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 | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 446 | 406 | 452 | 528 | 0 | 7267 | 0 | 7277 | 5692 | 19024 |
N.S. |
1 | 0.91 | 1.01 | 1.18 | 0.00 | 16.29 | 0.00 | 16.32 | 12.76 | 42.65 |
time (sec) |
N/A | 0.900 | 7.287 | 1.136 | 0.000 | 15.519 | 0.000 | 1.718 | 4.695 | 14.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 468 | 466 | 524 | 1556 | 0 | 9907 | 0 | 4621 | 6756 | 22946 |
N.S. |
1 | 1.00 | 1.12 | 3.32 | 0.00 | 21.17 | 0.00 | 9.87 | 14.44 | 49.03 |
time (sec) |
N/A | 0.994 | 4.900 | 1.540 | 0.000 | 41.298 | 0.000 | 1.363 | 4.977 | 15.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 664 | 578 | 628 | 762 | 0 | 12534 | 0 | 9534 | 8137 | 29137 |
N.S. |
1 | 0.87 | 0.95 | 1.15 | 0.00 | 18.88 | 0.00 | 14.36 | 12.25 | 43.88 |
time (sec) |
N/A | 1.267 | 12.507 | 1.206 | 0.000 | 122.439 | 0.000 | 1.704 | 3.100 | 17.819 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 367 | 348 | 349 | 413 | 0 | 843 | 1292 | 412 | 23 | 992 |
N.S. |
1 | 0.95 | 0.95 | 1.13 | 0.00 | 2.30 | 3.52 | 1.12 | 0.06 | 2.70 |
time (sec) |
N/A | 0.696 | 2.071 | 1.371 | 0.000 | 0.152 | 0.703 | 0.268 | 200.025 | 13.890 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 265 | 272 | 316 | 0 | 667 | 831 | 321 | 23 | 781 |
N.S. |
1 | 0.95 | 0.97 | 1.13 | 0.00 | 2.38 | 2.97 | 1.15 | 0.08 | 2.79 |
time (sec) |
N/A | 0.503 | 1.443 | 1.242 | 0.000 | 0.150 | 0.675 | 0.271 | 200.032 | 11.901 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 194 | 210 | 234 | 0 | 517 | 539 | 243 | 23 | 463 |
N.S. |
1 | 0.95 | 1.02 | 1.14 | 0.00 | 2.52 | 2.63 | 1.19 | 0.11 | 2.26 |
time (sec) |
N/A | 0.367 | 0.981 | 1.347 | 0.000 | 0.117 | 0.621 | 0.243 | 200.022 | 11.632 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 135 | 154 | 167 | 0 | 393 | 350 | 176 | 21 | 256 |
N.S. |
1 | 0.94 | 1.07 | 1.16 | 0.00 | 2.73 | 2.43 | 1.22 | 0.15 | 1.78 |
time (sec) |
N/A | 0.268 | 0.628 | 1.191 | 0.000 | 0.111 | 0.762 | 0.255 | 200.023 | 10.898 |
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 | 113 | 113 | 115 | 114 | 0 | 291 | 224 | 121 | 233 | 145 |
N.S. |
1 | 1.00 | 1.02 | 1.01 | 0.00 | 2.58 | 1.98 | 1.07 | 2.06 | 1.28 |
time (sec) |
N/A | 0.244 | 0.908 | 1.277 | 0.000 | 0.102 | 0.609 | 0.253 | 0.241 | 10.726 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 136 | 131 | 148 | 0 | 651 | 0 | 0 | 955 | 146 |
N.S. |
1 | 1.05 | 1.02 | 1.15 | 0.00 | 5.05 | 0.00 | 0.00 | 7.40 | 1.13 |
time (sec) |
N/A | 0.339 | 0.681 | 1.185 | 0.000 | 0.637 | 0.000 | 0.000 | 0.326 | 10.801 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 113 | 167 | 0 | 648 | 0 | 161 | 142 | 166 |
N.S. |
1 | 1.00 | 0.93 | 1.38 | 0.00 | 5.36 | 0.00 | 1.33 | 1.17 | 1.37 |
time (sec) |
N/A | 0.314 | 0.709 | 1.286 | 0.000 | 0.340 | 0.000 | 0.292 | 0.363 | 11.251 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 0 | 159 | 125 | 0 | 699 | 0 | 356 | 164 | 0 |
N.S. |
1 | 0.00 | 1.20 | 0.94 | 0.00 | 5.26 | 0.00 | 2.68 | 1.23 | 0.00 |
time (sec) |
N/A | 0.000 | 1.048 | 1.307 | 0.000 | 0.388 | 0.000 | 0.275 | 0.254 | 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 | 121 | 121 | 165 | 128 | 0 | 317 | 0 | 524 | 175 | 0 |
N.S. |
1 | 1.00 | 1.36 | 1.06 | 0.00 | 2.62 | 0.00 | 4.33 | 1.45 | 0.00 |
time (sec) |
