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 | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 385 | 459 | 276 | 592 | 0 | 600 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.19 | 0.72 | 1.54 | 0.00 | 1.56 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.023 | 15.081 | 3.078 | 0.000 | 0.099 | 0.000 | 0.000 | 3.540 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 406 | 442 | 382 | 589 | 0 | 641 | 0 | 0 | 873 | 0 |
N.S. |
1 | 1.09 | 0.94 | 1.45 | 0.00 | 1.58 | 0.00 | 0.00 | 2.15 | 0.00 |
time (sec) |
N/A | 0.936 | 20.494 | 1.747 | 0.000 | 0.125 | 0.000 | 0.000 | 3.459 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 318 | 352 | 310 | 474 | 0 | 532 | 0 | 0 | 487 | 0 |
N.S. |
1 | 1.11 | 0.97 | 1.49 | 0.00 | 1.67 | 0.00 | 0.00 | 1.53 | 0.00 |
time (sec) |
N/A | 0.802 | 14.776 | 1.658 | 0.000 | 0.127 | 0.000 | 0.000 | 1.966 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 277 | 240 | 404 | 0 | 439 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.14 | 0.99 | 1.66 | 0.00 | 1.81 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.639 | 11.253 | 1.539 | 0.000 | 0.117 | 0.000 | 0.000 | 0.972 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 159 | 145 | 360 | 0 | 382 | 0 | 0 | 61 | 0 |
N.S. |
1 | 0.79 | 0.72 | 1.79 | 0.00 | 1.90 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.428 | 6.639 | 1.566 | 0.000 | 0.087 | 0.000 | 0.000 | 1.140 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 152 | 130 | 218 | 0 | 382 | 0 | 0 | 71 | 0 |
N.S. |
1 | 0.74 | 0.63 | 1.06 | 0.00 | 1.86 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.501 | 6.559 | 2.178 | 0.000 | 0.086 | 0.000 | 0.000 | 1.923 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 296 | 220 | 471 | 0 | 493 | 0 | 0 | 329 | 0 |
N.S. |
1 | 1.20 | 0.89 | 1.91 | 0.00 | 2.00 | 0.00 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.734 | 10.948 | 2.689 | 0.000 | 0.084 | 0.000 | 0.000 | 1.729 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 319 | 416 | 276 | 537 | 0 | 616 | 0 | 0 | 741 | 0 |
N.S. |
1 | 1.30 | 0.87 | 1.68 | 0.00 | 1.93 | 0.00 | 0.00 | 2.32 | 0.00 |
time (sec) |
N/A | 0.901 | 13.839 | 3.337 | 0.000 | 0.098 | 0.000 | 0.000 | 2.996 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 406 | 520 | 348 | 622 | 0 | 743 | 0 | 0 | 1136 | 0 |
N.S. |
1 | 1.28 | 0.86 | 1.53 | 0.00 | 1.83 | 0.00 | 0.00 | 2.80 | 0.00 |
time (sec) |
N/A | 1.068 | 20.992 | 3.971 | 0.000 | 0.125 | 0.000 | 0.000 | 4.678 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 52 | 57 | 52 | 0 | 20 | 0 | 0 | 28 | 0 |
N.S. |
1 | 2.48 | 2.71 | 2.48 | 0.00 | 0.95 | 0.00 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.374 | 20.058 | 0.568 | 0.000 | 0.082 | 0.000 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 38 | 115 | 66 | 0 | 20 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.81 | 5.48 | 3.14 | 0.00 | 0.95 | 0.00 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.403 | 2.990 | 0.429 | 0.000 | 0.079 | 0.000 | 0.000 | 0.737 | 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 | 78 | 78 | 78 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.382 | 0.228 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 209 | 78 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 2.68 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.585 | 0.169 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.556 | 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 | 76 | 103 | 76 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.36 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.237 | 0.141 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.289 | 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 | 71 | 71 | 71 | 0 | 0 | 0 | 0 | 0 | 1580 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 22.25 | 0.00 |
time (sec) |
N/A | 0.371 | 0.150 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.237 | 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 | 79 | 79 | 76 | 0 | 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 | 0.00 |
time (sec) |
N/A | 0.377 | 0.174 | 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 | C | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 80 | 80 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.34 | 0.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.384 | 0.203 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.565 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 80 | 80 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.37 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.386 | 0.195 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.341 | 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 | 166 | 200 | 132 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.20 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.482 | 0.125 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 99 | 78 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.21 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.319 | 0.139 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 73 | 73 | 0 | 0 | 0 | 0 | 0 | 495 | 0 |
N.S. |
1 | 0.44 | 0.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.00 | 0.00 |
time (sec) |
N/A | 0.367 | 0.150 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 81 | 78 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.37 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.400 | 0.163 | 0.000 | 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 | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 57 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.373 | 0.154 | 0.000 | 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 | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 124 | 75 | 75 | 98 | 81 | 0 | 120 | 69 | 84 |
N.S. |
1 | 0.96 | 0.58 | 0.58 | 0.76 | 0.63 | 0.00 | 0.93 | 0.53 | 0.65 |
time (sec) |
N/A | 0.525 | 0.022 | 0.684 | 0.042 | 0.093 | 0.000 | 0.128 | 0.218 | 9.468 |
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 | 92 | 90 | 55 | 56 | 75 | 56 | 0 | 93 | 45 | 62 |
N.S. |
1 | 0.98 | 0.60 | 0.61 | 0.82 | 0.61 | 0.00 | 1.01 | 0.49 | 0.67 |
time (sec) |
N/A | 0.420 | 0.013 | 0.645 | 0.043 | 0.100 | 0.000 | 0.129 | 0.216 | 9.207 |
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 | 58 | 58 | 36 | 36 | 45 | 34 | 0 | 65 | 24 | 40 |
N.S. |
1 | 1.00 | 0.62 | 0.62 | 0.78 | 0.59 | 0.00 | 1.12 | 0.41 | 0.69 |
time (sec) |
N/A | 0.340 | 0.008 | 0.539 | 0.043 | 0.086 | 0.000 | 0.130 | 0.215 | 8.976 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 56 | 66 | 27 | 0 | 137 | 0 | 77 | 51 | 0 |
N.S. |
1 | 0.97 | 1.14 | 0.47 | 0.00 | 2.36 | 0.00 | 1.33 | 0.88 | 0.00 |
time (sec) |
N/A | 0.376 | 0.017 | 0.438 | 0.000 | 0.094 | 0.000 | 0.134 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 62 | 68 | 38 | 0 | 148 | 0 | 60 | 90 | 0 |
N.S. |
1 | 0.97 | 1.06 | 0.59 | 0.00 | 2.31 | 0.00 | 0.94 | 1.41 | 0.00 |
time (sec) |
N/A | 0.365 | 0.021 | 0.488 | 0.000 | 0.092 | 0.000 | 0.145 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 97 | 93 | 43 | 0 | 197 | 0 | 115 | 132 | 0 |
N.S. |
1 | 0.92 | 0.89 | 0.41 | 0.00 | 1.88 | 0.00 | 1.10 | 1.26 | 0.00 |
time (sec) |
N/A | 0.434 | 0.033 | 0.494 | 0.000 | 0.088 | 0.000 | 0.153 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 131 | 116 | 64 | 0 | 246 | 0 | 131 | 170 | 0 |
N.S. |
1 | 0.92 | 0.82 | 0.45 | 0.00 | 1.73 | 0.00 | 0.92 | 1.20 | 0.00 |
time (sec) |
N/A | 0.537 | 0.049 | 0.504 | 0.000 | 0.090 | 0.000 | 0.163 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 165 | 135 | 82 | 0 | 295 | 0 | 180 | 206 | 0 |
N.S. |
1 | 0.92 | 0.75 | 0.46 | 0.00 | 1.65 | 0.00 | 1.01 | 1.15 | 0.00 |
time (sec) |
N/A | 0.603 | 0.050 | 0.523 | 0.000 | 0.092 | 0.000 | 0.173 | 0.207 | 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 | 188 | 169 | 126 | 136 | 168 | 147 | 0 | 200 | 139 | 153 |
N.S. |
1 | 0.90 | 0.67 | 0.72 | 0.89 | 0.78 | 0.00 | 1.06 | 0.74 | 0.81 |
time (sec) |
N/A | 0.553 | 0.091 | 0.842 | 0.048 | 0.076 | 0.000 | 0.131 | 0.217 | 9.632 |
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 | 139 | 129 | 96 | 108 | 134 | 108 | 0 | 163 | 98 | 114 |
N.S. |
1 | 0.93 | 0.69 | 0.78 | 0.96 | 0.78 | 0.00 | 1.17 | 0.71 | 0.82 |
time (sec) |
N/A | 0.493 | 0.087 | 0.799 | 0.045 | 0.080 | 0.000 | 0.135 | 0.217 | 9.741 |
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 | 96 | 95 | 67 | 72 | 93 | 73 | 0 | 122 | 61 | 73 |
N.S. |
1 | 0.99 | 0.70 | 0.75 | 0.97 | 0.76 | 0.00 | 1.27 | 0.64 | 0.76 |
time (sec) |
N/A | 0.413 | 0.047 | 0.559 | 0.047 | 0.075 | 0.000 | 0.129 | 0.229 | 9.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 113 | 87 | 63 | 0 | 188 | 0 | 138 | 91 | 0 |
N.S. |
1 | 1.16 | 0.90 | 0.65 | 0.00 | 1.94 | 0.00 | 1.42 | 0.94 | 0.00 |
time (sec) |
N/A | 0.506 | 0.097 | 0.523 | 0.000 | 0.094 | 0.000 | 0.117 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 105 | 85 | 57 | 0 | 197 | 0 | 81 | 123 | 0 |
N.S. |
1 | 1.13 | 0.91 | 0.61 | 0.00 | 2.12 | 0.00 | 0.87 | 1.32 | 0.00 |
time (sec) |
N/A | 0.410 | 0.123 | 0.535 | 0.000 | 0.090 | 0.000 | 0.148 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 129 | 107 | 64 | 0 | 229 | 0 | 133 | 191 | 0 |
N.S. |
1 | 1.07 | 0.88 | 0.53 | 0.00 | 1.89 | 0.00 | 1.10 | 1.58 | 0.00 |
time (sec) |
N/A | 0.455 | 0.183 | 0.527 | 0.000 | 0.092 | 0.000 | 0.152 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 155 | 140 | 79 | 0 | 302 | 0 | 208 | 251 | 0 |
N.S. |
1 | 0.91 | 0.82 | 0.46 | 0.00 | 1.78 | 0.00 | 1.22 | 1.48 | 0.00 |
time (sec) |
N/A | 0.492 | 0.232 | 0.550 | 0.000 | 0.100 | 0.000 | 0.189 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 184 | 174 | 104 | 0 | 379 | 0 | 278 | 312 | 0 |
N.S. |
1 | 0.83 | 0.79 | 0.47 | 0.00 | 1.71 | 0.00 | 1.26 | 1.41 | 0.00 |
time (sec) |
N/A | 0.531 | 0.348 | 0.570 | 0.000 | 0.095 | 0.000 | 0.191 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 160 | 137 | 138 | 0 | 420 | 0 | 0 | 212 | 0 |
N.S. |
1 | 0.94 | 0.81 | 0.81 | 0.00 | 2.47 | 0.00 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.567 | 0.225 | 0.707 | 0.000 | 0.089 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 120 | 105 | 102 | 0 | 316 | 0 | 0 | 134 | 0 |
N.S. |
1 | 0.99 | 0.87 | 0.84 | 0.00 | 2.61 | 0.00 | 0.00 | 1.11 | 0.00 |
time (sec) |
N/A | 0.491 | 0.204 | 0.622 | 0.000 | 0.092 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 92 | 88 | 75 | 0 | 234 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.10 | 1.05 | 0.89 | 0.00 | 2.79 | 0.00 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.386 | 0.085 | 0.582 | 0.000 | 0.093 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 72 | 70 | 54 | 0 | 144 | 0 | 79 | 50 | 0 |
N.S. |
1 | 1.29 | 1.25 | 0.96 | 0.00 | 2.57 | 0.00 | 1.41 | 0.89 | 0.00 |
time (sec) |
N/A | 0.325 | 0.045 | 0.582 | 0.000 | 0.089 | 0.000 | 0.126 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 103 | 114 | 37 | 0 | 455 | 0 | 152 | 122 | 0 |
N.S. |
1 | 1.08 | 1.20 | 0.39 | 0.00 | 4.79 | 0.00 | 1.60 | 1.28 | 0.00 |
time (sec) |
N/A | 0.461 | 0.094 | 0.569 | 0.000 | 0.106 | 0.000 | 0.133 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 143 | 156 | 60 | 0 | 604 | 0 | 0 | 216 | 0 |
N.S. |
1 | 1.12 | 1.22 | 0.47 | 0.00 | 4.72 | 0.00 | 0.00 | 1.69 | 0.00 |
time (sec) |
N/A | 0.497 | 0.211 | 0.609 | 0.000 | 0.118 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 202 | 197 | 85 | 0 | 774 | 0 | 0 | 346 | 0 |
N.S. |
1 | 1.09 | 1.06 | 0.46 | 0.00 | 4.18 | 0.00 | 0.00 | 1.87 | 0.00 |
time (sec) |
N/A | 0.635 | 0.441 | 0.664 | 0.000 | 0.156 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 266 | 247 | 116 | 0 | 985 | 0 | 0 | 489 | 0 |
N.S. |
1 | 1.06 | 0.99 | 0.46 | 0.00 | 3.94 | 0.00 | 0.00 | 1.96 | 0.00 |
time (sec) |
N/A | 0.742 | 0.639 | 0.724 | 0.000 | 0.253 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 157 | 134 | 111 | 0 | 503 | 0 | 0 | 329 | 0 |
N.S. |
1 | 1.16 | 0.99 | 0.82 | 0.00 | 3.73 | 0.00 | 0.00 | 2.44 | 0.00 |
time (sec) |
N/A | 0.513 | 0.380 | 0.656 | 0.000 | 0.117 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 113 | 117 | 94 | 0 | 378 | 0 | 0 | 244 | 0 |
N.S. |
1 | 1.08 | 1.11 | 0.90 | 0.00 | 3.60 | 0.00 | 0.00 | 2.32 | 0.00 |
time (sec) |
N/A | 0.433 | 0.231 | 0.611 | 0.000 | 0.094 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 101 | 107 | 77 | 0 | 333 | 0 | 0 | 156 | 0 |
N.S. |
1 | 1.09 | 1.15 | 0.83 | 0.00 | 3.58 | 0.00 | 0.00 | 1.68 | 0.00 |
time (sec) |
N/A | 0.369 | 0.173 | 0.598 | 0.000 | 0.091 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 170 | 142 | 68 | 0 | 941 | 0 | 334 | 516 | 0 |
N.S. |
1 | 1.17 | 0.98 | 0.47 | 0.00 | 6.49 | 0.00 | 2.30 | 3.56 | 0.00 |
time (sec) |
N/A | 0.553 | 0.517 | 0.609 | 0.000 | 0.130 | 0.000 | 0.424 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 222 | 169 | 99 | 0 | 1256 | 0 | 0 | 743 | 0 |
N.S. |
1 | 1.14 | 0.87 | 0.51 | 0.00 | 6.44 | 0.00 | 0.00 | 3.81 | 0.00 |
time (sec) |
N/A | 0.671 | 0.636 | 0.710 | 0.000 | 0.284 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 296 | 240 | 123 | 0 | 1598 | 0 | 0 | 971 | 0 |
N.S. |
1 | 1.10 | 0.89 | 0.46 | 0.00 | 5.92 | 0.00 | 0.00 | 3.60 | 0.00 |
time (sec) |
N/A | 0.826 | 1.142 | 0.789 | 0.000 | 0.317 | 0.000 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 362 | 388 | 307 | 155 | 0 | 1979 | 0 | 0 | 1238 | 0 |
N.S. |
1 | 1.07 | 0.85 | 0.43 | 0.00 | 5.47 | 0.00 | 0.00 | 3.42 | 0.00 |
time (sec) |
N/A | 1.009 | 1.699 | 0.756 | 0.000 | 0.659 | 0.000 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 202 | 170 | 0 | 0 | 563 | 0 | 0 | 299 | 0 |
N.S. |
1 | 0.82 | 0.69 | 0.00 | 0.00 | 2.29 | 0.00 | 0.00 | 1.22 | 0.00 |
time (sec) |
N/A | 0.610 | 0.296 | 0.000 | 0.000 | 0.110 | 0.000 | 0.000 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 141 | 116 | 0 | 0 | 410 | 0 | 0 | 173 | 0 |
N.S. |
1 | 0.82 | 0.67 | 0.00 | 0.00 | 2.38 | 0.00 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 0.494 | 0.257 | 0.000 | 0.000 | 0.111 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 94 | 83 | 0 | 0 | 289 | 0 | 0 | 80 | 0 |
N.S. |
1 | 0.80 | 0.70 | 0.00 | 0.00 | 2.45 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.391 | 0.056 | 0.000 | 0.000 | 0.096 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 32 | 33 | 27 | 46 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.92 | 0.75 | 1.28 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.281 | 0.010 | 0.460 | 0.046 | 0.077 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 116 | 110 | 0 | 0 | 439 | 0 | 0 | 103 | 0 |
N.S. |
1 | 0.84 | 0.80 | 0.00 | 0.00 | 3.18 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.446 | 0.081 | 0.000 | 0.000 | 0.098 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 200 | 158 | 0 | 0 | 845 | 0 | 0 | 377 | 0 |
N.S. |
1 | 0.95 | 0.75 | 0.00 | 0.00 | 4.02 | 0.00 | 0.00 | 1.80 | 0.00 |
time (sec) |
N/A | 0.659 | 0.389 | 0.000 | 0.000 | 0.119 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 248 | 218 | 0 | 0 | 1473 | 0 | 0 | 865 | 0 |
N.S. |
1 | 0.83 | 0.73 | 0.00 | 0.00 | 4.93 | 0.00 | 0.00 | 2.89 | 0.00 |
time (sec) |
N/A | 0.649 | 0.763 | 0.000 | 0.000 | 0.212 | 0.000 | 0.000 | 0.225 | 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 | 99 | 100 | 111 | 0 | 0 | 108 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.01 | 1.12 | 0.00 | 0.00 | 1.09 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.405 | 4.917 | 0.000 | 0.000 | 0.082 | 0.000 | 0.000 | 0.307 | 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 | 99 | 99 | 113 | 0 | 0 | 109 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 1.14 | 0.00 | 0.00 | 1.10 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.405 | 4.939 | 0.000 | 0.000 | 0.076 | 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 | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 120 | 0 | 0 | 109 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 1.21 | 0.00 | 0.00 | 1.10 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.405 | 4.031 | 0.000 | 0.000 | 0.079 | 0.000 | 0.000 | 0.312 | 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 | 100 | 100 | 122 | 0 | 0 | 110 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.00 | 1.22 | 0.00 | 0.00 | 1.10 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.405 | 3.995 | 0.000 | 0.000 | 0.085 | 0.000 | 0.000 | 0.331 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 64 | 90 | 0 | 0 | 11 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.10 | 1.55 | 0.00 | 0.00 | 0.19 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.320 | 2.818 | 0.000 | 0.000 | 0.080 | 0.000 | 0.000 | 0.244 | 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 | 57 | 57 | 73 | 0 | 0 | 11 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.28 | 0.00 | 0.00 | 0.19 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.332 | 2.370 | 0.000 | 0.000 | 0.083 | 0.000 | 0.000 | 0.315 | 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 | 58 | 58 | 94 | 0 | 0 | 11 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.62 | 0.00 | 0.00 | 0.19 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.329 | 2.408 | 0.000 | 0.000 | 0.076 | 0.000 | 0.000 | 0.316 | 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 | 57 | 57 | 68 | 0 | 0 | 11 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.19 | 0.00 | 0.00 | 0.19 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.321 | 2.458 | 0.000 | 0.000 | 0.084 | 0.000 | 0.000 | 0.249 | 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 | 94 | 94 | 92 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.426 | 0.393 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.776 | 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 | 88 | 88 | 86 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.413 | 0.259 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.028 | 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 | 88 | 88 | 86 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.403 | 0.218 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 44.533 | 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 | 86 | 86 | 84 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.413 | 0.193 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.398 | 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 | 82 | 82 | 80 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.390 | 0.185 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.264 | 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 | 88 | 88 | 84 | 0 | 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 | 0.00 |
time (sec) |
N/A | 0.405 | 0.207 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.434 | 0.000 |