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 | B | F | A | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 95 | 142 | 210 | 0 | 303 | 0 | 0 | 63 | 0 |
| N.S. |
1 | 1.00 | 1.49 | 2.21 | 0.00 | 3.19 | 0.00 | 0.00 | 0.66 | 0.00 |
| time (sec) |
N/A | 0.516 | 1.559 | 1.809 | 0.000 | 0.162 | 0.000 | 0.000 | 0.209 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | A | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 143 | 142 | 172 | 285 | 0 | 260 | 0 | 0 | 56 | 0 |
| N.S. |
1 | 0.99 | 1.20 | 1.99 | 0.00 | 1.82 | 0.00 | 0.00 | 0.39 | 0.00 |
| time (sec) |
N/A | 0.747 | 1.863 | 1.886 | 0.000 | 0.123 | 0.000 | 0.000 | 0.203 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 191 | 195 | 271 | 303 | 0 | 375 | 0 | 0 | 83 | 0 |
| N.S. |
1 | 1.02 | 1.42 | 1.59 | 0.00 | 1.96 | 0.00 | 0.00 | 0.43 | 0.00 |
| time (sec) |
N/A | 0.981 | 2.391 | 1.850 | 0.000 | 0.133 | 0.000 | 0.000 | 0.187 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 237 | 240 | 202 | 222 | 0 | 0 | 0 | 188 | 313 | 0 |
| N.S. |
1 | 1.01 | 0.85 | 0.94 | 0.00 | 0.00 | 0.00 | 0.79 | 1.32 | 0.00 |
| time (sec) |
N/A | 1.255 | 15.099 | 1.948 | 0.000 | 0.000 | 0.000 | 0.158 | 0.209 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | F | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 193 | 195 | 187 | 206 | 0 | 0 | 0 | 154 | 252 | 0 |
| N.S. |
1 | 1.01 | 0.97 | 1.07 | 0.00 | 0.00 | 0.00 | 0.80 | 1.31 | 0.00 |
| time (sec) |
N/A | 0.981 | 10.518 | 2.049 | 0.000 | 0.000 | 0.000 | 0.157 | 0.200 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | F | F(-1) | A | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 143 | 149 | 172 | 190 | 183 | 0 | 0 | 129 | 187 | 0 |
| N.S. |
1 | 1.04 | 1.20 | 1.33 | 1.28 | 0.00 | 0.00 | 0.90 | 1.31 | 0.00 |
| time (sec) |
N/A | 0.765 | 3.862 | 1.990 | 0.129 | 0.000 | 0.000 | 0.142 | 0.180 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | B | F | F(-2) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 42 | 42 | 86 | 109 | 0 | 80 | 0 | 0 | 124 | 118 |
| N.S. |
1 | 1.00 | 2.05 | 2.60 | 0.00 | 1.90 | 0.00 | 0.00 | 2.95 | 2.81 |
| time (sec) |
N/A | 0.277 | 3.050 | 1.943 | 0.000 | 0.089 | 0.000 | 0.000 | 0.182 | 17.740 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | B | F | A | F | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 43 | 43 | 87 | 108 | 0 | 73 | 0 | 53 | 61 | 103 |
| N.S. |
1 | 1.00 | 2.02 | 2.51 | 0.00 | 1.70 | 0.00 | 1.23 | 1.42 | 2.40 |
| time (sec) |
N/A | 0.272 | 1.700 | 2.034 | 0.000 | 0.091 | 0.000 | 0.141 | 0.189 | 17.473 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 145 | 189 | 242 | 0 | 374 | 0 | 0 | 65 | 0 |
| N.S. |
1 | 1.04 | 1.35 | 1.73 | 0.00 | 2.67 | 0.00 | 0.00 | 0.46 | 0.00 |
| time (sec) |
N/A | 0.732 | 2.285 | 1.899 | 0.000 | 0.135 | 0.000 | 0.000 | 0.209 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 188 | 192 | 271 | 303 | 0 | 369 | 0 | 0 | 80 | 0 |
| N.S. |
1 | 1.02 | 1.44 | 1.61 | 0.00 | 1.96 | 0.00 | 0.00 | 0.43 | 0.00 |
| time (sec) |
N/A | 0.988 | 2.455 | 2.002 | 0.000 | 0.131 | 0.000 | 0.000 | 0.204 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 236 | 242 | 227 | 321 | 0 | 286 | 0 | 0 | 67 | 0 |
| N.S. |
1 | 1.03 | 0.96 | 1.36 | 0.00 | 1.21 | 0.00 | 0.00 | 0.28 | 0.00 |
| time (sec) |
N/A | 1.277 | 2.796 | 1.871 | 0.000 | 0.130 | 0.000 | 0.000 | 0.191 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 109 | 152 | 107 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
| N.S. |
1 | 1.39 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
| time (sec) |
N/A | 0.485 | 7.767 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 86 | 325 | 0 | 0 | 0 | 0 | 0 | 92 | 0 |
| N.S. |
1 | 1.00 | 3.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.07 | 0.00 |
| time (sec) |
N/A | 0.406 | 19.873 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 86 | 249 | 0 | 0 | 0 | 0 | 0 | 65 | 0 |
| N.S. |
1 | 1.00 | 2.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.76 | 0.00 |
| time (sec) |
N/A | 0.377 | 8.790 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 84 | 213 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
| N.S. |
1 | 1.02 | 2.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
| time (sec) |
N/A | 0.354 | 2.157 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 81 | 76 | 0 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
| N.S. |
1 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
| time (sec) |
N/A | 0.377 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 86 | 0 | 0 | 0 | 0 | 0 | 0 | 39 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
| time (sec) |
N/A | 0.373 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 86 | 86 | 0 | 0 | 0 | 0 | 0 | 0 | 50 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.58 | 0.00 |
| time (sec) |
N/A | 0.366 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | A | A | F(-1) | F | F | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 160 | 159 | 149 | 0 | 290 | 267 | 0 | 0 | 101 | 163 |
| N.S. |
1 | 0.99 | 0.93 | 0.00 | 1.81 | 1.67 | 0.00 | 0.00 | 0.63 | 1.02 |
| time (sec) |
N/A | 0.624 | 9.264 | 0.000 | 0.149 | 0.103 | 0.000 | 0.000 | 0.250 | 19.134 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | B | A | F(-1) | F | F | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 100 | 102 | 110 | 0 | 193 | 145 | 0 | 0 | 65 | 94 |
| N.S. |
1 | 1.02 | 1.10 | 0.00 | 1.93 | 1.45 | 0.00 | 0.00 | 0.65 | 0.94 |
| time (sec) |
N/A | 0.436 | 4.373 | 0.000 | 0.127 | 0.099 | 0.000 | 0.000 | 0.211 | 0.746 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | B | A | F | F | F | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 46 | 85 | 0 | 116 | 76 | 0 | 0 | 29 | 53 |
| N.S. |
1 | 1.00 | 1.85 | 0.00 | 2.52 | 1.65 | 0.00 | 0.00 | 0.63 | 1.15 |
| time (sec) |
N/A | 0.255 | 1.076 | 0.000 | 0.129 | 0.096 | 0.000 | 0.000 | 0.212 | 0.266 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 68 | 73 | 66 | 0 | 0 | 0 | 0 | 0 | 43 | 0 |
| N.S. |
1 | 1.07 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
| time (sec) |
N/A | 0.398 | 7.742 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.220 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 79 | 74 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
| N.S. |
1 | 1.07 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.70 | 0.00 |
| time (sec) |
N/A | 0.431 | 10.414 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 79 | 72 | 0 | 0 | 0 | 0 | 0 | 63 | 0 |
| N.S. |
1 | 1.07 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 |
| time (sec) |
N/A | 0.431 | 13.201 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 68 | 73 | 66 | 0 | 0 | 0 | 0 | 0 | 43 | 0 |
| N.S. |
1 | 1.07 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
| time (sec) |
N/A | 0.381 | 0.160 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 68 | 73 | 66 | 0 | 0 | 0 | 0 | 0 | 43 | 0 |
| N.S. |
1 | 1.07 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
| time (sec) |
N/A | 0.394 | 7.696 | 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 | A | F | F | F | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 164 | 162 | 109 | 0 | 0 | 101 | 0 | 0 | 104 | 149 |
| N.S. |
1 | 0.99 | 0.66 | 0.00 | 0.00 | 0.62 | 0.00 | 0.00 | 0.63 | 0.91 |
| time (sec) |
N/A | 0.630 | 0.354 | 0.000 | 0.000 | 0.111 | 0.000 | 0.000 | 0.172 | 17.410 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 101 | 103 | 81 | 0 | 0 | 72 | 0 | 0 | 78 | 111 |
| N.S. |
1 | 1.02 | 0.80 | 0.00 | 0.00 | 0.71 | 0.00 | 0.00 | 0.77 | 1.10 |
| time (sec) |
N/A | 0.430 | 0.279 | 0.000 | 0.000 | 0.108 | 0.000 | 0.000 | 0.183 | 0.530 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | A | F | F | F | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 46 | 46 | 52 | 0 | 0 | 44 | 0 | 0 | 58 | 58 |
| N.S. |
1 | 1.00 | 1.13 | 0.00 | 0.00 | 0.96 | 0.00 | 0.00 | 1.26 | 1.26 |
| time (sec) |
N/A | 0.276 | 0.158 | 0.000 | 0.000 | 0.094 | 0.000 | 0.000 | 0.179 | 0.242 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 113 | 150 | 122 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
| N.S. |
1 | 1.33 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
| time (sec) |
N/A | 0.455 | 2.113 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 153 | 114 | 0 | 0 | 0 | 0 | 0 | 71 | 0 |
| N.S. |
1 | 1.33 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.62 | 0.00 |
| time (sec) |
N/A | 0.455 | 0.475 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 152 | 117 | 0 | 0 | 0 | 0 | 0 | 111 | 0 |
| N.S. |
1 | 1.32 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.97 | 0.00 |
| time (sec) |
N/A | 0.479 | 0.536 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 227 | 240 | 207 | 190 | 250 | 204 | 580 | 263 | 329 | 559 |
| N.S. |
1 | 1.06 | 0.91 | 0.84 | 1.10 | 0.90 | 2.56 | 1.16 | 1.45 | 2.46 |
| time (sec) |
N/A | 0.809 | 1.882 | 94.385 | 0.036 | 0.094 | 0.343 | 0.148 | 0.206 | 18.635 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 162 | 170 | 124 | 140 | 175 | 145 | 386 | 184 | 216 | 460 |
| N.S. |
1 | 1.05 | 0.77 | 0.86 | 1.08 | 0.90 | 2.38 | 1.14 | 1.33 | 2.84 |
| time (sec) |
N/A | 0.560 | 1.104 | 12.776 | 0.034 | 0.093 | 0.334 | 0.130 | 0.193 | 17.335 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 99 | 102 | 89 | 115 | 112 | 90 | 199 | 112 | 125 | 108 |
| N.S. |
1 | 1.03 | 0.90 | 1.16 | 1.13 | 0.91 | 2.01 | 1.13 | 1.26 | 1.09 |
| time (sec) |
N/A | 0.358 | 0.606 | 0.417 | 0.035 | 0.086 | 0.145 | 0.128 | 0.191 | 16.578 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 48 | 48 | 45 | 44 | 57 | 48 | 94 | 52 | 55 | 100 |
| N.S. |
1 | 1.00 | 0.94 | 0.92 | 1.19 | 1.00 | 1.96 | 1.08 | 1.15 | 2.08 |
| time (sec) |
N/A | 0.215 | 0.236 | 0.991 | 0.028 | 0.084 | 0.095 | 0.122 | 0.163 | 16.553 |
| 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 | 16 | 16 | 27 | 17 | 16 | 18 | 19 | 16 | 17 | 25 |
| N.S. |
1 | 1.00 | 1.69 | 1.06 | 1.00 | 1.12 | 1.19 | 1.00 | 1.06 | 1.56 |
| time (sec) |
N/A | 0.156 | 0.004 | 0.312 | 0.026 | 0.086 | 0.058 | 0.120 | 0.159 | 16.395 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F(-2) | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 69 | 182 | 72 | 0 | 228 | 314 | 83 | 61 | 449 |
| N.S. |
1 | 1.10 | 2.89 | 1.14 | 0.00 | 3.62 | 4.98 | 1.32 | 0.97 | 7.13 |
| time (sec) |
N/A | 0.320 | 1.172 | 0.397 | 0.000 | 0.101 | 14.132 | 0.132 | 0.166 | 16.767 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F(-2) | A | F(-1) | A | B | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 83 | 89 | 220 | 113 | 0 | 362 | 0 | 124 | 185 | 140 |
| N.S. |
1 | 1.07 | 2.65 | 1.36 | 0.00 | 4.36 | 0.00 | 1.49 | 2.23 | 1.69 |
| time (sec) |
N/A | 0.370 | 1.605 | 0.501 | 0.000 | 0.101 | 0.000 | 0.139 | 0.172 | 16.503 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-2) | B | F(-1) | B | B | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 134 | 148 | 242 | 325 | 0 | 803 | 0 | 369 | 782 | 445 |
| N.S. |
1 | 1.10 | 1.81 | 2.43 | 0.00 | 5.99 | 0.00 | 2.75 | 5.84 | 3.32 |
| time (sec) |
N/A | 0.568 | 2.515 | 0.787 | 0.000 | 0.122 | 0.000 | 0.160 | 0.171 | 17.764 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F(-2) | B | F(-1) | B | B | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 192 | 215 | 428 | 641 | 0 | 1344 | 0 | 775 | 1580 | 877 |
| N.S. |
1 | 1.12 | 2.23 | 3.34 | 0.00 | 7.00 | 0.00 | 4.04 | 8.23 | 4.57 |
| time (sec) |
N/A | 0.823 | 4.653 | 1.434 | 0.000 | 0.145 | 0.000 | 0.178 | 0.189 | 18.538 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 318 | 329 | 262 | 462 | 451 | 299 | 1136 | 448 | 429 | 865 |
| N.S. |
1 | 1.03 | 0.82 | 1.45 | 1.42 | 0.94 | 3.57 | 1.41 | 1.35 | 2.72 |
| time (sec) |
N/A | 1.122 | 1.511 | 1.119 | 0.045 | 0.106 | 0.485 | 0.153 | 0.207 | 18.505 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 233 | 242 | 204 | 168 | 318 | 217 | 729 | 316 | 294 | 611 |
| N.S. |
1 | 1.04 | 0.88 | 0.72 | 1.36 | 0.93 | 3.13 | 1.36 | 1.26 | 2.62 |
| time (sec) |
N/A | 0.805 | 1.047 | 280.925 | 0.039 | 0.106 | 0.339 | 0.142 | 0.200 | 17.512 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 139 | 148 | 219 | 211 | 145 | 459 | 202 | 181 | 440 |
| N.S. |
1 | 0.89 | 0.95 | 1.40 | 1.35 | 0.93 | 2.94 | 1.29 | 1.16 | 2.82 |
| time (sec) |
N/A | 0.522 | 0.617 | 0.719 | 0.035 | 0.094 | 0.227 | 0.132 | 0.192 | 17.310 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 94 | 83 | 106 | 117 | 114 | 82 | 199 | 105 | 90 | 91 |
| N.S. |
1 | 0.88 | 1.13 | 1.24 | 1.21 | 0.87 | 2.12 | 1.12 | 0.96 | 0.97 |
| time (sec) |
N/A | 0.303 | 0.378 | 0.411 | 0.036 | 0.087 | 0.145 | 0.130 | 0.193 | 16.564 |
| 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 | 45 | 45 | 34 | 32 | 47 | 41 | 78 | 38 | 36 | 123 |
| N.S. |
1 | 1.00 | 0.76 | 0.71 | 1.04 | 0.91 | 1.73 | 0.84 | 0.80 | 2.73 |
| time (sec) |
N/A | 0.196 | 0.452 | 0.885 | 0.032 | 0.083 | 0.093 | 0.127 | 0.191 | 16.511 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 92 | 103 | 130 | 105 | 0 | 296 | 3709 | 132 | 136 | 940 |
| N.S. |
1 | 1.12 | 1.41 | 1.14 | 0.00 | 3.22 | 40.32 | 1.43 | 1.48 | 10.22 |
| time (sec) |
N/A | 0.501 | 5.391 | 0.635 | 0.000 | 0.102 | 123.609 | 0.130 | 0.189 | 16.983 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 128 | 139 | 160 | 0 | 476 | 0 | 198 | 321 | 2836 |
| N.S. |
1 | 1.14 | 1.24 | 1.43 | 0.00 | 4.25 | 0.00 | 1.77 | 2.87 | 25.32 |
| time (sec) |
N/A | 0.521 | 5.509 | 0.645 | 0.000 | 0.114 | 0.000 | 0.144 | 0.206 | 19.333 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 138 | 150 | 140 | 250 | 0 | 679 | 0 | 334 | 562 | 362 |
| N.S. |
1 | 1.09 | 1.01 | 1.81 | 0.00 | 4.92 | 0.00 | 2.42 | 4.07 | 2.62 |
| time (sec) |
N/A | 0.548 | 0.687 | 0.924 | 0.000 | 0.120 | 0.000 | 0.164 | 0.204 | 18.111 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 207 | 217 | 196 | 523 | 0 | 1366 | 0 | 750 | 1399 | 735 |
| N.S. |
1 | 1.05 | 0.95 | 2.53 | 0.00 | 6.60 | 0.00 | 3.62 | 6.76 | 3.55 |
| time (sec) |
N/A | 0.802 | 2.651 | 1.755 | 0.000 | 0.154 | 0.000 | 0.190 | 0.199 | 18.991 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 286 | 297 | 269 | 1056 | 0 | 2151 | 0 | 1493 | 2424 | 1411 |
| N.S. |
1 | 1.04 | 0.94 | 3.69 | 0.00 | 7.52 | 0.00 | 5.22 | 8.48 | 4.93 |
| time (sec) |
N/A | 1.150 | 5.253 | 2.841 | 0.000 | 0.180 | 0.000 | 0.238 | 0.338 | 19.119 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 215 | 342 | 233 | 481 | 469 | 261 | 1176 | 364 | 372 | 773 |
| N.S. |
1 | 1.59 | 1.08 | 2.24 | 2.18 | 1.21 | 5.47 | 1.69 | 1.73 | 3.60 |
| time (sec) |
N/A | 1.335 | 1.825 | 1.122 | 0.042 | 0.105 | 0.502 | 0.154 | 0.187 | 17.593 |
| 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 | 164 | 157 | 177 | 319 | 308 | 180 | 702 | 244 | 237 | 493 |
| N.S. |
1 | 0.96 | 1.08 | 1.95 | 1.88 | 1.10 | 4.28 | 1.49 | 1.45 | 3.01 |
| time (sec) |
N/A | 0.579 | 0.868 | 0.883 | 0.039 | 0.091 | 0.333 | 0.140 | 0.174 | 17.447 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 110 | 101 | 120 | 178 | 171 | 108 | 371 | 133 | 124 | 330 |
| N.S. |
1 | 0.92 | 1.09 | 1.62 | 1.55 | 0.98 | 3.37 | 1.21 | 1.13 | 3.00 |
| time (sec) |
N/A | 0.352 | 0.581 | 0.624 | 0.036 | 0.084 | 0.202 | 0.141 | 0.183 | 17.209 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 63 | 44 | 43 | 72 | 54 | 121 | 55 | 52 | 156 |
| N.S. |
1 | 1.00 | 0.70 | 0.68 | 1.14 | 0.86 | 1.92 | 0.87 | 0.83 | 2.48 |
| time (sec) |
N/A | 0.241 | 3.477 | 9.987 | 0.036 | 0.081 | 0.125 | 0.124 | 0.214 | 17.863 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 143 | 156 | 162 | 184 | 0 | 404 | 0 | 231 | 266 | 3382 |
| N.S. |
1 | 1.09 | 1.13 | 1.29 | 0.00 | 2.83 | 0.00 | 1.62 | 1.86 | 23.65 |
| time (sec) |
N/A | 0.891 | 5.623 | 1.737 | 0.000 | 0.114 | 0.000 | 0.144 | 0.198 | 17.927 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 161 | 176 | 162 | 209 | 0 | 645 | 0 | 380 | 574 | 5079 |
| N.S. |
1 | 1.09 | 1.01 | 1.30 | 0.00 | 4.01 | 0.00 | 2.36 | 3.57 | 31.55 |
| time (sec) |
N/A | 0.932 | 5.701 | 1.983 | 0.000 | 0.129 | 0.000 | 0.151 | 0.177 | 20.764 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 187 | 230 | 196 | 353 | 0 | 1064 | 0 | 503 | 1043 | 6246 |
| N.S. |
1 | 1.23 | 1.05 | 1.89 | 0.00 | 5.69 | 0.00 | 2.69 | 5.58 | 33.40 |
| time (sec) |
N/A | 1.061 | 6.094 | 1.917 | 0.000 | 0.136 | 0.000 | 0.175 | 0.172 | 21.383 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 207 | 251 | 178 | 466 | 0 | 1106 | 0 | 640 | 981 | 649 |
| N.S. |
1 | 1.21 | 0.86 | 2.25 | 0.00 | 5.34 | 0.00 | 3.09 | 4.74 | 3.14 |
| time (sec) |
N/A | 1.103 | 2.752 | 2.757 | 0.000 | 0.130 | 0.000 | 0.200 | 0.184 | 18.957 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 289 | 335 | 240 | 922 | 0 | 2009 | 0 | 1284 | 2057 | 1231 |
| N.S. |
1 | 1.16 | 0.83 | 3.19 | 0.00 | 6.95 | 0.00 | 4.44 | 7.12 | 4.26 |
| time (sec) |
N/A | 1.480 | 2.270 | 3.743 | 0.000 | 0.174 | 0.000 | 0.251 | 0.282 | 18.859 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 189 | 185 | 234 | 209 | 725 | 349 | 8605 | 293 | 497 | 451 |
| N.S. |
1 | 0.98 | 1.24 | 1.11 | 3.84 | 1.85 | 45.53 | 1.55 | 2.63 | 2.39 |
| time (sec) |
N/A | 0.611 | 0.459 | 10.344 | 0.122 | 0.088 | 4.366 | 0.139 | 0.215 | 18.353 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 117 | 192 | 148 | 425 | 236 | 3602 | 165 | 315 | 282 |
| N.S. |
1 | 0.97 | 1.59 | 1.22 | 3.51 | 1.95 | 29.77 | 1.36 | 2.60 | 2.33 |
| time (sec) |
N/A | 0.409 | 0.541 | 1.722 | 0.116 | 0.087 | 2.279 | 0.141 | 0.166 | 17.936 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 64 | 122 | 75 | 209 | 142 | 940 | 135 | 137 | 124 |
| N.S. |
1 | 1.03 | 1.97 | 1.21 | 3.37 | 2.29 | 15.16 | 2.18 | 2.21 | 2.00 |
| time (sec) |
N/A | 0.428 | 0.660 | 0.645 | 0.111 | 0.082 | 1.129 | 0.134 | 0.166 | 16.776 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 35 | 79 | 42 | 78 | 66 | 109 | 38 | 62 | 35 |
| N.S. |
1 | 1.00 | 2.26 | 1.20 | 2.23 | 1.89 | 3.11 | 1.09 | 1.77 | 1.00 |
| time (sec) |
N/A | 0.257 | 0.169 | 0.374 | 0.114 | 0.080 | 0.617 | 0.130 | 0.165 | 16.453 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | A | A | A | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 23 | 23 | 48 | 22 | 27 | 42 | 27 | 21 | 30 | 21 |
| N.S. |
1 | 1.00 | 2.09 | 0.96 | 1.17 | 1.83 | 1.17 | 0.91 | 1.30 | 0.91 |
| time (sec) |
N/A | 0.179 | 0.063 | 0.219 | 0.027 | 0.081 | 0.381 | 0.116 | 0.159 | 16.431 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 95 | 114 | 83 | 0 | 489 | 916 | 97 | 202 | 121 |
| N.S. |
1 | 1.07 | 1.28 | 0.93 | 0.00 | 5.49 | 10.29 | 1.09 | 2.27 | 1.36 |
| time (sec) |
N/A | 0.389 | 0.308 | 0.520 | 0.000 | 0.101 | 43.533 | 0.141 | 0.173 | 16.546 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 155 | 162 | 154 | 0 | 1120 | 0 | 298 | 1319 | 309 |
| N.S. |
1 | 1.03 | 1.08 | 1.03 | 0.00 | 7.47 | 0.00 | 1.99 | 8.79 | 2.06 |
| time (sec) |
N/A | 0.564 | 0.494 | 1.042 | 0.000 | 0.124 | 0.000 | 0.149 | 0.172 | 17.529 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 213 | 228 | 230 | 327 | 0 | 2365 | 0 | 466 | 3190 | 753 |
| N.S. |
1 | 1.07 | 1.08 | 1.54 | 0.00 | 11.10 | 0.00 | 2.19 | 14.98 | 3.54 |
| time (sec) |
N/A | 0.808 | 1.497 | 2.049 | 0.000 | 0.158 | 0.000 | 0.174 | 0.196 | 18.867 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 260 | 272 | 837 | 342 | 1312 | 578 | 17899 | 926 | 919 | 692 |
| N.S. |
1 | 1.05 | 3.22 | 1.32 | 5.05 | 2.22 | 68.84 | 3.56 | 3.53 | 2.66 |
| time (sec) |
N/A | 1.018 | 1.716 | 83.750 | 0.136 | 0.102 | 14.241 | 0.168 | 0.178 | 18.134 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 195 | 201 | 378 | 250 | 908 | 440 | 8950 | 322 | 661 | 478 |
| N.S. |
1 | 1.03 | 1.94 | 1.28 | 4.66 | 2.26 | 45.90 | 1.65 | 3.39 | 2.45 |
| time (sec) |
N/A | 0.762 | 1.831 | 10.707 | 0.132 | 0.092 | 8.238 | 0.151 | 0.165 | 17.948 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 120 | 126 | 212 | 157 | 591 | 308 | 3585 | 199 | 438 | 298 |
| N.S. |
1 | 1.05 | 1.77 | 1.31 | 4.92 | 2.57 | 29.88 | 1.66 | 3.65 | 2.48 |
| time (sec) |
N/A | 0.900 | 0.409 | 1.909 | 0.125 | 0.091 | 4.386 | 0.139 | 0.175 | 17.320 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 89 | 172 | 108 | 360 | 197 | 915 | 125 | 180 | 93 |
| N.S. |
1 | 1.05 | 2.02 | 1.27 | 4.24 | 2.32 | 10.76 | 1.47 | 2.12 | 1.09 |
| time (sec) |
N/A | 0.463 | 0.350 | 0.625 | 0.118 | 0.090 | 2.288 | 0.134 | 0.157 | 16.701 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 64 | 43 | 60 | 214 | 117 | 372 | 64 | 79 | 97 |
| N.S. |
1 | 0.98 | 0.66 | 0.92 | 3.29 | 1.80 | 5.72 | 0.98 | 1.22 | 1.49 |
| time (sec) |
N/A | 0.290 | 0.086 | 0.522 | 0.038 | 0.076 | 1.248 | 0.136 | 0.170 | 16.557 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 55 | 54 | 54 | 38 | 117 | 95 | 221 | 47 | 60 | 76 |
| N.S. |
1 | 0.98 | 0.98 | 0.69 | 2.13 | 1.73 | 4.02 | 0.85 | 1.09 | 1.38 |
| time (sec) |
N/A | 0.256 | 0.439 | 0.319 | 0.035 | 0.070 | 0.681 | 0.120 | 0.164 | 16.444 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 144 | 204 | 132 | 0 | 989 | 0 | 188 | 535 | 250 |
| N.S. |
1 | 1.10 | 1.56 | 1.01 | 0.00 | 7.55 | 0.00 | 1.44 | 4.08 | 1.91 |
| time (sec) |
N/A | 0.605 | 1.585 | 0.844 | 0.000 | 0.108 | 0.000 | 0.148 | 0.188 | 17.222 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 221 | 234 | 267 | 205 | 0 | 2297 | 0 | 310 | 2500 | 625 |
| N.S. |
1 | 1.06 | 1.21 | 0.93 | 0.00 | 10.39 | 0.00 | 1.40 | 11.31 | 2.83 |
| time (sec) |
N/A | 0.914 | 4.220 | 1.705 | 0.000 | 0.149 | 0.000 | 0.161 | 0.229 | 19.059 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 294 | 322 | 338 | 378 | 0 | 3540 | 0 | 594 | 4900 | 1199 |
| N.S. |
1 | 1.10 | 1.15 | 1.29 | 0.00 | 12.04 | 0.00 | 2.02 | 16.67 | 4.08 |
| time (sec) |
N/A | 1.282 | 4.305 | 3.615 | 0.000 | 0.290 | 0.000 | 0.188 | 0.248 | 19.385 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 354 | 374 | 560 | 468 | 1993 | 823 | 28065 | 738 | 1379 | 898 |
| N.S. |
1 | 1.06 | 1.58 | 1.32 | 5.63 | 2.32 | 79.28 | 2.08 | 3.90 | 2.54 |
| time (sec) |
N/A | 1.502 | 2.597 | 0.282 | 0.157 | 0.130 | 45.204 | 0.174 | 0.255 | 18.497 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 278 | 292 | 992 | 360 | 1504 | 653 | 15553 | 536 | 1041 | 652 |
| N.S. |
1 | 1.05 | 3.57 | 1.29 | 5.41 | 2.35 | 55.95 | 1.93 | 3.74 | 2.35 |
| time (sec) |
N/A | 1.172 | 8.410 | 84.606 | 0.148 | 0.113 | 27.569 | 0.169 | 0.179 | 18.324 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 195 | 207 | 683 | 248 | 1101 | 494 | 7373 | 375 | 740 | 440 |
| N.S. |
1 | 1.06 | 3.50 | 1.27 | 5.65 | 2.53 | 37.81 | 1.92 | 3.79 | 2.26 |
| time (sec) |
N/A | 1.407 | 1.446 | 10.753 | 0.136 | 0.093 | 16.253 | 0.161 | 0.217 | 17.830 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 142 | 152 | 408 | 194 | 784 | 352 | 2640 | 265 | 380 | 240 |
| N.S. |
1 | 1.07 | 2.87 | 1.37 | 5.52 | 2.48 | 18.59 | 1.87 | 2.68 | 1.69 |
| time (sec) |
N/A | 0.899 | 6.551 | 1.758 | 0.128 | 0.093 | 9.383 | 0.156 | 0.178 | 18.311 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 125 | 127 | 84 | 116 | 553 | 242 | 1365 | 171 | 207 | 218 |
| N.S. |
1 | 1.02 | 0.67 | 0.93 | 4.42 | 1.94 | 10.92 | 1.37 | 1.66 | 1.74 |
| time (sec) |
N/A | 0.522 | 0.156 | 0.726 | 0.045 | 0.080 | 5.110 | 0.149 | 0.168 | 16.835 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 102 | 99 | 63 | 95 | 387 | 190 | 1015 | 122 | 160 | 150 |
| N.S. |
1 | 0.97 | 0.62 | 0.93 | 3.79 | 1.86 | 9.95 | 1.20 | 1.57 | 1.47 |
| time (sec) |
N/A | 0.385 | 0.107 | 0.592 | 0.041 | 0.076 | 3.299 | 0.144 | 0.173 | 16.675 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | A | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 83 | 87 | 76 | 48 | 203 | 147 | 558 | 73 | 112 | 133 |
| N.S. |
1 | 1.05 | 0.92 | 0.58 | 2.45 | 1.77 | 6.72 | 0.88 | 1.35 | 1.60 |
| time (sec) |
N/A | 0.346 | 0.302 | 0.447 | 0.036 | 0.074 | 1.420 | 0.128 | 0.168 | 16.504 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 186 | 215 | 301 | 200 | 0 | 1744 | 0 | 349 | 1201 | 466 |
| N.S. |
1 | 1.16 | 1.62 | 1.08 | 0.00 | 9.38 | 0.00 | 1.88 | 6.46 | 2.51 |
| time (sec) |
N/A | 0.993 | 3.393 | 1.198 | 0.000 | 0.132 | 0.000 | 0.156 | 0.196 | 18.578 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 298 | 326 | 361 | 273 | 0 | 3235 | 0 | 499 | 3777 | 987 |
| N.S. |
1 | 1.09 | 1.21 | 0.92 | 0.00 | 10.86 | 0.00 | 1.67 | 12.67 | 3.31 |
| time (sec) |
N/A | 1.399 | 7.567 | 2.680 | 0.000 | 0.186 | 0.000 | 0.189 | 0.212 | 18.980 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | B | A | F(-2) | B | F(-1) | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 378 | 421 | 914 | 446 | 0 | 5226 | 0 | 766 | 6660 | 1660 |
| N.S. |
1 | 1.11 | 2.42 | 1.18 | 0.00 | 13.83 | 0.00 | 2.03 | 17.62 | 4.39 |
| time (sec) |
N/A | 1.848 | 10.848 | 5.587 | 0.000 | 0.266 | 0.000 | 0.255 | 0.450 | 20.004 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 71 | 55 | 80 | 309 | 150 | 889 | 112 | 155 | 94 |
| N.S. |
