Detailed conclusion table per each integral is given by 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 just an F.
In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | C | C | F | F | F | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 23 | 122 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 0.37 | 1.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
| time (sec) |
N/A | 0.008 | 1.387 | 0.037 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 46 | 48 | 117 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.04 | 2.54 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
| time (sec) |
N/A | 0.027 | 0.891 | 0.223 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | F | F | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 47 | 47 | 81 | 207 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.72 | 4.40 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
| time (sec) |
N/A | 0.043 | 2.063 | 0.431 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F | B | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 129 | 129 | 119 | 186 | 0 | 553 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.92 | 1.44 | 0.00 | 4.29 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.012 | 0.260 | 1.552 | 0.000 | 2.550 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F | B | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 120 | 120 | 119 | 186 | 0 | 553 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.99 | 1.55 | 0.00 | 4.61 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.011 | 0.250 | 1.516 | 0.000 | 2.417 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 129 | 129 | 119 | 0 | 0 | 755 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.92 | 0.00 | 0.00 | 5.85 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.015 | 0.219 | 0.028 | 0.000 | 7.246 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 124 | 124 | 123 | 0 | 0 | 776 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.99 | 0.00 | 0.00 | 6.26 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.014 | 0.220 | 0.030 | 0.000 | 6.057 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 120 | 120 | 121 | 0 | 0 | 286 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.01 | 0.00 | 0.00 | 2.38 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.013 | 0.211 | 0.025 | 0.000 | 4.687 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 120 | 120 | 121 | 0 | 0 | 286 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.01 | 0.00 | 0.00 | 2.38 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.012 | 0.204 | 0.029 | 0.000 | 5.024 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 120 | 120 | 119 | 0 | 0 | 337 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.99 | 0.00 | 0.00 | 2.81 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.015 | 0.217 | 0.031 | 0.000 | 30.378 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 124 | 124 | 123 | 0 | 0 | 343 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.99 | 0.00 | 0.00 | 2.77 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.015 | 0.226 | 0.029 | 0.000 | 28.580 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F | B | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 61 | 56 | 138 | 0 | 104 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.92 | 2.26 | 0.00 | 1.70 | 0.00 | 0.00 | -0.02 |
| time (sec) |
N/A | 0.006 | 0.102 | 1.000 | 0.000 | 3.391 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F | C | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 61 | 56 | 137 | 0 | 243 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.92 | 2.25 | 0.00 | 3.98 | 0.00 | 0.00 | -0.02 |
| time (sec) |
N/A | 0.006 | 0.099 | 0.961 | 0.000 | 3.487 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 77 | 77 | 67 | 0 | 0 | 274 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.87 | 0.00 | 0.00 | 3.56 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.009 | 0.119 | 0.030 | 0.000 | 7.383 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 79 | 79 | 69 | 0 | 0 | 273 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.87 | 0.00 | 0.00 | 3.46 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.010 | 0.119 | 0.027 | 0.000 | 6.816 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 85 | 77 | 0 | 0 | 276 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.91 | 0.00 | 0.00 | 3.25 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.012 | 0.125 | 0.026 | 0.000 | 4.843 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 85 | 77 | 0 | 0 | 278 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.91 | 0.00 | 0.00 | 3.27 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.010 | 0.153 | 0.026 | 0.000 | 6.415 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 101 | 101 | 88 | 0 | 0 | 338 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.87 | 0.00 | 0.00 | 3.35 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.014 | 0.140 | 0.027 | 0.000 | 26.002 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | B | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 90 | 0 | 0 | 350 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.87 | 0.00 | 0.00 | 3.40 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.014 | 0.131 | 0.028 | 0.000 | 25.812 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F | B | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 53 | 48 | 121 | 0 | 91 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.91 | 2.28 | 0.00 | 1.72 | 0.00 | 0.00 | -0.02 |
| time (sec) |
N/A | 0.005 | 0.081 | 1.112 | 0.000 | 3.416 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 362 | 362 | 346 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.188 | 10.333 | 0.011 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 302 | 302 | 348 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.142 | 9.823 | 0.013 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 244 | 244 | 161 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.105 | 8.792 | 0.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 199 | 199 | 160 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.103 | 7.409 | 0.027 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 167 | 160 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.073 | 6.994 | 0.028 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F(-1) | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 152 | 152 | 120 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.081 | 7.597 | 0.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 233 | 233 | 327 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.113 | 8.533 | 0.024 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 254 | 254 | 331 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.112 | 9.772 | 0.026 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 274 | 274 | 419 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.257 | 10.498 | 0.026 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 304 | 304 | 431 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.236 | 10.532 | 0.025 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 340 | 340 | 340 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.201 | 10.240 | 0.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 279 | 279 | 341 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.181 | 10.241 | 0.032 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 309 | 309 | 232 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.149 | 10.154 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 278 | 278 | 232 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.141 | 10.160 | 0.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 336 | 336 | 392 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.179 | 10.171 | 0.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 292 | 292 | 336 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.157 | 10.238 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 314 | 314 | 380 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.280 | 10.380 | 0.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 345 | 345 | 387 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.259 | 10.382 | 0.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 371 | 371 | 536 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.390 | 10.763 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | F | F | F(-1) | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 419 | 419 | 550 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.333 | 10.672 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | F | F(-1) | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 79 | 79 | 172 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 2.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.029 | 0.199 | 0.053 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F | C | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 296 | 296 | 136 | 0 | 0 | 0 | 121 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.46 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.197 | 5.131 | 0.039 | 0.000 | 0.000 | 20.037 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F | C | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 176 | 176 | 106 | 0 | 0 | 0 | 88 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.60 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.084 | 5.100 | 0.031 | 0.000 | 0.000 | 9.927 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F | C | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 85 | 90 | 0 | 0 | 0 | 53 | 0 | -1 |
| N.S. | 1 | 0.91 | 0.97 | 0.00 | 0.00 | 0.00 | 0.57 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.028 | 0.073 | 0.019 | 0.000 | 0.000 | 4.677 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | F | F | F | C | F | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 44 | 44 | 44 | 0 | 0 | 0 | 22 | 0 | 41 |
| N.S. | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.93 |
| time (sec) |
N/A | 0.007 | 0.004 | 0.000 | 0.000 | 0.000 | 1.070 | 0.000 | 5.567 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | F | F(-1) | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 162 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 2.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
| time (sec) |
N/A | 0.017 | 0.215 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | F | F(-1) | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 162 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 2.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
| time (sec) |
N/A | 0.018 | 0.247 | 0.040 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | F | F | F | F(-1) | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 162 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 2.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
| time (sec) |
N/A | 0.017 | 0.327 | 0.055 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | F | A | F | F | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 53 | 52 | 71 | 0 | 91 | 0 | 0 | 131 |
| N.S. | 1 | 1.00 | 0.98 | 1.34 | 0.00 | 1.72 | 0.00 | 0.00 | 2.47 |
| time (sec) |
N/A | 0.014 | 0.412 | 0.131 | 0.000 | 0.958 | 0.000 | 0.000 | 5.736 |