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 | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 34 | 32 | 0 | 34 | 0 | 0 | 34 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 0.00 | 1.06 | 0.00 | 0.00 | 1.06 |
time (sec) |
N/A | 0.447 | 0.900 | 0.428 | 0.000 | 0.313 | 0.000 | 0.000 | 1.666 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 231 | 231 | 223 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.571 | 0.469 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 149 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.460 | 0.287 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 77 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.327 | 0.111 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 16 | 15 | 25 | 34 | 16 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 1.67 | 2.27 | 1.07 | 1.00 |
time (sec) |
N/A | 0.163 | 0.003 | 1.417 | 0.197 | 0.308 | 0.534 | 0.526 | 1.438 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 34 | 32 | 75 | 33 | 0 | 34 | 34 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 2.34 | 1.03 | 0.00 | 1.06 | 1.06 |
time (sec) |
N/A | 0.437 | 0.172 | 0.045 | 0.318 | 0.315 | 0.000 | 0.426 | 1.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 34 | 32 | 240 | 57 | 0 | 34 | 34 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 7.50 | 1.78 | 0.00 | 1.06 | 1.06 |
time (sec) |
N/A | 0.471 | 0.450 | 0.063 | 0.330 | 0.393 | 0.000 | 0.398 | 1.472 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 34 | 32 | 1170 | 81 | 0 | 34 | 34 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 36.56 | 2.53 | 0.00 | 1.06 | 1.06 |
time (sec) |
N/A | 0.441 | 0.966 | 0.073 | 0.403 | 0.739 | 0.000 | 0.436 | 1.547 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 272 | 272 | 230 | 271 | 1115 | 655 | 411 | 766 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.00 | 4.10 | 2.41 | 1.51 | 2.82 | 0.00 |
time (sec) |
N/A | 0.524 | 0.148 | 12.893 | 0.243 | 0.320 | 24.793 | 0.354 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 125 | 115 | 129 | 530 | 267 | 216 | 286 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.03 | 4.24 | 2.14 | 1.73 | 2.29 | 0.00 |
time (sec) |
N/A | 0.344 | 0.075 | 2.968 | 0.226 | 0.324 | 13.323 | 0.324 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 41 | 47 | 186 | 81 | 65 | 73 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.15 | 4.54 | 1.98 | 1.59 | 1.78 | 0.00 |
time (sec) |
N/A | 0.231 | 0.026 | 0.817 | 0.211 | 0.333 | 8.604 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 13 | 13 | 65 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 4.33 | 0.87 | 0.87 |
time (sec) |
N/A | 0.146 | 0.002 | 0.485 | 0.204 | 0.315 | 1.171 | 0.307 | 1.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 28 | 28 | 30 | 28 | 30 | 29 | 24 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 1.04 | 0.86 | 1.07 | 1.07 |
time (sec) |
N/A | 0.390 | 1.297 | 0.046 | 0.258 | 0.376 | 5.883 | 0.337 | 1.426 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 28 | 28 | 30 | 28 | 343 | 51 | 26 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 12.25 | 1.82 | 0.93 | 1.07 | 1.07 |
time (sec) |
N/A | 0.388 | 1.127 | 0.060 | 0.275 | 0.354 | 10.042 | 0.375 | 1.533 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 28 | 28 | 30 | 28 | 1467 | 73 | 26 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 52.39 | 2.61 | 0.93 | 1.07 | 1.07 |
time (sec) |
N/A | 0.383 | 2.264 | 0.050 | 0.385 | 0.395 | 15.993 | 1.208 | 1.794 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 0 | 0 | 42 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 1.62 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.295 | 0.064 | 0.000 | 0.000 | 0.323 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F(-2) | B | B | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 204 | 0 | 65 | 61 | 0 | 20 |
N.S. |
1 | 1.00 | 1.00 | 9.27 | 0.00 | 2.95 | 2.77 | 0.00 | 0.91 |
time (sec) |
N/A | 0.291 | 0.031 | 0.081 | 0.000 | 0.357 | 66.404 | 0.000 | 1.911 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F(-2) | B | B | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 135 | 0 | 42 | 39 | 0 | 20 |
N.S. |
1 | 1.00 | 1.00 | 6.14 | 0.00 | 1.91 | 1.77 | 0.00 | 0.91 |
time (sec) |
N/A | 0.241 | 0.025 | 187.626 | 0.000 | 0.378 | 20.866 | 0.000 | 2.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 17 | 16 | 28 | 49 | 17 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.75 | 3.06 | 1.06 | 1.00 |
time (sec) |
N/A | 0.182 | 0.015 | 2.406 | 0.192 | 0.347 | 1.421 | 0.315 | 1.470 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 213 | 22 | 18 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 12.53 | 1.29 | 1.06 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.296 | 0.235 | 5.581 | 0.316 | 0.316 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 68 | 21 | 21 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 3.40 | 1.05 | 1.05 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.296 | 0.028 | 15.772 | 0.352 | 0.324 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 68 | 49 | 45 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 3.09 | 2.23 | 2.05 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.308 | 0.030 | 116.322 | 0.429 | 0.337 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 53 | 211 | 195 | 70 | 198 | 52 |
N.S. |
1 | 1.00 | 1.00 | 2.65 | 10.55 | 9.75 | 3.50 | 9.90 | 2.60 |
time (sec) |
N/A | 0.341 | 0.016 | 2.341 | 0.214 | 0.316 | 3.668 | 0.359 | 1.596 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 38 | 35 | 74 | 89 | 51 | 90 | 18 |
N.S. |
1 | 1.00 | 1.90 | 1.75 | 3.70 | 4.45 | 2.55 | 4.50 | 0.90 |
time (sec) |
N/A | 0.276 | 0.007 | 0.862 | 0.192 | 0.328 | 2.518 | 0.497 | 1.524 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 15 | 14 | 21 | 73 | 20 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 1.50 | 5.21 | 1.43 | 1.00 |
time (sec) |
N/A | 0.151 | 0.003 | 0.312 | 0.183 | 0.334 | 1.213 | 0.337 | 1.488 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 16 | 32 | 28 | 24 | 28 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 2.13 | 1.87 | 1.60 | 1.87 | 1.07 |
time (sec) |
N/A | 0.238 | 0.082 | 0.264 | 0.229 | 0.307 | 0.730 | 0.332 | 1.648 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 19 | 31 | 31 | 15 | 31 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.72 | 1.72 | 0.83 | 1.72 | 1.00 |
time (sec) |
N/A | 0.310 | 0.012 | 0.474 | 0.234 | 0.297 | 11.296 | 0.331 | 1.539 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 19 | 95 | 101 | 0 | 306 | 39 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 4.75 | 5.05 | 0.00 | 15.30 | 1.95 |
time (sec) |
N/A | 0.330 | 0.012 | 1.161 | 0.267 | 0.314 | 0.000 | 0.331 | 1.481 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 23 | 216 | 26 | 23 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.21 | 11.37 | 1.37 | 1.21 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.463 | 0.746 | 24.973 | 0.316 | 0.299 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 42 | 40 | 0 | 42 | 0 | 0 | 42 |
N.S. |
1 | 1.00 | 1.05 | 1.00 | 0.00 | 1.05 | 0.00 | 0.00 | 1.05 |
time (sec) |
N/A | 0.473 | 1.460 | 0.530 | 0.000 | 0.321 | 0.000 | 0.000 | 1.889 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 331 | 279 | 445 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.84 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.763 | 1.098 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 235 | 200 | 298 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.85 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.630 | 0.670 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 139 | 124 | 157 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.89 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.369 | 0.299 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 26 | 25 | 42 | 44 | 26 | 25 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.00 | 1.68 | 1.76 | 1.04 | 1.00 |
time (sec) |
N/A | 0.184 | 0.018 | 0.659 | 0.194 | 0.338 | 1.419 | 0.358 | 1.541 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 42 | 40 | 95 | 41 | 0 | 42 | 42 |
N.S. |
1 | 1.00 | 1.05 | 1.00 | 2.38 | 1.02 | 0.00 | 1.05 | 1.05 |
time (sec) |
N/A | 0.444 | 6.712 | 0.095 | 0.327 | 0.309 | 0.000 | 0.381 | 1.638 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 42 | 40 | 312 | 65 | 0 | 42 | 42 |
N.S. |
1 | 1.00 | 1.05 | 1.00 | 7.80 | 1.62 | 0.00 | 1.05 | 1.05 |
time (sec) |
N/A | 0.453 | 20.804 | 0.080 | 0.380 | 0.350 | 0.000 | 0.429 | 2.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 42 | 40 | 1583 | 89 | 0 | 42 | 42 |
N.S. |
1 | 1.00 | 1.05 | 1.00 | 39.58 | 2.22 | 0.00 | 1.05 | 1.05 |
time (sec) |
N/A | 0.458 | 58.910 | 0.090 | 0.496 | 0.742 | 0.000 | 0.472 | 1.953 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 27 | 31 | 30 | 22 | 0 | 26 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.19 | 1.15 | 0.85 | 0.00 | 1.00 |
time (sec) |
N/A | 0.379 | 0.499 | 10.788 | 0.359 | 0.357 | 22.160 | 0.000 | 1.517 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 29 | 29 | 31 | 29 | 59 | 52 | 26 | 31 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 2.03 | 1.79 | 0.90 | 1.07 | 1.07 |
time (sec) |
N/A | 0.358 | 79.503 | 0.008 | 0.355 | 0.373 | 15.640 | 0.364 | 1.625 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | F(-2) | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 625 | 238 | 0 | 44 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 12.76 | 4.86 | 0.00 | 0.90 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.241 | 0.305 | 1.491 | 0.000 | 0.372 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | F(-2) | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 642 | 243 | 0 | 45 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 12.84 | 4.86 | 0.00 | 0.90 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.232 | 0.299 | 1.354 | 0.000 | 0.341 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F(-2) | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 320 | 0 | 0 | 44 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 6.04 | 0.00 | 0.00 | 0.83 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.238 | 0.152 | 0.000 | 0.000 | 0.313 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F(-2) | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 316 | 0 | 0 | 43 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 6.08 | 0.00 | 0.00 | 0.83 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.219 | 0.131 | 0.000 | 0.000 | 0.309 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | F(-2) | A | F(-2) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 641 | 233 | 0 | 43 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 13.08 | 4.76 | 0.00 | 0.88 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.238 | 0.253 | 1.614 | 0.000 | 0.314 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | F(-2) | A | F(-2) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 645 | 238 | 0 | 44 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 12.90 | 4.76 | 0.00 | 0.88 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.219 | 0.177 | 1.480 | 0.000 | 0.355 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 56 | 0 | 0 | 83 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 1.24 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.280 | 0.160 | 0.000 | 0.000 | 0.352 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 59 | 0 | 0 | 90 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.75 | 0.00 | 0.00 | 1.14 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.289 | 0.121 | 0.000 | 0.000 | 0.333 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 49 | 0 | 0 | 70 | 0 | 56 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 1.27 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.250 | 0.053 | 0.000 | 0.000 | 0.309 | 0.000 | 0.353 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 49 | 0 | 0 | 70 | 0 | 56 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 1.27 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.237 | 0.051 | 0.000 | 0.000 | 0.332 | 0.000 | 0.330 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 43 | 0 | 0 | 53 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 1.18 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.174 | 0.042 | 0.000 | 0.000 | 0.355 | 0.000 | 0.335 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 40 | 39 | 64 | 45 | 0 | 54 | 32 |
N.S. |
1 | 1.00 | 1.25 | 1.22 | 2.00 | 1.41 | 0.00 | 1.69 | 1.00 |
time (sec) |
N/A | 0.163 | 0.028 | 1.661 | 0.196 | 0.349 | 0.000 | 0.340 | 1.690 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 45 | 0 | 0 | 46 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.238 | 0.043 | 0.000 | 0.000 | 0.317 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 49 | 0 | 0 | 53 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.244 | 0.043 | 0.000 | 0.000 | 0.383 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 49 | 0 | 0 | 53 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.238 | 0.044 | 0.000 | 0.000 | 0.339 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 26 | 23 | 26 | 19 | 26 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.18 | 1.05 | 1.18 | 0.86 | 1.18 | 1.00 |
time (sec) |
N/A | 0.159 | 0.013 | 0.404 | 0.233 | 0.351 | 0.420 | 0.307 | 1.570 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 23 | 22 | 24 | 0 | 32 | 20 |
N.S. |
1 | 1.00 | 1.10 | 1.15 | 1.10 | 1.20 | 0.00 | 1.60 | 1.00 |
time (sec) |
N/A | 0.157 | 0.006 | 0.547 | 0.188 | 0.295 | 0.000 | 0.351 | 1.493 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 39 | 0 | 0 | 45 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 1.12 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.204 | 0.015 | 0.000 | 0.000 | 0.331 | 0.000 | 0.331 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 34 | 33 | 55 | 37 | 0 | 43 | 27 |
N.S. |
1 | 1.00 | 1.26 | 1.22 | 2.04 | 1.37 | 0.00 | 1.59 | 1.00 |
time (sec) |
N/A | 0.161 | 0.009 | 1.289 | 0.195 | 0.302 | 0.000 | 0.331 | 1.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 66 | 74 | 48 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.12 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.218 | 0.017 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 99 | 94 | 85 | 86 | 87 | 98 | 112 | 89 | 85 |
N.S. |
1 | 0.95 | 0.86 | 0.87 | 0.88 | 0.99 | 1.13 | 0.90 | 0.86 |
time (sec) |
N/A | 0.250 | 0.034 | 0.349 | 0.197 | 0.338 | 4.447 | 0.331 | 1.570 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 81 | 74 | 75 | 75 | 86 | 97 | 75 | 73 |
N.S. |
1 | 0.95 | 0.87 | 0.88 | 0.88 | 1.01 | 1.14 | 0.88 | 0.86 |
time (sec) |
N/A | 0.238 | 0.028 | 0.225 | 0.187 | 0.321 | 2.437 | 0.310 | 1.481 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 68 | 63 | 64 | 65 | 74 | 85 | 65 | 61 |
N.S. |
1 | 0.96 | 0.89 | 0.90 | 0.92 | 1.04 | 1.20 | 0.92 | 0.86 |
time (sec) |
N/A | 0.230 | 0.021 | 0.172 | 0.197 | 0.285 | 1.307 | 0.315 | 1.494 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 51 | 49 | 53 | 51 | 59 | 70 | 51 | 49 |
N.S. |
1 | 0.89 | 0.86 | 0.93 | 0.89 | 1.04 | 1.23 | 0.89 | 0.86 |
time (sec) |
N/A | 0.213 | 0.016 | 0.145 | 0.192 | 0.283 | 0.723 | 0.327 | 1.522 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 36 | 31 | 37 | 36 | 38 | 44 | 37 | 33 |
N.S. |
1 | 1.09 | 0.94 | 1.12 | 1.09 | 1.15 | 1.33 | 1.12 | 1.00 |
time (sec) |
N/A | 0.184 | 0.007 | 0.105 | 0.194 | 0.304 | 0.368 | 0.356 | 1.570 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 51 | 50 | 62 | 80 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.94 | 1.17 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.321 | 0.015 | 0.130 | 0.190 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 45 | 48 | 46 | 46 | 66 | 47 | 43 |
N.S. |
1 | 1.00 | 0.96 | 1.02 | 0.98 | 0.98 | 1.40 | 1.00 | 0.91 |
time (sec) |
N/A | 0.210 | 0.010 | 0.122 | 0.192 | 0.288 | 0.981 | 0.335 | 1.981 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 67 | 65 | 62 | 62 | 70 | 94 | 65 | 54 |
N.S. |
1 | 0.93 | 0.90 | 0.86 | 0.86 | 0.97 | 1.31 | 0.90 | 0.75 |
time (sec) |
N/A | 0.221 | 0.022 | 0.187 | 0.196 | 0.330 | 1.902 | 0.402 | 1.661 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 79 | 77 | 72 | 75 | 82 | 112 | 80 | 68 |
N.S. |
1 | 0.92 | 0.90 | 0.84 | 0.87 | 0.95 | 1.30 | 0.93 | 0.79 |
time (sec) |
N/A | 0.235 | 0.023 | 0.237 | 0.194 | 0.305 | 3.846 | 0.362 | 1.677 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 93 | 87 | 84 | 86 | 94 | 122 | 92 | 79 |
N.S. |
1 | 0.93 | 0.87 | 0.84 | 0.86 | 0.94 | 1.22 | 0.92 | 0.79 |
time (sec) |
N/A | 0.249 | 0.033 | 0.335 | 0.190 | 0.333 | 7.517 | 0.347 | 1.759 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 157 | 154 | 137 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.356 | 0.123 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 207 | 201 | 190 | 238 | 0 | 444 | 0 | 221 | 395 |
N.S. |
1 | 0.97 | 0.92 | 1.15 | 0.00 | 2.14 | 0.00 | 1.07 | 1.91 |
time (sec) |
N/A | 0.403 | 0.135 | 1.056 | 0.000 | 0.324 | 0.000 | 0.419 | 1.652 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 167 | 162 | 151 | 190 | 0 | 364 | 0 | 176 | 288 |
N.S. |
1 | 0.97 | 0.90 | 1.14 | 0.00 | 2.18 | 0.00 | 1.05 | 1.72 |
time (sec) |
N/A | 0.367 | 0.097 | 0.753 | 0.000 | 0.335 | 0.000 | 0.351 | 1.644 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 136 | 132 | 122 | 154 | 0 | 299 | 0 | 146 | 229 |
N.S. |
1 | 0.97 | 0.90 | 1.13 | 0.00 | 2.20 | 0.00 | 1.07 | 1.68 |
time (sec) |
N/A | 0.324 | 0.073 | 0.623 | 0.000 | 0.347 | 0.000 | 0.332 | 1.660 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 102 | 94 | 122 | 0 | 245 | 359 | 113 | 166 |
N.S. |
1 | 0.94 | 0.86 | 1.12 | 0.00 | 2.25 | 3.29 | 1.04 | 1.52 |
time (sec) |
N/A | 0.287 | 0.057 | 0.543 | 0.000 | 0.349 | 90.937 | 0.343 | 1.649 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 81 | 78 | 89 | 0 | 190 | 274 | 92 | 120 |
N.S. |
1 | 1.03 | 0.99 | 1.13 | 0.00 | 2.41 | 3.47 | 1.16 | 1.52 |
time (sec) |
N/A | 0.246 | 0.038 | 0.466 | 0.000 | 0.333 | 34.757 | 0.353 | 1.504 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 123 | 150 | 166 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 1.16 | 1.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.373 | 0.135 | 0.247 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 87 | 95 | 0 | 199 | 211 | 99 | 262 |
N.S. |
1 | 1.00 | 1.01 | 1.10 | 0.00 | 2.31 | 2.45 | 1.15 | 3.05 |
time (sec) |
N/A | 0.287 | 0.070 | 0.579 | 0.000 | 0.368 | 152.532 | 0.377 | 2.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 117 | 105 | 145 | 0 | 261 | 0 | 129 | 474 |
N.S. |
1 | 0.97 | 0.87 | 1.20 | 0.00 | 2.16 | 0.00 | 1.07 | 3.92 |
time (sec) |
N/A | 0.329 | 0.153 | 0.574 | 0.000 | 0.359 | 0.000 | 0.332 | 1.886 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 149 | 141 | 132 | 181 | 0 | 318 | 0 | 164 | 505 |
N.S. |
1 | 0.95 | 0.89 | 1.21 | 0.00 | 2.13 | 0.00 | 1.10 | 3.39 |
time (sec) |
N/A | 0.369 | 0.232 | 0.850 | 0.000 | 0.361 | 0.000 | 0.336 | 2.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 190 | 184 | 172 | 225 | 0 | 404 | 0 | 210 | 627 |
N.S. |
1 | 0.97 | 0.91 | 1.18 | 0.00 | 2.13 | 0.00 | 1.11 | 3.30 |
time (sec) |
N/A | 0.404 | 0.288 | 1.049 | 0.000 | 0.357 | 0.000 | 0.344 | 2.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 35 | 38 | 37 | 33 | 46 | 37 | 39 |
N.S. |
1 | 1.00 | 0.83 | 0.90 | 0.88 | 0.79 | 1.10 | 0.88 | 0.93 |
time (sec) |
N/A | 0.198 | 0.013 | 0.248 | 0.285 | 0.284 | 0.072 | 0.317 | 0.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 485 | 483 | 468 | 876 | 0 | 1270 | 0 | 741 | 1240 |
N.S. |
1 | 1.00 | 0.96 | 1.81 | 0.00 | 2.62 | 0.00 | 1.53 | 2.56 |
time (sec) |