N/A | 0.260 | 1.231 | 1.346 | 0.000 | 0.230 | 0.000 | 0.289 | 0.270 | 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 | 172 | 171 | 198 | 185 | 0 | 425 | 0 | 991 | 274 | 0 |
N.S. |
1 | 0.99 | 1.15 | 1.08 | 0.00 | 2.47 | 0.00 | 5.76 | 1.59 | 0.00 |
time (sec) |
N/A | 0.347 | 1.791 | 1.486 | 0.000 | 0.408 | 0.000 | 0.261 | 0.406 | 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 | 235 | 230 | 264 | 257 | 0 | 553 | 0 | 1407 | 343 | 0 |
N.S. |
1 | 0.98 | 1.12 | 1.09 | 0.00 | 2.35 | 0.00 | 5.99 | 1.46 | 0.00 |
time (sec) |
N/A | 0.451 | 2.544 | 1.425 | 0.000 | 0.927 | 0.000 | 0.267 | 0.669 | 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 | 310 | 302 | 329 | 344 | 0 | 709 | 0 | 1955 | 467 | 0 |
N.S. |
1 | 0.97 | 1.06 | 1.11 | 0.00 | 2.29 | 0.00 | 6.31 | 1.51 | 0.00 |
time (sec) |
N/A | 0.572 | 3.554 | 1.559 | 0.000 | 1.709 | 0.000 | 0.249 | 1.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 455 | 391 | 505 | 652 | 0 | 1263 | 4983 | 637 | 23 | 0 |
N.S. |
1 | 0.86 | 1.11 | 1.43 | 0.00 | 2.78 | 10.95 | 1.40 | 0.05 | 0.00 |
time (sec) |
N/A | 0.751 | 4.121 | 1.375 | 0.000 | 0.220 | 0.778 | 0.264 | 200.084 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 356 | 308 | 412 | 525 | 0 | 1037 | 3089 | 522 | 23 | 0 |
N.S. |
1 | 0.87 | 1.16 | 1.47 | 0.00 | 2.91 | 8.68 | 1.47 | 0.06 | 0.00 |
time (sec) |
N/A | 0.579 | 2.894 | 1.389 | 0.000 | 0.191 | 0.763 | 0.259 | 200.049 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 269 | 237 | 328 | 413 | 0 | 845 | 1911 | 420 | 23 | 0 |
N.S. |
1 | 0.88 | 1.22 | 1.54 | 0.00 | 3.14 | 7.10 | 1.56 | 0.09 | 0.00 |
time (sec) |
N/A | 0.420 | 2.111 | 1.333 | 0.000 | 0.154 | 0.698 | 0.263 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 178 | 254 | 316 | 0 | 669 | 1175 | 330 | 21 | 0 |
N.S. |
1 | 0.90 | 1.28 | 1.60 | 0.00 | 3.38 | 5.93 | 1.67 | 0.11 | 0.00 |
time (sec) |
N/A | 0.315 | 1.473 | 1.155 | 0.000 | 0.130 | 0.902 | 0.254 | 200.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 156 | 192 | 234 | 0 | 515 | 711 | 249 | 20 | 305 |
N.S. |
1 | 0.99 | 1.22 | 1.48 | 0.00 | 3.26 | 4.50 | 1.58 | 0.13 | 1.93 |
time (sec) |
N/A | 0.271 | 2.277 | 1.180 | 0.000 | 0.123 | 0.597 | 0.256 | 200.031 | 10.979 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 234 | 208 | 271 | 0 | 1023 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.07 | 0.95 | 1.24 | 0.00 | 4.69 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.528 | 1.249 | 1.204 | 0.000 | 2.627 | 0.000 | 0.000 | 200.026 | 0.000 |
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 | 193 | 203 | 182 | 331 | 0 | 917 | 0 | 238 | 274 | 0 |
N.S. |
1 | 1.05 | 0.94 | 1.72 | 0.00 | 4.75 | 0.00 | 1.23 | 1.42 | 0.00 |
time (sec) |
N/A | 0.454 | 1.309 | 1.234 | 0.000 | 1.173 | 0.000 | 0.284 | 0.355 | 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 | 179 | 182 | 159 | 290 | 0 | 921 | 0 | 412 | 267 | 0 |
N.S. |
1 | 1.02 | 0.89 | 1.62 | 0.00 | 5.15 | 0.00 | 2.30 | 1.49 | 0.00 |
time (sec) |
N/A | 0.426 | 1.649 | 1.361 | 0.000 | 0.917 | 0.000 | 0.294 | 0.404 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 0 | 181 | 254 | 0 | 953 | 0 | 627 | 264 | 0 |
N.S. |
1 | 0.00 | 0.88 | 1.23 | 0.00 | 4.63 | 0.00 | 3.04 | 1.28 | 0.00 |
time (sec) |
N/A | 0.000 | 1.762 | 1.327 | 0.000 | 0.986 | 0.000 | 0.293 | 0.440 | 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 | 217 | 235 | 240 | 225 | 0 | 1083 | 0 | 1016 | 310 | 0 |
N.S. |
1 | 1.08 | 1.11 | 1.04 | 0.00 | 4.99 | 0.00 | 4.68 | 1.43 | 0.00 |
time (sec) |
N/A | 0.512 | 2.298 | 1.364 | 0.000 | 1.325 | 0.000 | 0.352 | 0.566 | 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 | 170 | 168 | 261 | 256 | 0 | 555 | 0 | 1357 | 343 | 0 |
N.S. |
1 | 0.99 | 1.54 | 1.51 | 0.00 | 3.26 | 0.00 | 7.98 | 2.02 | 0.00 |
time (sec) |
N/A | 0.325 | 2.777 | 1.481 | 0.000 | 0.922 | 0.000 | 0.253 | 0.885 | 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 | 230 | 218 | 324 | 344 | 0 | 709 | 0 | 2059 | 467 | 0 |
N.S. |
1 | 0.95 | 1.41 | 1.50 | 0.00 | 3.08 | 0.00 | 8.95 | 2.03 | 0.00 |
time (sec) |
N/A | 0.412 | 4.096 | 1.568 | 0.000 | 1.826 | 0.000 | 0.283 | 1.687 | 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 | 303 | 277 | 412 | 446 | 0 | 889 | 0 | 2713 | 561 | 0 |
N.S. |
1 | 0.91 | 1.36 | 1.47 | 0.00 | 2.93 | 0.00 | 8.95 | 1.85 | 0.00 |
time (sec) |
N/A | 0.513 | 5.176 | 1.652 | 0.000 | 2.332 | 0.000 | 0.277 | 3.082 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 543 | 434 | 698 | 951 | 0 | 1775 | 17279 | 906 | 23 | 0 |
N.S. |
1 | 0.80 | 1.29 | 1.75 | 0.00 | 3.27 | 31.82 | 1.67 | 0.04 | 0.00 |
time (sec) |
N/A | 0.806 | 9.785 | 1.394 | 0.000 | 0.326 | 0.980 | 0.267 | 200.019 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 432 | 351 | 585 | 794 | 0 | 1511 | 10654 | 767 | 23 | 0 |
N.S. |
1 | 0.81 | 1.35 | 1.84 | 0.00 | 3.50 | 24.66 | 1.78 | 0.05 | 0.00 |
time (sec) |
N/A | 0.636 | 6.284 | 1.249 | 0.000 | 0.285 | 0.907 | 0.278 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 333 | 280 | 482 | 652 | 0 | 1263 | 6552 | 641 | 23 | 0 |
N.S. |
1 | 0.84 | 1.45 | 1.96 | 0.00 | 3.79 | 19.68 | 1.92 | 0.07 | 0.00 |
time (sec) |
N/A | 0.461 | 4.064 | 1.290 | 0.000 | 0.223 | 0.945 | 0.267 | 200.060 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 221 | 390 | 511 | 0 | 1039 | 4009 | 526 | 21 | 0 |
N.S. |
1 | 0.88 | 1.55 | 2.03 | 0.00 | 4.12 | 15.91 | 2.09 | 0.08 | 0.00 |
time (sec) |
N/A | 0.363 | 2.771 | 1.233 | 0.000 | 0.171 | 0.962 | 0.281 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 199 | 311 | 314 | 0 | 843 | 2428 | 423 | 20 | 0 |
N.S. |
1 | 0.98 | 1.53 | 1.55 | 0.00 | 4.15 | 11.96 | 2.08 | 0.10 | 0.00 |
time (sec) |
N/A | 0.311 | 4.243 | 1.230 | 0.000 | 0.151 | 0.695 | 0.266 | 200.049 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 346 | 374 | 324 | 433 | 0 | 1575 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.08 | 0.94 | 1.25 | 0.00 | 4.55 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.780 | 2.495 | 1.179 | 0.000 | 8.646 | 0.000 | 0.000 | 200.040 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 310 | 329 | 287 | 600 | 0 | 1393 | 0 | 368 | 449 | 0 |
N.S. |
1 | 1.06 | 0.93 | 1.94 | 0.00 | 4.49 | 0.00 | 1.19 | 1.45 | 0.00 |
time (sec) |
N/A | 0.660 | 2.192 | 1.285 | 0.000 | 4.339 | 0.000 | 0.274 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 288 | 253 | 505 | 0 | 1269 | 0 | 527 | 433 | 0 |
N.S. |
1 | 1.05 | 0.93 | 1.85 | 0.00 | 4.65 | 0.00 | 1.93 | 1.59 | 0.00 |
time (sec) |
N/A | 0.591 | 2.447 | 1.347 | 0.000 | 2.877 | 0.000 | 0.288 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 263 | 234 | 456 | 0 | 1293 | 0 | 765 | 396 | 0 |
N.S. |
1 | 1.03 | 0.92 | 1.79 | 0.00 | 5.07 | 0.00 | 3.00 | 1.55 | 0.00 |
time (sec) |
N/A | 0.600 | 2.700 | 1.323 | 0.000 | 1.624 | 0.000 | 0.326 | 0.304 | 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 | 284 | 294 | 286 | 453 | 0 | 1305 | 0 | 1163 | 409 | 0 |
N.S. |
1 | 1.04 | 1.01 | 1.60 | 0.00 | 4.60 | 0.00 | 4.10 | 1.44 | 0.00 |
time (sec) |
N/A | 0.689 | 3.552 | 1.372 | 0.000 | 2.314 | 0.000 | 0.350 | 0.490 | 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 | 346 | 361 | 313 | 389 | 0 | 1445 | 0 | 1525 | 441 | 0 |
N.S. |
1 | 1.04 | 0.90 | 1.12 | 0.00 | 4.18 | 0.00 | 4.41 | 1.27 | 0.00 |
time (sec) |
N/A | 0.833 | 4.982 | 1.500 | 0.000 | 3.508 | 0.000 | 0.408 | 0.786 | 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 | 332 | 358 | 360 | 384 | 0 | 1659 | 0 | 2086 | 505 | 0 |
N.S. |
1 | 1.08 | 1.08 | 1.16 | 0.00 | 5.00 | 0.00 | 6.28 | 1.52 | 0.00 |
time (sec) |
N/A | 0.758 | 4.680 | 1.552 | 0.000 | 4.427 | 0.000 | 0.543 | 1.727 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 215 | 402 | 446 | 0 | 887 | 0 | 2598 | 561 | 0 |
N.S. |
1 | 0.98 | 1.84 | 2.04 | 0.00 | 4.05 | 0.00 | 11.86 | 2.56 | 0.00 |
time (sec) |
N/A | 0.384 | 5.628 | 1.816 | 0.000 | 2.199 | 0.000 | 0.293 | 6.773 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 288 | 265 | 490 | 563 | 0 | 1091 | 0 | 3603 | 710 | 0 |
N.S. |
1 | 0.92 | 1.70 | 1.95 | 0.00 | 3.79 | 0.00 | 12.51 | 2.47 | 0.00 |
time (sec) |
N/A | 0.457 | 7.669 | 1.849 | 0.000 | 4.076 | 0.000 | 0.309 | 19.106 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 375 | 324 | 292 | 695 | 0 | 1315 | 0 | 4427 | 829 | 0 |
N.S. |
1 | 0.86 | 0.78 | 1.85 | 0.00 | 3.51 | 0.00 | 11.81 | 2.21 | 0.00 |
time (sec) |
N/A | 0.594 | 10.969 | 2.036 | 0.000 | 5.002 | 0.000 | 0.311 | 96.887 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 222 | 173 | 167 | 0 | 395 | 423 | 181 | 23 | 0 |
N.S. |
1 | 1.08 | 0.84 | 0.81 | 0.00 | 1.92 | 2.05 | 0.88 | 0.11 | 0.00 |
time (sec) |
N/A | 0.456 | 0.777 | 1.316 | 0.000 | 0.122 | 0.640 | 0.252 | 200.059 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 151 | 124 | 115 | 0 | 295 | 292 | 126 | 233 | 0 |
N.S. |
1 | 1.06 | 0.87 | 0.80 | 0.00 | 2.06 | 2.04 | 0.88 | 1.63 | 0.00 |
time (sec) |
N/A | 0.326 | 0.565 | 1.230 | 0.000 | 0.110 | 0.578 | 0.247 | 0.248 | 0.000 |
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 | 92 | 92 | 92 | 80 | 0 | 213 | 204 | 88 | 144 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.00 | 2.32 | 2.22 | 0.96 | 1.57 | 0.00 |
time (sec) |
N/A | 0.226 | 0.505 | 1.220 | 0.000 | 0.100 | 0.831 | 0.250 | 0.224 | 0.000 |
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 | 67 | 67 | 66 | 58 | 0 | 162 | 146 | 60 | 106 | 80 |
N.S. |
1 | 1.00 | 0.99 | 0.87 | 0.00 | 2.42 | 2.18 | 0.90 | 1.58 | 1.19 |
time (sec) |
N/A | 0.209 | 0.449 | 1.163 | 0.000 | 0.091 | 0.425 | 0.253 | 0.216 | 11.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 74 | 67 | 0 | 468 | 0 | 0 | 794 | 66 |
N.S. |
1 | 1.00 | 0.96 | 0.87 | 0.00 | 6.08 | 0.00 | 0.00 | 10.31 | 0.86 |
time (sec) |
N/A | 0.247 | 0.330 | 1.167 | 0.000 | 0.151 | 0.000 | 0.000 | 0.238 | 10.796 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 68 | 65 | 0 | 177 | 0 | 110 | 60 | 87 |
N.S. |
1 | 1.00 | 0.94 | 0.90 | 0.00 | 2.46 | 0.00 | 1.53 | 0.83 | 1.21 |
time (sec) |
N/A | 0.213 | 0.487 | 1.210 | 0.000 | 0.118 | 0.000 | 0.222 | 0.263 | 10.851 |
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 | 116 | 122 | 122 | 88 | 0 | 235 | 0 | 303 | 130 | 0 |
N.S. |
1 | 1.05 | 1.05 | 0.76 | 0.00 | 2.03 | 0.00 | 2.61 | 1.12 | 0.00 |
