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 [5] had the largest ratio of
[.380952000000000013]
| | | | | | |
# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\) |
| | | | | | |
|
|
|
|
|
|
|
1 |
A |
6 |
5 |
0.75 |
21 |
0.238 |
| | | | | | |
2 |
A |
5 |
4 |
0.93 |
21 |
0.190 |
| | | | | | |
3 |
A |
7 |
6 |
0.67 |
21 |
0.286 |
| | | | | | |
4 |
A |
5 |
4 |
1.05 |
19 |
0.211 |
| | | | | | |
5 |
A |
9 |
8 |
1.22 |
21 |
0.381 |
| | | | | | |
6 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
7 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
8 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
9 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
10 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
11 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
12 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
13 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
14 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
15 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
16 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
17 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
18 |
A |
6 |
5 |
0.75 |
21 |
0.238 |
| | | | | | |
19 |
A |
5 |
4 |
0.93 |
21 |
0.190 |
| | | | | | |
20 |
A |
7 |
6 |
0.67 |
21 |
0.286 |
| | | | | | |
21 |
A |
5 |
4 |
1.05 |
19 |
0.211 |
| | | | | | |
22 |
A |
9 |
8 |
1.27 |
21 |
0.381 |
| | | | | | |
23 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
24 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
25 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
26 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
27 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
28 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
29 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
30 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
31 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
32 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
33 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
34 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
35 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
36 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
37 |
A |
6 |
5 |
0.92 |
30 |
0.167 |
| | | | | | |
38 |
A |
5 |
4 |
0.92 |
30 |
0.133 |
| | | | | | |
39 |
A |
7 |
6 |
0.94 |
30 |
0.200 |
| | | | | | |
40 |
A |
5 |
4 |
0.95 |
28 |
0.143 |
| | | | | | |
41 |
A |
6 |
5 |
0.80 |
30 |
0.167 |
| | | | | | |
42 |
A |
5 |
4 |
0.90 |
30 |
0.133 |
| | | | | | |
43 |
A |
6 |
5 |
0.95 |
30 |
0.167 |
| | | | | | |
44 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
45 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
46 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
47 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
48 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
49 |
C |
5 |
4 |
1.56 |
30 |
0.133 |
| | | | | | |
50 |
C |
5 |
4 |
1.84 |
30 |
0.133 |
| | | | | | |
51 |
C |
5 |
4 |
1.80 |
30 |
0.133 |
| | | | | | |
52 |
C |
2 |
2 |
2.53 |
28 |
0.071 |
| | | | | | |
53 |
C |
5 |
4 |
1.15 |
30 |
0.133 |
| | | | | | |
54 |
C |
6 |
5 |
1.32 |
30 |
0.167 |
| | | | | | |
55 |
C |
7 |
6 |
1.56 |
30 |
0.200 |
| | | | | | |
56 |
C |
5 |
5 |
1.86 |
30 |
0.167 |
| | | | | | |
57 |
C |
4 |
4 |
1.63 |
30 |
0.133 |
| | | | | | |
58 |
A |
3 |
2 |
1.00 |
27 |
0.074 |
| | | | | | |
59 |
C |
2 |
2 |
2.23 |
30 |
0.067 |
| | | | | | |
60 |
C |
3 |
3 |
4.29 |
30 |
0.100 |
| | | | | | |
61 |
C |
4 |
4 |
3.20 |
30 |
0.133 |
| | | | | | |
62 |
C |
5 |
5 |
2.89 |
30 |
0.167 |
| | | | | | |
63 |
C |
6 |
6 |
2.73 |
30 |
0.200 |
| | | | | | |
64 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
65 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
66 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
67 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
68 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
69 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
70 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
71 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
72 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
73 |
A |
6 |
5 |
0.90 |
30 |
0.167 |
| | | | | | |
74 |
A |
5 |
4 |
0.94 |
30 |
0.133 |
| | | | | | |
75 |
A |
6 |
5 |
0.98 |
30 |
0.167 |
| | | | | | |
76 |
A |
4 |
3 |
1.00 |
28 |
0.107 |
| | | | | | |
77 |
A |
8 |
7 |
1.15 |
30 |
0.233 |
| | | | | | |
78 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
79 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
80 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
81 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
82 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
83 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
84 |
A |
1 |
1 |
1.00 |
30 |
0.033 |
| | | | | | |
85 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
86 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
87 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
88 |
F |
0 |
0 |
N/A |
0.000 |
N/A |
| | | | | | |
89 |
C |
5 |
5 |
1.32 |
32 |
0.156 |
| | | | | | |
90 |
C |
4 |
4 |
1.69 |
30 |
0.133 |
| | | | | | |
91 |
A |
3 |
2 |
1.00 |
27 |
0.074 |
| | | | | | |
92 |
C |
4 |
3 |
0.35 |
32 |
0.094 |
| | | | | | |
93 |
C |
5 |
5 |
1.23 |
34 |
0.147 |
| | | | | | |
94 |
C |
4 |
4 |
1.51 |
32 |
0.125 |
| | | | | | |
95 |
A |
3 |
2 |
1.00 |
29 |
0.069 |
| | | | | | |
96 |
C |
4 |
3 |
0.33 |
34 |
0.088 |
| | | | | | |
97 |
C |
2 |
2 |
1.17 |
34 |
0.059 |
| | | | | | |
98 |
C |
2 |
2 |
1.18 |
36 |
0.056 |
| | | | | | |
| | | | | | |