1 | 0.95 | 0.73 | 1.07 | 4.12 | 2.00 | 11.85 | 1.49 | 2.07 | 1.25 |
| time (sec) |
N/A | 0.385 | 0.047 | 0.466 | 0.039 | 0.089 | 3.523 | 0.120 | 0.204 | 16.636 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | C | B | B | B | A | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 81 | 77 | 54 | 80 | 309 | 150 | 887 | 112 | 155 | 97 |
| N.S. |
1 | 0.95 | 0.67 | 0.99 | 3.81 | 1.85 | 10.95 | 1.38 | 1.91 | 1.20 |
| time (sec) |
N/A | 0.414 | 0.050 | 0.449 | 0.039 | 0.094 | 3.492 | 0.133 | 0.227 | 16.630 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 290 | 301 | 3531 | 1315 | 0 | 567 | 0 | 0 | 146 | 0 |
| N.S. |
1 | 1.04 | 12.18 | 4.53 | 0.00 | 1.96 | 0.00 | 0.00 | 0.50 | 0.00 |
| time (sec) |
N/A | 1.520 | 6.901 | 5.003 | 0.000 | 0.115 | 0.000 | 0.000 | 0.252 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 231 | 237 | 2625 | 1034 | 0 | 497 | 0 | 0 | 86 | 0 |
| N.S. |
1 | 1.03 | 11.36 | 4.48 | 0.00 | 2.15 | 0.00 | 0.00 | 0.37 | 0.00 |
| time (sec) |
N/A | 1.106 | 6.623 | 2.817 | 0.000 | 0.115 | 0.000 | 0.000 | 0.198 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 179 | 180 | 1736 | 657 | 0 | 431 | 0 | 0 | 36 | 0 |
| N.S. |
1 | 1.01 | 9.70 | 3.67 | 0.00 | 2.41 | 0.00 | 0.00 | 0.20 | 0.00 |
| time (sec) |
N/A | 0.823 | 6.678 | 1.972 | 0.000 | 0.103 | 0.000 | 0.000 | 0.188 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | C | F | F | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 138 | 138 | 880 | 205 | 0 | 369 | 0 | 0 | 61 | 176 |
| N.S. |
1 | 1.00 | 6.38 | 1.49 | 0.00 | 2.67 | 0.00 | 0.00 | 0.44 | 1.28 |
| time (sec) |
N/A | 0.615 | 6.607 | 2.133 | 0.000 | 0.095 | 0.000 | 0.000 | 0.193 | 16.995 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 169 | 191 | 938 | 246 | 0 | 500 | 0 | 0 | 93 | 0 |
| N.S. |
1 | 1.13 | 5.55 | 1.46 | 0.00 | 2.96 | 0.00 | 0.00 | 0.55 | 0.00 |
| time (sec) |
N/A | 0.855 | 6.859 | 1.545 | 0.000 | 0.104 | 0.000 | 0.000 | 0.179 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 237 | 251 | 1870 | 881 | 0 | 876 | 0 | 0 | 125 | 0 |
| N.S. |
1 | 1.06 | 7.89 | 3.72 | 0.00 | 3.70 | 0.00 | 0.00 | 0.53 | 0.00 |
| time (sec) |
N/A | 1.212 | 7.217 | 2.078 | 0.000 | 0.120 | 0.000 | 0.000 | 0.199 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 318 | 334 | 2815 | 1043 | 0 | 1395 | 0 | 0 | 157 | 0 |
| N.S. |
1 | 1.05 | 8.85 | 3.28 | 0.00 | 4.39 | 0.00 | 0.00 | 0.49 | 0.00 |
| time (sec) |
N/A | 1.670 | 7.796 | 2.856 | 0.000 | 0.159 | 0.000 | 0.000 | 0.196 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 378 | 388 | 322 | 1614 | 0 | 713 | 0 | 0 | 228 | 0 |
| N.S. |
1 | 1.03 | 0.85 | 4.27 | 0.00 | 1.89 | 0.00 | 0.00 | 0.60 | 0.00 |
| time (sec) |
N/A | 1.943 | 4.760 | 12.618 | 0.000 | 0.135 | 0.000 | 0.000 | 0.237 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 298 | 306 | 262 | 1316 | 0 | 614 | 0 | 0 | 138 | 0 |
| N.S. |
1 | 1.03 | 0.88 | 4.42 | 0.00 | 2.06 | 0.00 | 0.00 | 0.46 | 0.00 |
| time (sec) |
N/A | 1.507 | 3.909 | 4.490 | 0.000 | 0.182 | 0.000 | 0.000 | 0.231 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 239 | 245 | 244 | 1035 | 0 | 532 | 0 | 0 | 62 | 0 |
| N.S. |
1 | 1.03 | 1.02 | 4.33 | 0.00 | 2.23 | 0.00 | 0.00 | 0.26 | 0.00 |
| time (sec) |
N/A | 1.147 | 1.191 | 3.073 | 0.000 | 0.116 | 0.000 | 0.000 | 0.194 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
| size | 189 | 193 | 193 | 719 | 0 | 453 | 0 | 0 | 99 | 0 |
| N.S. |
1 | 1.02 | 1.02 | 3.80 | 0.00 | 2.40 | 0.00 | 0.00 | 0.52 | 0.00 |
| time (sec) |
N/A | 0.858 | 3.202 | 1.641 | 0.000 | 0.099 | 0.000 | 0.000 | 0.179 | 0.000 |