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 | C | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 355 | 281 | 0 | 0 | 0 | 0 | 0 | 143 | 0 |
N.S. |
1 | 1.39 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 2.083 | 0.412 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 340 | 491 | 526 | 0 | 0 | 0 | 0 | 0 | 317 | 0 |
N.S. |
1 | 1.44 | 1.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 3.397 | 0.711 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-2) | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 406 | 671 | 608 | 0 | 0 | 0 | 0 | 0 | 1064 | 0 |
N.S. |
1 | 1.65 | 1.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.62 | 0.00 |
time (sec) |
N/A | 5.047 | 0.905 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 381 | 695 | 556 | 416 | 0 | 0 | 0 | 0 | 398 | 0 |
N.S. |
1 | 1.82 | 1.46 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 5.310 | 1.027 | 4.714 | 0.000 | 0.000 | 0.000 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 323 | 499 | 534 | 256 | 0 | 0 | 0 | 0 | 160 | 0 |
N.S. |
1 | 1.54 | 1.65 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 3.497 | 0.448 | 4.244 | 0.000 | 0.000 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 242 | 345 | 369 | 155 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.43 | 1.52 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 2.148 | 0.249 | 4.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 316 | 471 | 547 | 243 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.49 | 1.73 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 3.473 | 0.425 | 4.324 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 372 | 641 | 568 | 370 | 0 | 0 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.72 | 1.53 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 4.884 | 0.702 | 4.381 | 0.000 | 0.000 | 0.000 | 0.000 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 34 | 32 | 34 | 35 | 0 | 0 | 34 | 34 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 1.09 | 0.00 | 0.00 | 1.06 | 1.06 |
time (sec) |
N/A | 0.451 | 0.269 | 1.250 | 0.092 | 0.100 | 0.000 | 0.000 | 200.048 | 26.299 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 305 | 288 | 242 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.331 | 1.843 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 199 | 185 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.076 | 0.612 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 110 | 114 | 0 | 0 | 118 | 0 | 0 | 711 | 0 |
N.S. |
1 | 0.96 | 0.99 | 0.00 | 0.00 | 1.03 | 0.00 | 0.00 | 6.18 | 0.00 |
time (sec) |
N/A | 0.758 | 0.406 | 0.000 | 0.000 | 0.100 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 32 | 32 | 41 | 0 | 32 | 43 | 31 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.03 | 1.32 | 0.00 | 1.03 | 1.39 | 1.00 |
time (sec) |
N/A | 0.403 | 0.014 | 1.276 | 0.035 | 0.083 | 0.000 | 0.122 | 0.184 | 26.878 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 34 | 32 | 34 | 43 | 37 | 34 | 34 | 34 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 1.34 | 1.16 | 1.06 | 1.06 | 1.06 |
time (sec) |
N/A | 0.473 | 0.310 | 1.310 | 0.115 | 0.095 | 102.269 | 0.138 | 200.031 | 27.381 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 34 | 32 | 34 | 68 | 0 | 0 | 62 | 34 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 2.12 | 0.00 | 0.00 | 1.94 | 1.06 |
time (sec) |
N/A | 0.471 | 1.218 | 1.234 | 0.146 | 0.086 | 0.000 | 0.000 | 0.243 | 26.496 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 34 | 32 | 34 | 92 | 0 | 34 | 34 | 34 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 2.88 | 0.00 | 1.06 | 1.06 | 1.06 |
time (sec) |
N/A | 0.463 | 1.083 | 1.230 | 0.167 | 0.093 | 0.000 | 0.176 | 200.016 | 26.437 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 402 | 402 | 379 | 1208 | 0 | 0 | 0 | 0 | 1082 | 0 |
N.S. |
1 | 1.00 | 0.94 | 3.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.69 | 0.00 |
time (sec) |
N/A | 1.147 | 0.589 | 3.986 | 0.000 | 0.000 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 241 | 224 | 721 | 0 | 0 | 0 | 0 | 620 | 0 |
N.S. |
1 | 1.00 | 0.93 | 2.99 | 0.00 | 0.00 | 0.00 | 0.00 | 2.57 | 0.00 |
time (sec) |
N/A | 0.819 | 0.284 | 2.430 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 110 | 394 | 0 | 0 | 0 | 0 | 298 | 0 |
N.S. |
1 | 1.00 | 0.92 | 3.31 | 0.00 | 0.00 | 0.00 | 0.00 | 2.50 | 0.00 |
time (sec) |
N/A | 0.591 | 0.118 | 1.596 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 62 | 217 | 0 | 0 | 0 | 0 | 111 | 0 |
N.S. |
1 | 1.00 | 0.98 | 3.44 | 0.00 | 0.00 | 0.00 | 0.00 | 1.76 | 0.00 |
time (sec) |
N/A | 0.482 | 0.005 | 1.052 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 155 | 111 | 378 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 0.72 | 2.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.721 | 0.075 | 2.701 | 0.000 | 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 | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 252 | 196 | 494 | 0 | 0 | 0 | 0 | 100 | 0 |
N.S. |
1 | 1.00 | 0.78 | 1.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.899 | 0.178 | 3.763 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 402 | 402 | 311 | 771 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 0.77 | 1.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.174 | 0.332 | 6.534 | 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 | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 469 | 469 | 876 | 0 | 0 | 0 | 0 | 0 | 1408 | 0 |
N.S. |
1 | 1.00 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.00 | 0.00 |
time (sec) |
N/A | 1.519 | 0.541 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 215 | 460 | 0 | 0 | 0 | 0 | 0 | 639 | 0 |
N.S. |
1 | 1.00 | 2.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.97 | 0.00 |
time (sec) |
N/A | 0.894 | 0.400 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 106 | 194 | 737 | 0 | 0 | 0 | 0 | 219 | 0 |
N.S. |
1 | 0.95 | 1.75 | 6.64 | 0.00 | 0.00 | 0.00 | 0.00 | 1.97 | 0.00 |
time (sec) |
N/A | 0.793 | 0.080 | 1.372 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 264 | 353 | 1427 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.34 | 5.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.099 | 0.294 | 7.827 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 427 | 427 | 630 | 0 | 0 | 0 | 0 | 0 | 163 | 0 |
N.S. |
1 | 1.00 | 1.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 1.415 | 0.603 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 660 | 660 | 1521 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.001 | 0.886 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 308 | 799 | 0 | 0 | 0 | 0 | 0 | 1041 | 0 |
N.S. |
1 | 1.00 | 2.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.38 | 0.00 |
time (sec) |
N/A | 1.120 | 0.442 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 149 | 335 | 1396 | 0 | 0 | 0 | 0 | 331 | 0 |
N.S. |
1 | 0.94 | 2.12 | 8.84 | 0.00 | 0.00 | 0.00 | 0.00 | 2.09 | 0.00 |
time (sec) |
N/A | 1.036 | 0.155 | 2.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 372 | 372 | 599 | 2696 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.61 | 7.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.439 | 0.448 | 13.373 | 0.000 | 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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 602 | 602 | 1025 | 0 | 0 | 0 | 0 | 0 | 226 | 0 |
N.S. |
1 | 1.00 | 1.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 1.964 | 1.042 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 31 | 37 | 24 | 31 | 434 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 1.28 | 0.83 | 1.07 | 14.97 | 1.07 |
time (sec) |
N/A | 0.689 | 0.172 | 0.082 | 0.137 | 0.075 | 2.579 | 0.120 | 0.212 | 26.607 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 26 | 31 | 20 | 26 | 211 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.29 | 0.83 | 1.08 | 8.79 | 1.08 |
time (sec) |
N/A | 0.338 | 0.012 | 0.026 | 0.109 | 0.088 | 1.192 | 0.112 | 0.192 | 26.413 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 31 | 33 | 61 | 26 | 33 | 87 | 33 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 1.97 | 0.84 | 1.06 | 2.81 | 1.06 |
time (sec) |
N/A | 0.659 | 0.896 | 1.266 | 0.120 | 0.089 | 2.799 | 0.114 | 0.203 | 27.459 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 31 | 33 | 111 | 27 | 33 | 151 | 33 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 3.58 | 0.87 | 1.06 | 4.87 | 1.06 |
time (sec) |
N/A | 0.767 | 2.764 | 0.065 | 0.110 | 0.091 | 7.649 | 0.121 | 0.187 | 26.709 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 223 | 69 | 26 | 31 | 1620 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 7.69 | 2.38 | 0.90 | 1.07 | 55.86 | 1.07 |
time (sec) |
N/A | 0.754 | 0.828 | 0.032 | 0.171 | 0.096 | 8.387 | 0.123 | 0.223 | 26.496 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 188 | 63 | 22 | 26 | 805 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 7.83 | 2.62 | 0.92 | 1.08 | 33.54 | 1.08 |
time (sec) |
N/A | 0.329 | 0.049 | 0.027 | 0.116 | 0.104 | 2.945 | 0.117 | 0.202 | 26.406 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 31 | 488 | 118 | 27 | 33 | 180 | 33 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 15.74 | 3.81 | 0.87 | 1.06 | 5.81 | 1.06 |
time (sec) |
N/A | 0.628 | 7.848 | 0.066 | 0.135 | 0.090 | 9.053 | 0.165 | 0.203 | 26.465 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | F(-1) | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 0 | 723 | 203 | 29 | 33 | 298 | 33 |
N.S. |
1 | 1.00 | 1.06 | 0.00 | 23.32 | 6.55 | 0.94 | 1.06 | 9.61 | 1.06 |
time (sec) |
N/A | 0.746 | 16.916 | 0.000 | 0.177 | 0.106 | 46.914 | 0.178 | 0.184 | 26.853 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 281 | 281 | 241 | 507 | 0 | 0 | 0 | 0 | 399 | 0 |
N.S. |
1 | 1.00 | 0.86 | 1.80 | 0.00 | 0.00 | 0.00 | 0.00 | 1.42 | 0.00 |
time (sec) |
N/A | 0.933 | 0.268 | 1.931 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 181 | 170 | 388 | 0 | 0 | 0 | 0 | 280 | 0 |
N.S. |
1 | 1.00 | 0.94 | 2.14 | 0.00 | 0.00 | 0.00 | 0.00 | 1.55 | 0.00 |
time (sec) |
N/A | 0.714 | 0.150 | 1.616 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 95 | 284 | 0 | 0 | 0 | 0 | 174 | 0 |
N.S. |
1 | 1.00 | 0.91 | 2.73 | 0.00 | 0.00 | 0.00 | 0.00 | 1.67 | 0.00 |
time (sec) |
N/A | 0.553 | 0.082 | 1.442 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 62 | 217 | 0 | 0 | 0 | 0 | 111 | 0 |
N.S. |
1 | 1.00 | 0.98 | 3.44 | 0.00 | 0.00 | 0.00 | 0.00 | 1.76 | 0.00 |
time (sec) |
N/A | 0.464 | 0.007 | 0.994 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 85 | 276 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 0.79 | 2.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.581 | 0.047 | 1.260 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 162 | 141 | 338 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.00 | 0.87 | 2.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.712 | 0.093 | 1.622 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 250 | 208 | 429 | 0 | 0 | 0 | 0 | 82 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.893 | 0.244 | 1.974 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 265 | 265 | 220 | 550 | 0 | 0 | 0 | 0 | 1405 | 0 |
N.S. |
1 | 1.00 | 0.83 | 2.08 | 0.00 | 0.00 | 0.00 | 0.00 | 5.30 | 0.00 |
time (sec) |
N/A | 0.925 | 0.295 | 1.889 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 186 | 153 | 435 | 0 | 0 | 0 | 0 | 1165 | 0 |
N.S. |
1 | 1.00 | 0.82 | 2.34 | 0.00 | 0.00 | 0.00 | 0.00 | 6.26 | 0.00 |
time (sec) |
N/A | 0.750 | 0.150 | 1.632 | 0.000 | 0.000 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 114 | 311 | 0 | 0 | 0 | 0 | 896 | 0 |
N.S. |
1 | 1.00 | 0.83 | 2.25 | 0.00 | 0.00 | 0.00 | 0.00 | 6.49 | 0.00 |
time (sec) |
N/A | 0.633 | 0.098 | 1.563 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 70 | 57 | 127 | 85 | 95 | 333 | 88 | 135 | 84 |
N.S. |
1 | 0.95 | 0.77 | 1.72 | 1.15 | 1.28 | 4.50 | 1.19 | 1.82 | 1.14 |
time (sec) |
N/A | 0.348 | 0.057 | 1.177 | 0.043 | 0.091 | 2.812 | 0.116 | 0.169 | 26.662 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 179 | 152 | 354 | 0 | 0 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.749 | 0.120 | 1.406 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 240 | 199 | 437 | 0 | 0 | 0 | 0 | 165 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.873 | 0.204 | 2.287 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 335 | 335 | 269 | 549 | 0 | 0 | 0 | 0 | 186 | 0 |
N.S. |
1 | 1.00 | 0.80 | 1.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 1.052 | 0.420 | 3.233 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 397 | 397 | 331 | 549 | 0 | 0 | 0 | 0 | 346 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 1.311 | 0.336 | 3.622 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 278 | 243 | 431 | 0 | 0 | 0 | 0 | 211 | 0 |
N.S. |
1 | 1.00 | 0.87 | 1.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.959 | 0.188 | 1.862 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 203 | 172 | 356 | 0 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.718 | 0.053 | 1.335 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 245 | 224 | 415 | 0 | 0 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.00 | 0.91 | 1.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.960 | 0.103 | 1.325 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 331 | 331 | 279 | 499 | 0 | 0 | 0 | 0 | 140 | 0 |
N.S. |
1 | 1.00 | 0.84 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 1.122 | 0.189 | 2.500 | 0.000 | 0.000 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 369 | 369 | 339 | 606 | 0 | 0 | 0 | 0 | 273 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 1.118 | 0.364 | 2.368 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 276 | 263 | 491 | 0 | 0 | 0 | 0 | 155 | 0 |
N.S. |
1 | 1.00 | 0.95 | 1.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.941 | 0.174 | 1.658 | 0.000 | 0.000 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 239 | 184 | 405 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 0.77 | 1.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.730 | 0.074 | 1.526 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 290 | 290 | 280 | 492 | 0 | 0 | 0 | 0 | 64 | 0 |
N.S. |
1 | 1.00 | 0.97 | 1.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.979 | 0.223 | 2.292 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 388 | 388 | 350 | 598 | 0 | 0 | 0 | 0 | 179 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 1.119 | 0.412 | 3.670 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 417 | 417 | 530 | 624 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.27 | 1.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.356 | 1.498 | 3.109 | 0.000 | 0.000 | 0.000 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 344 | 344 | 455 | 496 | 0 | 0 | 0 | 0 | 1514 | 0 |
N.S. |
1 | 1.00 | 1.32 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | 4.40 | 0.00 |
time (sec) |
N/A | 1.143 | 1.190 | 2.363 | 0.000 | 0.000 | 0.000 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 120 | 165 | 765 | 130 | 373 | 0 | 194 | 231 | 366 |
N.S. |
1 | 0.86 | 1.19 | 5.50 | 0.94 | 2.68 | 0.00 | 1.40 | 1.66 | 2.63 |
time (sec) |
N/A | 0.449 | 0.216 | 2.904 | 0.121 | 0.118 | 0.000 | 0.138 | 0.179 | 27.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 383 | 383 | 521 | 556 | 0 | 0 | 0 | 0 | 150 | 0 |
N.S. |
1 | 1.00 | 1.36 | 1.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 1.256 | 1.375 | 1.763 | 0.000 | 0.000 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 460 | 460 | 596 | 656 | 0 | 0 | 0 | 0 | 767 | 0 |
N.S. |
1 | 1.00 | 1.30 | 1.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.67 | 0.00 |
time (sec) |
N/A | 1.417 | 1.711 | 5.859 | 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 | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 534 | 534 | 433 | 1619 | 0 | 0 | 0 | 0 | 699 | 0 |
N.S. |
1 | 1.00 | 0.81 | 3.03 | 0.00 | 0.00 | 0.00 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 1.891 | 0.851 | 2.599 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 491 | 491 | 382 | 1521 | 0 | 0 | 0 | 0 | 518 | 0 |
N.S. |
1 | 1.00 | 0.78 | 3.10 | 0.00 | 0.00 | 0.00 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 1.721 | 0.671 | 2.674 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 503 | 503 | 407 | 1406 | 0 | 0 | 0 | 0 | 149 | 0 |
N.S. |
1 | 1.00 | 0.81 | 2.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 1.268 | 0.972 | 2.655 | 0.000 | 0.000 | 0.000 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 560 | 560 | 475 | 1619 | 0 | 0 | 0 | 0 | 629 | 0 |
N.S. |
1 | 1.00 | 0.85 | 2.89 | 0.00 | 0.00 | 0.00 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 1.929 | 0.806 | 4.820 | 0.000 | 0.000 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 326 | 313 | 275 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 0.96 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.546 | 0.241 | 0.000 | 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 | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 506 | 349 | 0 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.771 | 0.000 | 0.000 | 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 | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 295 | 307 | 0 | 0 | 0 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.06 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 1.542 | 0.040 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 510 | 336 | 631 | 0 | 0 | 0 | 0 | 0 | 58 | 0 |
N.S. |
1 | 0.66 | 1.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.900 | 14.949 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 27 | 20 | 120 | 21 | 0 | 0 | 28 | 19 |
N.S. |
1 | 1.00 | 1.12 | 0.83 | 5.00 | 0.88 | 0.00 | 0.00 | 1.17 | 0.79 |
time (sec) |
N/A | 0.345 | 0.011 | 2.092 | 0.047 | 0.096 | 0.000 | 0.000 | 0.161 | 26.444 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 81 | 62 | 119 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.00 | 1.93 | 1.48 | 2.83 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.463 | 0.022 | 1.852 | 0.037 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 82 | 44 | 0 | 43 | 0 | 0 | 63 | 43 |
N.S. |
1 | 1.00 | 2.00 | 1.07 | 0.00 | 1.05 | 0.00 | 0.00 | 1.54 | 1.05 |
time (sec) |
N/A | 0.458 | 0.042 | 2.060 | 0.000 | 0.095 | 0.000 | 0.000 | 0.170 | 28.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 80 | 85 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.00 | 1.70 | 1.81 | 0.00 | 0.00 | 0.00 | 0.00 | 1.32 | 0.00 |
time (sec) |
N/A | 0.475 | 0.035 | 2.057 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 371 | 371 | 376 | 153 | 0 | 0 | 0 | 0 | 158 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 1.319 | 0.303 | 1.639 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 292 | 297 | 77 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.878 | 0.053 | 1.402 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 324 | 324 | 330 | 106 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.054 | 0.105 | 2.045 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 414 | 414 | 405 | 186 | 0 | 0 | 0 | 0 | 92 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.250 | 0.235 | 2.419 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 416 | 416 | 403 | 148 | 0 | 0 | 0 | 0 | 72 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 1.515 | 0.394 | 1.487 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 383 | 383 | 369 | 127 | 0 | 0 | 0 | 0 | 103 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 1.167 | 0.188 | 1.438 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 359 | 359 | 297 | 86 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.011 | 0.100 | 1.430 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 359 | 359 | 294 | 94 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.882 | 0.088 | 1.369 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 398 | 398 | 378 | 124 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.293 | 0.208 | 1.608 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 423 | 423 | 371 | 150 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.205 | 0.287 | 1.633 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 498 | 498 | 480 | 175 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.779 | 0.263 | 1.878 | 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 | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 401 | 401 | 383 | 85 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.285 | 0.084 | 1.454 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 433 | 433 | 416 | 114 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.446 | 0.113 | 2.193 | 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 | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 530 | 530 | 484 | 163 | 0 | 0 | 0 | 0 | 72 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 1.613 | 0.280 | 1.540 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 473 | 473 | 348 | 102 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 0.74 | 0.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.339 | 0.123 | 1.452 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 537 | 537 | 506 | 158 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.598 | 0.255 | 1.704 | 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 | A | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 521 | 521 | 458 | 145 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.724 | 0.280 | 1.501 | 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 | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 497 | 497 | 464 | 94 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.424 | 0.363 | 1.438 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |