2.3 Detailed conclusion table specific for Rubi results
The following table is specific to Rubi only. It gives additional statistics for each integral. the
column steps is the number of steps used by Rubi to obtain the antiderivative. The rules
column is the number of unique rules used. The integrand size column is the leaf size
of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is also given. The larger this ratio is, the harder
the integral is to solve. In this test file, problem number [18] had the largest ratio of
[.500000000000000000]
| | | | | | |
| # |
grade |
|
|
| normalized | | antiderivative |
| leaf size |
|
|
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\) |
| | | | | | |
|
|
|
|
|
|
|
|
| 1 |
A |
1 |
1 |
1.00 |
8 |
0.125 |
| | | | | | |
| 2 |
A |
1 |
1 |
1.00 |
8 |
0.125 |
| | | | | | |
| 3 |
A |
1 |
1 |
1.00 |
6 |
0.167 |
| | | | | | |
| 4 |
A |
1 |
1 |
1.00 |
4 |
0.250 |
| | | | | | |
| 5 |
A |
1 |
1 |
1.00 |
8 |
0.125 |
| | | | | | |
| 6 |
A |
1 |
1 |
1.00 |
8 |
0.125 |
| | | | | | |
| 7 |
A |
1 |
1 |
1.00 |
8 |
0.125 |
| | | | | | |
| 8 |
A |
2 |
2 |
1.16 |
10 |
0.200 |
| | | | | | |
| 9 |
A |
2 |
2 |
1.16 |
10 |
0.200 |
| | | | | | |
| 10 |
A |
2 |
2 |
1.00 |
8 |
0.250 |
| | | | | | |
| 11 |
A |
2 |
2 |
1.11 |
6 |
0.333 |
| | | | | | |
| 12 |
A |
3 |
2 |
1.00 |
10 |
0.200 |
| | | | | | |
| 13 |
A |
2 |
2 |
1.12 |
10 |
0.200 |
| | | | | | |
| 14 |
A |
2 |
2 |
1.00 |
10 |
0.200 |
| | | | | | |
| 15 |
A |
3 |
3 |
1.22 |
10 |
0.300 |
| | | | | | |
| 16 |
A |
3 |
3 |
1.11 |
10 |
0.300 |
| | | | | | |
| 17 |
A |
3 |
3 |
1.11 |
8 |
0.375 |
| | | | | | |
| 18 |
A |
3 |
3 |
1.14 |
6 |
0.500 |
| | | | | | |
| 19 |
A |
3 |
2 |
1.00 |
10 |
0.200 |
| | | | | | |
| 20 |
A |
3 |
3 |
1.16 |
10 |
0.300 |
| | | | | | |
| 21 |
A |
3 |
3 |
1.11 |
10 |
0.300 |
| | | | | | |
| 22 |
A |
3 |
2 |
1.00 |
10 |
0.200 |
| | | | | | |
| 23 |
A |
3 |
2 |
1.00 |
10 |
0.200 |
| | | | | | |
| 24 |
A |
3 |
2 |
1.00 |
8 |
0.250 |
| | | | | | |
| 25 |
A |
1 |
1 |
1.00 |
6 |
0.167 |
| | | | | | |
| 26 |
A |
3 |
2 |
1.00 |
10 |
0.200 |
| | | | | | |
| 27 |
A |
3 |
2 |
1.00 |
10 |
0.200 |
| | | | | | |
| 28 |
A |
3 |
2 |
1.00 |
10 |
0.200 |
| | | | | | |
| 29 |
A |
4 |
3 |
1.00 |
10 |
0.300 |
| | | | | | |
| 30 |
A |
4 |
3 |
1.00 |
10 |
0.300 |
| | | | | | |
| 31 |
A |
4 |
3 |
1.00 |
8 |
0.375 |
| | | | | | |
| 32 |
A |
2 |
2 |
1.00 |
6 |
0.333 |
| | | | | | |
| 33 |
A |
3 |
2 |
1.00 |
10 |
0.200 |
| | | | | | |
| 34 |
A |
4 |
3 |
1.00 |
10 |
0.300 |
| | | | | | |
| 35 |
A |
4 |
3 |
1.00 |
10 |
0.300 |
| | | | | | |
| 36 |
A |
5 |
4 |
1.08 |
10 |
0.400 |
| | | | | | |
| 37 |
A |
5 |
4 |
1.02 |
10 |
0.400 |
| | | | | | |
| 38 |
A |
5 |
4 |
1.00 |
8 |
0.500 |
| | | | | | |
| 39 |
A |
3 |
3 |
1.00 |
6 |
0.500 |
| | | | | | |
| 40 |
A |
3 |
2 |
1.00 |
10 |
0.200 |
| | | | | | |
| 41 |
A |
5 |
4 |
0.97 |
10 |
0.400 |
| | | | | | |
| 42 |
A |
5 |
4 |
1.00 |
10 |
0.400 |
| | | | | | |
| 43 |
A |
1 |
1 |
1.00 |
14 |
0.071 |
| | | | | | |
| 44 |
A |
1 |
1 |
1.00 |
14 |
0.071 |
| | | | | | |
| 45 |
A |
1 |
1 |
1.00 |
12 |
0.083 |
| | | | | | |
| 46 |
A |
1 |
1 |
1.00 |
10 |
0.100 |
| | | | | | |
| 47 |
A |
1 |
1 |
1.00 |
14 |
0.071 |
| | | | | | |
| 48 |
A |
1 |
1 |
1.00 |
14 |
0.071 |
| | | | | | |
| 49 |
A |
1 |
1 |
1.00 |
14 |
0.071 |
| | | | | | |
| 50 |
A |
2 |
2 |
1.02 |
16 |
0.125 |
| | | | | | |
| 51 |
A |
2 |
2 |
1.02 |
16 |
0.125 |
| | | | | | |
| 52 |
A |
2 |
2 |
0.98 |
14 |
0.143 |
| | | | | | |
| 53 |
A |
2 |
2 |
0.86 |
12 |
0.167 |
| | | | | | |
| 54 |
A |
3 |
2 |
1.00 |
16 |
0.125 |
| | | | | | |
| 55 |
A |
2 |
2 |
0.98 |
16 |
0.125 |
| | | | | | |
| 56 |
A |
2 |
2 |
0.96 |
16 |
0.125 |
| | | | | | |
| 57 |
A |
3 |
3 |
1.03 |
16 |
0.188 |
| | | | | | |
| 58 |
A |
3 |
3 |
1.00 |
16 |
0.188 |
| | | | | | |
| 59 |
A |
3 |
3 |
1.00 |
14 |
0.214 |
| | | | | | |
| 60 |
A |
3 |
3 |
0.85 |
12 |
0.250 |
| | | | | | |
| 61 |
A |
3 |
2 |
1.00 |
16 |
0.125 |
| | | | | | |
| 62 |
A |
3 |
3 |
0.97 |
16 |
0.188 |
| | | | | | |
| 63 |
A |
3 |
3 |
0.99 |
16 |
0.188 |
| | | | | | |
| 64 |
A |
3 |
3 |
0.99 |
16 |
0.188 |
| | | | | | |
| 65 |
A |
3 |
2 |
1.00 |
16 |
0.125 |
| | | | | | |
| 66 |
A |
3 |
2 |
1.00 |
16 |
0.125 |
| | | | | | |
| 67 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
| | | | | | |
| 68 |
A |
3 |
2 |
1.00 |
12 |
0.167 |
| | | | | | |
| 69 |
A |
3 |
2 |
1.00 |
16 |
0.125 |
| | | | | | |
| 70 |
A |
3 |
2 |
1.00 |
16 |
0.125 |
| | | | | | |
| 71 |
A |
3 |
2 |
1.00 |
16 |
0.125 |
| | | | | | |
| 72 |
A |
3 |
2 |
1.00 |
16 |
0.125 |
| | | | | | |
| 73 |
A |
4 |
3 |
1.00 |
16 |
0.188 |
| | | | | | |
| 74 |
A |
4 |
3 |
1.00 |
16 |
0.188 |
| | | | | | |
| 75 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
| | | | | | |
| 76 |
A |
4 |
3 |
1.00 |
12 |
0.250 |
| | | | | | |
| 77 |
A |
3 |
2 |
1.00 |
16 |
0.125 |
| | | | | | |
| 78 |
A |
4 |
3 |
1.00 |
16 |
0.188 |
| | | | | | |
| 79 |
A |
4 |
3 |
1.00 |
16 |
0.188 |
| | | | | | |
| 80 |
A |
4 |
3 |
1.00 |
16 |
0.188 |
| | | | | | |
| 81 |
A |
5 |
4 |
1.09 |
16 |
0.250 |
| | | | | | |
| 82 |
A |
5 |
4 |
1.07 |
16 |
0.250 |
| | | | | | |
| 83 |
A |
5 |
4 |
1.08 |
14 |
0.286 |
| | | | | | |
| 84 |
A |
5 |
4 |
1.06 |
12 |
0.333 |
| | | | | | |
| 85 |
A |
3 |
2 |
1.00 |
16 |
0.125 |
| | | | | | |
| 86 |
A |
5 |
4 |
1.07 |
16 |
0.250 |
| | | | | | |
| 87 |
A |
5 |
4 |
1.10 |
16 |
0.250 |
| | | | | | |
| 88 |
A |
5 |
4 |
1.07 |
16 |
0.250 |
| | | | | | |
| 89 |
A |
1 |
1 |
1.00 |
18 |
0.056 |
| | | | | | |
| 90 |
A |
1 |
1 |
1.00 |
18 |
0.056 |
| | | | | | |
| 91 |
A |
1 |
1 |
1.00 |
18 |
0.056 |
| | | | | | |
| 92 |
A |
1 |
1 |
1.00 |
18 |
0.056 |
| | | | | | |
| 93 |
A |
1 |
1 |
1.00 |
18 |
0.056 |
| | | | | | |
| 94 |
A |
1 |
1 |
1.00 |
18 |
0.056 |
| | | | | | |
| 95 |
A |
2 |
2 |
1.01 |
20 |
0.100 |
| | | | | | |
| 96 |
A |
2 |
2 |
1.01 |
20 |
0.100 |
| | | | | | |
| 97 |
A |
2 |
2 |
1.01 |
20 |
0.100 |
| | | | | | |
| 98 |
A |
2 |
2 |
0.99 |
20 |
0.100 |
| | | | | | |
| 99 |
A |
2 |
2 |
0.99 |
20 |
0.100 |
| | | | | | |
| 100 |
A |
2 |
2 |
1.01 |
20 |
0.100 |
| | | | | | |
| 101 |
A |
3 |
2 |
1.00 |
20 |
0.100 |
| | | | | | |
| 102 |
A |
3 |
2 |
1.00 |
20 |
0.100 |
| | | | | | |
| 103 |
A |
3 |
2 |
1.00 |
20 |
0.100 |
| | | | | | |
| 104 |
A |
3 |
2 |
1.00 |
20 |
0.100 |
| | | | | | |
| 105 |
A |
3 |
2 |
0.96 |
20 |
0.100 |
| | | | | | |
| 106 |
A |
3 |
2 |
1.00 |
20 |
0.100 |
| | | | | | |
| 107 |
A |
4 |
3 |
1.00 |
20 |
0.150 |
| | | | | | |
| 108 |
A |
4 |
3 |
1.00 |
20 |
0.150 |
| | | | | | |
| 109 |
A |
4 |
3 |
1.00 |
20 |
0.150 |
| | | | | | |
| 110 |
A |
4 |
3 |
1.00 |
20 |
0.150 |
| | | | | | |
| 111 |
A |
4 |
3 |
0.97 |
20 |
0.150 |
| | | | | | |
| 112 |
A |
4 |
3 |
1.00 |
20 |
0.150 |
| | | | | | |
| 113 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
| | | | | | |
| 114 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
| | | | | | |
| 115 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
| | | | | | |
| 116 |
A |
5 |
4 |
1.00 |
12 |
0.333 |
| | | | | | |
| 117 |
A |
5 |
4 |
1.00 |
10 |
0.400 |
| | | | | | |
| 118 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
| | | | | | |
| 119 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
| | | | | | |
| 120 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
| | | | | | |
| 121 |
A |
6 |
5 |
1.06 |
14 |
0.357 |
| | | | | | |
| 122 |
A |
6 |
5 |
1.06 |
14 |
0.357 |
| | | | | | |
| 123 |
A |
6 |
5 |
1.06 |
12 |
0.417 |
| | | | | | |
| 124 |
A |
6 |
5 |
1.03 |
10 |
0.500 |
| | | | | | |
| 125 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
| | | | | | |
| 126 |
A |
6 |
5 |
1.04 |
14 |
0.357 |
| | | | | | |
| 127 |
A |
6 |
5 |
1.06 |
14 |
0.357 |
| | | | | | |
| 128 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
| | | | | | |
| 129 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
| | | | | | |
| 130 |
A |
4 |
3 |
1.00 |
12 |
0.250 |
| | | | | | |
| 131 |
A |
4 |
3 |
1.00 |
10 |
0.300 |
| | | | | | |
| 132 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
| | | | | | |
| 133 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
| | | | | | |
| 134 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
| | | | | | |
| 135 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
| | | | | | |
| 136 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
| | | | | | |
| 137 |
A |
5 |
4 |
1.00 |
12 |
0.333 |
| | | | | | |
| 138 |
A |
5 |
4 |
1.00 |
10 |
0.400 |
| | | | | | |
| 139 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
| | | | | | |
| 140 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
| | | | | | |
| 141 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
| | | | | | |
| 142 |
A |
6 |
5 |
1.05 |
14 |
0.357 |
| | | | | | |
| 143 |
A |
6 |
5 |
1.07 |
14 |
0.357 |
| | | | | | |
| 144 |
A |
6 |
5 |
1.04 |
12 |
0.417 |
| | | | | | |
| 145 |
A |
6 |
5 |
1.05 |
10 |
0.500 |
| | | | | | |
| 146 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
| | | | | | |
| 147 |
A |
6 |
5 |
1.05 |
14 |
0.357 |
| | | | | | |
| 148 |
A |
6 |
5 |
1.04 |
14 |
0.357 |
| | | | | | |
| 149 |
A |
1 |
1 |
1.00 |
22 |
0.045 |
| | | | | | |
| 150 |
A |
3 |
3 |
1.05 |
18 |
0.167 |
| | | | | | |
| 151 |
A |
2 |
2 |
1.04 |
18 |
0.111 |
| | | | | | |
| 152 |
A |
1 |
1 |
1.00 |
16 |
0.062 |
| | | | | | |
| 153 |
A |
3 |
2 |
1.00 |
18 |
0.111 |
| | | | | | |
| 154 |
A |
4 |
3 |
1.00 |
18 |
0.167 |
| | | | | | |
| 155 |
A |
5 |
4 |
1.03 |
18 |
0.222 |
| | | | | | |
| 156 |
A |
3 |
3 |
1.05 |
16 |
0.188 |
| | | | | | |
| 157 |
A |
2 |
2 |
1.04 |
16 |
0.125 |
| | | | | | |
| 158 |
A |
1 |
1 |
1.00 |
14 |
0.071 |
| | | | | | |
| 159 |
A |
4 |
3 |
1.00 |
16 |
0.188 |
| | | | | | |
| 160 |
A |
5 |
4 |
1.00 |
16 |
0.250 |
| | | | | | |
| 161 |
A |
6 |
5 |
1.00 |
16 |
0.312 |
| | | | | | |
| 162 |
A |
6 |
5 |
1.06 |
14 |
0.357 |
| | | | | | |
| 163 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
| | | | | | |
| 164 |
A |
4 |
3 |
1.00 |
14 |
0.214 |
| | | | | | |
| 165 |
A |
5 |
4 |
1.00 |
14 |
0.286 |
| | | | | | |
| 166 |
A |
6 |
5 |
1.04 |
14 |
0.357 |
| | | | | | |
| 167 |
A |
3 |
2 |
1.00 |
18 |
0.111 |
| | | | | | |
| 168 |
A |
3 |
2 |
1.00 |
16 |
0.125 |
| | | | | | |
| 169 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
| | | | | | |
| 170 |
A |
3 |
2 |
1.00 |
12 |
0.167 |
| | | | | | |
| 171 |
A |
3 |
2 |
1.00 |
16 |
0.125 |
| | | | | | |
| 172 |
A |
3 |
2 |
1.00 |
16 |
0.125 |
| | | | | | |
| 173 |
A |
3 |
2 |
1.00 |
16 |
0.125 |
| | | | | | |
| 174 |
A |
3 |
2 |
1.00 |
16 |
0.125 |
| | | | | | |
| 175 |
A |
3 |
2 |
1.00 |
16 |
0.125 |
| | | | | | |
| 176 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
| | | | | | |
| 177 |
A |
3 |
2 |
1.00 |
12 |
0.167 |
| | | | | | |
| 178 |
A |
3 |
2 |
1.00 |
10 |
0.200 |
| | | | | | |
| 179 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
| | | | | | |
| 180 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
| | | | | | |
| 181 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
| | | | | | |
| 182 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
| | | | | | |
| 183 |
A |
3 |
2 |
1.00 |
20 |
0.100 |
| | | | | | |
| 184 |
A |
3 |
2 |
1.00 |
18 |
0.111 |
| | | | | | |
| 185 |
A |
3 |
2 |
1.00 |
16 |
0.125 |
| | | | | | |
| 186 |
A |
3 |
2 |
1.00 |
14 |
0.143 |
| | | | | | |
| 187 |
A |
3 |
2 |
1.00 |
18 |
0.111 |
| | | | | | |
| 188 |
A |
3 |
2 |
1.00 |
18 |
0.111 |
| | | | | | |
| 189 |
A |
3 |
2 |
1.00 |
18 |
0.111 |
| | | | | | |
| 190 |
A |
3 |
2 |
1.00 |
18 |
0.111 |
| | | | | | |
| 191 |
A |
3 |
2 |
1.00 |
18 |
0.111 |
| | | | | | |
| 192 |
A |
4 |
3 |
1.00 |
20 |
0.150 |
| | | | | | |
| 193 |
A |
4 |
3 |
1.00 |
27 |
0.111 |
| | | | | | |
| | | | | | |