time (sec) |
N/A | 0.287 | 0.885 | 1.216 | 0.000 | 0.169 | 0.000 | 0.239 | 0.238 | 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 | 167 | 181 | 161 | 128 | 0 | 321 | 0 | 511 | 175 | 0 |
N.S. |
1 | 1.08 | 0.96 | 0.77 | 0.00 | 1.92 | 0.00 | 3.06 | 1.05 | 0.00 |
time (sec) |
N/A | 0.388 | 1.251 | 1.263 | 0.000 | 0.234 | 0.000 | 0.253 | 0.314 | 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 | 231 | 253 | 201 | 185 | 0 | 425 | 0 | 884 | 274 | 0 |
N.S. |
1 | 1.10 | 0.87 | 0.80 | 0.00 | 1.84 | 0.00 | 3.83 | 1.19 | 0.00 |
time (sec) |
N/A | 0.533 | 1.631 | 1.348 | 0.000 | 0.396 | 0.000 | 0.264 | 0.393 | 0.000 |
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 | 280 | 291 | 298 | 447 | 0 | 1035 | 0 | 365 | 1083 | 0 |
N.S. |
1 | 1.04 | 1.06 | 1.60 | 0.00 | 3.70 | 0.00 | 1.30 | 3.87 | 0.00 |
time (sec) |
N/A | 0.546 | 1.584 | 1.296 | 0.000 | 0.288 | 0.000 | 0.257 | 0.369 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 210 | 223 | 359 | 0 | 793 | 0 | 266 | 23 | 0 |
N.S. |
1 | 1.07 | 1.13 | 1.82 | 0.00 | 4.03 | 0.00 | 1.35 | 0.12 | 0.00 |
time (sec) |
N/A | 0.389 | 1.118 | 1.311 | 0.000 | 0.253 | 0.000 | 0.227 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 166 | 147 | 244 | 0 | 603 | 0 | 175 | 709 | 0 |
N.S. |
1 | 1.08 | 0.96 | 1.59 | 0.00 | 3.94 | 0.00 | 1.14 | 4.63 | 0.00 |
time (sec) |
N/A | 0.347 | 0.842 | 1.298 | 0.000 | 0.192 | 0.000 | 0.247 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 104 | 168 | 0 | 405 | 0 | 108 | 456 | 111 |
N.S. |
1 | 1.00 | 1.08 | 1.75 | 0.00 | 4.22 | 0.00 | 1.12 | 4.75 | 1.16 |
time (sec) |
N/A | 0.236 | 0.648 | 1.227 | 0.000 | 0.182 | 0.000 | 0.276 | 0.204 | 11.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 44 | 45 | 0 | 74 | 0 | 55 | 157 | 44 |
N.S. |
1 | 1.00 | 0.98 | 1.00 | 0.00 | 1.64 | 0.00 | 1.22 | 3.49 | 0.98 |
time (sec) |
N/A | 0.171 | 0.440 | 1.169 | 0.000 | 0.128 | 0.000 | 0.236 | 0.194 | 10.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 105 | 124 | 0 | 412 | 0 | 125 | 2230 | 0 |
N.S. |
1 | 1.00 | 1.09 | 1.29 | 0.00 | 4.29 | 0.00 | 1.30 | 23.23 | 0.00 |
time (sec) |
N/A | 0.244 | 0.718 | 1.158 | 0.000 | 0.203 | 0.000 | 0.261 | 0.649 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 171 | 145 | 243 | 0 | 657 | 0 | 220 | 451 | 0 |
N.S. |
1 | 1.15 | 0.97 | 1.63 | 0.00 | 4.41 | 0.00 | 1.48 | 3.03 | 0.00 |
time (sec) |
N/A | 0.356 | 0.950 | 1.247 | 0.000 | 0.301 | 0.000 | 0.252 | 0.232 | 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 | 219 | 239 | 210 | 369 | 0 | 869 | 0 | 467 | 696 | 0 |
N.S. |
1 | 1.09 | 0.96 | 1.68 | 0.00 | 3.97 | 0.00 | 2.13 | 3.18 | 0.00 |
time (sec) |
N/A | 0.484 | 1.548 | 1.196 | 0.000 | 0.463 | 0.000 | 0.250 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 322 | 293 | 460 | 0 | 1093 | 0 | 798 | 796 | 0 |
N.S. |
1 | 1.10 | 1.00 | 1.58 | 0.00 | 3.74 | 0.00 | 2.73 | 2.73 | 0.00 |
time (sec) |
N/A | 0.683 | 2.443 | 1.300 | 0.000 | 0.969 | 0.000 | 0.252 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 313 | 287 | 1246 | 0 | 1601 | 0 | 456 | 23 | 0 |
N.S. |
1 | 1.10 | 1.01 | 4.37 | 0.00 | 5.62 | 0.00 | 1.60 | 0.08 | 0.00 |
time (sec) |
N/A | 0.593 | 2.408 | 1.342 | 0.000 | 0.646 | 0.000 | 0.254 | 200.076 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 214 | 204 | 765 | 0 | 1061 | 0 | 312 | 23 | 0 |
N.S. |
1 | 1.13 | 1.08 | 4.05 | 0.00 | 5.61 | 0.00 | 1.65 | 0.12 | 0.00 |
time (sec) |
N/A | 0.403 | 1.760 | 1.224 | 0.000 | 0.613 | 0.000 | 0.265 | 200.032 | 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 | 94 | 94 | 110 | 132 | 0 | 248 | 0 | 195 | 503 | 131 |
N.S. |
1 | 1.00 | 1.17 | 1.40 | 0.00 | 2.64 | 0.00 | 2.07 | 5.35 | 1.39 |
time (sec) |
N/A | 0.233 | 1.209 | 1.341 | 0.000 | 0.460 | 0.000 | 0.259 | 0.301 | 10.898 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 114 | 114 | 129 | 0 | 244 | 0 | 196 | 401 | 128 |
N.S. |
1 | 0.99 | 0.99 | 1.12 | 0.00 | 2.12 | 0.00 | 1.70 | 3.49 | 1.11 |
time (sec) |
N/A | 0.245 | 1.033 | 1.230 | 0.000 | 0.510 | 0.000 | 0.255 | 0.272 | 10.813 |
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 | 90 | 90 | 99 | 123 | 0 | 245 | 0 | 193 | 435 | 121 |
N.S. |
1 | 1.00 | 1.10 | 1.37 | 0.00 | 2.72 | 0.00 | 2.14 | 4.83 | 1.34 |
time (sec) |
N/A | 0.212 | 1.160 | 1.161 | 0.000 | 0.480 | 0.000 | 0.247 | 0.360 | 10.697 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 208 | 191 | 253 | 0 | 1077 | 0 | 333 | 7582 | 0 |
N.S. |
1 | 1.13 | 1.04 | 1.38 | 0.00 | 5.85 | 0.00 | 1.81 | 41.21 | 0.00 |
time (sec) |
N/A | 0.380 | 1.607 | 1.214 | 0.000 | 1.146 | 0.000 | 0.256 | 17.965 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 317 | 284 | 467 | 0 | 1655 | 0 | 483 | 1284 | 0 |
N.S. |
1 | 1.14 | 1.03 | 1.69 | 0.00 | 5.97 | 0.00 | 1.74 | 4.64 | 0.00 |
time (sec) |
N/A | 0.612 | 2.332 | 1.225 | 0.000 | 1.606 | 0.000 | 0.265 | 0.340 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 366 | 408 | 424 | 780 | 0 | 2057 | 0 | 765 | 1748 | 0 |
N.S. |
1 | 1.11 | 1.16 | 2.13 | 0.00 | 5.62 | 0.00 | 2.09 | 4.78 | 0.00 |
time (sec) |
N/A | 0.844 | 4.079 | 1.261 | 0.000 | 4.431 | 0.000 | 0.276 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 141 | 215 | 258 | 0 | 550 | 0 | 436 | 1120 | 395 |
N.S. |
1 | 1.04 | 1.59 | 1.91 | 0.00 | 4.07 | 0.00 | 3.23 | 8.30 | 2.93 |
time (sec) |
N/A | 0.271 | 3.913 | 1.268 | 0.000 | 2.624 | 0.000 | 0.270 | 2.220 | 11.315 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 191 | 349 | 354 | 0 | 941 | 0 | 768 | 1920 | 599 |
N.S. |
1 | 1.06 | 1.93 | 1.96 | 0.00 | 5.20 | 0.00 | 4.24 | 10.61 | 3.31 |
time (sec) |
N/A | 0.313 | 8.132 | 1.207 | 0.000 | 13.605 | 0.000 | 0.253 | 41.342 | 11.794 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 40 | 38 | 48 | 47 | 0 | 56 | 71 | 41 |
N.S. |
1 | 1.00 | 2.11 | 2.00 | 2.53 | 2.47 | 0.00 | 2.95 | 3.74 | 2.16 |
time (sec) |
N/A | 0.166 | 0.122 | 0.981 | 0.026 | 0.074 | 0.000 | 0.259 | 0.268 | 11.485 |
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 | 548 | 441 | 638 | 871 | 0 | 265 | 0 | 0 | 292 | 0 |
N.S. |
1 | 0.80 | 1.16 | 1.59 | 0.00 | 0.48 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.742 | 27.302 | 1.921 | 0.000 | 0.100 | 0.000 | 0.000 | 1.651 | 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 | 476 | 362 | 550 | 795 | 0 | 215 | 0 | 0 | 138 | 0 |
N.S. |
1 | 0.76 | 1.16 | 1.67 | 0.00 | 0.45 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.547 | 26.269 | 1.582 | 0.000 | 0.097 | 0.000 | 0.000 | 1.429 | 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 | 336 | 491 | 769 | 0 | 190 | 0 | 0 | 142 | 0 |
N.S. |
1 | 0.78 | 1.14 | 1.78 | 0.00 | 0.44 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.475 | 24.498 | 1.698 | 0.000 | 0.091 | 0.000 | 0.000 | 8.405 | 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 | 456 | 348 | 499 | 791 | 0 | 198 | 0 | 0 | 160 | 0 |
