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 | B | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 722 | 1467 | 823 | 1210 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 2.03 | 1.14 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 2.917 | 35.061 | 7.855 | 0.000 | 0.000 | 0.000 | 0.000 | 200.037 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 343 | 266 | 430 | 373 | 0 | 55 | 0 | 0 | 133 | 0 |
N.S. |
1 | 0.78 | 1.25 | 1.09 | 0.00 | 0.16 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.571 | 34.246 | 4.677 | 0.000 | 0.071 | 0.000 | 0.000 | 0.575 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 318 | 234 | 425 | 368 | 0 | 50 | 0 | 0 | 113 | 0 |
N.S. |
1 | 0.74 | 1.34 | 1.16 | 0.00 | 0.16 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.464 | 33.948 | 2.667 | 0.000 | 0.080 | 0.000 | 0.000 | 0.571 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 203 | 419 | 362 | 0 | 45 | 0 | 0 | 95 | 0 |
N.S. |
1 | 0.69 | 1.43 | 1.24 | 0.00 | 0.15 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.365 | 23.162 | 2.926 | 0.000 | 0.071 | 0.000 | 0.000 | 0.492 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 87 | 238 | 287 | 0 | 26 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.35 | 0.94 | 1.14 | 0.00 | 0.10 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.215 | 30.340 | 2.843 | 0.000 | 0.069 | 0.000 | 0.000 | 0.406 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 313 | 244 | 201 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.09 | 0.85 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.644 | 20.572 | 2.606 | 0.000 | 0.000 | 0.000 | 0.000 | 200.044 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 339 | 438 | 615 | 373 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.29 | 1.81 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.898 | 24.449 | 3.556 | 0.000 | 0.000 | 0.000 | 0.000 | 200.045 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 499 | 788 | 620 | 504 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.58 | 1.24 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.689 | 24.551 | 3.451 | 0.000 | 0.000 | 0.000 | 0.000 | 200.042 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 653 | 309 | 385 | 225 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.47 | 0.59 | 0.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.744 | 22.779 | 3.145 | 0.000 | 0.000 | 0.000 | 0.000 | 0.339 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 324 | 234 | 425 | 368 | 0 | 50 | 0 | 0 | 113 | 0 |
N.S. |
1 | 0.72 | 1.31 | 1.14 | 0.00 | 0.15 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.482 | 34.165 | 2.866 | 0.000 | 0.075 | 0.000 | 0.000 | 0.539 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 203 | 420 | 362 | 0 | 45 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.68 | 1.40 | 1.21 | 0.00 | 0.15 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.413 | 33.972 | 2.556 | 0.000 | 0.082 | 0.000 | 0.000 | 0.449 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 173 | 391 | 216 | 0 | 26 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.65 | 1.46 | 0.81 | 0.00 | 0.10 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.337 | 22.543 | 2.953 | 0.000 | 0.071 | 0.000 | 0.000 | 0.439 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 85 | 153 | 150 | 0 | 11 | 0 | 0 | 35 | 0 |
