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 | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 108 | 108 | 75 | 238 | 0 | 139 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.69 | 2.20 | 0.00 | 1.29 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.100 | 0.153 | 5.516 | 0.000 | 0.104 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 80 | 80 | 55 | 161 | 0 | 119 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.69 | 2.01 | 0.00 | 1.49 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.094 | 0.136 | 4.773 | 0.000 | 0.110 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 105 | 105 | 73 | 215 | 0 | 170 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.70 | 2.05 | 0.00 | 1.62 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.145 | 0.406 | 5.150 | 0.000 | 0.098 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 136 | 136 | 85 | 403 | 0 | 189 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.62 | 2.96 | 0.00 | 1.39 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.186 | 0.413 | 6.514 | 0.000 | 0.108 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 169 | 169 | 107 | 576 | 0 | 202 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.63 | 3.41 | 0.00 | 1.20 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.228 | 0.615 | 8.326 | 0.000 | 0.110 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 169 | 169 | 103 | 301 | 0 | 165 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.61 | 1.78 | 0.00 | 0.98 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.261 | 0.457 | 8.392 | 0.000 | 0.111 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 140 | 88 | 273 | 0 | 153 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.63 | 1.95 | 0.00 | 1.09 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.181 | 0.101 | 6.963 | 0.000 | 0.116 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 112 | 76 | 240 | 0 | 140 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.68 | 2.14 | 0.00 | 1.25 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.157 | 0.054 | 5.895 | 0.000 | 0.112 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 83 | 83 | 57 | 163 | 0 | 119 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.69 | 1.96 | 0.00 | 1.43 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.167 | 0.045 | 5.002 | 0.000 | 0.111 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 110 | 110 | 73 | 217 | 0 | 171 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.66 | 1.97 | 0.00 | 1.55 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.250 | 0.461 | 5.147 | 0.000 | 0.122 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 141 | 141 | 87 | 404 | 0 | 192 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.62 | 2.87 | 0.00 | 1.36 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.314 | 0.342 | 6.386 | 0.000 | 0.119 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 174 | 174 | 107 | 577 | 0 | 205 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.61 | 3.32 | 0.00 | 1.18 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.237 | 0.550 | 8.298 | 0.000 | 0.108 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 171 | 171 | 100 | 301 | 0 | 171 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.58 | 1.76 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.138 | 0.107 | 9.010 | 0.000 | 0.127 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 145 | 145 | 89 | 273 | 0 | 157 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.61 | 1.88 | 0.00 | 1.08 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.152 | 0.146 | 8.884 | 0.000 | 0.117 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 116 | 78 | 240 | 0 | 142 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.67 | 2.07 | 0.00 | 1.22 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.134 | 0.056 | 15.668 | 0.000 | 0.117 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 85 | 54 | 163 | 0 | 119 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.64 | 1.92 | 0.00 | 1.40 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.117 | 0.391 | 53.232 | 0.000 | 0.111 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 112 | 73 | 217 | 0 | 173 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.65 | 1.94 | 0.00 | 1.54 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.147 | 0.371 | 158.889 | 0.000 | 0.106 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 143 | 143 | 87 | 406 | 0 | 196 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.61 | 2.84 | 0.00 | 1.37 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.165 | 0.376 | 2.429 | 0.000 | 0.117 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 176 | 176 | 102 | 579 | 0 | 211 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.58 | 3.29 | 0.00 | 1.20 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.192 | 0.665 | 3.174 | 0.000 | 0.115 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 173 | 173 | 101 | 298 | 0 | 165 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.58 | 1.72 | 0.00 | 0.95 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.164 | 0.667 | 7.524 | 0.000 | 0.120 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 144 | 144 | 88 | 270 | 0 | 154 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.61 | 1.88 | 0.00 | 1.07 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.136 | 0.413 | 6.289 | 0.000 | 0.105 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 113 | 113 | 78 | 237 | 0 | 142 | 0 | 0 | 94 |
| N.S. |
1 | 1.00 | 0.69 | 2.10 | 0.00 | 1.26 | 0.00 | 0.00 | 0.83 |
| time (sec) |
N/A | 0.116 | 0.067 | 5.129 | 0.000 | 0.110 | 0.000 | 0.000 | 0.290 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 82 | 82 | 54 | 160 | 0 | 122 | 0 | 0 | 48 |
| N.S. |
1 | 1.00 | 0.66 | 1.95 | 0.00 | 1.49 | 0.00 | 0.00 | 0.59 |
| time (sec) |
N/A | 0.088 | 0.037 | 3.629 | 0.000 | 0.094 | 0.000 | 0.000 | 0.347 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 106 | 106 | 73 | 214 | 0 | 173 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.69 | 2.02 | 0.00 | 1.63 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.141 | 0.286 | 5.145 | 0.000 | 0.115 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 135 | 84 | 406 | 0 | 192 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.62 | 3.01 | 0.00 | 1.42 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.183 | 0.239 | 6.363 | 0.000 | 0.099 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 168 | 168 | 101 | 579 | 0 | 205 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.60 | 3.45 | 0.00 | 1.22 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.207 | 0.409 | 8.488 | 0.000 | 0.105 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 176 | 176 | 104 | 301 | 0 | 165 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.59 | 1.71 | 0.00 | 0.94 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.184 | 0.626 | 8.567 | 0.000 | 0.123 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 147 | 147 | 88 | 273 | 0 | 154 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.60 | 1.86 | 0.00 | 1.05 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.154 | 0.639 | 6.761 | 0.000 | 0.109 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 116 | 75 | 240 | 0 | 142 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.65 | 2.07 | 0.00 | 1.22 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.132 | 0.406 | 5.583 | 0.000 | 0.109 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 85 | 57 | 163 | 0 | 122 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.67 | 1.92 | 0.00 | 1.44 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.101 | 0.040 | 4.540 | 0.000 | 0.102 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 112 | 76 | 217 | 0 | 173 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.68 | 1.94 | 0.00 | 1.54 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.105 | 0.141 | 4.831 | 0.000 | 0.105 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 140 | 87 | 406 | 0 | 192 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.62 | 2.90 | 0.00 | 1.37 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.155 | 0.117 | 6.595 | 0.000 | 0.101 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 171 | 171 | 104 | 579 | 0 | 205 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.61 | 3.39 | 0.00 | 1.20 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.203 | 0.239 | 8.145 | 0.000 | 0.118 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 176 | 176 | 104 | 301 | 0 | 165 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.59 | 1.71 | 0.00 | 0.94 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.175 | 0.884 | 8.294 | 0.000 | 0.119 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 147 | 147 | 91 | 273 | 0 | 154 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.62 | 1.86 | 0.00 | 1.05 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.134 | 0.633 | 7.046 | 0.000 | 0.122 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 116 | 78 | 240 | 0 | 142 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.67 | 2.07 | 0.00 | 1.22 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.113 | 0.465 | 5.699 | 0.000 | 0.107 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 85 | 85 | 57 | 163 | 0 | 122 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.67 | 1.92 | 0.00 | 1.44 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.089 | 0.038 | 4.594 | 0.000 | 0.117 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 112 | 76 | 217 | 0 | 173 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.68 | 1.94 | 0.00 | 1.54 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.118 | 0.059 | 4.664 | 0.000 | 0.103 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 