N/A | 0.925 | 0.532 | 3.810 | 0.000 | 0.376 | 0.000 | 0.386 | 2.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 338 | 337 | 324 | 594 | 0 | 880 | 0 | 495 | 775 |
N.S. |
1 | 1.00 | 0.96 | 1.76 | 0.00 | 2.60 | 0.00 | 1.46 | 2.29 |
time (sec) |
N/A | 0.677 | 0.319 | 2.378 | 0.000 | 0.329 | 0.000 | 0.361 | 1.920 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 226 | 226 | 204 | 384 | 0 | 567 | 0 | 307 | 457 |
N.S. |
1 | 1.00 | 0.90 | 1.70 | 0.00 | 2.51 | 0.00 | 1.36 | 2.02 |
time (sec) |
N/A | 0.481 | 0.238 | 1.608 | 0.000 | 0.316 | 0.000 | 0.343 | 1.753 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 154 | 152 | 123 | 170 | 0 | 336 | 379 | 167 | 242 |
N.S. |
1 | 0.99 | 0.80 | 1.10 | 0.00 | 2.18 | 2.46 | 1.08 | 1.57 |
time (sec) |
N/A | 0.355 | 0.122 | 0.674 | 0.000 | 0.327 | 88.720 | 0.345 | 1.643 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 81 | 78 | 89 | 0 | 190 | 274 | 92 | 120 |
N.S. |
1 | 1.03 | 0.99 | 1.13 | 0.00 | 2.41 | 3.47 | 1.16 | 1.52 |
time (sec) |
N/A | 0.254 | 0.030 | 0.148 | 0.000 | 0.319 | 33.635 | 0.458 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 228 | 213 | 200 | 300 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.88 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.580 | 0.268 | 1.367 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 165 | 163 | 166 | 184 | 0 | 429 | 0 | 189 | 590 |
N.S. |
1 | 0.99 | 1.01 | 1.12 | 0.00 | 2.60 | 0.00 | 1.15 | 3.58 |
time (sec) |
N/A | 0.406 | 0.201 | 1.747 | 0.000 | 0.374 | 0.000 | 0.358 | 4.536 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 259 | 248 | 215 | 310 | 0 | 1341 | 0 | 490 | 1715 |
N.S. |
1 | 0.96 | 0.83 | 1.20 | 0.00 | 5.18 | 0.00 | 1.89 | 6.62 |
time (sec) |
N/A | 0.539 | 0.337 | 2.734 | 0.000 | 1.549 | 0.000 | 0.396 | 5.921 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 356 | 341 | 310 | 486 | 0 | 3013 | 0 | 1128 | 2707 |
N.S. |
1 | 0.96 | 0.87 | 1.37 | 0.00 | 8.46 | 0.00 | 3.17 | 7.60 |
time (sec) |
N/A | 0.739 | 0.635 | 4.726 | 0.000 | 9.965 | 0.000 | 0.459 | 12.796 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 519 | 500 | 469 | 725 | 0 | 5824 | 0 | 2191 | 4334 |
N.S. |
1 | 0.96 | 0.90 | 1.40 | 0.00 | 11.22 | 0.00 | 4.22 | 8.35 |
time (sec) |
N/A | 1.031 | 1.135 | 8.090 | 0.000 | 48.896 | 0.000 | 0.591 | 20.485 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 175 | 174 | 131 | 292 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.75 | 1.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.541 | 0.042 | 1.603 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 258 | 248 | 339 | 433 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 1.31 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.825 | 0.222 | 2.460 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 762 | 762 | 626 | 555 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.466 | 0.640 | 1.878 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 782 | 782 | 663 | 637 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.574 | 0.739 | 2.783 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 144 | 136 | 111 | 0 | 123 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.77 | 0.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.463 | 0.045 | 0.000 | 0.198 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 587 | 583 | 478 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.111 | 0.557 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 311 | 311 | 290 | 279 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.663 | 0.123 | 1.385 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 371 | 386 | 365 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.700 | 0.112 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 443 | 443 | 826 | 219 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.86 | 0.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.910 | 0.457 | 0.321 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |