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 | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 96 | 97 | 95 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
| N.S. |
1 | 1.01 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
| time (sec) |
N/A | 0.395 | 0.174 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 70 | 85 | 110 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.21 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.347 | 0.068 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.277 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 134 | 145 | 125 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.425 | 5.209 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.211 | 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 | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 230 | 232 | 206 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
| N.S. |
1 | 1.01 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
| time (sec) |
N/A | 0.633 | 5.345 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.031 | 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 | 91 | 91 | 111 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.504 | 0.412 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 5.839 | 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 | 91 | 91 | 111 | 0 | 0 | 0 | 0 | 0 | 432 | 0 |
| N.S. |
1 | 1.00 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.75 | 0.00 |
| time (sec) |
N/A | 0.494 | 0.321 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.208 | 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 | 89 | 89 | 111 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.488 | 0.341 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 3.417 | 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 | 89 | 89 | 111 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.455 | 0.411 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 12.803 | 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 | 91 | 91 | 111 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.493 | 0.399 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 47.495 | 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 | 105 | 101 | 115 | 0 | 0 | 0 | 0 | 0 | 1332 | 0 |
| N.S. |
1 | 0.96 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 12.69 | 0.00 |
| time (sec) |
N/A | 0.456 | 0.237 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.470 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | C | C | F | F | F(-2) | F | F | F | F(-1) |
| verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 533 | 67 | 68 | 0 | 0 | 0 | 0 | 0 | 39 | 0 |
| N.S. |
1 | 0.13 | 0.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
| time (sec) |
N/A | 0.356 | 10.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.281 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | C | A | F | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 162 | 67 | 126 | 0 | 0 | 0 | 0 | 0 | 39 | 0 |
| N.S. |
1 | 0.41 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
| time (sec) |
N/A | 0.360 | 8.339 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.326 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | C | A | F | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 214 | 67 | 218 | 0 | 0 | 0 | 0 | 0 | 37 | 0 |
| N.S. |
1 | 0.31 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
| time (sec) |
N/A | 0.344 | 5.773 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.273 | 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 | 31 | 31 | 47 | 29 | 0 | 121 | 0 | 35 | 78 | 0 |
| N.S. |
