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 | A | A | B | A | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 263 | 263 | 187 | 887 | 320 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.71 | 3.37 | 1.22 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.237 | 1.285 | 2.180 | 0.265 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | B | A | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 204 | 204 | 463 | 666 | 259 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 2.27 | 3.26 | 1.27 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.190 | 1.595 | 0.082 | 0.260 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | A | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 136 | 136 | 98 | 312 | 202 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.72 | 2.29 | 1.49 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.142 | 0.204 | 0.070 | 0.262 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 81 | 81 | 55 | 91 | 139 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.68 | 1.12 | 1.72 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.060 | 0.050 | 1.846 | 0.262 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 148 | 148 | 634 | 931 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 4.28 | 6.29 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.062 | 2.169 | 20.375 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | A | A | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 251 | 251 | 208 | 356 | 244 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.83 | 1.42 | 0.97 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.488 | 1.020 | 2.449 | 0.260 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | A | A | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 370 | 370 | 271 | 449 | 360 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.73 | 1.21 | 0.97 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.586 | 2.091 | 0.213 | 0.270 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 56 | 56 | 75 | 160 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.34 | 2.86 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
| time (sec) |
N/A | 0.093 | 0.071 | 10.561 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | B | B | B | B | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 72 | 78 | 88 | 349 | 500 | 231 | 363 | 414 |
| N.S. | 1 | 1.00 | 1.08 | 1.22 | 4.85 | 6.94 | 3.21 | 5.04 | 5.75 |
| time (sec) |
N/A | 0.045 | 0.039 | 1.542 | 0.260 | 0.383 | 1.422 | 0.450 | 1.421 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | B | B | B | B | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 69 | 59 | 77 | 219 | 348 | 180 | 322 | 237 |
| N.S. | 1 | 1.00 | 0.86 | 1.12 | 3.17 | 5.04 | 2.61 | 4.67 | 3.43 |
| time (sec) |
N/A | 0.044 | 0.032 | 0.562 | 0.257 | 0.385 | 1.074 | 0.436 | 0.618 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | B | B | B | B | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 48 | 48 | 77 | 65 | 117 | 121 | 95 | 180 | 73 |
| N.S. | 1 | 1.00 | 1.60 | 1.35 | 2.44 | 2.52 | 1.98 | 3.75 | 1.52 |
| time (sec) |
N/A | 0.023 | 0.022 | 0.040 | 0.266 | 0.344 | 0.681 | 0.422 | 1.842 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | A | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 54 | 54 | 288 | 78 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 5.33 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
| time (sec) |
N/A | 0.031 | 0.089 | 0.793 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | B | B | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 63 | 69 | 75 | 88 | 114 | 235 | 152 | 122 |
| N.S. | 1 | 1.00 | 1.10 | 1.19 | 1.40 | 1.81 | 3.73 | 2.41 | 1.94 |
| time (sec) |
N/A | 0.039 | 0.078 | 0.591 | 0.262 | 0.432 | 1.204 | 0.412 | 1.369 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | B | B | B | B | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 63 | 100 | 77 | 121 | 166 | 313 | 194 | 67 |
| N.S. | 1 | 1.00 | 1.59 | 1.22 | 1.92 | 2.63 | 4.97 | 3.08 | 1.06 |
| time (sec) |
N/A | 0.034 | 0.034 | 0.577 | 0.259 | 0.368 | 1.464 | 0.408 | 1.732 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 159 | 159 | 148 | 357 | 755 | 1288 | 581 | 733 | 1730 |
| N.S. | 1 | 1.00 | 0.93 | 2.25 | 4.75 | 8.10 | 3.65 | 4.61 | 10.88 |
| time (sec) |
N/A | 0.177 | 0.058 | 2.698 | 0.459 | 0.379 | 2.384 | 0.462 | 2.124 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | B | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 179 | 179 | 150 | 342 | 572 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.84 | 1.91 | 3.20 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.168 | 0.290 | 4.122 | 0.452 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 95 | 134 | 272 | 320 | 333 | 238 | 351 | 432 |
| N.S. | 1 | 1.00 | 1.41 | 2.86 | 3.37 | 3.51 | 2.51 | 3.69 | 4.55 |
| time (sec) |
N/A | 0.091 | 0.041 | 0.078 | 0.443 | 0.403 | 1.100 | 0.423 | 1.563 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 168 | 168 | 424 | 840 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 2.52 | 5.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.219 | 0.262 | 11.776 | 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 | 104 | 104 | 126 | 346 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.21 | 3.33 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.131 | 0.170 | 1.792 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 119 | 136 | 324 | 309 | 348 | 1102 | 375 | 776 |
| N.S. | 1 | 1.00 | 1.14 | 2.72 | 2.60 | 2.92 | 9.26 | 3.15 | 6.52 |
| time (sec) |
N/A | 0.128 | 0.116 | 0.769 | 0.279 | 0.385 | 1.587 | 0.419 | 2.418 |
| 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 | 180 | 180 | 218 | 427 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.21 | 2.37 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.190 | 0.359 | 1.750 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 172 | 172 | 218 | 375 | 582 | 789 | 3516 | 730 | 2746 |
| N.S. | 1 | 1.00 | 1.27 | 2.18 | 3.38 | 4.59 | 20.44 | 4.24 | 15.97 |
| time (sec) |
N/A | 0.189 | 0.158 | 0.790 | 0.307 | 0.388 | 5.387 | 0.428 | 3.424 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 263 | 263 | 336 | 1345 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.28 | 5.11 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.337 | 0.445 | 15.654 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | C | B | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 160 | 160 | 213 | 6414 | 628 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.33 | 40.09 | 3.92 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.189 | 0.760 | 2.888 | 0.457 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 257 | 257 | 599 | 1738 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 2.33 | 6.76 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.349 | 0.561 | 3.531 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 143 | 143 | 248 | 1867 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.73 | 13.06 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.208 | 0.626 | 2.885 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 166 | 166 | 335 | 5530 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 2.02 | 33.31 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.235 | 0.829 | 3.134 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 269 | 269 | 393 | 2080 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.46 | 7.73 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.364 | 0.914 | 6.384 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | B | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 21 | 21 | 31 | 34 | 58 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.48 | 1.62 | 2.76 | 0.00 | 0.00 | 0.00 | -0.05 |
| time (sec) |
N/A | 0.017 | 0.005 | 0.934 | 0.251 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | B | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 32 | 32 | 52 | 62 | 132 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.62 | 1.94 | 4.12 | 0.00 | 0.00 | 0.00 | -0.03 |
| time (sec) |
N/A | 0.022 | 0.007 | 0.874 | 0.260 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 168 | 168 | 270 | 982 | 331 | 818 | 644 | 2336 | 737 |
| N.S. | 1 | 1.00 | 1.61 | 5.85 | 1.97 | 4.87 | 3.83 | 13.90 | 4.39 |
| time (sec) |
N/A | 0.238 | 0.160 | 1.395 | 0.256 | 0.408 | 2.073 | 0.460 | 1.724 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | A | B | B | B | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 120 | 120 | 174 | 590 | 207 | 421 | 369 | 976 | 381 |
| N.S. | 1 | 1.00 | 1.45 | 4.92 | 1.72 | 3.51 | 3.08 | 8.13 | 3.18 |
| time (sec) |
N/A | 0.148 | 0.119 | 0.699 | 0.261 | 0.405 | 2.258 | 0.430 | 1.387 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | A | A | B | B | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 97 | 97 | 138 | 185 | 111 | 177 | 173 | 341 | 136 |
| N.S. | 1 | 1.00 | 1.42 | 1.91 | 1.14 | 1.82 | 1.78 | 3.52 | 1.40 |
| time (sec) |
N/A | 0.122 | 0.074 | 0.194 | 0.255 | 0.368 | 1.037 | 0.429 | 1.337 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 40 | 40 | 48 | 44 | 36 | 61 | 46 | 200 | 48 |
| N.S. | 1 | 1.00 | 1.20 | 1.10 | 0.90 | 1.52 | 1.15 | 5.00 | 1.20 |
| time (sec) |
N/A | 0.019 | 0.021 | 0.584 | 0.264 | 0.383 | 0.235 | 0.398 | 1.440 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | A | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 130 | 130 | 329 | 220 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 2.53 | 1.69 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.098 | 0.365 | 13.642 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | B | B | B | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 115 | 125 | 170 | 128 | 517 | 1658 | 474 | 170 |
| N.S. | 1 | 1.00 | 1.09 | 1.48 | 1.11 | 4.50 | 14.42 | 4.12 | 1.48 |
| time (sec) |
N/A | 0.118 | 0.132 | 0.760 | 0.259 | 0.497 | 4.616 | 0.428 | 1.638 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | B | B | B | B |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 167 | 174 | 266 | 316 | 2443 | 19912 | 2567 | 417 |
| N.S. | 1 | 1.00 | 1.04 | 1.59 | 1.89 | 14.63 | 119.23 | 15.37 | 2.50 |
| time (sec) |
N/A | 0.178 | 0.261 | 0.844 | 0.283 | 1.086 | 12.566 | 0.499 | 3.034 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | B | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 562 | 562 | 1082 | 4769 | 1438 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.93 | 8.49 | 2.56 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.713 | 5.988 | 1.096 | 0.464 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | B | B | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 374 | 374 | 795 | 2890 | 857 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 2.13 | 7.73 | 2.29 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.438 | 2.900 | 0.722 | 0.452 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | B | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 221 | 220 | 271 | 812 | 435 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.23 | 3.67 | 1.97 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.319 | 0.322 | 0.317 | 0.448 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 97 | 97 | 107 | 140 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.10 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.080 | 0.154 | 1.751 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | F | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 