N.S. |
1 | 0.76 | 1.09 | 1.73 | 0.00 | 0.43 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.515 | 24.859 | 1.860 | 0.000 | 0.101 | 0.000 | 0.000 | 3.109 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 527 | 0 | 576 | 842 | 0 | 255 | 0 | 0 | 254 | 0 |
N.S. |
1 | 0.00 | 1.09 | 1.60 | 0.00 | 0.48 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.000 | 26.209 | 2.293 | 0.000 | 0.089 | 0.000 | 0.000 | 1.006 | 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 | 634 | 502 | 660 | 903 | 0 | 325 | 0 | 0 | 220 | 0 |
N.S. |
1 | 0.79 | 1.04 | 1.42 | 0.00 | 0.51 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.847 | 27.221 | 2.678 | 0.000 | 0.100 | 0.000 | 0.000 | 3.846 | 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 | 247 | 277 | 178 | 137 | 0 | 68 | 0 | 0 | 169 | 0 |
N.S. |
1 | 1.12 | 0.72 | 0.55 | 0.00 | 0.28 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.489 | 21.261 | 1.110 | 0.000 | 0.081 | 0.000 | 0.000 | 0.492 | 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 | 224 | 249 | 170 | 132 | 0 | 63 | 0 | 0 | 151 | 0 |
N.S. |
1 | 1.11 | 0.76 | 0.59 | 0.00 | 0.28 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.459 | 21.204 | 1.102 | 0.000 | 0.087 | 0.000 | 0.000 | 0.623 | 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 | 201 | 221 | 165 | 127 | 0 | 58 | 0 | 0 | 133 | 0 |
N.S. |
1 | 1.10 | 0.82 | 0.63 | 0.00 | 0.29 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.409 | 21.193 | 1.062 | 0.000 | 0.084 | 0.000 | 0.000 | 0.554 | 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 | 178 | 193 | 163 | 122 | 0 | 53 | 0 | 0 | 115 | 0 |
N.S. |
1 | 1.08 | 0.92 | 0.69 | 0.00 | 0.30 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.372 | 21.209 | 1.124 | 0.000 | 0.080 | 0.000 | 0.000 | 0.553 | 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 | 155 | 165 | 158 | 117 | 0 | 48 | 0 | 0 | 97 | 0 |
N.S. |
1 | 1.06 | 1.02 | 0.75 | 0.00 | 0.31 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.330 | 21.197 | 1.067 | 0.000 | 0.077 | 0.000 | 0.000 | 0.681 | 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 | 155 | 165 | 153 | 113 | 0 | 55 | 0 | 0 | 102 | 0 |
N.S. |
1 | 1.06 | 0.99 | 0.73 | 0.00 | 0.35 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.337 | 21.210 | 1.032 | 0.000 | 0.088 | 0.000 | 0.000 | 0.676 | 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 | 153 | 163 | 153 | 115 | 0 | 59 | 0 | 0 | 111 | 0 |
N.S. |
1 | 1.07 | 1.00 | 0.75 | 0.00 | 0.39 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.328 | 21.206 | 0.945 | 0.000 | 0.075 | 0.000 | 0.000 | 0.515 | 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 | 176 | 189 | 153 | 124 | 0 | 64 | 0 | 0 | 174 | 0 |
N.S. |
1 | 1.07 | 0.87 | 0.70 | 0.00 | 0.36 | 0.00 | 0.00 | 0.99 | 0.00 |
time (sec) |
N/A | 0.381 | 21.211 | 1.078 | 0.000 | 0.086 | 0.000 | 0.000 | 0.478 | 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 | 201 | 217 | 155 | 129 | 0 | 69 | 0 | 0 | 168 | 0 |
N.S. |
1 | 1.08 | 0.77 | 0.64 | 0.00 | 0.34 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.410 | 21.201 | 0.948 | 0.000 | 0.083 | 0.000 | 0.000 | 0.523 | 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 | 224 | 245 | 160 | 134 | 0 | 74 | 0 | 0 | 245 | 0 |
N.S. |
1 | 1.09 | 0.71 | 0.60 | 0.00 | 0.33 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.450 | 21.205 | 1.019 | 0.000 | 0.120 | 0.000 | 0.000 | 0.711 | 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 | 252 | 282 | 183 | 142 | 0 | 73 | 0 | 0 | 187 | 0 |
N.S. |
1 | 1.12 | 0.73 | 0.56 | 0.00 | 0.29 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.521 | 21.242 | 1.119 | 0.000 | 0.082 | 0.000 | 0.000 | 0.441 | 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 | 229 | 254 | 178 | 137 | 0 | 68 | 0 | 0 | 169 | 0 |
N.S. |
1 | 1.11 | 0.78 | 0.60 | 0.00 | 0.30 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.465 | 21.230 | 1.049 | 0.000 | 0.086 | 0.000 | 0.000 | 0.441 | 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 | 206 | 226 | 173 | 132 | 0 | 63 | 0 | 0 | 151 | 0 |
N.S. |
1 | 1.10 | 0.84 | 0.64 | 0.00 | 0.31 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.423 | 21.226 | 1.053 | 0.000 | 0.080 | 0.000 | 0.000 | 0.429 | 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 | 183 | 198 | 165 | 127 | 0 | 58 | 0 | 0 | 133 | 0 |
N.S. |
1 | 1.08 | 0.90 | 0.69 | 0.00 | 0.32 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.377 | 21.214 | 1.178 | 0.000 | 0.087 | 0.000 | 0.000 | 0.415 | 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 | 183 | 198 | 163 | 123 | 0 | 65 | 0 | 0 | 134 | 0 |
N.S. |
1 | 1.08 | 0.89 | 0.67 | 0.00 | 0.36 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.377 | 21.218 | 1.056 | 0.000 | 0.089 | 0.000 | 0.000 | 0.486 | 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 | 172 | 189 | 163 | 125 | 0 | 69 | 0 | 0 | 145 | 0 |
N.S. |
1 | 1.10 | 0.95 | 0.73 | 0.00 | 0.40 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.374 | 21.250 | 1.014 | 0.000 | 0.081 | 0.000 | 0.000 | 0.403 | 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 | 181 | 194 | 163 | 129 | 0 | 69 | 0 | 0 | 190 | 0 |
N.S. |
1 | 1.07 | 0.90 | 0.71 | 0.00 | 0.38 | 0.00 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 0.382 | 21.217 | 0.941 | 0.000 | 0.085 | 0.000 | 0.000 | 0.481 | 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 | 183 | 193 | 163 | 129 | 0 | 69 | 0 | 0 | 200 | 0 |
N.S. |
1 | 1.05 | 0.89 | 0.70 | 0.00 | 0.38 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.398 | 21.219 | 1.003 | 0.000 | 0.081 | 0.000 | 0.000 | 0.550 | 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 | 206 | 222 | 160 | 134 | 0 | 74 | 0 | 0 | 261 | 0 |
N.S. |
1 | 1.08 | 0.78 | 0.65 | 0.00 | 0.36 | 0.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.433 | 21.216 | 1.034 | 0.000 | 0.085 | 0.000 | 0.000 | 0.731 | 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 | 229 | 250 | 165 | 139 | 0 | 79 | 0 | 0 | 249 | 0 |
N.S. |
1 | 1.09 | 0.72 | 0.61 | 0.00 | 0.34 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.467 | 21.218 | 1.043 | 0.000 | 0.076 | 0.000 | 0.000 | 0.830 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 278 | 170 | 144 | 0 | 84 | 0 | 0 | 249 | 0 |
N.S. |
1 | 1.10 | 0.67 | 0.57 | 0.00 | 0.33 | 0.00 | 0.00 | 0.99 | 0.00 |
time (sec) |
N/A | 0.509 | 21.229 | 0.960 | 0.000 | 0.083 | 0.000 | 0.000 | 1.128 | 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 | 401 | 291 | 444 | 538 | 0 | 144 | 0 | 0 | 71 | 0 |
N.S. |
1 | 0.73 | 1.11 | 1.34 | 0.00 | 0.36 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.421 | 23.955 | 1.543 | 0.000 | 0.098 | 0.000 | 0.000 | 1.119 | 0.000 |