143 | 143 | 87 | 406 | 0 | 192 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.61 | 2.84 | 0.00 | 1.34 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.121 | 0.097 | 6.412 | 0.000 | 0.109 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 173 | 173 | 104 | 579 | 0 | 205 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.60 | 3.35 | 0.00 | 1.18 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.193 | 0.098 | 8.424 | 0.000 | 0.116 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 176 | 176 | 104 | 579 | 0 | 205 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.59 | 3.29 | 0.00 | 1.16 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.160 | 0.036 | 8.385 | 0.000 | 0.118 | 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 | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 172 | 172 | 81 | 91 | 93 | 252 | 0 | 278 | 105 |
| N.S. |
1 | 1.00 | 0.47 | 0.53 | 0.54 | 1.47 | 0.00 | 1.62 | 0.61 |
| time (sec) |
N/A | 0.096 | 0.404 | 5.223 | 0.481 | 0.363 | 0.000 | 3.404 | 16.238 |
| 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 | 136 | 136 | 69 | 74 | 68 | 230 | 202 | 194 | 92 |
| N.S. |
1 | 1.00 | 0.51 | 0.54 | 0.50 | 1.69 | 1.49 | 1.43 | 0.68 |
| time (sec) |
N/A | 0.071 | 0.281 | 4.900 | 0.417 | 0.326 | 81.203 | 2.583 | 16.086 |
| 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 | 98 | 98 | 57 | 55 | 40 | 204 | 165 | 142 | 79 |
| N.S. |
1 | 1.00 | 0.58 | 0.56 | 0.41 | 2.08 | 1.68 | 1.45 | 0.81 |
| time (sec) |
N/A | 0.028 | 0.224 | 5.025 | 0.410 | 0.343 | 2.901 | 1.878 | 14.954 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 42 | 39 | 40 | 181 | 80 | 0 | 35 |
| N.S. |
1 | 1.00 | 0.71 | 0.66 | 0.68 | 3.07 | 1.36 | 0.00 | 0.59 |
| time (sec) |
N/A | 0.014 | 0.036 | 4.966 | 0.368 | 0.341 | 1.354 | 0.000 | 0.319 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 60 | 60 | 40 | 52 | 92 | 210 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.67 | 0.87 | 1.53 | 3.50 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.027 | 0.026 | 4.677 | 0.375 | 0.357 | 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) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 68 | 68 | 50 | 57 | 120 | 205 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.74 | 0.84 | 1.76 | 3.01 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.051 | 0.037 | 5.058 | 0.421 | 0.333 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 107 | 65 | 103 | 716 | 225 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.61 | 0.96 | 6.69 | 2.10 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.064 | 0.084 | 5.139 | 0.617 | 0.339 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 145 | 145 | 76 | 122 | 957 | 253 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.52 | 0.84 | 6.60 | 1.74 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.074 | 0.222 | 4.929 | 0.719 | 0.328 | 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 | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 177 | 177 | 81 | 92 | 100 | 261 | 0 | 279 | 106 |
| N.S. |
1 | 1.00 | 0.46 | 0.52 | 0.56 | 1.47 | 0.00 | 1.58 | 0.60 |
| time (sec) |
N/A | 0.080 | 0.365 | 5.076 | 0.466 | 0.351 | 0.000 | 3.459 | 16.238 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 140 | 69 | 75 | 74 | 237 | 0 | 195 | 93 |
| N.S. |
1 | 1.00 | 0.49 | 0.54 | 0.53 | 1.69 | 0.00 | 1.39 | 0.66 |
| time (sec) |
N/A | 0.063 | 0.231 | 5.034 | 0.447 | 0.351 | 0.000 | 2.590 | 1.226 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 101 | 101 | 58 | 56 | 43 | 209 | 151 | 0 | 50 |
| N.S. |
1 | 1.00 | 0.57 | 0.55 | 0.43 | 2.07 | 1.50 | 0.00 | 0.50 |
| time (sec) |
N/A | 0.025 | 0.033 | 4.899 | 0.443 | 0.320 | 31.582 | 0.000 | 0.549 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 61 | 42 | 40 | 40 | 184 | 80 | 0 | 36 |
| N.S. |
1 | 1.00 | 0.69 | 0.66 | 0.66 | 3.02 | 1.31 | 0.00 | 0.59 |
| time (sec) |
N/A | 0.015 | 0.048 | 5.104 | 0.364 | 0.341 | 31.981 | 0.000 | 14.774 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 62 | 40 | 53 | 95 | 212 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.65 | 0.85 | 1.53 | 3.42 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.029 | 0.031 | 4.959 | 0.439 | 0.383 | 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) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 70 | 70 | 50 | 58 | 123 | 208 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.71 | 0.83 | 1.76 | 2.97 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.051 | 0.043 | 4.567 | 0.547 | 0.358 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 110 | 110 | 65 | 104 | 747 | 232 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.59 | 0.95 | 6.79 | 2.11 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.073 | 0.079 | 4.993 | 0.548 | 0.371 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 149 | 149 | 77 | 123 | 992 | 260 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.52 | 0.83 | 6.66 | 1.74 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.070 | 0.013 | 5.112 | 0.538 | 0.346 | 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 | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 187 | 187 | 81 | 94 | 110 | 279 | 0 | 278 | 108 |
| N.S. |
1 | 1.00 | 0.43 | 0.50 | 0.59 | 1.49 | 0.00 | 1.49 | 0.58 |
| time (sec) |
N/A | 0.079 | 0.396 | 5.095 | 0.510 | 0.357 | 0.000 | 3.702 | 15.839 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 148 | 148 | 69 | 77 | 82 | 251 | 0 | 0 | 64 |
| N.S. |
1 | 1.00 | 0.47 | 0.52 | 0.55 | 1.70 | 0.00 | 0.00 | 0.43 |
| time (sec) |
N/A | 0.069 | 0.994 | 5.217 | 0.484 | 0.347 | 0.000 | 0.000 | 0.763 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 107 | 57 | 58 | 47 | 219 | 0 | 0 | 52 |
| N.S. |
1 | 1.00 | 0.53 | 0.54 | 0.44 | 2.05 | 0.00 | 0.00 | 0.49 |
| time (sec) |
N/A | 0.030 | 0.268 | 5.108 | 0.471 | 0.343 | 0.000 | 0.000 | 14.910 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 42 | 42 | 40 | 190 | 0 | 0 | 38 |
| N.S. |
1 | 1.00 | 0.65 | 0.65 | 0.62 | 2.92 | 0.00 | 0.00 | 0.58 |
| time (sec) |
N/A | 0.016 | 0.059 | 4.914 | 0.445 | 0.318 | 0.000 | 0.000 | 0.373 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 66 | 66 | 40 | 55 | 99 | 216 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.61 | 0.83 | 1.50 | 3.27 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.030 | 0.049 | 4.920 | 0.402 | 0.360 | 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) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 74 | 50 | 60 | 127 | 214 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.68 | 0.81 | 1.72 | 2.89 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.051 | 0.060 | 4.875 | 0.488 | 0.328 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 116 | 65 | 106 | 803 | 242 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.56 | 0.91 | 6.92 | 2.09 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.064 | 0.109 | 4.719 | 0.440 | 0.340 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 157 | 157 | 76 | 125 | 1060 | 274 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.48 | 0.80 | 6.75 | 1.75 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.073 | 0.222 | 5.031 | 0.443 | 0.367 | 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) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 136 | 136 | 69 | 74 | 68 | 236 | 0 | 0 | 95 |
| N.S. |
1 | 1.00 | 0.51 | 0.54 | 0.50 | 1.74 | 0.00 | 0.00 | 0.70 |
| time (sec) |
N/A | 0.060 | 0.418 | 5.041 | 0.430 | 0.348 | 0.000 | 0.000 | 16.110 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 98 | 57 | 55 | 40 | 210 | 151 | 0 | 82 |
| N.S. |
1 | 1.00 | 0.58 | 0.56 | 0.41 | 2.14 | 1.54 | 0.00 | 0.84 |
| time (sec) |
N/A | 0.025 | 0.350 | 4.762 | 0.415 | 0.313 | 36.742 | 0.000 | 0.902 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 59 | 59 | 42 | 39 | 40 | 187 | 80 | 0 | 61 |
| N.S. |
1 | 1.00 | 0.71 | 0.66 | 0.68 | 3.17 | 1.36 | 0.00 | 1.03 |
| time (sec) |
N/A | 0.016 | 0.033 | 5.020 | 0.395 | 0.338 | 1.431 | 0.000 | 0.593 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 60 | 60 | 40 | 52 | 92 | 215 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.67 | 0.87 | 1.53 | 3.58 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.031 | 0.027 | 4.914 | 0.413 | 0.368 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 68 | 68 | 50 | 57 | 125 | 211 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.74 | 0.84 | 1.84 | 3.10 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.045 | 0.034 | 5.027 | 0.419 | 0.331 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 107 | 65 | 103 | 722 | 231 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.61 | 0.96 | 6.75 | 2.16 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.063 | 0.060 | 5.033 | 0.421 | 0.344 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 145 | 145 | 76 | 122 | 957 | 259 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.52 | 0.84 | 6.60 | 1.79 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.077 | 0.113 | 5.042 | 0.424 | 0.343 | 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) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 148 | 148 | 69 | 77 | 68 | 236 | 0 | 0 | 95 |
| N.S. |
1 | 1.00 | 0.47 | 0.52 | 0.46 | 1.59 | 0.00 | 0.00 | 0.64 |
| time (sec) |
N/A | 0.061 | 0.505 | 5.014 | 0.417 | 0.368 | 0.000 | 0.000 | 15.809 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 107 | 57 | 58 | 40 | 210 | 0 | 0 | 82 |
| N.S. |
1 | 1.00 | 0.53 | 0.54 | 0.37 | 1.96 | 0.00 | 0.00 | 0.77 |
| time (sec) |
N/A | 0.027 | 0.346 | 4.952 | 0.415 | 0.335 | 0.000 | 0.000 | 0.829 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | A | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 42 | 42 | 40 | 187 | 80 | 0 | 61 |
| N.S. |
1 | 1.00 | 0.65 | 0.65 | 0.62 | 2.88 | 1.23 | 0.00 | 0.94 |
| time (sec) |
N/A | 0.015 | 0.043 | 4.902 | 0.371 | 0.346 | 36.756 | 0.000 | 0.510 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 66 | 66 | 40 | 55 | 92 | 215 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.61 | 0.83 | 1.39 | 3.26 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.030 | 0.032 | 5.212 | 0.384 | 0.377 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 74 | 50 | 60 | 133 | 211 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.68 | 0.81 | 1.80 | 2.85 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.046 | 0.042 | 5.048 | 0.409 | 0.333 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 116 | 65 | 106 | 739 | 231 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.56 | 0.91 | 6.37 | 1.99 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.070 | 0.060 | 4.837 | 0.443 | 0.349 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 157 | 157 | 76 | 125 | 983 | 259 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.48 | 0.80 | 6.26 | 1.65 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.076 | 0.118 | 5.118 | 0.439 | 0.330 | 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) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 148 | 148 | 72 | 77 | 68 | 236 | 0 | 0 | 95 |
| N.S. |
1 | 1.00 | 0.49 | 0.52 | 0.46 | 1.59 | 0.00 | 0.00 | 0.64 |
| time (sec) |
N/A | 0.067 | 0.775 | 5.200 | 0.422 | 0.369 | 0.000 | 0.000 | 16.106 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 107 | 60 | 58 | 40 | 210 | 0 | 0 | 82 |
| N.S. |
1 | 1.00 | 0.56 | 0.54 | 0.37 | 1.96 | 0.00 | 0.00 | 0.77 |
| time (sec) |
N/A | 0.028 | 0.463 | 4.760 | 0.411 | 0.370 | 0.000 | 0.000 | 0.742 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 65 | 45 | 42 | 40 | 187 | 0 | 0 | 61 |
| N.S. |
1 | 1.00 | 0.69 | 0.65 | 0.62 | 2.88 | 0.00 | 0.00 | 0.94 |
| time (sec) |
N/A | 0.016 | 0.040 | 4.957 | 0.362 | 0.325 | 0.000 | 0.000 | 0.521 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 66 | 66 | 43 | 55 | 92 | 215 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.65 | 0.83 | 1.39 | 3.26 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.034 | 0.034 | 4.964 | 0.386 | 0.396 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 74 | 50 | 60 | 133 | 211 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.68 | 0.81 | 1.80 | 2.85 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.051 | 0.042 | 5.105 | 0.418 | 0.356 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 116 | 65 | 106 | 757 | 231 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.56 | 0.91 | 6.53 | 1.99 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.063 | 0.069 | 5.110 | 0.444 | 0.389 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 157 | 157 | 76 | 125 | 1033 | 259 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.48 | 0.80 | 6.58 | 1.65 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.079 | 0.141 | 5.222 | 0.434 | 0.338 | 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 | 119 | 119 | 94 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.089 | 0.143 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 119 | 89 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.090 | 0.097 | 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 | 119 | 119 | 86 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.073 | 0.056 | 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 | 114 | 114 | 86 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.098 | 0.068 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 112 | 86 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.113 | 0.090 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 117 | 117 | 94 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.110 | 0.065 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 119 | 94 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.096 | 0.141 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 119 | 89 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.093 | 0.126 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 119 | 86 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.074 | 0.005 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 116 | 87 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.109 | 0.005 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 112 | 88 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.115 | 0.011 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 115 | 88 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.123 | 0.080 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 119 | 94 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.101 | 0.128 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 119 | 89 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.091 | 0.009 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |