Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 201 | 190 | 173 | 0 | 0 | 204 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.86 | 0.00 | 0.00 | 1.01 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.288 | 0.413 | 0.000 | 0.000 | 0.279 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 141 | 134 | 123 | 0 | 0 | 113 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.87 | 0.00 | 0.00 | 0.80 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.265 | 0.224 | 0.000 | 0.000 | 0.279 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 81 | 78 | 73 | 0 | 0 | 51 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.90 | 0.00 | 0.00 | 0.63 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.232 | 0.193 | 0.000 | 0.000 | 0.284 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 20 | 20 | 20 | 19 | 0 | 18 | 41 | 18 | 18 |
| N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.00 | 0.90 | 2.05 | 0.90 | 0.90 |
| time (sec) |
N/A | 0.196 | 0.025 | 0.950 | 0.000 | 0.270 | 0.953 | 0.323 | 17.024 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 63 | 65 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.217 | 0.082 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 63 | 65 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.218 | 0.096 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 365 | 327 | 280 | 0 | 0 | 654 | 0 | 0 | 0 |
| N.S. |
1 | 0.90 | 0.77 | 0.00 | 0.00 | 1.79 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.503 | 4.201 | 0.000 | 0.000 | 0.311 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 239 | 217 | 186 | 0 | 0 | 239 | 0 | 0 | 0 |
| N.S. |
1 | 0.91 | 0.78 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.372 | 1.496 | 0.000 | 0.000 | 0.311 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 104 | 89 | 0 | 0 | 80 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.83 | 0.00 | 0.00 | 0.75 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.256 | 0.997 | 0.000 | 0.000 | 0.317 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 122 | 122 | 112 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.372 | 1.212 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 122 | 122 | 112 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.359 | 1.334 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 104 | 89 | 0 | 0 | 80 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.83 | 0.00 | 0.00 | 0.75 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.309 | 0.009 | 0.000 | 0.000 | 0.288 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 122 | 122 | 112 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.532 | 0.007 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 297 | 266 | 228 | 0 | 0 | 377 | 0 | 0 | 0 |
| N.S. |
1 | 0.90 | 0.77 | 0.00 | 0.00 | 1.27 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.471 | 6.541 | 0.000 | 0.000 | 0.298 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 171 | 156 | 135 | 0 | 0 | 122 | 0 | 0 | 0 |
| N.S. |
1 | 0.91 | 0.79 | 0.00 | 0.00 | 0.71 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.414 | 2.242 | 0.000 | 0.000 | 0.335 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 41 | 41 | 36 | 0 | 0 | 41 | 0 | 0 | 41 |
| N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 1.00 |
| time (sec) |
N/A | 0.342 | 0.252 | 0.000 | 0.000 | 0.273 | 0.000 | 0.000 | 17.344 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 122 | 122 | 112 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.387 | 3.108 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F(-1) | F | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 41 | 41 | 36 | 0 | 0 | 41 | 0 | 0 | 39 |
| N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.95 |
| time (sec) |
N/A | 0.507 | 0.008 | 0.000 | 0.000 | 0.274 | 0.000 | 0.000 | 16.689 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 327 | 208 | 175 | 0 | 0 | 231 | 0 | 0 | 0 |
| N.S. |
1 | 0.64 | 0.54 | 0.00 | 0.00 | 0.71 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.677 | 0.165 | 0.000 | 0.000 | 0.309 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 93 | 76 | 0 | 0 | 117 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 1.26 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.605 | 0.034 | 0.000 | 0.000 | 0.290 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 177 | 177 | 152 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.659 | 0.130 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 93 | 76 | 0 | 0 | 117 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 1.26 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.796 | 0.021 | 0.000 | 0.000 | 0.282 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 191 | 191 | 772 | 272 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 4.04 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.701 | 4.191 | 4.541 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 81 | 81 | 191 | 74 | 0 | 141 | 70 | 266 | 50 |
| N.S. |
1 | 1.00 | 2.36 | 0.91 | 0.00 | 1.74 | 0.86 | 3.28 | 0.62 |
| time (sec) |
N/A | 0.246 | 0.087 | 0.159 | 0.000 | 0.332 | 0.318 | 0.403 | 0.111 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 73 | 73 | 233 | 66 | 0 | 146 | 63 | 282 | 28 |
| N.S. |
1 | 1.00 | 3.19 | 0.90 | 0.00 | 2.00 | 0.86 | 3.86 | 0.38 |
| time (sec) |
N/A | 0.217 | 0.097 | 0.148 | 0.000 | 0.367 | 0.334 | 0.405 | 17.812 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 38 | 38 | 87 | 70 | 0 | 153 | 70 | 67 | 54 |
| N.S. |
1 | 1.00 | 2.29 | 1.84 | 0.00 | 4.03 | 1.84 | 1.76 | 1.42 |
| time (sec) |
N/A | 0.232 | 0.047 | 0.080 | 0.000 | 0.325 | 0.382 | 0.334 | 0.221 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 38 | 38 | 87 | 72 | 0 | 155 | 63 | 63 | 67 |
| N.S. |
1 | 1.00 | 2.29 | 1.89 | 0.00 | 4.08 | 1.66 | 1.66 | 1.76 |
| time (sec) |
N/A | 0.225 | 0.041 | 0.081 | 0.000 | 0.323 | 0.407 | 0.329 | 17.550 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 38 | 54 | 38 | 78 | 0 | 144 | 109 | 0 | 196 |
| N.S. |
1 | 1.42 | 1.00 | 2.05 | 0.00 | 3.79 | 2.87 | 0.00 | 5.16 |
| time (sec) |
N/A | 0.268 | 0.279 | 0.334 | 0.000 | 0.356 | 15.540 | 0.000 | 17.515 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 38 | 54 | 38 | 72 | 0 | 144 | 99 | 0 | 139 |
| N.S. |
1 | 1.42 | 1.00 | 1.89 | 0.00 | 3.79 | 2.61 | 0.00 | 3.66 |
| time (sec) |
N/A | 0.257 | 0.259 | 0.328 | 0.000 | 0.371 | 15.593 | 0.000 | 20.079 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 49 | 42 | 42 | 36 | 155 | 78 | 39 | 42 |
| N.S. |
1 | 1.17 | 1.00 | 1.00 | 0.86 | 3.69 | 1.86 | 0.93 | 1.00 |
| time (sec) |
N/A | 0.189 | 0.016 | 0.075 | 0.271 | 0.329 | 0.351 | 0.421 | 0.113 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 44 | 51 | 46 | 42 | 67 | 168 | 75 | 42 | 199 |
| N.S. |
1 | 1.16 | 1.05 | 0.95 | 1.52 | 3.82 | 1.70 | 0.95 | 4.52 |
| time (sec) |
N/A | 0.187 | 0.018 | 0.064 | 0.262 | 0.294 | 0.391 | 0.398 | 17.483 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | B | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 40 | 40 | 85 | 74 | 0 | 208 | 90 | 0 | 278 |
| N.S. |
1 | 1.00 | 2.12 | 1.85 | 0.00 | 5.20 | 2.25 | 0.00 | 6.95 |
| time (sec) |