214 | 214 | 2404 | 1872 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 11.23 | 8.75 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.109 | 20.621 | 30.398 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | A | F | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 480 | 485 | 425 | 857 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.01 | 0.89 | 1.79 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.241 | 5.923 | 4.883 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F | F | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 750 | 750 | 1968 | 1491 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 2.62 | 1.99 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.559 | 14.704 | 2.155 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | B | C | F | F | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 546 | 546 | 1646 | 12235 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 3.01 | 22.41 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.746 | 8.067 | 50.183 | 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 | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 326 | 325 | 566 | 19935 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.74 | 61.15 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.577 | 0.718 | 3.832 | 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 | 132 | 132 | 205 | 284 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.55 | 2.15 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.163 | 0.178 | 0.496 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | F | C | F | F | F | F | F |
| verified |
N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 308 | 308 | 0 | 3825 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.00 | 12.42 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.132 | 46.229 | 7.704 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | F | F | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 1089 | 1094 | 2701 | 5732 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 2.48 | 5.26 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 2.066 | 20.885 | 4.011 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | A |
| verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
| time (sec) |
N/A | 0.046 | 3.608 | 2.539 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | A |
| verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
| time (sec) |
N/A | 0.045 | 0.235 | 2.371 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | F | F | F | F | F | F | F |
| verified |
N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 162 | 162 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.195 | 0.048 | 1.927 | 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 | F | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 780 | 780 | 623 | 743 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.80 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.978 | 0.532 | 5.955 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | B | C | F | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 481 | 481 | 365 | 1289 | 591 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.76 | 2.68 | 1.23 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.437 | 0.222 | 4.041 | 0.591 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | A | A | A | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 120 | 120 | 138 | 184 | 192 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 1.15 | 1.53 | 1.60 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.091 | 0.011 | 12.585 | 0.259 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | A | A | F | F | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 186 | 186 | 759 | 305 | 192 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 4.08 | 1.64 | 1.03 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.173 | 3.163 | 8.188 | 0.265 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | C | F | F(-1) | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 545 | 545 | 1456 | 10288 | 651 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 2.67 | 18.88 | 1.19 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.649 | 20.077 | 2.897 | 0.555 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | C | F | F | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 832 | 832 | 917 | 638 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 1.10 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 1.103 | 4.662 | 1.975 | 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 | F | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 585 | 585 | 549 | 773 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.94 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.869 | 0.380 | 2.066 | 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 | F | F(-1) | F | F |
| verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 661 | 661 | 598 | 1001 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 0.90 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.790 | 0.445 | 1.604 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
A | A | C | B | F(-2) | F | F(-1) | F | F |
| verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 335 | 335 | 1208 | 2132 | 0 | 0 | 0 | 0 | -1 |
| N.S. |
1 | 1.00 | 3.61 | 6.36 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
| time (sec) |
N/A | 0.522 | 27.371 | 5.385 | 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 | 83 | 83 | 76 | 168 | 0 | 0 | 0 | 0 | -1 |
| N.S. | 1 | 1.00 | 0.92 | 2.02 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
| time (sec) |
N/A | 0.180 | 0.059 | 2.027 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |