.00 | 2.20 | 0.13 | 0.00 |
time (sec) |
N/A | 0.990 | 1.671 | 0.311 | 0.000 | 6.313 | 0.000 | 0.144 | 209.917 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 330 | 398 | 323 | 398 | 0 | 2207 | 0 | 1161 | 1280 | 0 |
N.S. |
1 | 1.21 | 0.98 | 1.21 | 0.00 | 6.69 | 0.00 | 3.52 | 3.88 | 0.00 |
time (sec) |
N/A | 1.214 | 2.718 | 0.339 | 0.000 | 19.907 | 0.000 | 0.208 | 0.362 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F(-1) | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 335 | 419 | 350 | 525 | 719 | 0 | 0 | 0 | 2937 | 0 |
N.S. |
1 | 1.25 | 1.04 | 1.57 | 2.15 | 0.00 | 0.00 | 0.00 | 8.77 | 0.00 |
time (sec) |
N/A | 3.080 | 2.315 | 0.330 | 0.133 | 0.000 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F(-1) | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 324 | 286 | 473 | 611 | 0 | 0 | 0 | 2568 | 0 |
N.S. |
1 | 1.21 | 1.07 | 1.76 | 2.28 | 0.00 | 0.00 | 0.00 | 9.58 | 0.00 |
time (sec) |
N/A | 1.882 | 2.547 | 0.296 | 0.110 | 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 | B | F(-1) | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 245 | 215 | 430 | 522 | 0 | 0 | 0 | 1717 | 0 |
N.S. |
1 | 1.20 | 1.05 | 2.11 | 2.56 | 0.00 | 0.00 | 0.00 | 8.42 | 0.00 |
time (sec) |
N/A | 1.171 | 1.256 | 0.242 | 0.092 | 0.000 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 186 | 177 | 390 | 419 | 0 | 0 | 0 | 1148 | 0 |
N.S. |
1 | 1.11 | 1.05 | 2.32 | 2.49 | 0.00 | 0.00 | 0.00 | 6.83 | 0.00 |
time (sec) |
N/A | 0.718 | 1.170 | 0.192 | 0.077 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 285 | 183 | 408 | 0 | 1585 | 0 | 0 | 1093 | 0 |
N.S. |
1 | 1.71 | 1.10 | 2.44 | 0.00 | 9.49 | 0.00 | 0.00 | 6.54 | 0.00 |
time (sec) |
N/A | 1.050 | 1.107 | 0.223 | 0.000 | 7.932 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 252 | 226 | 430 | 0 | 2210 | 0 | 0 | 1767 | 0 |
N.S. |
1 | 1.22 | 1.10 | 2.09 | 0.00 | 10.73 | 0.00 | 0.00 | 8.58 | 0.00 |
time (sec) |
N/A | 0.944 | 1.345 | 0.309 | 0.000 | 11.544 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 335 | 334 | 479 | 0 | 3165 | 0 | 0 | 2620 | 0 |
N.S. |
1 | 1.24 | 1.24 | 1.77 | 0.00 | 11.72 | 0.00 | 0.00 | 9.70 | 0.00 |
time (sec) |
N/A | 1.167 | 2.549 | 0.345 | 0.000 | 31.181 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 338 | 418 | 403 | 536 | 0 | 3853 | 0 | 0 | 3070 | 0 |
N.S. |
1 | 1.24 | 1.19 | 1.59 | 0.00 | 11.40 | 0.00 | 0.00 | 9.08 | 0.00 |
time (sec) |
N/A | 1.287 | 3.418 | 0.396 | 0.000 | 33.924 | 0.000 | 0.000 | 0.254 | 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 | 221 | 220 | 170 | 207 | 256 | 517 | 449 | 218 | 531 | 0 |
N.S. |
1 | 1.00 | 0.77 | 0.94 | 1.16 | 2.34 | 2.03 | 0.99 | 2.40 | 0.00 |
time (sec) |
N/A | 1.626 | 0.964 | 0.296 | 0.040 | 0.112 | 12.029 | 0.137 | 0.187 | 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 | 184 | 182 | 146 | 171 | 205 | 411 | 359 | 176 | 456 | 0 |
N.S. |
1 | 0.99 | 0.79 | 0.93 | 1.11 | 2.23 | 1.95 | 0.96 | 2.48 | 0.00 |
time (sec) |
N/A | 1.136 | 1.037 | 0.287 | 0.043 | 0.101 | 8.847 | 0.142 | 0.187 | 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 | 150 | 136 | 115 | 130 | 158 | 360 | 280 | 140 | 395 | 0 |
N.S. |
1 | 0.91 | 0.77 | 0.87 | 1.05 | 2.40 | 1.87 | 0.93 | 2.63 | 0.00 |
time (sec) |
N/A | 0.740 | 0.696 | 0.212 | 0.037 | 0.106 | 7.605 | 0.138 | 0.180 | 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 | 114 | 106 | 104 | 112 | 126 | 276 | 209 | 113 | 275 | 151 |
N.S. |
1 | 0.93 | 0.91 | 0.98 | 1.11 | 2.42 | 1.83 | 0.99 | 2.41 | 1.32 |
time (sec) |