1 | 1.00 | 1.52 | 0.94 | 0.00 | 3.90 | 0.00 | 1.13 | 2.52 | 0.00 |
| time (sec) |
N/A | 0.253 | 0.065 | 0.587 | 0.000 | 0.132 | 0.000 | 0.130 | 0.267 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 38 | 38 | 38 | 27 | 38 | 27 | 29 | 41 | 25 | 33 |
| N.S. |
1 | 1.00 | 1.00 | 0.71 | 1.00 | 0.71 | 0.76 | 1.08 | 0.66 | 0.87 |
| time (sec) |
N/A | 0.304 | 0.009 | 0.112 | 0.025 | 0.086 | 0.203 | 0.118 | 0.283 | 3.984 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 47 | 61 | 61 | 46 | 49 | 47 | 37 | 54 | 47 | 38 |
| N.S. |
1 | 1.30 | 1.30 | 0.98 | 1.04 | 1.00 | 0.79 | 1.15 | 1.00 | 0.81 |
| time (sec) |
N/A | 0.358 | 0.009 | 0.067 | 0.031 | 0.122 | 0.145 | 0.125 | 0.294 | 0.112 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 61 | 61 | 46 | 49 | 47 | 37 | 54 | 47 | 38 |
| N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.80 | 0.77 | 0.61 | 0.89 | 0.77 | 0.62 |
| time (sec) |
N/A | 0.316 | 0.009 | 0.085 | 0.025 | 0.104 | 0.161 | 0.122 | 0.251 | 3.242 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 76 | 176 | 0 | 174 | 0 | 48 | 133 | 0 |
| N.S. |
1 | 1.00 | 1.29 | 2.98 | 0.00 | 2.95 | 0.00 | 0.81 | 2.25 | 0.00 |
| time (sec) |
N/A | 0.374 | 0.086 | 0.286 | 0.000 | 0.146 | 0.000 | 0.134 | 0.248 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 76 | 176 | 0 | 174 | 0 | 48 | 133 | 0 |
| N.S. |
1 | 1.00 | 1.29 | 2.98 | 0.00 | 2.95 | 0.00 | 0.81 | 2.25 | 0.00 |
| time (sec) |
N/A | 0.410 | 0.063 | 0.086 | 0.000 | 0.107 | 0.000 | 0.135 | 0.260 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | C | C | F | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 270 | 67 | 96 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
| N.S. |
1 | 0.25 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
| time (sec) |
N/A | 0.413 | 11.057 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.299 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | C | C | F | F | F(-1) | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 270 | 67 | 96 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
| N.S. |
1 | 0.25 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
| time (sec) |
N/A | 0.460 | 11.072 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.257 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | C | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 79 | 47 | 50 | 45 | 37 | 119 | 59 | 36 | 58 |
| N.S. |
1 | 1.05 | 0.63 | 0.67 | 0.60 | 0.49 | 1.59 | 0.79 | 0.48 | 0.77 |
| time (sec) |
N/A | 0.317 | 0.684 | 0.184 | 0.109 | 0.093 | 35.451 | 0.146 | 0.280 | 4.489 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | C | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 34 | 34 | 34 | 25 | 19 | 24 | 102 | 24 | 22 | 36 |
| N.S. |
1 | 1.00 | 1.00 | 0.74 | 0.56 | 0.71 | 3.00 | 0.71 | 0.65 | 1.06 |
| time (sec) |
N/A | 0.267 | 0.389 | 0.374 | 0.108 | 0.105 | 2.871 | 0.142 | 0.274 | 4.113 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | C | A | A | C | F(-2) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 39 | 39 | 79 | 67 | 35 | 56 | 73 | 0 | 36 | 82 |
| N.S. |
1 | 1.00 | 2.03 | 1.72 | 0.90 | 1.44 | 1.87 | 0.00 | 0.92 | 2.10 |
| time (sec) |
N/A | 0.300 | 0.279 | 0.160 | 0.044 | 0.108 | 18.060 | 0.000 | 0.280 | 5.445 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | A | A | F(-1) | B | F | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 84 | 77 | 0 | 61 | 94 | 0 | 370 | 72 | 344 |
| N.S. |
1 | 1.05 | 0.96 | 0.00 | 0.76 | 1.18 | 0.00 | 4.62 | 0.90 | 4.30 |
| time (sec) |
N/A | 0.353 | 0.477 | 0.000 | 0.105 | 0.099 | 0.000 | 0.380 | 0.464 | 8.069 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 309 | 317 | 73 | 0 | 0 | 67 | 141 | 0 | 93 | 0 |
| N.S. |
1 | 1.03 | 0.24 | 0.00 | 0.00 | 0.22 | 0.46 | 0.00 | 0.30 | 0.00 |
| time (sec) |
N/A | 0.617 | 7.346 | 0.000 | 0.000 | 0.153 | 103.154 | 0.000 | 0.462 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 269 | 269 | 73 | 0 | 0 | 53 | 138 | 0 | 64 | 0 |
| N.S. |
1 | 1.00 | 0.27 | 0.00 | 0.00 | 0.20 | 0.51 | 0.00 | 0.24 | 0.00 |
| time (sec) |
N/A | 0.503 | 5.729 | 0.000 | 0.000 | 0.089 | 5.960 | 0.000 | 0.366 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 228 | 228 | 66 | 0 | 0 | 23 | 114 | 0 | 34 | 0 |
| N.S. |
1 | 1.00 | 0.29 | 0.00 | 0.00 | 0.10 | 0.50 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 0.429 | 4.269 | 0.000 | 0.000 | 0.144 | 3.366 | 0.000 | 0.311 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 271 | 271 | 73 | 0 | 0 | 51 | 107 | 0 | 38 | 0 |
| N.S. |
1 | 1.00 | 0.27 | 0.00 | 0.00 | 0.19 | 0.39 | 0.00 | 0.14 | 0.00 |
| time (sec) |
N/A | 0.506 | 5.646 | 0.000 | 0.000 | 0.083 | 15.342 | 0.000 | 0.334 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | A | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 311 | 319 | 73 | 0 | 0 | 69 | 0 | 0 | 38 | 0 |
| N.S. |
1 | 1.03 | 0.23 | 0.00 | 0.00 | 0.22 | 0.00 | 0.00 | 0.12 | 0.00 |
| time (sec) |
N/A | 0.602 | 7.044 | 0.000 | 0.000 | 0.108 | 0.000 | 0.000 | 0.347 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | A | A | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 579 | 601 | 73 | 0 | 0 | 65 | 141 | 0 | 68 | 0 |
| N.S. |
1 | 1.04 | 0.13 | 0.00 | 0.00 | 0.11 | 0.24 | 0.00 | 0.12 | 0.00 |
| time (sec) |
N/A | 1.025 | 6.540 | 0.000 | 0.000 | 0.091 | 15.348 | 0.000 | 0.432 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | A | A | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 533 | 554 | 73 | 0 | 0 | 33 | 121 | 0 | 35 | 0 |
| N.S. |
1 | 1.04 | 0.14 | 0.00 | 0.00 | 0.06 | 0.23 | 0.00 | 0.07 | 0.00 |
| time (sec) |
N/A | 0.933 | 3.861 | 0.000 | 0.000 | 0.115 | 2.957 | 0.000 | 0.266 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | A | A | F | F | F(-1) |
| verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 573 | 599 | 71 | 0 | 0 | 59 | 107 | 0 | 38 | 0 |
| N.S. |
1 | 1.05 | 0.12 | 0.00 | 0.00 | 0.10 | 0.19 | 0.00 | 0.07 | 0.00 |
| time (sec) |
N/A | 1.027 | 4.992 | 0.000 | 0.000 | 0.100 | 5.405 | 0.000 | 0.361 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 143 | 99 | 75 | 57 | 62 | 0 | 162 | 83 | 831 |
| N.S. |
1 | 1.06 | 0.73 | 0.56 | 0.42 | 0.46 | 0.00 | 1.20 | 0.61 | 6.16 |
| time (sec) |
N/A | 0.438 | 1.376 | 0.145 | 0.026 | 0.143 | 0.000 | 0.140 | 0.270 | 49.472 |
| 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 104 | 107 | 87 | 65 | 47 | 57 | 0 | 127 | 66 | 632 |
| N.S. |
1 | 1.03 | 0.84 | 0.62 | 0.45 | 0.55 | 0.00 | 1.22 | 0.63 | 6.08 |
| time (sec) |
N/A | 0.370 | 1.151 | 0.085 | 0.031 | 0.085 | 0.000 | 0.139 | 0.246 | 27.174 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | A | A | F | B | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 73 | 74 | 404 | 52 | 37 | 52 | 0 | 92 | 49 | 0 |
| N.S. |
1 | 1.01 | 5.53 | 0.71 | 0.51 | 0.71 | 0.00 | 1.26 | 0.67 | 0.00 |
| time (sec) |
N/A | 0.323 | 1.406 | 0.081 | 0.029 | 0.100 | 0.000 | 0.140 | 0.199 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 37 | 37 | 264 | 72 | 26 | 46 | 61 | 57 | 33 | 41 |
| N.S. |
1 | 1.00 | 7.14 | 1.95 | 0.70 | 1.24 | 1.65 | 1.54 | 0.89 | 1.11 |
| time (sec) |
N/A | 0.271 | 1.136 | 0.088 | 0.031 | 0.091 | 1.743 | 0.129 | 0.218 | 3.994 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | A | B | F | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 38 | 69 | 184 | 47 | 27 | 55 | 0 | 0 | 44 | 129 |
| N.S. |
1 | 1.82 | 4.84 | 1.24 | 0.71 | 1.45 | 0.00 | 0.00 | 1.16 | 3.39 |
| time (sec) |
N/A | 0.343 | 0.958 | 0.091 | 0.102 | 0.090 | 0.000 | 0.000 | 0.198 | 5.141 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 31 | 31 | 421 | 23 | 10 | 30 | 0 | 48 | 38 | 31 |
| N.S. |
1 | 1.00 | 13.58 | 0.74 | 0.32 | 0.97 | 0.00 | 1.55 | 1.23 | 1.00 |
| time (sec) |
N/A | 0.249 | 1.945 | 0.093 | 0.102 | 0.103 | 0.000 | 0.120 | 0.220 | 3.899 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | A | A | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 63 | 693 | 28 | 21 | 37 | 0 | 90 | 56 | 43 |
| N.S. |
1 | 1.00 | 11.00 | 0.44 | 0.33 | 0.59 | 0.00 | 1.43 | 0.89 | 0.68 |
| time (sec) |
N/A | 0.279 | 8.071 | 0.092 | 0.102 | 0.109 | 0.000 | 0.133 | 0.215 | 3.771 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 94 | 99 | 41 | 33 | 31 | 44 | 0 | 111 | 72 | 55 |
| N.S. |
1 | 1.05 | 0.44 | 0.35 | 0.33 | 0.47 | 0.00 | 1.18 | 0.77 | 0.59 |
| time (sec) |
N/A | 0.330 | 10.041 | 0.093 | 0.103 | 0.086 | 0.000 | 0.139 | 0.211 | 3.868 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 125 | 135 | 46 | 38 | 41 | 49 | 0 | 132 | 87 | 67 |
| N.S. |
1 | 1.08 | 0.37 | 0.30 | 0.33 | 0.39 | 0.00 | 1.06 | 0.70 | 0.54 |
| time (sec) |
N/A | 0.379 | 10.057 | 0.105 | 0.107 | 0.086 | 0.000 | 0.139 | 0.210 | 3.911 |
| 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 104 | 107 | 88 | 65 | 47 | 57 | 0 | 76 | 66 | 632 |
| N.S. |
1 | 1.03 | 0.85 | 0.62 | 0.45 | 0.55 | 0.00 | 0.73 | 0.63 | 6.08 |
| time (sec) |
N/A | 0.373 | 1.163 | 0.138 | 0.031 | 0.087 | 0.000 | 0.123 | 0.177 | 23.791 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | A | A | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 73 | 71 | 406 | 55 | 37 | 52 | 0 | 59 | 49 | 429 |
| N.S. |
1 | 0.97 | 5.56 | 0.75 | 0.51 | 0.71 | 0.00 | 0.81 | 0.67 | 5.88 |
| time (sec) |
N/A | 0.324 | 1.518 | 0.102 | 0.024 | 0.094 | 0.000 | 0.107 | 0.205 | 16.816 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | A | A | F | A | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 35 | 265 | 41 | 24 | 46 | 0 | 39 | 33 | 0 |
| N.S. |
1 | 1.00 | 7.57 | 1.17 | 0.69 | 1.31 | 0.00 | 1.11 | 0.94 | 0.00 |
| time (sec) |
N/A | 0.267 | 1.407 | 0.095 | 0.034 | 0.101 | 0.000 | 0.119 | 0.212 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | B | B | F | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 8 | 8 | 38 | 40 | 16 | 27 | 0 | 20 | 19 | 6 |
| N.S. |
1 | 1.00 | 4.75 | 5.00 | 2.00 | 3.38 | 0.00 | 2.50 | 2.38 | 0.75 |
| time (sec) |
N/A | 0.223 | 0.860 | 0.100 | 0.025 | 0.088 | 0.000 | 0.110 | 0.200 | 4.068 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | A | A | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 29 | 29 | 146 | 20 | 10 | 25 | 0 | 25 | 20 | 19 |
| N.S. |
1 | 1.00 | 5.03 | 0.69 | 0.34 | 0.86 | 0.00 | 0.86 | 0.69 | 0.66 |
| time (sec) |
N/A | 0.235 | 0.906 | 0.106 | 0.103 | 0.084 | 0.000 | 0.112 | 0.204 | 4.224 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | A | A | F | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 63 | 407 | 25 | 21 | 34 | 0 | 48 | 39 | 33 |
| N.S. |
1 | 1.00 | 6.46 | 0.40 | 0.33 | 0.54 | 0.00 | 0.76 | 0.62 | 0.52 |
| time (sec) |
N/A | 0.275 | 1.976 | 0.106 | 0.104 | 0.092 | 0.000 | 0.118 | 0.188 | 4.283 |
| 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 | 94 | 99 | 41 | 30 | 31 | 39 | 0 | 69 | 57 | 43 |
| N.S. |
1 | 1.05 | 0.44 | 0.32 | 0.33 | 0.41 | 0.00 | 0.73 | 0.61 | 0.46 |
| time (sec) |
N/A | 0.327 | 1.126 | 0.103 | 0.102 | 0.092 | 0.000 | 0.124 | 0.203 | 4.312 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 44 | 44 | 46 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.291 | 0.145 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 16.236 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 49 | 45 | 47 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
| N.S. |
1 | 0.92 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 |
| time (sec) |
N/A | 0.333 | 0.195 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.030 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 104 | 104 | 104 | 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 | 0.379 | 0.176 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 42.809 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F(-2) | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 109 | 105 | 105 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.417 | 0.211 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 41.908 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 45 | 45 | 45 | 46 | 51 | 82 | 274 | 107 | 72 | 45 |
| N.S. |
1 | 1.00 | 1.00 | 1.02 | 1.13 | 1.82 | 6.09 | 2.38 | 1.60 | 1.00 |
| time (sec) |
N/A | 0.313 | 0.081 | 0.165 | 0.030 | 0.093 | 0.530 | 0.132 | 0.195 | 3.506 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 46 | 41 | 45 | 50 | 75 | 255 | 103 | 70 | 45 |
| N.S. |
1 | 1.00 | 0.89 | 0.98 | 1.09 | 1.63 | 5.54 | 2.24 | 1.52 | 0.98 |
| time (sec) |
N/A | 0.316 | 0.070 | 0.129 | 0.035 | 0.096 | 0.365 | 0.126 | 0.189 | 3.493 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 40 | 40 | 37 | 39 | 48 | 69 | 236 | 83 | 66 | 38 |
| N.S. |
1 | 1.00 | 0.92 | 0.98 | 1.20 | 1.72 | 5.90 | 2.08 | 1.65 | 0.95 |
| time (sec) |
N/A | 0.290 | 0.069 | 0.116 | 0.028 | 0.087 | 0.301 | 0.122 | 0.186 | 3.435 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 34 | 34 | 36 | 34 | 36 | 33 | 44 | 0 | 30 | 32 |
| N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 0.97 | 1.29 | 0.00 | 0.88 | 0.94 |
| time (sec) |
N/A | 0.288 | 0.031 | 0.123 | 0.025 | 0.105 | 0.159 | 0.000 | 0.251 | 4.217 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 47 | 47 | 40 | 45 | 0 | 70 | 248 | 0 | 71 | 45 |
| N.S. |
1 | 1.00 | 0.85 | 0.96 | 0.00 | 1.49 | 5.28 | 0.00 | 1.51 | 0.96 |
| time (sec) |
N/A | 0.322 | 0.084 | 0.139 | 0.000 | 0.080 | 0.347 | 0.000 | 0.187 | 3.510 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 53 | 42 | 44 | 0 | 69 | 313 | 0 | 70 | 45 |
| N.S. |
1 | 1.00 | 0.79 | 0.83 | 0.00 | 1.30 | 5.91 | 0.00 | 1.32 | 0.85 |
| time (sec) |
N/A | 0.308 | 0.082 | 0.144 | 0.000 | 0.082 | 0.320 | 0.000 | 0.195 | 3.935 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 49 | 49 | 45 | 45 | 0 | 74 | 332 | 0 | 73 | 45 |
| N.S. |
1 | 1.00 | 0.92 | 0.92 | 0.00 | 1.51 | 6.78 | 0.00 | 1.49 | 0.92 |
| time (sec) |
N/A | 0.315 | 0.085 | 0.141 | 0.000 | 0.086 | 0.548 | 0.000 | 0.204 | 3.537 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 76 | 76 | 70 | 76 | 96 | 189 | 770 | 275 | 151 | 80 |
| N.S. |
1 | 1.00 | 0.92 | 1.00 | 1.26 | 2.49 | 10.13 | 3.62 | 1.99 | 1.05 |
| time (sec) |
N/A | 0.378 | 0.121 | 0.256 | 0.027 | 0.113 | 0.686 | 0.126 | 0.202 | 3.734 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 76 | 76 | 70 | 76 | 93 | 189 | 767 | 275 | 151 | 80 |
| N.S. |
1 | 1.00 | 0.92 | 1.00 | 1.22 | 2.49 | 10.09 | 3.62 | 1.99 | 1.05 |
| time (sec) |
N/A | 0.373 | 0.101 | 0.240 | 0.031 | 0.087 | 0.531 | 0.130 | 0.210 | 3.677 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 70 | 70 | 70 | 68 | 94 | 175 | 726 | 232 | 146 | 71 |
| N.S. |
1 | 1.00 | 1.00 | 0.97 | 1.34 | 2.50 | 10.37 | 3.31 | 2.09 | 1.01 |
| time (sec) |
N/A | 0.348 | 0.105 | 0.211 | 0.056 | 0.088 | 0.552 | 0.129 | 0.235 | 3.754 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | A | F | B | B |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 55 | 52 | 59 | 62 | 70 | 60 | 80 | 0 | 44 | 61 |
| N.S. |
1 | 0.95 | 1.07 | 1.13 | 1.27 | 1.09 | 1.45 | 0.00 | 0.80 | 1.11 |
| time (sec) |
N/A | 0.316 | 0.059 | 0.210 | 0.031 | 0.113 | 0.177 | 0.000 | 0.213 | 3.702 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 78 | 78 | 68 | 75 | 0 | 177 | 785 | 0 | 148 | 80 |
| N.S. |
1 | 1.00 | 0.87 | 0.96 | 0.00 | 2.27 | 10.06 | 0.00 | 1.90 | 1.03 |
| time (sec) |
N/A | 0.378 | 0.128 | 0.231 | 0.000 | 0.081 | 0.483 | 0.000 | 0.207 | 3.698 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 84 | 71 | 76 | 0 | 179 | 955 | 0 | 152 | 80 |
| N.S. |
1 | 1.00 | 0.85 | 0.90 | 0.00 | 2.13 | 11.37 | 0.00 | 1.81 | 0.95 |
| time (sec) |
N/A | 0.382 | 0.123 | 0.233 | 0.000 | 0.084 | 0.599 | 0.000 | 0.222 | 3.679 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 84 | 71 | 76 | 0 | 179 | 959 | 0 | 152 | 80 |
| N.S. |
1 | 1.00 | 0.85 | 0.90 | 0.00 | 2.13 | 11.42 | 0.00 | 1.81 | 0.95 |
| time (sec) |
N/A | 0.389 | 0.124 | 0.230 | 0.000 | 0.093 | 0.621 | 0.000 | 0.191 | 3.793 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | B | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 56 | 56 | 75 | 0 | 0 | 0 | 162 | 0 | 5 | 0 |
| N.S. |
1 | 1.00 | 1.34 | 0.00 | 0.00 | 0.00 | 2.89 | 0.00 | 0.09 | 0.00 |
| time (sec) |
N/A | 0.307 | 0.078 | 0.000 | 0.000 | 0.000 | 1.789 | 0.000 | 0.189 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | B | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 56 | 56 | 75 | 0 | 0 | 0 | 162 | 0 | 5 | 0 |
| N.S. |
1 | 1.00 | 1.34 | 0.00 | 0.00 | 0.00 | 2.89 | 0.00 | 0.09 | 0.00 |
| time (sec) |
N/A | 0.298 | 0.064 | 0.000 | 0.000 | 0.000 | 1.720 | 0.000 | 0.192 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | B | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 42 | 40 | 0 | 0 | 0 | 110 | 0 | 1 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 2.62 | 0.00 | 0.02 | 0.00 |
| time (sec) |
N/A | 0.280 | 0.090 | 0.000 | 0.000 | 0.000 | 1.219 | 0.000 | 0.186 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 38 | 38 | 38 | 50 | 34 | 83 | 0 | 2 | 35 |
| N.S. |
1 | 1.09 | 1.09 | 1.09 | 1.43 | 0.97 | 2.37 | 0.00 | 0.06 | 1.00 |
| time (sec) |
N/A | 0.323 | 0.043 | 0.104 | 0.034 | 0.091 | 0.562 | 0.000 | 0.183 | 3.621 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | B | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 55 | 55 | 73 | 0 | 0 | 0 | 0 | 0 | 5 | 0 |
| N.S. |
1 | 1.00 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
| time (sec) |
N/A | 0.307 | 0.082 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | B | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 76 | 0 | 0 | 0 | 0 | 0 | 5 | 0 |
| N.S. |
1 | 1.00 | 1.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
| time (sec) |
N/A | 0.315 | 0.074 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.207 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | B | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 76 | 0 | 0 | 0 | 0 | 0 | 5 | 0 |
| N.S. |
1 | 1.00 | 1.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
| time (sec) |
N/A | 0.319 | 0.082 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.202 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 84 | 75 | 0 | 0 | 0 | 767 | 0 | 15 | 0 |
| N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 9.13 | 0.00 | 0.18 | 0.00 |
| time (sec) |
N/A | 0.361 | 0.075 | 0.000 | 0.000 | 0.000 | 6.193 | 0.000 | 0.191 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 84 | 75 | 0 | 0 | 0 | 767 | 0 | 13 | 0 |
| N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 9.13 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 0.355 | 0.067 | 0.000 | 0.000 | 0.000 | 4.266 | 0.000 | 0.199 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 71 | 72 | 56 | 0 | 0 | 0 | 741 | 0 | 11 | 0 |
| N.S. |
1 | 1.01 | 0.79 | 0.00 | 0.00 | 0.00 | 10.44 | 0.00 | 0.15 | 0.00 |
| time (sec) |
N/A | 0.335 | 0.051 | 0.000 | 0.000 | 0.000 | 3.844 | 0.000 | 0.216 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 52 | 52 | 47 | 54 | 63 | 73 | 248 | 0 | 22 | 52 |
| N.S. |
1 | 1.00 | 0.90 | 1.04 | 1.21 | 1.40 | 4.77 | 0.00 | 0.42 | 1.00 |
| time (sec) |
N/A | 0.350 | 0.077 | 0.122 | 0.035 | 0.086 | 1.107 | 0.000 | 0.187 | 3.612 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 81 | 81 | 73 | 0 | 0 | 0 | 780 | 0 | 18 | 0 |
| N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 9.63 | 0.00 | 0.22 | 0.00 |
| time (sec) |
N/A | 0.373 | 0.080 | 0.000 | 0.000 | 0.000 | 12.449 | 0.000 | 0.210 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 85 | 76 | 0 | 0 | 0 | 821 | 0 | 18 | 0 |
| N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 9.66 | 0.00 | 0.21 | 0.00 |
| time (sec) |
N/A | 0.352 | 0.087 | 0.000 | 0.000 | 0.000 | 27.407 | 0.000 | 0.219 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 85 | 76 | 0 | 0 | 0 | 821 | 0 | 18 | 0 |
| N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 9.66 | 0.00 | 0.21 | 0.00 |
| time (sec) |
N/A | 0.353 | 0.078 | 0.000 | 0.000 | 0.000 | 49.214 | 0.000 | 0.208 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 87 | 75 | 0 | 0 | 0 | 2360 | 0 | 28 | 0 |
| N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 27.13 | 0.00 | 0.32 | 0.00 |
| time (sec) |
N/A | 0.351 | 0.081 | 0.000 | 0.000 | 0.000 | 68.190 | 0.000 | 0.268 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 86 | 75 | 0 | 0 | 0 | 2315 | 0 | 26 | 0 |
| N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 26.92 | 0.00 | 0.30 | 0.00 |
| time (sec) |
N/A | 0.348 | 0.069 | 0.000 | 0.000 | 0.000 | 49.539 | 0.000 | 0.187 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 78 | 58 | 0 | 0 | 0 | 2319 | 0 | 24 | 0 |
| N.S. |
1 | 1.28 | 0.95 | 0.00 | 0.00 | 0.00 | 38.02 | 0.00 | 0.39 | 0.00 |
| time (sec) |
N/A | 0.335 | 0.061 | 0.000 | 0.000 | 0.000 | 49.664 | 0.000 | 0.192 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 69 | 64 | 68 | 106 | 133 | 542 | 0 | 61 | 83 |
| N.S. |
1 | 0.96 | 0.89 | 0.94 | 1.47 | 1.85 | 7.53 | 0.00 | 0.85 | 1.15 |
| time (sec) |
N/A | 0.364 | 0.102 | 0.154 | 0.036 | 0.090 | 2.041 | 0.000 | 0.197 | 3.715 |
| 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 | 89 | 89 | 73 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
| N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
| time (sec) |
N/A | 0.361 | 0.088 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 87 | 76 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
| N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
| time (sec) |
N/A | 0.356 | 0.086 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 90 | 76 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
| N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
| time (sec) |
N/A | 0.352 | 0.087 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.209 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | A | A | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 55 | 55 | 55 | 243 | 58 | 83 | 0 | 71 | 75 | 50 |
| N.S. |
1 | 1.00 | 1.00 | 4.42 | 1.05 | 1.51 | 0.00 | 1.29 | 1.36 | 0.91 |
| time (sec) |
N/A | 0.314 | 0.173 | 0.198 | 0.030 | 0.093 | 0.000 | 0.137 | 0.213 | 3.970 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | A | A | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 55 | 55 | 55 | 243 | 58 | 83 | 0 | 71 | 75 | 50 |
| N.S. |
1 | 1.00 | 1.00 | 4.42 | 1.05 | 1.51 | 0.00 | 1.29 | 1.36 | 0.91 |
| time (sec) |
N/A | 0.322 | 0.163 | 0.165 | 0.031 | 0.098 | 0.000 | 0.134 | 0.188 | 3.958 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 55 | 55 | 55 | 243 | 58 | 83 | 301 | 71 | 75 | 50 |
| N.S. |
1 | 1.00 | 1.00 | 4.42 | 1.05 | 1.51 | 5.47 | 1.29 | 1.36 | 0.91 |
| time (sec) |
N/A | 0.312 | 0.203 | 0.138 | 0.032 | 0.096 | 16.262 | 0.130 | 0.187 | 4.555 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 55 | 55 | 55 | 209 | 58 | 83 | 126 | 71 | 73 | 50 |
| N.S. |
1 | 1.00 | 1.00 | 3.80 | 1.05 | 1.51 | 2.29 | 1.29 | 1.33 | 0.91 |
| time (sec) |
N/A | 0.319 | 0.154 | 0.144 | 0.027 | 0.101 | 1.397 | 0.126 | 0.257 | 3.988 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 53 | 52 | 240 | 58 | 77 | 134 | 58 | 69 | 50 |
| N.S. |
1 | 1.00 | 0.98 | 4.53 | 1.09 | 1.45 | 2.53 | 1.09 | 1.30 | 0.94 |
| time (sec) |
N/A | 0.320 | 0.130 | 0.139 | 0.030 | 0.116 | 1.806 | 0.121 | 0.197 | 4.183 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-2) | A | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 53 | 53 | 55 | 243 | 0 | 83 | 366 | 0 | 74 | 52 |
| N.S. |
1 | 1.00 | 1.04 | 4.58 | 0.00 | 1.57 | 6.91 | 0.00 | 1.40 | 0.98 |
| time (sec) |
N/A | 0.320 | 0.262 | 0.139 | 0.000 | 0.106 | 1.289 | 0.000 | 0.209 | 4.418 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-2) | A | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 55 | 55 | 57 | 243 | 0 | 87 | 389 | 0 | 77 | 52 |
| N.S. |
1 | 1.00 | 1.04 | 4.42 | 0.00 | 1.58 | 7.07 | 0.00 | 1.40 | 0.95 |
| time (sec) |
N/A | 0.317 | 0.175 | 0.142 | 0.000 | 0.092 | 6.349 | 0.000 | 0.188 | 4.407 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-2) | A | B | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 55 | 55 | 57 | 243 | 0 | 87 | 389 | 0 | 77 | 52 |
| N.S. |
1 | 1.00 | 1.04 | 4.42 | 0.00 | 1.58 | 7.07 | 0.00 | 1.40 | 0.95 |
| time (sec) |
N/A | 0.316 | 0.176 | 0.143 | 0.000 | 0.090 | 25.563 | 0.000 | 0.196 | 4.328 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | A | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 88 | 88 | 87 | 621 | 104 | 191 | 0 | 123 | 154 | 85 |
| N.S. |
1 | 1.00 | 0.99 | 7.06 | 1.18 | 2.17 | 0.00 | 1.40 | 1.75 | 0.97 |
| time (sec) |
N/A | 0.392 | 0.281 | 0.447 | 0.031 | 0.104 | 0.000 | 0.139 | 0.189 | 4.198 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | A | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 88 | 88 | 87 | 621 | 104 | 191 | 842 | 123 | 154 | 85 |
| N.S. |
1 | 1.00 | 0.99 | 7.06 | 1.18 | 2.17 | 9.57 | 1.40 | 1.75 | 0.97 |
| time (sec) |
N/A | 0.379 | 0.305 | 0.284 | 0.032 | 0.098 | 177.029 | 0.135 | 0.216 | 4.222 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | A | B | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 90 | 87 | 564 | 104 | 190 | 218 | 123 | 152 | 85 |
| N.S. |
1 | 1.00 | 0.97 | 6.27 | 1.16 | 2.11 | 2.42 | 1.37 | 1.69 | 0.94 |
| time (sec) |
N/A | 0.361 | 0.266 | 0.285 | 0.032 | 0.119 | 1.957 | 0.139 | 0.189 | 4.043 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | A | B | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 86 | 84 | 614 | 104 | 184 | 233 | 104 | 148 | 85 |
| N.S. |
1 | 1.00 | 0.98 | 7.14 | 1.21 | 2.14 | 2.71 | 1.21 | 1.72 | 0.99 |
| time (sec) |
N/A | 0.374 | 0.213 | 0.279 | 0.031 | 0.107 | 3.032 | 0.131 | 0.203 | 4.132 |