N.S. |
1 | 0.84 | 1.51 | 1.49 | 0.00 | 0.11 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.235 | 31.359 | 2.314 | 0.000 | 0.071 | 0.000 | 0.000 | 0.462 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 301 | 229 | 228 | 158 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 0.76 | 0.76 | 0.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.502 | 21.649 | 2.765 | 0.000 | 0.000 | 0.000 | 0.000 | 200.042 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 462 | 438 | 615 | 373 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 0.95 | 1.33 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.856 | 24.402 | 3.085 | 0.000 | 0.000 | 0.000 | 0.000 | 200.046 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 496 | 788 | 585 | 504 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.59 | 1.18 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 2.826 | 25.529 | 3.135 | 0.000 | 0.000 | 0.000 | 0.000 | 200.040 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 202 | 172 | 469 | 426 | 709 | 10479 | 1304 | 836 | 553 |
N.S. |
1 | 1.00 | 0.85 | 2.32 | 2.11 | 3.51 | 51.88 | 6.46 | 4.14 | 2.74 |
time (sec) |
N/A | 0.713 | 0.324 | 0.755 | 0.047 | 0.086 | 2.471 | 0.238 | 0.247 | 10.991 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 137 | 374 | 312 | 498 | 6195 | 921 | 582 | 419 |
N.S. |
1 | 1.00 | 0.85 | 2.32 | 1.94 | 3.09 | 38.48 | 5.72 | 3.61 | 2.60 |
time (sec) |
N/A | 0.602 | 0.231 | 0.698 | 0.046 | 0.083 | 1.516 | 0.211 | 0.260 | 10.818 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 142 | 281 | 215 | 342 | 3267 | 604 | 373 | 300 |
N.S. |
1 | 1.00 | 1.17 | 2.32 | 1.78 | 2.83 | 27.00 | 4.99 | 3.08 | 2.48 |
time (sec) |
N/A | 0.505 | 0.334 | 0.743 | 0.047 | 0.082 | 0.977 | 0.234 | 0.256 | 10.757 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 83 | 135 | 132 | 201 | 1416 | 350 | 206 | 201 |
N.S. |
1 | 1.00 | 1.01 | 1.65 | 1.61 | 2.45 | 17.27 | 4.27 | 2.51 | 2.45 |
time (sec) |
N/A | 0.425 | 0.145 | 0.682 | 0.034 | 0.086 | 0.610 | 0.242 | 0.259 | 10.653 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 72 | 0 | 0 | 0 | 308 | 0 | 271 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 3.71 | 0.00 | 3.27 | 0.00 |
time (sec) |
N/A | 0.396 | 0.143 | 0.000 | 0.000 | 0.000 | 3.062 | 0.000 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 87 | 69 | 0 | 0 | 0 | 250 | 0 | 207 | 0 |
N.S. |
1 | 1.07 | 0.85 | 0.00 | 0.00 | 0.00 | 3.09 | 0.00 | 2.56 | 0.00 |
time (sec) |
N/A | 0.372 | 0.127 | 0.000 | 0.000 | 0.000 | 2.939 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 119 | 83 | 0 | 0 | 0 | 1006 | 0 | 194 | 0 |
N.S. |
1 | 1.13 | 0.79 | 0.00 | 0.00 | 0.00 | 9.58 | 0.00 | 1.85 | 0.00 |
time (sec) |
N/A | 0.425 | 0.143 | 0.000 | 0.000 | 0.000 | 5.067 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 123 | 77 | 0 | 0 | 0 | 1527 | 0 | 572 | 0 |
N.S. |
1 | 1.03 | 0.65 | 0.00 | 0.00 | 0.00 | 12.83 | 0.00 | 4.81 | 0.00 |
time (sec) |
N/A | 0.449 | 0.196 | 0.000 | 0.000 | 0.000 | 13.504 | 0.000 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 290 | 290 | 320 | 0 | 0 | 0 | 0 | 0 | 1239 | 0 |
N.S. |
1 | 1.00 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.27 | 0.00 |
time (sec) |
N/A | 1.253 | 1.474 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.311 | 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 | 237 | 237 | 289 | 0 | 0 | 0 | 0 | 0 | 487 | 0 |
N.S. |
1 | 1.00 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.05 | 0.00 |
time (sec) |
N/A | 0.808 | 0.577 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.308 | 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 | 218 | 198 | 183 | 0 | 0 | 0 | 0 | 0 | 170 | 0 |
N.S. |
1 | 0.91 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.624 | 0.380 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.281 | 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 | 191 | 191 | 163 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.664 | 0.298 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.268 | 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 | 264 | 242 | 207 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 0.92 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.849 | 0.550 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.259 | 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 | 307 | 296 | 246 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.96 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.987 | 0.640 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 176 | 122 | 0 | 0 | 0 | 121 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 0.77 | 0.00 | 0.00 | 0.00 | 0.76 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.614 | 0.180 | 0.000 | 0.000 | 0.000 | 9.392 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 211 | 0 | 0 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.895 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 650 | 639 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 2.215 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.042 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 471 | 469 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.044 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.039 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 377 | 377 | 0 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.768 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.034 | 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 | 187 | 187 | 205 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.477 | 0.052 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 7.697 | 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) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 25 | 0 | 25 | 4722 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.00 | 1.09 | 205.30 | 1.09 |
time (sec) |
N/A | 0.266 | 3.098 | 0.873 | 0.076 | 0.092 | 0.000 | 0.215 | 0.547 | 10.879 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 25 | 0 | 25 | 8766 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.00 | 1.09 | 381.13 | 1.09 |
time (sec) |
N/A | 0.271 | 2.735 | 0.893 | 0.076 | 0.164 | 0.000 | 0.203 | 0.753 | 10.961 |
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 | 55 | 55 | 55 | 52 | 51 | 51 | 54 | 53 | 35 | 51 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.93 | 0.93 | 0.98 | 0.96 | 0.64 | 0.93 |
time (sec) |
N/A | 0.396 | 0.011 | 0.214 | 0.032 | 0.066 | 0.030 | 0.216 | 0.300 | 0.060 |
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 | 55 | 55 | 55 | 52 | 51 | 51 | 54 | 53 | 35 | 51 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.93 | 0.93 | 0.98 | 0.96 | 0.64 | 0.93 |
time (sec) |
N/A | 0.372 | 0.010 | 0.218 | 0.028 | 0.064 | 0.020 | 0.203 | 0.270 | 0.046 |
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 | 55 | 55 | 50 | 52 | 51 | 51 | 54 | 53 | 35 | 51 |
N.S. |
1 | 1.00 | 0.91 | 0.95 | 0.93 | 0.93 | 0.98 | 0.96 | 0.64 | 0.93 |
time (sec) |
N/A | 0.351 | 0.013 | 0.211 | 0.025 | 0.063 | 0.022 | 0.225 | 0.270 | 0.049 |
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 | 55 | 55 | 50 | 52 | 51 | 51 | 54 | 53 | 35 | 51 |
N.S. |
1 | 1.00 | 0.91 | 0.95 | 0.93 | 0.93 | 0.98 | 0.96 | 0.64 | 0.93 |
time (sec) |
N/A | 0.354 | 0.012 | 0.217 | 0.026 | 0.062 | 0.020 | 0.203 | 0.270 | 0.047 |
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 | 38 | 38 | 46 | 48 | 48 | 48 | 49 | 49 | 32 | 47 |
N.S. |
1 | 1.00 | 1.21 | 1.26 | 1.26 | 1.26 | 1.29 | 1.29 | 0.84 | 1.24 |
time (sec) |
N/A | 0.326 | 0.011 | 0.207 | 0.026 | 0.063 | 0.021 | 0.219 | 0.278 | 0.045 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 43 | 46 | 46 | 46 | 46 | 46 | 31 | 45 |
N.S. |
1 | 1.00 | 1.08 | 1.15 | 1.15 | 1.15 | 1.15 | 1.15 | 0.78 | 1.12 |
time (sec) |
N/A | 0.312 | 0.018 | 0.072 | 0.034 | 0.068 | 0.056 | 0.198 | 0.292 | 0.041 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 43 | 44 | 46 | 52 | 42 | 46 | 36 | 46 |
N.S. |
1 | 1.00 | 0.98 | 1.00 | 1.05 | 1.18 | 0.95 | 1.05 | 0.82 | 1.05 |
time (sec) |
N/A | 0.330 | 0.026 | 0.081 | 0.034 | 0.065 | 0.088 | 0.190 | 0.267 | 0.046 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 43 | 43 | 46 | 53 | 46 | 47 | 37 | 46 |
N.S. |
1 | 1.00 | 0.98 | 0.98 | 1.05 | 1.20 | 1.05 | 1.07 | 0.84 | 1.05 |
time (sec) |
N/A | 0.324 | 0.028 | 0.090 | 0.032 | 0.067 | 0.169 | 0.231 | 0.281 | 0.058 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 48 | 46 | 50 | 53 | 54 | 51 | 37 | 48 |
N.S. |
1 | 1.00 | 0.98 | 0.94 | 1.02 | 1.08 | 1.10 | 1.04 | 0.76 | 0.98 |
time (sec) |
N/A | 0.333 | 0.029 | 0.065 | 0.026 | 0.070 | 0.281 | 0.204 | 0.280 | 0.054 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 47 | 48 | 51 | 51 | 56 | 51 | 35 | 49 |
N.S. |
1 | 1.00 | 1.07 | 1.09 | 1.16 | 1.16 | 1.27 | 1.16 | 0.80 | 1.11 |
time (sec) |
N/A | 0.291 | 0.019 | 0.060 | 0.026 | 0.063 | 0.371 | 0.233 | 0.283 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 50 | 48 | 51 | 51 | 56 | 51 | 35 | 51 |
N.S. |
1 | 1.00 | 0.91 | 0.87 | 0.93 | 0.93 | 1.02 | 0.93 | 0.64 | 0.93 |
time (sec) |
N/A | 0.336 | 0.018 | 0.064 | 0.029 | 0.064 | 0.527 | 0.212 | 0.291 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 50 | 48 | 51 | 51 | 56 | 51 | 35 | 51 |
N.S. |
1 | 1.00 | 0.91 | 0.87 | 0.93 | 0.93 | 1.02 | 0.93 | 0.64 | 0.93 |
time (sec) |
N/A | 0.333 | 0.019 | 0.062 | 0.030 | 0.064 | 0.545 | 0.227 | 0.280 | 0.036 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 50 | 48 | 51 | 51 | 56 | 51 | 35 | 51 |
N.S. |
1 | 1.00 | 0.91 | 0.87 | 0.93 | 0.93 | 1.02 | 0.93 | 0.64 | 0.93 |
time (sec) |
N/A | 0.330 | 0.018 | 0.073 | 0.035 | 0.065 | 0.654 | 0.203 | 0.270 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 99 | 98 | 99 | 99 | 109 | 101 | 57 | 91 |
N.S. |