N/A | 0.500 | 0.600 | 0.204 | 0.029 | 0.096 | 6.001 | 0.144 | 0.177 | 17.956 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 114 | 114 | 150 | 131 | 706 | 332 | 0 | 344 | 0 |
N.S. |
1 | 0.94 | 0.94 | 1.24 | 1.08 | 5.83 | 2.74 | 0.00 | 2.84 | 0.00 |
time (sec) |
N/A | 0.626 | 0.753 | 0.185 | 0.037 | 0.222 | 10.241 | 0.000 | 0.174 | 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 | 120 | 112 | 118 | 137 | 130 | 292 | 500 | 149 | 454 | 0 |
N.S. |
1 | 0.93 | 0.98 | 1.14 | 1.08 | 2.43 | 4.17 | 1.24 | 3.78 | 0.00 |
time (sec) |
N/A | 0.610 | 0.665 | 0.240 | 0.044 | 0.147 | 10.837 | 0.121 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 149 | 153 | 158 | 164 | 379 | 578 | 265 | 650 | 0 |
N.S. |
1 | 0.94 | 0.97 | 1.00 | 1.04 | 2.40 | 3.66 | 1.68 | 4.11 | 0.00 |
time (sec) |
N/A | 0.898 | 1.048 | 0.214 | 0.046 | 0.312 | 9.222 | 0.151 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 195 | 186 | 205 | 212 | 440 | 683 | 444 | 703 | 0 |
N.S. |
1 | 0.98 | 0.94 | 1.04 | 1.07 | 2.22 | 3.45 | 2.24 | 3.55 | 0.00 |
time (sec) |
N/A | 1.310 | 1.248 | 0.273 | 0.045 | 0.290 | 21.732 | 0.131 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 230 | 225 | 225 | 263 | 539 | 789 | 764 | 754 | 0 |
N.S. |
1 | 0.97 | 0.95 | 0.95 | 1.11 | 2.28 | 3.34 | 3.24 | 3.19 | 0.00 |
time (sec) |
N/A | 1.769 | 1.776 | 0.286 | 0.040 | 0.292 | 14.490 | 0.142 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 301 | 301 | 281 | 299 | 357 | 739 | 0 | 311 | 32 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.99 | 1.19 | 2.46 | 0.00 | 1.03 | 0.11 | 0.00 |
time (sec) |
N/A | 1.648 | 1.803 | 0.418 | 0.054 | 0.124 | 0.000 | 0.139 | 200.054 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 203 | 235 | 229 | 277 | 564 | 0 | 244 | 645 | 0 |
N.S. |
1 | 0.84 | 0.98 | 0.95 | 1.15 | 2.34 | 0.00 | 1.01 | 2.68 | 0.00 |
time (sec) |
N/A | 1.027 | 1.047 | 0.285 | 0.045 | 0.110 | 0.000 | 0.126 | 0.431 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 168 | 165 | 178 | 227 | 538 | 0 | 215 | 29 | 0 |
N.S. |
1 | 0.84 | 0.83 | 0.89 | 1.14 | 2.70 | 0.00 | 1.08 | 0.15 | 0.00 |
time (sec) |
N/A | 0.692 | 0.903 | 0.290 | 0.041 | 0.109 | 0.000 | 0.145 | 200.035 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 178 | 163 | 257 | 217 | 1003 | 0 | 0 | 535 | 0 |
N.S. |
1 | 0.98 | 0.90 | 1.42 | 1.20 | 5.54 | 0.00 | 0.00 | 2.96 | 0.00 |
time (sec) |
N/A | 1.022 | 1.039 | 0.255 | 0.041 | 0.535 | 0.000 | 0.000 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 181 | 169 | 223 | 219 | 1034 | 0 | 233 | 990 | 0 |
N.S. |
1 | 0.97 | 0.91 | 1.20 | 1.18 | 5.56 | 0.00 | 1.25 | 5.32 | 0.00 |
time (sec) |
N/A | 1.015 | 1.103 | 0.327 | 0.047 | 0.543 | 0.000 | 0.124 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 204 | 223 | 216 | 234 | 557 | 0 | 341 | 917 | 0 |
N.S. |
1 | 0.99 | 1.08 | 1.04 | 1.13 | 2.69 | 0.00 | 1.65 | 4.43 | 0.00 |
time (sec) |
N/A | 1.126 | 1.517 | 0.278 | 0.040 | 0.293 | 0.000 | 0.151 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 252 | 225 | 262 | 284 | 586 | 0 | 586 | 1071 | 0 |
N.S. |
1 | 0.99 | 0.89 | 1.03 | 1.12 | 2.31 | 0.00 | 2.31 | 4.22 | 0.00 |
time (sec) |
N/A | 1.832 | 1.396 | 0.316 | 0.041 | 0.285 | 0.000 | 0.137 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 313 | 312 | 305 | 323 | 366 | 764 | 0 | 1078 | 1210 | 0 |
N.S. |
1 | 1.00 | 0.97 | 1.03 | 1.17 | 2.44 | 0.00 | 3.44 | 3.87 | 0.00 |
time (sec) |
N/A | 2.604 | 2.113 | 0.336 | 0.039 | 0.296 | 0.000 | 0.142 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 311 | 354 | 383 | 508 | 983 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.14 | 1.23 | 1.63 | 3.16 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 2.990 | 3.133 | 0.340 | 0.353 | 0.000 | 0.000 | 0.000 | 200.033 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 269 | 275 | 472 | 804 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.11 | 1.13 | 1.94 | 3.31 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.873 | 2.106 | 0.311 | 0.229 | 0.000 | 0.000 | 0.000 | 200.038 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 212 | 221 | 417 | 652 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.08 | 1.13 | 2.13 | 3.33 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 1.189 | 1.447 | 0.290 | 0.174 | 0.000 | 0.000 | 0.000 | 200.023 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 168 | 177 | 457 | 544 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.04 | 1.09 | 2.82 | 3.36 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.782 | 0.911 | 0.208 | 0.115 | 0.000 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 147 | 386 | 453 | 721 | 0 | 290 | 29 | 0 |
N.S. |
1 | 1.00 | 1.07 | 2.80 | 3.28 | 5.22 | 0.00 | 2.10 | 0.21 | 0.00 |
time (sec) |
N/A | 0.562 | 0.841 | 0.194 | 0.095 | 0.863 | 0.000 | 0.144 | 200.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 264 | 181 | 401 | 0 | 1847 | 0 | 0 | 1103 | 0 |
N.S. |
1 | 1.64 | 1.12 | 2.49 | 0.00 | 11.47 | 0.00 | 0.00 | 6.85 | 0.00 |
time (sec) |
N/A | 1.091 | 0.871 | 0.201 | 0.000 | 5.014 | 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 | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 239 | 228 | 429 | 0 | 2398 | 0 | 389 | 32 | 0 |
N.S. |
1 | 1.11 | 1.06 | 2.00 | 0.00 | 11.15 | 0.00 | 1.81 | 0.15 | 0.00 |
time (sec) |
N/A | 0.938 | 1.152 | 0.269 | 0.000 | 8.515 | 0.000 | 0.136 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 350 | 326 | 474 | 0 | 3317 | 0 | 535 | 2277 | 0 |
N.S. |
1 | 1.19 | 1.11 | 1.62 | 0.00 | 11.32 | 0.00 | 1.83 | 7.77 | 0.00 |
time (sec) |
N/A | 1.137 | 2.428 | 0.305 | 0.000 | 21.320 | 0.000 | 0.138 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 368 | 440 | 446 | 751 | 1610 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.20 | 1.21 | 2.04 | 4.38 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 3.953 | 3.854 | 0.448 | 0.316 | 0.000 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 303 | 359 | 543 | 737 | 1459 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.18 | 1.79 | 2.43 | 4.82 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 2.651 | 11.879 | 0.349 | 0.233 | 0.000 | 0.000 | 0.000 | 200.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 316 | 304 | 993 | 1347 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.14 | 1.09 | 3.57 | 4.85 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.832 | 2.183 | 0.275 | 0.205 | 0.000 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 233 | 255 | 919 | 1242 | 1571 | 0 | 0 | 2422 | 0 |
N.S. |
1 | 1.01 | 1.10 | 3.98 | 5.38 | 6.80 | 0.00 | 0.00 | 10.48 | 0.00 |
time (sec) |
N/A | 1.065 | 2.180 | 0.236 | 0.168 | 1.559 | 0.000 | 0.000 | 35.345 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 239 | 246 | 872 | 1085 | 1583 | 0 | 0 | 2371 | 0 |
N.S. |
1 | 1.01 | 1.04 | 3.69 | 4.60 | 6.71 | 0.00 | 0.00 | 10.05 | 0.00 |
time (sec) |
N/A | 0.919 | 1.984 | 0.216 | 0.143 | 1.628 | 0.000 | 0.000 | 15.838 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 515 | 320 | 913 | 0 | 4367 | 0 | 0 | 3375 | 0 |
N.S. |
1 | 1.92 | 1.19 | 3.41 | 0.00 | 16.29 | 0.00 | 0.00 | 12.59 | 0.00 |
time (sec) |
N/A | 1.686 | 1.905 | 0.256 | 0.000 | 34.619 | 0.000 | 0.000 | 1.549 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 351 | 430 | 359 | 747 | 0 | 5706 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.23 | 1.02 | 2.13 | 0.00 | 16.26 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.268 | 3.099 | 0.334 | 0.000 | 55.645 | 0.000 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 456 | 565 | 495 | 777 | 0 | 7645 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.24 | 1.09 | 1.70 | 0.00 | 16.77 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.562 | 4.308 | 0.381 | 0.000 | 145.908 | 0.000 | 0.000 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 498 | 1057 | 1192 | 888 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 2.12 | 2.39 | 1.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 4.637 | 27.332 | 5.919 | 0.000 | 0.000 | 0.000 | 0.000 | 200.036 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 459 | 0 | 1049 | 958 | 0 | 0 | 0 | 0 | 136 | 0 |
N.S. |
1 | 0.00 | 2.29 | 2.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.000 | 26.662 | 6.069 | 0.000 | 0.000 | 0.000 | 0.000 | 104.868 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 831 | 834 | 982 | 2091 | 0 | 739 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.18 | 2.52 | 0.00 | 0.89 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 4.068 | 32.625 | 9.378 | 0.000 | 0.098 | 0.000 | 0.000 | 200.015 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 700 | 694 | 830 | 1405 | 0 | 609 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.99 | 1.19 | 2.01 | 0.00 | 0.87 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 2.755 | 29.972 | 7.000 | 0.000 | 0.087 | 0.000 | 0.000 | 200.017 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 577 | 560 | 726 | 1018 | 0 | 468 | 0 | 0 | 1048 | 0 |
N.S. |
1 | 0.97 | 1.26 | 1.76 | 0.00 | 0.81 | 0.00 | 0.00 | 1.82 | 0.00 |
time (sec) |
N/A | 2.033 | 28.710 | 5.286 | 0.000 | 0.096 | 0.000 | 0.000 | 3.906 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 468 | 457 | 597 | 802 | 0 | 381 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.98 | 1.28 | 1.71 | 0.00 | 0.81 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.377 | 27.064 | 3.238 | 0.000 | 0.083 | 0.000 | 0.000 | 200.015 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 519 | 792 | 750 | 903 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.53 | 1.45 | 1.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 2.781 | 26.432 | 1.253 | 0.000 | 0.000 | 0.000 | 0.000 | 200.014 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 505 | 1365 | 994 | 867 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 2.70 | 1.97 | 1.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 7.875 | 28.076 | 3.978 | 0.000 | 0.000 | 0.000 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 532 | 1470 | 1530 | 849 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 2.76 | 2.88 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 9.427 | 28.755 | 3.053 | 0.000 | 0.000 | 0.000 | 0.000 | 200.018 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 617 | 1676 | 1895 | 999 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 2.72 | 3.07 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 11.599 | 30.832 | 6.302 | 0.000 | 0.000 | 0.000 | 0.000 | 200.016 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 738 | 1907 | 2679 | 1132 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 2.58 | 3.63 | 1.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 14.331 | 32.737 | 7.956 | 0.000 | 0.000 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 990 | 962 | 1335 | 2610 | 0 | 916 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.97 | 1.35 | 2.64 | 0.00 | 0.93 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 3.616 | 33.820 | 9.048 | 0.000 | 0.104 | 0.000 | 0.000 | 200.018 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 831 | 795 | 980 | 2094 | 0 | 738 | 0 | 0 | 31 | 0 |
N.S. |
1 | 0.96 | 1.18 | 2.52 | 0.00 | 0.89 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 2.597 | 32.543 | 6.653 | 0.000 | 0.090 | 0.000 | 0.000 | 200.020 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 692 | 662 | 831 | 1540 | 0 | 608 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.96 | 1.20 | 2.23 | 0.00 | 0.88 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.943 | 30.357 | 6.655 | 0.000 | 0.085 | 0.000 | 0.000 | 200.017 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 709 | 0 | 1669 | 1318 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 2.35 | 1.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.000 | 30.670 | 3.916 | 0.000 | 0.000 | 0.000 | 0.000 | 200.012 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 667 | 0 | 1658 | 1119 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 2.49 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.000 | 29.912 | 8.476 | 0.000 | 0.000 | 0.000 | 0.000 | 200.017 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 664 | 0 | 1990 | 1047 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 3.00 | 1.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.000 | 30.324 | 5.756 | 0.000 | 0.000 | 0.000 | 0.000 | 200.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 693 | 0 | 2192 | 1052 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 3.16 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.000 | 30.897 | 6.189 | 0.000 | 0.000 | 0.000 | 0.000 | 200.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 757 | 0 | 2808 | 1135 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 3.71 | 1.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.000 | 33.407 | 7.380 | 0.000 | 0.000 | 0.000 | 0.000 | 200.032 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 893 | 0 | 3014 | 1288 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 3.38 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.000 | 33.782 | 10.721 | 0.000 | 0.000 | 0.000 | 0.000 | 200.024 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 594 | 620 | 738 | 974 | 0 | 467 | 0 | 0 | 1048 | 0 |
N.S. |
1 | 1.04 | 1.24 | 1.64 | 0.00 | 0.79 | 0.00 | 0.00 | 1.76 | 0.00 |
time (sec) |
N/A | 3.668 | 28.565 | 6.402 | 0.000 | 0.091 | 0.000 | 0.000 | 5.592 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 493 | 509 | 615 | 778 | 0 | 381 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.03 | 1.25 | 1.58 | 0.00 | 0.77 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 2.464 | 26.949 | 6.027 | 0.000 | 0.089 | 0.000 | 0.000 | 200.017 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 398 | 407 | 536 | 663 | 0 | 283 | 0 | 0 | 437 | 0 |
N.S. |
1 | 1.02 | 1.35 | 1.67 | 0.00 | 0.71 | 0.00 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 1.533 | 25.615 | 3.625 | 0.000 | 0.091 | 0.000 | 0.000 | 2.371 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 333 | 338 | 454 | 588 | 0 | 237 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.02 | 1.36 | 1.77 | 0.00 | 0.71 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.951 | 23.952 | 3.501 | 0.000 | 0.086 | 0.000 | 0.000 | 200.013 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 389 | 443 | 669 | 672 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.14 | 1.72 | 1.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.622 | 24.664 | 2.990 | 0.000 | 0.000 | 0.000 | 0.000 | 200.014 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 429 | 491 | 870 | 645 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.14 | 2.03 | 1.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 2.078 | 25.763 | 4.028 | 0.000 | 0.000 | 0.000 | 0.000 | 200.036 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 515 | 570 | 1392 | 903 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.11 | 2.70 | 1.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 2.833 | 27.690 | 5.217 | 0.000 | 0.000 | 0.000 | 0.000 | 200.033 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 597 | 663 | 791 | 1101 | 0 | 878 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.11 | 1.32 | 1.84 | 0.00 | 1.47 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 3.901 | 30.543 | 9.518 | 0.000 | 0.109 | 0.000 | 0.000 | 200.012 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 507 | 549 | 728 | 888 | 0 | 662 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.08 | 1.44 | 1.75 | 0.00 | 1.31 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 2.602 | 27.242 | 7.652 | 0.000 | 0.089 | 0.000 | 0.000 | 200.016 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 432 | 459 | 611 | 763 | 0 | 537 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.06 | 1.41 | 1.77 | 0.00 | 1.24 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.909 | 25.972 | 5.959 | 0.000 | 0.090 | 0.000 | 0.000 | 200.018 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 367 | 372 | 533 | 696 | 0 | 399 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.01 | 1.45 | 1.90 | 0.00 | 1.09 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.099 | 25.690 | 3.658 | 0.000 | 0.084 | 0.000 | 0.000 | 200.020 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 473 | 706 | 435 | 912 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.49 | 0.92 | 1.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 2.427 | 24.346 | 3.936 | 0.000 | 0.000 | 0.000 | 0.000 | 200.014 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 524 | 1131 | 1699 | 960 | 0 | 0 | 0 | 0 | 633 | 0 |
N.S. |
1 | 2.16 | 3.24 | 1.83 | 0.00 | 0.00 | 0.00 | 0.00 | 1.21 | 0.00 |
time (sec) |
N/A | 5.568 | 30.434 | 6.609 | 0.000 | 0.000 | 0.000 | 0.000 | 52.975 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 615 | 1401 | 2647 | 1051 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 2.28 | 4.30 | 1.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 8.576 | 32.463 | 7.412 | 0.000 | 0.000 | 0.000 | 0.000 | 200.020 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 681 | 733 | 921 | 1106 | 0 | 1336 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.08 | 1.35 | 1.62 | 0.00 | 1.96 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 4.138 | 32.742 | 11.754 | 0.000 | 0.145 | 0.000 | 0.000 | 200.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 603 | 634 | 794 | 981 | 0 | 1125 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.05 | 1.32 | 1.63 | 0.00 | 1.87 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 3.108 | 30.810 | 10.179 | 0.000 | 0.132 | 0.000 | 0.000 | 200.016 | 0.000 |