N/A | 0.284 | 0.034 | 0.222 | 0.000 | 0.310 | 0.651 | 0.000 | 17.466 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | B | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 40 | 40 | 85 | 77 | 0 | 213 | 80 | 0 | 30 |
| N.S. |
1 | 1.00 | 2.12 | 1.92 | 0.00 | 5.32 | 2.00 | 0.00 | 0.75 |
| time (sec) |
N/A | 0.280 | 0.035 | 0.222 | 0.000 | 0.296 | 0.680 | 0.000 | 0.155 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 78 | 42 | 78 | 0 | 146 | 122 | 0 | 0 |
| N.S. |
1 | 1.86 | 1.00 | 1.86 | 0.00 | 3.48 | 2.90 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.366 | 1.017 | 1.106 | 0.000 | 0.287 | 98.471 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | B | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 78 | 42 | 74 | 0 | 146 | 112 | 0 | 0 |
| N.S. |
1 | 1.86 | 1.00 | 1.76 | 0.00 | 3.48 | 2.67 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.349 | 0.247 | 1.091 | 0.000 | 0.316 | 97.943 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 40 | 40 | 86 | 74 | 0 | 153 | 73 | 71 | 233 |
| N.S. |
1 | 1.00 | 2.15 | 1.85 | 0.00 | 3.82 | 1.82 | 1.78 | 5.82 |
| time (sec) |
N/A | 0.245 | 0.033 | 0.079 | 0.000 | 0.300 | 0.611 | 0.355 | 16.921 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 40 | 40 | 86 | 74 | 0 | 155 | 66 | 67 | 67 |
| N.S. |
1 | 1.00 | 2.15 | 1.85 | 0.00 | 3.88 | 1.65 | 1.68 | 1.68 |
| time (sec) |
N/A | 0.256 | 0.032 | 0.093 | 0.000 | 0.303 | 0.615 | 0.340 | 17.371 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 49 | 42 | 42 | 36 | 155 | 78 | 39 | 42 |
| N.S. |
1 | 1.17 | 1.00 | 1.00 | 0.86 | 3.69 | 1.86 | 0.93 | 1.00 |
| time (sec) |
N/A | 0.186 | 0.015 | 0.064 | 0.266 | 0.312 | 0.454 | 0.363 | 17.469 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 44 | 51 | 46 | 42 | 67 | 168 | 75 | 42 | 923 |
| N.S. |
1 | 1.16 | 1.05 | 0.95 | 1.52 | 3.82 | 1.70 | 0.95 | 20.98 |
| time (sec) |
N/A | 0.191 | 0.016 | 0.067 | 0.268 | 0.306 | 0.485 | 0.362 | 17.355 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 42 | 42 | 78 | 0 | 146 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.86 | 0.00 | 3.48 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.374 | 2.304 | 2.569 | 0.000 | 0.314 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 42 | 42 | 74 | 0 | 146 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.76 | 0.00 | 3.48 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.363 | 0.415 | 2.591 | 0.000 | 0.312 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 70 | 42 | 84 | 0 | 165 | 0 | 0 | 0 |
| N.S. |
1 | 1.67 | 1.00 | 2.00 | 0.00 | 3.93 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.391 | 0.470 | 3.539 | 0.000 | 0.324 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 70 | 42 | 78 | 0 | 165 | 0 | 0 | 0 |
| N.S. |
1 | 1.67 | 1.00 | 1.86 | 0.00 | 3.93 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.393 | 0.570 | 3.455 | 0.000 | 0.313 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | A | A | A | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 134 | 109 | 108 | 1812 | 125 | 233 | 138 | 155 | 167 |
| N.S. |
1 | 0.81 | 0.81 | 13.52 | 0.93 | 1.74 | 1.03 | 1.16 | 1.25 |
| time (sec) |
N/A | 0.500 | 0.163 | 0.135 | 0.191 | 0.292 | 1.913 | 0.341 | 17.478 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | A | A | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 69 | 64 | 66 | 1699 | 62 | 161 | 85 | 72 | 123 |
| N.S. |
1 | 0.93 | 0.96 | 24.62 | 0.90 | 2.33 | 1.23 | 1.04 | 1.78 |
| time (sec) |
N/A | 0.407 | 0.055 | 0.075 | 0.194 | 0.305 | 1.586 | 0.329 | 17.310 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 23 | 23 | 26 | 1628 | 21 | 105 | 46 | 22 | 45 |
| N.S. |
1 | 1.00 | 1.13 | 70.78 | 0.91 | 4.57 | 2.00 | 0.96 | 1.96 |
| time (sec) |
N/A | 0.303 | 0.024 | 0.070 | 0.183 | 0.290 | 1.206 | 0.365 | 18.109 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | A | A | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 88 | 86 | 69 | 1697 | 0 | 316 | 139 | 94 | 1270 |
| N.S. |
1 | 0.98 | 0.78 | 19.28 | 0.00 | 3.59 | 1.58 | 1.07 | 14.43 |
| time (sec) |
N/A | 0.430 | 0.077 | 0.078 | 0.000 | 0.360 | 2.932 | 0.333 | 18.189 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F | A | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 151 | 184 | 139 | 1910 | 0 | 530 | 0 | 210 | 4602 |
| N.S. |
1 | 1.22 | 0.92 | 12.65 | 0.00 | 3.51 | 0.00 | 1.39 | 30.48 |
| time (sec) |
N/A | 0.558 | 0.219 | 0.105 | 0.000 | 0.737 | 0.000 | 0.334 | 19.544 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 147 | 156 | 99 | 1780 | 0 | 1168 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.67 | 12.11 | 0.00 | 7.95 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.430 | 0.258 | 0.083 | 0.000 | 0.395 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 63 | 1718 | 0 | 510 | 0 | 107 | 0 |
| N.S. |
1 | 1.00 | 0.61 | 16.68 | 0.00 | 4.95 | 0.00 | 1.04 | 0.00 |
| time (sec) |
N/A | 0.249 | 0.209 | 0.076 | 0.000 | 0.315 | 0.000 | 0.329 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 160 | 168 | 105 | 1811 | 0 | 581 | 0 | 211 | 0 |
| N.S. |
1 | 1.05 | 0.66 | 11.32 | 0.00 | 3.63 | 0.00 | 1.32 | 0.00 |
| time (sec) |
N/A | 0.398 | 0.360 | 0.086 | 0.000 | 0.374 | 0.000 | 0.344 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | A | A | A | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 112 | 108 | 332 | 125 | 191 | 146 | 156 | 200 |
| N.S. |
1 | 0.80 | 0.77 | 2.37 | 0.89 | 1.36 | 1.04 | 1.11 | 1.43 |
| time (sec) |
N/A | 0.497 | 0.163 | 0.390 | 0.182 | 0.300 | 2.082 | 0.317 | 17.830 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | A | A | A | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 73 | 67 | 66 | 246 | 62 | 118 | 92 | 72 | 119 |
| N.S. |
1 | 0.92 | 0.90 | 3.37 | 0.85 | 1.62 | 1.26 | 0.99 | 1.63 |
| time (sec) |
N/A | 0.409 | 0.054 | 0.163 | 0.184 | 0.282 | 1.632 | 0.331 | 18.044 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | A | B | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 26 | 26 | 29 | 160 | 22 | 61 | 49 | 23 | 60 |
| N.S. |
1 | 1.00 | 1.12 | 6.15 | 0.85 | 2.35 | 1.88 | 0.88 | 2.31 |
| time (sec) |
N/A | 0.295 | 0.027 | 0.147 | 0.182 | 0.303 | 1.226 | 0.318 | 17.253 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | A | A | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 90 | 69 | 223 | 0 | 232 | 150 | 94 | 156 |
| N.S. |
1 | 0.97 | 0.74 | 2.40 | 0.00 | 2.49 | 1.61 | 1.01 | 1.68 |
| time (sec) |
N/A | 0.437 | 0.076 | 1.111 | 0.000 | 0.301 | 2.973 | 0.383 | 17.758 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F | A | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 154 | 187 | 139 | 405 | 0 | 445 | 0 | 211 | 248 |
| N.S. |
1 | 1.21 | 0.90 | 2.63 | 0.00 | 2.89 | 0.00 | 1.37 | 1.61 |
| time (sec) |
N/A | 0.549 | 0.210 | 0.970 | 0.000 | 0.367 | 0.000 | 0.320 | 18.896 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 311 | 325 | 296 | 994 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.95 | 3.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.778 | 10.432 | 0.992 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 304 | 307 | 252 | 665 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.83 | 2.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.626 | 10.205 | 0.881 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F(-2) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 300 | 312 | 425 | 665 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.42 | 2.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.670 | 10.461 | 0.863 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 319 | 342 | 496 | 1200 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 1.55 | 3.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.741 | 10.523 | 0.834 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 324 | 337 | 604 | 1049 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 1.86 | 3.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.715 | 13.067 | 0.914 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 135 | 320 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.329 | 0.550 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 167 | 156 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.420 | 0.407 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | B | A | B | A | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 27 | 27 | 32 | 0 | 61 | 25 | 49 | 26 | 25 |
| N.S. |
1 | 1.00 | 1.19 | 0.00 | 2.26 | 0.93 | 1.81 | 0.96 | 0.93 |
| time (sec) |
N/A | 0.297 | 0.059 | 0.000 | 0.199 | 0.263 | 6.000 | 0.311 | 16.922 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 8 | 8 | 8 | 7 | 6 | 6 | 7 | 6 | 6 |
| N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.88 | 0.75 | 0.75 |
| time (sec) |
N/A | 0.143 | 0.014 | 0.945 | 0.276 | 0.267 | 0.087 | 0.322 | 0.047 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 13 | 23 | 13 | 10 | 21 | 21 | 26 | 22 | 9 |
| N.S. |
1 | 1.77 | 1.00 | 0.77 | 1.62 | 1.62 | 2.00 | 1.69 | 0.69 |
| time (sec) |
N/A | 0.158 | 0.028 | 0.954 | 0.276 | 0.266 | 0.122 | 0.325 | 16.488 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 27 | 27 | 25 | 20 | 19 | 19 | 22 | 20 | 19 |
| N.S. |
1 | 1.00 | 0.93 | 0.74 | 0.70 | 0.70 | 0.81 | 0.74 | 0.70 |
| time (sec) |
N/A | 0.173 | 0.019 | 0.957 | 0.182 | 0.255 | 0.089 | 0.333 | 16.555 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 32 | 36 | 33 | 25 | 24 | 24 | 0 | 24 | 24 |
| N.S. |
1 | 1.12 | 1.03 | 0.78 | 0.75 | 0.75 | 0.00 | 0.75 | 0.75 |
| time (sec) |
N/A | 0.173 | 0.005 | 0.954 | 0.183 | 0.245 | 0.000 | 0.325 | 0.031 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 25 | 27 | 25 | 20 | 19 | 19 | 22 | 19 | 19 |
| N.S. |
1 | 1.08 | 1.00 | 0.80 | 0.76 | 0.76 | 0.88 | 0.76 | 0.76 |
| time (sec) |
N/A | 0.166 | 0.018 | 0.947 | 0.187 | 0.273 | 0.092 | 0.347 | 0.030 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 20 | 18 | 18 | 15 | 14 | 14 | 15 | 15 | 14 |
| N.S. |
1 | 0.90 | 0.90 | 0.75 | 0.70 | 0.70 | 0.75 | 0.75 | 0.70 |
| time (sec) |
N/A | 0.166 | 0.013 | 0.951 | 0.179 | 0.276 | 0.062 | 0.336 | 0.082 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 71 | 62 | 46 | 45 | 47 | 68 | 45 | 73 |
| N.S. |
1 | 1.15 | 1.00 | 0.74 | 0.73 | 0.76 | 1.10 | 0.73 | 1.18 |
| time (sec) |
N/A | 0.228 | 0.010 | 0.941 | 0.274 | 0.269 | 0.196 | 0.369 | 0.051 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 73 | 81 | 72 | 50 | 49 | 49 | 0 | 49 | 49 |
| N.S. |
1 | 1.11 | 0.99 | 0.68 | 0.67 | 0.67 | 0.00 | 0.67 | 0.67 |
| time (sec) |
N/A | 0.198 | 0.036 | 1.035 | 0.185 | 0.251 | 0.000 | 0.320 | 0.036 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 130 | 140 | 117 | 83 | 82 | 76 | 121 | 82 | 82 |
| N.S. |
1 | 1.08 | 0.90 | 0.64 | 0.63 | 0.58 | 0.93 | 0.63 | 0.63 |
| time (sec) |
N/A | 0.235 | 0.013 | 0.988 | 0.185 | 0.252 | 1.125 | 0.326 | 0.193 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | B | B | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 200 | 205 | 126 | 124 | 272 | 638 | 0 | 139 | 223 |
| N.S. |
1 | 1.02 | 0.63 | 0.62 | 1.36 | 3.19 | 0.00 | 0.70 | 1.12 |
| time (sec) |
N/A | 0.436 | 0.011 | 1.033 | 0.270 | 0.983 | 0.000 | 0.431 | 0.095 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 8 | 8 | 8 | 7 | 6 | 6 | 7 | 6 | 6 |
| N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.88 | 0.75 | 0.75 |
| time (sec) |
N/A | 0.130 | 0.002 | 1.009 | 0.275 | 0.281 | 0.106 | 0.346 | 0.143 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 19 | 25 | 19 | 16 | 15 | 15 | 17 | 15 | 15 |
| N.S. |
1 | 1.32 | 1.00 | 0.84 | 0.79 | 0.79 | 0.89 | 0.79 | 0.79 |
| time (sec) |
N/A | 0.161 | 0.014 | 0.942 | 0.197 | 0.250 | 0.066 | 0.329 | 17.757 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | C | F | A | B |
| verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 108 | 124 | 62 | 66 | 83 | 74 | 0 | 83 | 42 |
| N.S. |
1 | 1.15 | 0.57 | 0.61 | 0.77 | 0.69 | 0.00 | 0.77 | 0.39 |
| time (sec) |
N/A | 0.306 | 0.078 | 0.950 | 0.275 | 0.267 | 0.000 | 0.350 | 0.088 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 76 | 83 | 83 | 61 | 60 | 62 | 0 | 60 | 78 |
| N.S. |
1 | 1.09 | 1.09 | 0.80 | 0.79 | 0.82 | 0.00 | 0.79 | 1.03 |
| time (sec) |
N/A | 0.196 | 0.046 | 1.026 | 0.274 | 0.272 | 0.000 | 0.341 | 0.071 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 131 | 110 | 76 | 75 | 71 | 0 | 75 | 75 |
| N.S. |
1 | 1.10 | 0.92 | 0.64 | 0.63 | 0.60 | 0.00 | 0.63 | 0.63 |
| time (sec) |
N/A | 0.216 | 0.028 | 1.004 | 0.194 | 0.258 | 0.000 | 0.351 | 0.173 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | B | B | F | A | B |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 201 | 208 | 127 | 132 | 293 | 547 | 0 | 140 | 208 |
| N.S. |
1 | 1.03 | 0.63 | 0.66 | 1.46 | 2.72 | 0.00 | 0.70 | 1.03 |
| time (sec) |
N/A | 0.431 | 0.007 | 1.032 | 0.279 | 0.940 | 0.000 | 0.439 | 17.040 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | C | A | F | F(-2) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 36 | 36 | 35 | 36 | 15 | 44 | 0 | 0 | 32 |
| N.S. |
1 | 1.00 | 0.97 | 1.00 | 0.42 | 1.22 | 0.00 | 0.00 | 0.89 |
| time (sec) |
N/A | 0.179 | 1.170 | 0.691 | 0.214 | 0.262 | 0.000 | 0.000 | 16.998 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | C | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 29 | 29 | 29 | 27 | 5 | 35 | 0 | 76 | 23 |
| N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.17 | 1.21 | 0.00 | 2.62 | 0.79 |
| time (sec) |
N/A | 0.168 | 8.770 | 0.974 | 0.213 | 0.285 | 0.000 | 0.352 | 16.946 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | C | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 29 | 29 | 27 | 27 | 5 | 35 | 0 | 56 | 23 |
| N.S. |
1 | 1.00 | 0.93 | 0.93 | 0.17 | 1.21 | 0.00 | 1.93 | 0.79 |
| time (sec) |
N/A | 0.159 | 5.582 | 0.947 | 0.215 | 0.284 | 0.000 | 0.351 | 17.306 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | C | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 25 | 25 | 24 | 25 | 5 | 33 | 0 | 51 | 21 |
| N.S. |
1 | 1.00 | 0.96 | 1.00 | 0.20 | 1.32 | 0.00 | 2.04 | 0.84 |
| time (sec) |
N/A | 0.152 | 4.391 | 0.962 | 0.211 | 0.266 | 0.000 | 0.339 | 17.040 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | C | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 24 | 24 | 24 | 24 | 5 | 32 | 0 | 42 | 20 |
| N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.21 | 1.33 | 0.00 | 1.75 | 0.83 |
| time (sec) |
N/A | 0.161 | 1.511 | 0.987 | 0.220 | 0.250 | 0.000 | 0.337 | 16.883 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | C | A | F | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 29 | 29 | 26 | 27 | 5 | 35 | 0 | 60 | 23 |
| N.S. |
1 | 1.00 | 0.90 | 0.93 | 0.17 | 1.21 | 0.00 | 2.07 | 0.79 |
| time (sec) |
N/A | 0.163 | 3.142 | 1.041 | 0.214 | 0.251 | 0.000 | 0.377 | 16.739 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 80 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.206 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 138 | 143 | 112 | 0 | 0 | 0 | 117 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.81 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.268 | 0.153 | 0.000 | 0.000 | 0.000 | 11.738 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 79 | 79 | 73 | 0 | 0 | 0 | 73 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.194 | 0.102 | 0.000 | 0.000 | 0.000 | 2.666 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | C | F | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 40 | 40 | 50 | 0 | 0 | 0 | 34 | 0 | 51 |
| N.S. |
1 | 1.00 | 1.25 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 | 1.28 |
| time (sec) |
N/A | 0.155 | 0.043 | 0.000 | 0.000 | 0.000 | 0.800 | 0.000 | 16.892 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 101 | 101 | 97 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.223 | 0.136 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 56 | 56 | 57 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.189 | 0.116 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 112 | 99 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.226 | 0.146 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 185 | 197 | 155 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.349 | 0.204 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | C | A | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 33 | 33 | 33 | 35 | 8 | 44 | 0 | 0 | 29 |
| N.S. |
1 | 1.00 | 1.00 | 1.06 | 0.24 | 1.33 | 0.00 | 0.00 | 0.88 |
| time (sec) |
N/A | 0.189 | 0.073 | 1.061 | 0.216 | 0.267 | 0.000 | 0.000 | 16.812 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | C | A | F | C | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 31 | 31 | 32 | 31 | 5 | 41 | 0 | 15 | 25 |
| N.S. |
1 | 1.00 | 1.03 | 1.00 | 0.16 | 1.32 | 0.00 | 0.48 | 0.81 |
| time (sec) |
N/A | 0.178 | 0.041 | 1.038 | 0.220 | 0.237 | 0.000 | 0.381 | 16.672 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | C | A | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 28 | 28 | 28 | 30 | 7 | 41 | 0 | 0 | 27 |
| N.S. |
1 | 1.00 | 1.00 | 1.07 | 0.25 | 1.46 | 0.00 | 0.00 | 0.96 |
| time (sec) |
N/A | 0.162 | 0.045 | 1.043 | 0.220 | 0.264 | 0.000 | 0.000 | 17.076 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | C | B | F | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 28 | 28 | 28 | 30 | 4 | 51 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 1.07 | 0.14 | 1.82 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.164 | 0.056 | 0.935 | 0.217 | 0.277 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | C | A | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 26 | 26 | 26 | 28 | 7 | 41 | 0 | 0 | 22 |
| N.S. |
1 | 1.00 | 1.00 | 1.08 | 0.27 | 1.58 | 0.00 | 0.00 | 0.85 |
| time (sec) |
N/A | 0.174 | 0.048 | 0.980 | 0.211 | 0.254 | 0.000 | 0.000 | 16.821 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | C | A | F | C | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 31 | 31 | 31 | 31 | 5 | 44 | 0 | 5 | 25 |
| N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.16 | 1.42 | 0.00 | 0.16 | 0.81 |
| time (sec) |
N/A | 0.181 | 0.055 | 0.988 | 0.217 | 0.262 | 0.000 | 0.348 | 17.282 |