1 | 1.00 | 1.00 | 0.99 | 1.00 | 1.00 | 1.10 | 1.02 | 0.58 | 0.92 |
time (sec) |
N/A | 0.505 | 0.017 | 0.967 | 0.028 | 0.064 | 0.024 | 0.203 | 0.265 | 0.048 |
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 | 99 | 99 | 99 | 97 | 99 | 99 | 105 | 100 | 57 | 91 |
N.S. |
1 | 1.00 | 1.00 | 0.98 | 1.00 | 1.00 | 1.06 | 1.01 | 0.58 | 0.92 |
time (sec) |
N/A | 0.461 | 0.014 | 0.959 | 0.027 | 0.073 | 0.027 | 0.188 | 0.287 | 0.035 |
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 | 87 | 87 | 88 | 96 | 99 | 99 | 104 | 99 | 57 | 90 |
N.S. |
1 | 1.00 | 1.01 | 1.10 | 1.14 | 1.14 | 1.20 | 1.14 | 0.66 | 1.03 |
time (sec) |
N/A | 0.438 | 0.029 | 0.998 | 0.028 | 0.062 | 0.025 | 0.199 | 0.291 | 0.036 |
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 | 61 | 61 | 88 | 97 | 99 | 99 | 107 | 100 | 57 | 91 |
N.S. |
1 | 1.00 | 1.44 | 1.59 | 1.62 | 1.62 | 1.75 | 1.64 | 0.93 | 1.49 |
time (sec) |
N/A | 0.385 | 0.026 | 0.916 | 0.034 | 0.067 | 0.026 | 0.212 | 0.289 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 84 | 94 | 96 | 96 | 100 | 97 | 54 | 88 |
N.S. |
1 | 1.00 | 2.21 | 2.47 | 2.53 | 2.53 | 2.63 | 2.55 | 1.42 | 2.32 |
time (sec) |
N/A | 0.316 | 0.017 | 0.852 | 0.047 | 0.064 | 0.027 | 0.191 | 0.289 | 0.036 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 64 | 83 | 92 | 93 | 93 | 95 | 94 | 53 | 84 |
N.S. |
1 | 0.97 | 1.26 | 1.39 | 1.41 | 1.41 | 1.44 | 1.42 | 0.80 | 1.27 |
time (sec) |
N/A | 0.352 | 0.026 | 0.872 | 0.032 | 0.066 | 0.091 | 0.208 | 0.277 | 0.040 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 85 | 93 | 94 | 101 | 94 | 95 | 59 | 86 |
N.S. |
1 | 1.00 | 0.99 | 1.08 | 1.09 | 1.17 | 1.09 | 1.10 | 0.69 | 1.00 |
time (sec) |
N/A | 0.420 | 0.040 | 0.934 | 0.034 | 0.064 | 0.118 | 0.192 | 0.286 | 0.044 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 86 | 90 | 96 | 101 | 97 | 96 | 59 | 91 |
N.S. |
1 | 1.00 | 0.96 | 1.00 | 1.07 | 1.12 | 1.08 | 1.07 | 0.66 | 1.01 |
time (sec) |
N/A | 0.415 | 0.037 | 0.842 | 0.027 | 0.065 | 0.212 | 0.201 | 0.300 | 10.734 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 86 | 85 | 96 | 101 | 99 | 96 | 59 | 94 |
N.S. |
1 | 1.00 | 0.97 | 0.96 | 1.08 | 1.13 | 1.11 | 1.08 | 0.66 | 1.06 |
time (sec) |
N/A | 0.437 | 0.038 | 0.911 | 0.032 | 0.063 | 0.393 | 0.213 | 0.286 | 10.623 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 85 | 83 | 95 | 101 | 99 | 96 | 59 | 93 |
N.S. |
1 | 1.00 | 0.99 | 0.97 | 1.10 | 1.17 | 1.15 | 1.12 | 0.69 | 1.08 |
time (sec) |
N/A | 0.413 | 0.041 | 0.868 | 0.036 | 0.067 | 0.648 | 0.165 | 0.280 | 0.076 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 69 | 87 | 86 | 98 | 101 | 105 | 99 | 59 | 94 |
N.S. |
1 | 0.97 | 1.23 | 1.21 | 1.38 | 1.42 | 1.48 | 1.39 | 0.83 | 1.32 |
time (sec) |
N/A | 0.356 | 0.055 | 0.921 | 0.036 | 0.066 | 0.975 | 0.228 | 0.278 | 10.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 85 | 88 | 99 | 99 | 107 | 99 | 57 | 95 |
N.S. |
1 | 1.00 | 1.93 | 2.00 | 2.25 | 2.25 | 2.43 | 2.25 | 1.30 | 2.16 |
time (sec) |
N/A | 0.293 | 0.029 | 0.860 | 0.033 | 0.064 | 1.225 | 0.215 | 0.295 | 0.052 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 88 | 88 | 99 | 99 | 107 | 99 | 57 | 96 |
N.S. |
1 | 1.00 | 0.89 | 0.89 | 1.00 | 1.00 | 1.08 | 1.00 | 0.58 | 0.97 |
time (sec) |
N/A | 0.420 | 0.027 | 0.852 | 0.032 | 0.060 | 1.565 | 0.192 | 0.302 | 10.586 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 88 | 88 | 99 | 99 | 107 | 99 | 57 | 95 |
N.S. |
1 | 1.00 | 0.89 | 0.89 | 1.00 | 1.00 | 1.08 | 1.00 | 0.58 | 0.96 |
time (sec) |
N/A | 0.426 | 0.028 | 0.900 | 0.033 | 0.060 | 1.938 | 0.242 | 0.278 | 10.661 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 88 | 88 | 99 | 99 | 107 | 99 | 57 | 96 |
N.S. |
1 | 1.00 | 0.89 | 0.89 | 1.00 | 1.00 | 1.08 | 1.00 | 0.58 | 0.97 |
time (sec) |
N/A | 0.418 | 0.028 | 0.858 | 0.037 | 0.062 | 2.394 | 0.205 | 0.298 | 10.646 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 88 | 88 | 99 | 99 | 107 | 99 | 57 | 97 |
N.S. |
1 | 1.00 | 0.89 | 0.89 | 1.00 | 1.00 | 1.08 | 1.00 | 0.58 | 0.98 |
time (sec) |
N/A | 0.411 | 0.028 | 0.907 | 0.037 | 0.062 | 2.790 | 0.235 | 0.291 | 10.568 |
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 | 143 | 143 | 143 | 144 | 147 | 147 | 162 | 149 | 79 | 131 |
N.S. |
1 | 1.00 | 1.00 | 1.01 | 1.03 | 1.03 | 1.13 | 1.04 | 0.55 | 0.92 |
time (sec) |
N/A | 0.602 | 0.025 | 0.998 | 0.032 | 0.062 | 0.029 | 0.243 | 0.279 | 0.066 |
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 | 139 | 139 | 143 | 143 | 147 | 147 | 162 | 148 | 79 | 130 |
N.S. |
1 | 1.00 | 1.03 | 1.03 | 1.06 | 1.06 | 1.17 | 1.06 | 0.57 | 0.94 |
time (sec) |
N/A | 0.569 | 0.020 | 0.992 | 0.026 | 0.064 | 0.035 | 0.176 | 0.274 | 10.517 |
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 | 112 | 112 | 143 | 143 | 147 | 147 | 162 | 148 | 79 | 131 |
N.S. |
1 | 1.00 | 1.28 | 1.28 | 1.31 | 1.31 | 1.45 | 1.32 | 0.71 | 1.17 |
time (sec) |
N/A | 0.510 | 0.021 | 0.937 | 0.037 | 0.063 | 0.029 | 0.209 | 0.274 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 143 | 144 | 147 | 147 | 163 | 149 | 79 | 131 |
N.S. |
1 | 1.00 | 1.64 | 1.66 | 1.69 | 1.69 | 1.87 | 1.71 | 0.91 | 1.51 |
time (sec) |
N/A | 0.452 | 0.021 | 0.931 | 0.031 | 0.062 | 0.031 | 0.274 | 0.305 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 140 | 144 | 146 | 146 | 160 | 149 | 79 | 130 |
N.S. |
1 | 1.00 | 2.30 | 2.36 | 2.39 | 2.39 | 2.62 | 2.44 | 1.30 | 2.13 |
time (sec) |
N/A | 0.378 | 0.019 | 1.007 | 0.026 | 0.064 | 0.031 | 0.283 | 0.289 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 122 | 140 | 142 | 142 | 148 | 145 | 76 | 126 |
N.S. |
1 | 1.00 | 3.21 | 3.68 | 3.74 | 3.74 | 3.89 | 3.82 | 2.00 | 3.32 |
time (sec) |
N/A | 0.325 | 0.038 | 0.937 | 0.035 | 0.064 | 0.032 | 0.196 | 0.282 | 0.049 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 92 | 128 | 138 | 142 | 142 | 148 | 142 | 75 | 125 |
N.S. |
1 | 0.96 | 1.33 | 1.44 | 1.48 | 1.48 | 1.54 | 1.48 | 0.78 | 1.30 |
time (sec) |
N/A | 0.399 | 0.037 | 0.995 | 0.044 | 0.066 | 0.131 | 0.210 | 0.273 | 0.056 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 129 | 141 | 143 | 149 | 148 | 143 | 81 | 127 |
N.S. |
1 | 1.00 | 0.97 | 1.06 | 1.08 | 1.12 | 1.11 | 1.08 | 0.61 | 0.95 |
time (sec) |
N/A | 0.511 | 0.065 | 0.944 | 0.032 | 0.066 | 0.144 | 0.197 | 0.257 | 10.511 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 128 | 138 | 143 | 149 | 148 | 144 | 81 | 130 |
N.S. |
1 | 1.00 | 0.98 | 1.05 | 1.09 | 1.14 | 1.13 | 1.10 | 0.62 | 0.99 |
time (sec) |
N/A | 0.503 | 0.069 | 0.924 | 0.028 | 0.065 | 0.254 | 0.209 | 0.257 | 10.514 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 127 | 134 | 145 | 149 | 150 | 145 | 81 | 135 |
N.S. |
1 | 1.00 | 0.95 | 1.00 | 1.08 | 1.11 | 1.12 | 1.08 | 0.60 | 1.01 |
time (sec) |
N/A | 0.515 | 0.232 | 0.873 | 0.030 | 0.066 | 0.434 | 0.189 | 0.264 | 0.057 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 128 | 130 | 145 | 149 | 150 | 145 | 81 | 138 |
N.S. |
1 | 1.00 | 0.96 | 0.97 | 1.08 | 1.11 | 1.12 | 1.08 | 0.60 | 1.03 |
time (sec) |
N/A | 0.507 | 0.089 | 0.920 | 0.041 | 0.070 | 0.795 | 0.228 | 0.265 | 10.560 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 128 | 125 | 144 | 149 | 150 | 144 | 81 | 140 |
N.S. |
1 | 1.00 | 0.98 | 0.95 | 1.10 | 1.14 | 1.15 | 1.10 | 0.62 | 1.07 |
time (sec) |
N/A | 0.511 | 0.062 | 0.892 | 0.033 | 0.068 | 1.187 | 0.188 | 0.287 | 0.070 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 132 | 125 | 123 | 143 | 149 | 150 | 144 | 81 | 139 |
N.S. |
1 | 1.00 | 0.95 | 0.93 | 1.08 | 1.13 | 1.14 | 1.09 | 0.61 | 1.05 |
time (sec) |
N/A | 0.491 | 0.072 | 0.943 | 0.027 | 0.067 | 1.752 | 0.186 | 0.291 | 10.634 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 97 | 132 | 126 | 146 | 149 | 156 | 147 | 81 | 140 |
N.S. |
1 | 0.96 | 1.31 | 1.25 | 1.45 | 1.48 | 1.54 | 1.46 | 0.80 | 1.39 |
time (sec) |
N/A | 0.401 | 0.064 | 0.876 | 0.027 | 0.066 | 2.379 | 0.126 | 0.292 | 10.768 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 123 | 128 | 147 | 147 | 158 | 147 | 79 | 141 |
N.S. |
1 | 1.00 | 2.80 | 2.91 | 3.34 | 3.34 | 3.59 | 3.34 | 1.80 | 3.20 |
time (sec) |
N/A | 0.303 | 0.038 | 0.903 | 0.034 | 0.065 | 2.972 | 0.189 | 0.299 | 10.786 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 71 | 126 | 128 | 147 | 147 | 158 | 147 | 79 | 143 |
N.S. |
1 | 0.99 | 1.75 | 1.78 | 2.04 | 2.04 | 2.19 | 2.04 | 1.10 | 1.99 |
time (sec) |
N/A | 0.324 | 0.037 | 0.894 | 0.027 | 0.077 | 3.909 | 0.179 | 0.281 | 0.075 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 143 | 126 | 128 | 147 | 147 | 158 | 147 | 79 | 143 |
N.S. |
1 | 1.00 | 0.88 | 0.90 | 1.03 | 1.03 | 1.10 | 1.03 | 0.55 | 1.00 |
time (sec) |
N/A | 0.515 | 0.038 | 0.837 | 0.035 | 0.064 | 4.808 | 0.159 | 0.292 | 0.075 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 143 | 126 | 128 | 147 | 147 | 158 | 147 | 79 | 142 |
N.S. |
1 | 1.00 | 0.88 | 0.90 | 1.03 | 1.03 | 1.10 | 1.03 | 0.55 | 0.99 |
time (sec) |
N/A | 0.494 | 0.040 | 0.929 | 0.039 | 0.065 | 6.008 | 0.150 | 0.302 | 10.861 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 143 | 126 | 128 | 147 | 147 | 158 | 147 | 79 | 142 |
N.S. |
1 | 1.00 | 0.88 | 0.90 | 1.03 | 1.03 | 1.10 | 1.03 | 0.55 | 0.99 |
time (sec) |
N/A | 0.496 | 0.038 | 0.852 | 0.028 | 0.067 | 7.887 | 0.140 | 0.306 | 0.076 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 143 | 126 | 128 | 147 | 147 | 158 | 147 | 79 | 143 |
N.S. |
1 | 1.00 | 0.88 | 0.90 | 1.03 | 1.03 | 1.10 | 1.03 | 0.55 | 1.00 |
time (sec) |
N/A | 0.506 | 0.039 | 0.932 | 0.035 | 0.064 | 10.150 | 0.152 | 0.302 | 10.843 |
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 | 131 | 131 | 149 | 122 | 129 | 129 | 133 | 132 | 131 | 121 |
N.S. |
1 | 1.00 | 1.14 | 0.93 | 0.98 | 0.98 | 1.02 | 1.01 | 1.00 | 0.92 |
time (sec) |
N/A | 0.572 | 0.031 | 0.815 | 0.028 | 0.061 | 0.042 | 0.124 | 0.291 | 10.960 |
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 | 119 | 119 | 150 | 124 | 128 | 128 | 134 | 133 | 131 | 123 |
N.S. |
1 | 1.00 | 1.26 | 1.04 | 1.08 | 1.08 | 1.13 | 1.12 | 1.10 | 1.03 |
time (sec) |
N/A | 0.499 | 0.021 | 0.862 | 0.032 | 0.065 | 0.040 | 0.188 | 0.284 | 0.095 |
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 | 99 | 99 | 151 | 124 | 129 | 129 | 136 | 133 | 131 | 123 |
N.S. |
1 | 1.00 | 1.53 | 1.25 | 1.30 | 1.30 | 1.37 | 1.34 | 1.32 | 1.24 |
time (sec) |
N/A | 0.480 | 0.021 | 0.886 | 0.026 | 0.079 | 0.036 | 0.199 | 0.263 | 0.095 |
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 | 87 | 87 | 153 | 124 | 129 | 129 | 139 | 133 | 131 | 123 |
N.S. |
1 | 1.00 | 1.76 | 1.43 | 1.48 | 1.48 | 1.60 | 1.53 | 1.51 | 1.41 |
time (sec) |
N/A | 0.458 | 0.020 | 0.807 | 0.029 | 0.063 | 0.035 | 0.139 | 0.284 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 153 | 124 | 129 | 129 | 136 | 133 | 131 | 123 |
N.S. |
1 | 1.00 | 2.22 | 1.80 | 1.87 | 1.87 | 1.97 | 1.93 | 1.90 | 1.78 |
time (sec) |
N/A | 0.396 | 0.020 | 0.873 | 0.029 | 0.063 | 0.037 | 0.162 | 0.297 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 148 | 124 | 128 | 128 | 133 | 133 | 131 | 123 |
N.S. |
1 | 1.00 | 2.69 | 2.25 | 2.33 | 2.33 | 2.42 | 2.42 | 2.38 | 2.24 |
time (sec) |
N/A | 0.372 | 0.022 | 0.803 | 0.028 | 0.063 | 0.036 | 0.142 | 0.316 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 147 | 124 | 129 | 129 | 133 | 133 | 131 | 123 |
N.S. |
1 | 1.00 | 3.77 | 3.18 | 3.31 | 3.31 | 3.41 | 3.41 | 3.36 | 3.15 |
time (sec) |
N/A | 0.343 | 0.018 | 0.885 | 0.031 | 0.063 | 0.034 | 0.180 | 0.281 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 113 | 119 | 126 | 126 | 119 | 129 | 129 | 118 |
N.S. |
1 | 1.00 | 4.52 | 4.76 | 5.04 | 5.04 | 4.76 | 5.16 | 5.16 | 4.72 |
time (sec) |
N/A | 0.285 | 0.024 | 0.807 | 0.038 | 0.065 | 0.042 | 0.217 | 0.282 | 0.096 |
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 | 87 | 78 | 85 | 116 | 124 | 124 | 117 | 126 | 125 | 115 |
N.S. |
1 | 0.90 | 0.98 | 1.33 | 1.43 | 1.43 | 1.34 | 1.45 | 1.44 | 1.32 |
time (sec) |
N/A | 0.333 | 0.038 | 0.903 | 0.030 | 0.075 | 0.123 | 0.186 | 0.278 | 0.103 |
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 | 139 | 139 | 139 | 123 | 125 | 131 | 121 | 126 | 135 | 118 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.90 | 0.94 | 0.87 | 0.91 | 0.97 | 0.85 |
time (sec) |
N/A | 0.506 | 0.044 | 0.786 | 0.031 | 0.065 | 0.135 | 0.192 | 0.282 | 0.105 |
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 | 138 | 138 | 139 | 123 | 125 | 131 | 122 | 126 | 135 | 119 |
N.S. |
1 | 1.00 | 1.01 | 0.89 | 0.91 | 0.95 | 0.88 | 0.91 | 0.98 | 0.86 |
time (sec) |
N/A | 0.514 | 0.047 | 0.852 | 0.029 | 0.064 | 0.210 | 0.166 | 0.272 | 10.984 |
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 | 138 | 138 | 140 | 123 | 127 | 131 | 124 | 128 | 135 | 121 |
N.S. |
1 | 1.00 | 1.01 | 0.89 | 0.92 | 0.95 | 0.90 | 0.93 | 0.98 | 0.88 |
time (sec) |
N/A | 0.514 | 0.039 | 0.868 | 0.036 | 0.066 | 0.329 | 0.204 | 0.271 | 0.085 |
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 | 137 | 137 | 139 | 123 | 126 | 131 | 122 | 128 | 135 | 121 |
N.S. |
1 | 1.00 | 1.01 | 0.90 | 0.92 | 0.96 | 0.89 | 0.93 | 0.99 | 0.88 |
time (sec) |
N/A | 0.502 | 0.046 | 0.856 | 0.027 | 0.066 | 0.525 | 0.156 | 0.303 | 0.066 |