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 | A | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 122 | 107 | 177 | 162 | 116 | 221 | 8644 | 19 | 0 |
N.S. |
1 | 1.07 | 0.94 | 1.55 | 1.42 | 1.02 | 1.94 | 75.82 | 0.17 | 0.00 |
time (sec) |
N/A | 0.264 | 0.099 | 0.254 | 0.038 | 0.136 | 10.597 | 0.983 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 97 | 72 | 79 | 81 | 63 | 153 | 3862 | 19 | 0 |
N.S. |
1 | 1.09 | 0.81 | 0.89 | 0.91 | 0.71 | 1.72 | 43.39 | 0.21 | 0.00 |
time (sec) |
N/A | 0.255 | 0.063 | 0.174 | 0.034 | 0.109 | 2.267 | 0.170 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 93 | 97 | 141 | 131 | 107 | 175 | 4828 | 19 | 0 |
N.S. |
1 | 1.04 | 1.09 | 1.58 | 1.47 | 1.20 | 1.97 | 54.25 | 0.21 | 0.00 |
time (sec) |
N/A | 0.244 | 0.053 | 0.176 | 0.028 | 0.131 | 3.777 | 0.583 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 68 | 62 | 70 | 60 | 53 | 107 | 1926 | 19 | 0 |
N.S. |
1 | 1.06 | 0.97 | 1.09 | 0.94 | 0.83 | 1.67 | 30.09 | 0.30 | 0.00 |
time (sec) |
N/A | 0.233 | 0.073 | 0.174 | 0.026 | 0.110 | 1.518 | 0.159 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 85 | 94 | 98 | 94 | 107 | 2101 | 19 | 0 |
N.S. |
1 | 1.00 | 1.33 | 1.47 | 1.53 | 1.47 | 1.67 | 32.83 | 0.30 | 0.00 |
time (sec) |
N/A | 0.236 | 0.043 | 0.172 | 0.027 | 0.131 | 2.135 | 0.441 | 0.260 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 50 | 61 | 37 | 40 | 58 | 634 | 17 | 40 |
N.S. |
1 | 1.00 | 1.28 | 1.56 | 0.95 | 1.03 | 1.49 | 16.26 | 0.44 | 1.03 |
time (sec) |
N/A | 0.196 | 0.021 | 0.168 | 0.034 | 0.107 | 0.956 | 0.142 | 0.227 | 0.836 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 59 | 38 | 53 | 63 | 32 | 63 | 12 | 34 |
N.S. |
1 | 1.00 | 1.84 | 1.19 | 1.66 | 1.97 | 1.00 | 1.97 | 0.38 | 1.06 |
time (sec) |
N/A | 0.176 | 0.041 | 0.070 | 0.030 | 0.113 | 1.374 | 0.124 | 0.253 | 1.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 87 | 59 | 84 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.36 | 0.92 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.450 | 0.020 | 0.466 | 0.000 | 0.000 | 0.000 | 0.000 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 40 | 58 | 33 | 27 | 36 | 43 | 21 | 36 |
N.S. |
1 | 1.00 | 1.29 | 1.87 | 1.06 | 0.87 | 1.16 | 1.39 | 0.68 | 1.16 |
time (sec) |
N/A | 0.207 | 0.026 | 0.176 | 0.024 | 0.093 | 0.419 | 0.132 | 0.242 | 0.788 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 64 | 66 | 96 | 83 | 39 | 119 | 58 | 25 | 50 |
N.S. |
1 | 1.25 | 1.29 | 1.88 | 1.63 | 0.76 | 2.33 | 1.14 | 0.49 | 0.98 |
time (sec) |
N/A | 0.234 | 0.031 | 0.172 | 0.121 | 0.104 | 2.151 | 0.129 | 0.241 | 0.929 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 65 | 59 | 71 | 58 | 40 | 110 | 65 | 25 | 0 |
N.S. |
1 | 1.08 | 0.98 | 1.18 | 0.97 | 0.67 | 1.83 | 1.08 | 0.42 | 0.00 |
time (sec) |
N/A | 0.247 | 0.039 | 0.181 | 0.034 | 0.099 | 2.249 | 0.136 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 96 | 78 | 138 | 125 | 52 | 192 | 83 | 25 | 0 |
N.S. |
1 | 1.26 | 1.03 | 1.82 | 1.64 | 0.68 | 2.53 | 1.09 | 0.33 | 0.00 |
time (sec) |
N/A | 0.257 | 0.046 | 0.183 | 0.118 | 0.094 | 4.974 | 0.135 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 86 | 69 | 79 | 76 | 51 | 156 | 87 | 25 | 0 |
N.S. |
1 | 1.05 | 0.84 | 0.96 | 0.93 | 0.62 | 1.90 | 1.06 | 0.30 | 0.00 |
time (sec) |
N/A | 0.278 | 0.048 | 0.177 | 0.028 | 0.109 | 4.220 | 0.133 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 128 | 88 | 174 | 165 | 62 | 241 | 104 | 25 | 0 |
N.S. |
1 | 1.27 | 0.87 | 1.72 | 1.63 | 0.61 | 2.39 | 1.03 | 0.25 | 0.00 |
time (sec) |
N/A | 0.290 | 0.056 | 0.176 | 0.114 | 0.091 | 9.989 | 0.133 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 114 | 124 | 170 | 163 | 146 | 0 | 6625 | 39 | 0 |
N.S. |
1 | 1.07 | 1.16 | 1.59 | 1.52 | 1.36 | 0.00 | 61.92 | 0.36 | 0.00 |
time (sec) |
N/A | 0.563 | 0.138 | 0.527 | 0.316 | 0.124 | 0.000 | 0.388 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 140 | 226 | 285 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 0.95 | 1.54 | 1.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.548 | 0.852 | 0.850 | 0.000 | 0.000 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 64 | 90 | 123 | 87 | 111 | 0 | 2181 | 35 | 0 |
N.S. |
1 | 1.14 | 1.61 | 2.20 | 1.55 | 1.98 | 0.00 | 38.95 | 0.62 | 0.00 |
time (sec) |
N/A | 0.413 | 0.165 | 0.507 | 0.049 | 0.123 | 0.000 | 0.246 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 87 | 163 | 194 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.95 | 1.77 | 2.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.411 | 0.158 | 0.357 | 0.000 | 0.000 | 0.000 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 107 | 129 | 206 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.15 | 1.39 | 2.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.530 | 0.085 | 0.512 | 0.000 | 0.000 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 56 | 75 | 114 | 78 | 57 | 0 | 105 | 42 | 89 |
N.S. |
1 | 1.12 | 1.50 | 2.28 | 1.56 | 1.14 | 0.00 | 2.10 | 0.84 | 1.78 |
time (sec) |
N/A | 0.379 | 0.083 | 0.377 | 0.034 | 0.110 | 0.000 | 0.145 | 0.237 | 0.969 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 97 | 102 | 145 | 0 | 82 | 0 | 147 | 48 | 0 |
N.S. |
1 | 1.18 | 1.24 | 1.77 | 0.00 | 1.00 | 0.00 | 1.79 | 0.59 | 0.00 |
time (sec) |
N/A | 0.344 | 0.075 | 0.502 | 0.000 | 0.115 | 0.000 | 0.144 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 110 | 108 | 153 | 164 | 93 | 0 | 168 | 48 | 0 |
N.S. |
1 | 1.08 | 1.06 | 1.50 | 1.61 | 0.91 | 0.00 | 1.65 | 0.47 | 0.00 |
time (sec) |
N/A | 0.494 | 0.122 | 0.680 | 0.319 | 0.108 | 0.000 | 0.173 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 139 | 148 | 265 | 0 | 120 | 0 | 215 | 48 | 0 |
N.S. |
1 | 1.14 | 1.21 | 2.17 | 0.00 | 0.98 | 0.00 | 1.76 | 0.39 | 0.00 |
time (sec) |
N/A | 0.453 | 0.112 | 0.624 | 0.000 | 0.115 | 0.000 | 0.141 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 213 | 288 | 365 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.03 | 1.39 | 1.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.871 | 0.539 | 0.890 | 0.000 | 0.000 | 0.000 | 0.000 | 0.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 227 | 403 | 574 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 0.96 | 1.71 | 2.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.869 | 1.009 | 1.076 | 0.000 | 0.000 | 0.000 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 132 | 184 | 252 | 0 | 0 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.05 | 1.46 | 2.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.611 | 0.403 | 0.769 | 0.000 | 0.000 | 0.000 | 0.000 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 149 | 289 | 446 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 0.94 | 1.83 | 2.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.590 | 0.221 | 1.153 | 0.000 | 0.000 | 0.000 | 0.000 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 145 | 204 | 364 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.13 | 1.59 | 2.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.661 | 0.118 | 0.608 | 0.000 | 0.000 | 0.000 | 0.000 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 86 | 141 | 196 | 146 | 98 | 0 | 196 | 63 | 156 |
N.S. |
1 | 1.08 | 1.76 | 2.45 | 1.82 | 1.22 | 0.00 | 2.45 | 0.79 | 1.95 |
time (sec) |
N/A | 0.499 | 0.118 | 0.451 | 0.049 | 0.103 | 0.000 | 0.145 | 0.256 | 0.984 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 149 | 185 | 207 | 0 | 150 | 0 | 278 | 71 | 0 |
N.S. |
1 | 1.09 | 1.35 | 1.51 | 0.00 | 1.09 | 0.00 | 2.03 | 0.52 | 0.00 |
time (sec) |
N/A | 0.445 | 0.144 | 0.561 | 0.000 | 0.111 | 0.000 | 0.163 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 189 | 204 | 299 | 575 | 172 | 0 | 336 | 71 | 0 |
N.S. |
1 | 1.11 | 1.20 | 1.76 | 3.38 | 1.01 | 0.00 | 1.98 | 0.42 | 0.00 |
time (sec) |
N/A | 0.752 | 0.180 | 0.886 | 0.654 | 0.112 | 0.000 | 0.161 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 268 | 283 | 470 | 0 | 225 | 0 | 427 | 71 | 0 |
N.S. |
1 | 1.29 | 1.36 | 2.26 | 0.00 | 1.08 | 0.00 | 2.05 | 0.34 | 0.00 |
time (sec) |
N/A | 0.793 | 0.207 | 0.885 | 0.000 | 0.113 | 0.000 | 0.155 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 12 | 14 | 14 | 10 | 14 | 14 | 18 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 0.83 | 1.17 | 1.17 | 1.50 |
time (sec) |
N/A | 0.189 | 2.391 | 0.604 | 0.147 | 0.085 | 0.475 | 46.736 | 0.235 | 0.759 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 16 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.60 |
time (sec) |
N/A | 0.171 | 0.021 | 0.431 | 0.146 | 0.091 | 0.478 | 7.276 | 0.238 | 0.759 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 14 | 16 | 15 | 12 | 16 | 15 | 20 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.07 | 0.86 | 1.14 | 1.07 | 1.43 |
time (sec) |
N/A | 0.197 | 0.214 | 0.348 | 0.172 | 0.090 | 1.101 | 1.818 | 0.251 | 0.825 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 43 | 47 | 0 | 0 | 0 | 55 | 19 | 0 |
N.S. |
1 | 1.00 | 0.93 | 1.02 | 0.00 | 0.00 | 0.00 | 1.20 | 0.41 | 0.00 |
time (sec) |
N/A | 0.444 | 0.060 | 0.291 | 0.000 | 0.000 | 0.000 | 0.138 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 59 | 56 | 58 | 0 | 0 | 0 | 95 | 19 | 0 |
N.S. |
1 | 0.94 | 0.89 | 0.92 | 0.00 | 0.00 | 0.00 | 1.51 | 0.30 | 0.00 |
time (sec) |
N/A | 0.523 | 0.055 | 0.420 | 0.000 | 0.000 | 0.000 | 0.143 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 109 | 91 | 102 | 0 | 0 | 0 | 199 | 19 | 0 |
N.S. |
1 | 0.93 | 0.78 | 0.87 | 0.00 | 0.00 | 0.00 | 1.70 | 0.16 | 0.00 |
time (sec) |
N/A | 0.479 | 0.125 | 0.254 | 0.000 | 0.000 | 0.000 | 0.147 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 12 | 583 | 28 | 12 | 14 | 28 | 18 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 48.58 | 2.33 | 1.00 | 1.17 | 2.33 | 1.50 |
time (sec) |
N/A | 0.178 | 10.362 | 0.515 | 0.872 | 0.087 | 1.091 | 98.444 | 0.262 | 0.793 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 577 | 26 | 12 | 0 | 26 | 16 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 57.70 | 2.60 | 1.20 | 0.00 | 2.60 | 1.60 |
time (sec) |
N/A | 0.169 | 20.706 | 0.450 | 0.859 | 0.086 | 1.183 | 0.000 | 0.259 | 0.791 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 14 | 560 | 30 | 14 | 16 | 30 | 20 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 40.00 | 2.14 | 1.00 | 1.14 | 2.14 | 1.43 |
time (sec) |
N/A | 0.188 | 2.753 | 0.368 | 0.630 | 0.085 | 2.147 | 5.398 | 0.261 | 0.865 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 79 | 69 | 78 | 0 | 0 | 0 | 226 | 36 | 0 |
N.S. |
1 | 1.05 | 0.92 | 1.04 | 0.00 | 0.00 | 0.00 | 3.01 | 0.48 | 0.00 |
time (sec) |
N/A | 0.541 | 0.243 | 0.331 | 0.000 | 0.000 | 0.000 | 0.171 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 86 | 80 | 77 | 0 | 0 | 0 | 357 | 36 | 0 |
N.S. |
1 | 1.02 | 0.95 | 0.92 | 0.00 | 0.00 | 0.00 | 4.25 | 0.43 | 0.00 |
time (sec) |
N/A | 0.646 | 0.286 | 0.466 | 0.000 | 0.000 | 0.000 | 0.175 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 164 | 223 | 153 | 0 | 0 | 0 | 694 | 36 | 0 |
N.S. |
1 | 0.92 | 1.25 | 0.86 | 0.00 | 0.00 | 0.00 | 3.90 | 0.20 | 0.00 |
time (sec) |
N/A | 0.535 | 0.520 | 0.296 | 0.000 | 0.000 | 0.000 | 0.184 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 12 | 1790 | 42 | 12 | 0 | 42 | 18 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 149.17 | 3.50 | 1.00 | 0.00 | 3.50 | 1.50 |
time (sec) |
N/A | 0.173 | 2.401 | 0.477 | 34.090 | 0.089 | 2.169 | 0.000 | 0.229 | 0.812 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 1744 | 40 | 12 | 12 | 40 | 16 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 174.40 | 4.00 | 1.20 | 1.20 | 4.00 | 1.60 |
time (sec) |
N/A | 0.168 | 8.510 | 0.525 | 34.687 | 0.097 | 2.279 | 48.664 | 0.282 | 0.835 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 14 | 1568 | 45 | 14 | 16 | 45 | 20 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 112.00 | 3.21 | 1.00 | 1.14 | 3.21 | 1.43 |
time (sec) |
N/A | 0.185 | 1.198 | 0.350 | 25.694 | 0.089 | 4.386 | 9.590 | 0.287 | 1.008 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 112 | 88 | 154 | 0 | 0 | 0 | 580 | 53 | 0 |
N.S. |
1 | 1.09 | 0.85 | 1.50 | 0.00 | 0.00 | 0.00 | 5.63 | 0.51 | 0.00 |
time (sec) |
N/A | 0.645 | 0.270 | 0.307 | 0.000 | 0.000 | 0.000 | 0.210 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 116 | 114 | 157 | 0 | 0 | 0 | 929 | 53 | 0 |
N.S. |
1 | 1.04 | 1.02 | 1.40 | 0.00 | 0.00 | 0.00 | 8.29 | 0.47 | 0.00 |
time (sec) |
N/A | 0.783 | 0.275 | 0.431 | 0.000 | 0.000 | 0.000 | 0.213 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 211 | 169 | 307 | 0 | 0 | 0 | 1640 | 53 | 0 |
N.S. |
1 | 0.93 | 0.74 | 1.35 | 0.00 | 0.00 | 0.00 | 7.19 | 0.23 | 0.00 |
time (sec) |
N/A | 0.600 | 0.312 | 0.288 | 0.000 | 0.000 | 0.000 | 0.228 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 16 | 991 | 44 | 15 | 18 | 121 | 22 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 61.94 | 2.75 | 0.94 | 1.12 | 7.56 | 1.38 |
time (sec) |
N/A | 0.196 | 3.879 | 0.524 | 17.407 | 0.120 | 26.310 | 0.562 | 0.284 | 1.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 16 | 512 | 30 | 15 | 18 | 80 | 22 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 32.00 | 1.88 | 0.94 | 1.12 | 5.00 | 1.38 |
time (sec) |
N/A | 0.187 | 2.494 | 0.505 | 7.296 | 0.135 | 12.049 | 0.404 | 0.285 | 1.079 |
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 | 67 | 67 | 82 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.00 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.254 | 0.176 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 16 | 18 | 18 | 14 | 18 | 20 | 22 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.88 | 1.12 | 1.25 | 1.38 |
time (sec) |
N/A | 0.204 | 0.612 | 1.835 | 0.203 | 0.098 | 1.323 | 0.741 | 0.283 | 0.702 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 16 | 643 | 32 | 15 | 18 | 34 | 22 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 40.19 | 2.00 | 0.94 | 1.12 | 2.12 | 1.38 |
time (sec) |
N/A | 0.201 | 1.248 | 1.144 | 1.942 | 0.091 | 6.412 | 1.509 | 0.232 | 0.732 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 168 | 166 | 402 | 272 | 291 | 362 | 9430 | 93 | 0 |
N.S. |
1 | 1.01 | 0.99 | 2.41 | 1.63 | 1.74 | 2.17 | 56.47 | 0.56 | 0.00 |
time (sec) |
N/A | 0.801 | 0.165 | 0.240 | 0.039 | 0.226 | 4.794 | 2.376 | 0.253 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 130 | 124 | 306 | 200 | 209 | 228 | 6416 | 62 | 0 |
N.S. |
1 | 1.05 | 1.00 | 2.47 | 1.61 | 1.69 | 1.84 | 51.74 | 0.50 | 0.00 |
time (sec) |
N/A | 0.568 | 0.108 | 0.237 | 0.043 | 0.182 | 4.172 | 2.814 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 87 | 114 | 110 | 93 | 130 | 104 | 1547 | 32 | 77 |
N.S. |
1 | 1.04 | 1.36 | 1.31 | 1.11 | 1.55 | 1.24 | 18.42 | 0.38 | 0.92 |
time (sec) |
N/A | 0.377 | 0.135 | 0.209 | 0.036 | 0.154 | 2.689 | 0.315 | 0.261 | 1.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 59 | 38 | 53 | 63 | 32 | 63 | 12 | 34 |
N.S. |
1 | 1.00 | 1.84 | 1.19 | 1.66 | 1.97 | 1.00 | 1.97 | 0.38 | 1.06 |
time (sec) |
N/A | 0.181 | 0.027 | 0.071 | 0.038 | 0.134 | 1.467 | 0.121 | 0.271 | 0.988 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 247 | 333 | 453 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 1.35 | 1.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.754 | 0.413 | 1.483 | 0.000 | 0.000 | 0.000 | 0.000 | 0.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 111 | 142 | 193 | 0 | 477 | 0 | 0 | 75 | 0 |
N.S. |
1 | 1.07 | 1.37 | 1.86 | 0.00 | 4.59 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.380 | 0.132 | 1.971 | 0.000 | 0.151 | 0.000 | 0.000 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 199 | 247 | 574 | 0 | 1117 | 0 | 0 | 159 | 0 |
N.S. |
1 | 1.16 | 1.44 | 3.34 | 0.00 | 6.49 | 0.00 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.492 | 0.286 | 1.888 | 0.000 | 0.449 | 0.000 | 0.000 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 372 | 396 | 333 | 798 | 0 | 0 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.06 | 0.90 | 2.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.033 | 12.204 | 11.148 | 0.000 | 0.000 | 0.000 | 0.000 | 0.359 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 315 | 350 | 277 | 386 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.11 | 0.88 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.849 | 32.672 | 9.150 | 0.000 | 0.000 | 0.000 | 0.000 | 0.329 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 237 | 212 | 252 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.12 | 1.00 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.599 | 15.807 | 6.211 | 0.000 | 0.000 | 0.000 | 0.000 | 0.328 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 137 | 124 | 215 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.15 | 1.04 | 1.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.451 | 0.197 | 4.076 | 0.000 | 0.000 | 0.000 | 0.000 | 0.353 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 320 | 326 | 875 | 0 | 0 | 0 | 0 | 136 | 0 |
N.S. |
1 | 1.07 | 1.09 | 2.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.727 | 29.494 | 9.631 | 0.000 | 0.000 | 0.000 | 0.000 | 0.523 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 498 | 516 | 407 | 1618 | 0 | 0 | 0 | 0 | 260 | 0 |
N.S. |
1 | 1.04 | 0.82 | 3.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 1.092 | 32.667 | 14.467 | 0.000 | 0.000 | 0.000 | 0.000 | 0.867 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 167 | 141 | 328 | 296 | 192 | 408 | 17474 | 41 | 0 |
N.S. |
1 | 0.81 | 0.68 | 1.59 | 1.44 | 0.93 | 1.98 | 84.83 | 0.20 | 0.00 |
time (sec) |
N/A | 0.359 | 0.164 | 0.436 | 0.056 | 0.232 | 12.798 | 2.397 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 136 | 123 | 254 | 232 | 170 | 294 | 9792 | 41 | 0 |
N.S. |
1 | 0.84 | 0.76 | 1.58 | 1.44 | 1.06 | 1.83 | 60.82 | 0.25 | 0.00 |
time (sec) |
N/A | 0.325 | 0.122 | 0.429 | 0.053 | 0.227 | 5.498 | 1.519 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 101 | 150 | 132 | 154 | 141 | 153 | 4051 | 34 | 0 |
N.S. |
1 | 0.93 | 1.38 | 1.21 | 1.41 | 1.29 | 1.40 | 37.17 | 0.31 | 0.00 |
time (sec) |
N/A | 0.270 | 0.166 | 0.209 | 0.064 | 0.167 | 3.626 | 1.039 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 83 | 104 | 116 | 89 | 123 | 73 | 1088 | 39 | 72 |
N.S. |
1 | 0.95 | 1.20 | 1.33 | 1.02 | 1.41 | 0.84 | 12.51 | 0.45 | 0.83 |
time (sec) |
N/A | 0.286 | 0.091 | 0.213 | 0.033 | 0.180 | 3.059 | 0.450 | 0.214 | 0.961 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 101 | 69 | 108 | 94 | 67 | 150 | 113 | 51 | 0 |
N.S. |
1 | 0.96 | 0.66 | 1.03 | 0.90 | 0.64 | 1.43 | 1.08 | 0.49 | 0.00 |
time (sec) |
N/A | 0.292 | 0.072 | 0.223 | 0.059 | 0.149 | 2.354 | 0.128 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 131 | 94 | 127 | 137 | 89 | 279 | 158 | 51 | 0 |
N.S. |
1 | 0.86 | 0.62 | 0.84 | 0.90 | 0.59 | 1.84 | 1.04 | 0.34 | 0.00 |
time (sec) |
N/A | 0.309 | 0.096 | 0.216 | 0.043 | 0.115 | 6.191 | 0.135 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 159 | 110 | 145 | 172 | 110 | 371 | 202 | 51 | 0 |
N.S. |
1 | 0.81 | 0.56 | 0.74 | 0.87 | 0.56 | 1.88 | 1.03 | 0.26 | 0.00 |
time (sec) |
N/A | 0.335 | 0.112 | 0.216 | 0.036 | 0.135 | 34.505 | 0.134 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 161 | 118 | 139 | 185 | 128 | 364 | 13018 | 41 | 0 |
N.S. |
1 | 0.82 | 0.60 | 0.71 | 0.94 | 0.65 | 1.86 | 66.42 | 0.21 | 0.00 |
time (sec) |
N/A | 0.377 | 0.169 | 0.401 | 0.042 | 0.144 | 4.386 | 0.263 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 131 | 98 | 121 | 144 | 107 | 272 | 7820 | 41 | 0 |
N.S. |
1 | 0.86 | 0.64 | 0.79 | 0.94 | 0.70 | 1.78 | 51.11 | 0.27 | 0.00 |
time (sec) |
N/A | 0.352 | 0.203 | 0.568 | 0.038 | 0.129 | 2.756 | 0.211 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 116 | 79 | 217 | 100 | 86 | 177 | 3346 | 39 | 0 |
N.S. |
1 | 0.84 | 0.57 | 1.57 | 0.72 | 0.62 | 1.28 | 24.25 | 0.28 | 0.00 |
time (sec) |
N/A | 0.327 | 0.083 | 0.573 | 0.046 | 0.179 | 1.848 | 0.178 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 152 | 115 | 137 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.23 | 0.93 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.683 | 0.071 | 1.224 | 0.000 | 0.000 | 0.000 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 175 | 132 | 143 | 0 | 0 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.28 | 0.96 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.687 | 0.087 | 1.101 | 0.000 | 0.000 | 0.000 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 215 | 186 | 459 | 405 | 273 | 542 | 4760 | 72 | 0 |
N.S. |
1 | 0.85 | 0.74 | 1.82 | 1.61 | 1.08 | 2.15 | 18.89 | 0.29 | 0.00 |
time (sec) |
N/A | 0.464 | 0.217 | 0.450 | 0.054 | 0.443 | 13.468 | 5.800 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 179 | 153 | 340 | 296 | 237 | 355 | 14166 | 65 | 0 |
N.S. |
1 | 0.94 | 0.80 | 1.78 | 1.55 | 1.24 | 1.86 | 74.17 | 0.34 | 0.00 |
time (sec) |
N/A | 0.386 | 0.138 | 0.240 | 0.049 | 0.291 | 6.647 | 4.168 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 146 | 136 | 249 | 198 | 230 | 207 | 6018 | 74 | 0 |
N.S. |
1 | 0.90 | 0.84 | 1.54 | 1.22 | 1.42 | 1.28 | 37.15 | 0.46 | 0.00 |
time (sec) |
N/A | 0.393 | 0.124 | 0.266 | 0.045 | 0.192 | 5.063 | 2.423 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 147 | 127 | 231 | 159 | 221 | 211 | 4968 | 81 | 0 |
N.S. |
1 | 0.93 | 0.80 | 1.46 | 1.01 | 1.40 | 1.34 | 31.44 | 0.51 | 0.00 |
time (sec) |
N/A | 0.379 | 0.132 | 0.247 | 0.036 | 0.158 | 5.668 | 96.738 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 171 | 127 | 175 | 181 | 127 | 333 | 222 | 85 | 0 |
N.S. |
1 | 0.93 | 0.69 | 0.96 | 0.99 | 0.69 | 1.82 | 1.21 | 0.46 | 0.00 |
time (sec) |
N/A | 0.401 | 0.139 | 0.247 | 0.039 | 0.104 | 5.873 | 0.132 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 201 | 153 | 207 | 241 | 159 | 508 | 293 | 85 | 0 |
N.S. |
1 | 0.83 | 0.63 | 0.86 | 1.00 | 0.66 | 2.11 | 1.22 | 0.35 | 0.00 |
time (sec) |
N/A | 0.430 | 0.147 | 0.259 | 0.037 | 0.102 | 46.474 | 0.138 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 242 | 207 | 162 | 198 | 256 | 187 | 493 | 17666 | 72 | 0 |
N.S. |
1 | 0.86 | 0.67 | 0.82 | 1.06 | 0.77 | 2.04 | 73.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.484 | 0.165 | 0.625 | 0.051 | 0.138 | 4.998 | 0.335 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 160 | 125 | 352 | 192 | 153 | 352 | 11858 | 70 | 0 |
N.S. |
1 | 0.82 | 0.64 | 1.81 | 0.98 | 0.78 | 1.81 | 60.81 | 0.36 | 0.00 |
time (sec) |
N/A | 0.371 | 0.173 | 0.616 | 0.042 | 0.137 | 3.306 | 0.250 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 217 | 160 | 231 | 0 | 0 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.17 | 0.86 | 1.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.837 | 0.222 | 1.702 | 0.000 | 0.000 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 228 | 194 | 216 | 0 | 0 | 0 | 0 | 84 | 0 |
N.S. |
1 | 1.21 | 1.03 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.823 | 0.565 | 1.482 | 0.000 | 0.000 | 0.000 | 0.000 | 0.253 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 546 | 598 | 1023 | 374 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.10 | 1.87 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 1.665 | 1.640 | 29.015 | 0.000 | 0.000 | 0.000 | 0.000 | 0.253 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 499 | 547 | 891 | 446 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.10 | 1.79 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.527 | 0.411 | 1.791 | 0.000 | 0.000 | 0.000 | 0.000 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 509 | 557 | 871 | 272 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.09 | 1.71 | 0.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.331 | 0.428 | 15.122 | 0.000 | 0.000 | 0.000 | 0.000 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 459 | 511 | 876 | 1970 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.11 | 1.91 | 4.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 1.377 | 0.118 | 1.966 | 0.000 | 0.000 | 0.000 | 0.000 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 551 | 603 | 997 | 331 | 0 | 0 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.09 | 1.81 | 0.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.544 | 1.635 | 25.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 617 | 676 | 1255 | 701 | 0 | 0 | 0 | 0 | 137 | 0 |
N.S. |
1 | 1.10 | 2.03 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.770 | 2.576 | 6.415 | 0.000 | 0.000 | 0.000 | 0.000 | 0.271 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 582 | 634 | 1213 | 577 | 0 | 0 | 0 | 0 | 123 | 0 |
N.S. |
1 | 1.09 | 2.08 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 1.682 | 0.974 | 2.094 | 0.000 | 0.000 | 0.000 | 0.000 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 118 | 286 | 263 | 0 | 390 | 0 | 0 | 90 | 0 |
N.S. |
1 | 0.90 | 2.18 | 2.01 | 0.00 | 2.98 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.315 | 0.423 | 4.262 | 0.000 | 0.152 | 0.000 | 0.000 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 546 | 602 | 1190 | 2108 | 0 | 0 | 0 | 0 | 138 | 0 |
N.S. |
1 | 1.10 | 2.18 | 3.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.578 | 0.726 | 6.215 | 0.000 | 0.000 | 0.000 | 0.000 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 784 | 844 | 1331 | 941 | 0 | 0 | 0 | 0 | 149 | 0 |
N.S. |
1 | 1.08 | 1.70 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 2.883 | 1.434 | 67.161 | 0.000 | 0.000 | 0.000 | 0.000 | 0.260 | 0.000 |