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 [1] had the largest ratio of
[1]
| | | | | | |
# |
grade |
|
|
normalized | antiderivative |
leaf size | |
|
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\) |
| | | | | | |
|
|
|
|
|
|
|
1 |
A |
11 |
10 |
1.11 |
10 |
1.000 |
| | | | | | |
2 |
A |
8 |
7 |
1.08 |
10 |
0.700 |
| | | | | | |
3 |
A |
9 |
8 |
1.06 |
8 |
1.000 |
| | | | | | |
4 |
A |
4 |
3 |
0.94 |
6 |
0.500 |
| | | | | | |
5 |
A |
9 |
8 |
1.00 |
10 |
0.800 |
| | | | | | |
6 |
A |
6 |
5 |
1.06 |
10 |
0.500 |
| | | | | | |
7 |
A |
8 |
7 |
1.06 |
10 |
0.700 |
| | | | | | |
8 |
A |
9 |
8 |
1.13 |
10 |
0.800 |
| | | | | | |
9 |
A |
6 |
5 |
0.96 |
8 |
0.625 |
| | | | | | |
10 |
A |
5 |
4 |
1.11 |
8 |
0.500 |
| | | | | | |
11 |
A |
5 |
4 |
1.00 |
8 |
0.500 |
| | | | | | |
12 |
A |
6 |
5 |
0.95 |
8 |
0.625 |
| | | | | | |
13 |
A |
7 |
6 |
0.89 |
8 |
0.750 |
| | | | | | |
14 |
A |
9 |
8 |
0.95 |
10 |
0.800 |
| | | | | | |
15 |
A |
8 |
7 |
0.94 |
10 |
0.700 |
| | | | | | |
16 |
A |
7 |
6 |
0.96 |
10 |
0.600 |
| | | | | | |
17 |
A |
6 |
5 |
1.00 |
10 |
0.500 |
| | | | | | |
18 |
A |
7 |
6 |
0.97 |
10 |
0.600 |
| | | | | | |
19 |
A |
8 |
7 |
0.96 |
10 |
0.700 |
| | | | | | |
20 |
A |
12 |
11 |
1.02 |
14 |
0.786 |
| | | | | | |
21 |
A |
11 |
10 |
1.01 |
15 |
0.667 |
| | | | | | |
22 |
A |
9 |
8 |
0.97 |
19 |
0.421 |
| | | | | | |
23 |
A |
3 |
3 |
1.00 |
14 |
0.214 |
| | | | | | |
24 |
A |
6 |
5 |
1.12 |
10 |
0.500 |
| | | | | | |
25 |
A |
4 |
4 |
1.11 |
10 |
0.400 |
| | | | | | |
26 |
A |
4 |
3 |
0.97 |
8 |
0.375 |
| | | | | | |
27 |
A |
6 |
6 |
1.07 |
6 |
1.000 |
| | | | | | |
28 |
A |
7 |
6 |
1.15 |
10 |
0.600 |
| | | | | | |
29 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
| | | | | | |
30 |
A |
7 |
6 |
1.02 |
10 |
0.600 |
| | | | | | |
31 |
A |
3 |
3 |
1.00 |
8 |
0.375 |
| | | | | | |
32 |
A |
6 |
5 |
1.00 |
6 |
0.833 |
| | | | | | |
33 |
A |
7 |
6 |
1.12 |
10 |
0.600 |
| | | | | | |
34 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
| | | | | | |
35 |
A |
6 |
5 |
1.12 |
10 |
0.500 |
| | | | | | |
36 |
A |
6 |
5 |
1.07 |
10 |
0.500 |
| | | | | | |
37 |
A |
9 |
8 |
1.17 |
10 |
0.800 |
| | | | | | |
38 |
A |
8 |
7 |
1.13 |
8 |
0.875 |
| | | | | | |
39 |
A |
7 |
6 |
1.08 |
6 |
1.000 |
| | | | | | |
40 |
A |
7 |
6 |
1.23 |
10 |
0.600 |
| | | | | | |
41 |
A |
3 |
3 |
1.00 |
10 |
0.300 |
| | | | | | |
42 |
A |
4 |
4 |
1.10 |
10 |
0.400 |
| | | | | | |
43 |
A |
5 |
5 |
1.15 |
10 |
0.500 |
| | | | | | |
44 |
A |
6 |
6 |
1.17 |
10 |
0.600 |
| | | | | | |
45 |
A |
4 |
3 |
1.04 |
12 |
0.250 |
| | | | | | |
46 |
A |
7 |
6 |
1.06 |
10 |
0.600 |
| | | | | | |
47 |
A |
7 |
6 |
1.15 |
10 |
0.600 |
| | | | | | |
48 |
A |
5 |
4 |
0.79 |
12 |
0.333 |
| | | | | | |
49 |
A |
5 |
4 |
0.81 |
14 |
0.286 |
| | | | | | |
50 |
A |
3 |
3 |
1.00 |
14 |
0.214 |
| | | | | | |
51 |
A |
2 |
2 |
0.97 |
14 |
0.143 |
| | | | | | |
52 |
A |
2 |
2 |
1.00 |
14 |
0.143 |
| | | | | | |
53 |
A |
1 |
1 |
1.00 |
12 |
0.083 |
| | | | | | |
54 |
A |
1 |
1 |
1.00 |
14 |
0.071 |
| | | | | | |
55 |
A |
1 |
1 |
1.00 |
14 |
0.071 |
| | | | | | |
56 |
A |
2 |
2 |
1.01 |
14 |
0.143 |
| | | | | | |
57 |
A |
3 |
3 |
1.00 |
14 |
0.214 |
| | | | | | |
58 |
A |
2 |
2 |
0.97 |
14 |
0.143 |
| | | | | | |
59 |
A |
2 |
2 |
1.00 |
14 |
0.143 |
| | | | | | |
60 |
A |
1 |
1 |
1.00 |
12 |
0.083 |
| | | | | | |
61 |
A |
1 |
1 |
1.00 |
14 |
0.071 |
| | | | | | |
62 |
A |
1 |
1 |
1.00 |
14 |
0.071 |
| | | | | | |
63 |
A |
2 |
2 |
1.02 |
14 |
0.143 |
| | | | | | |
64 |
A |
2 |
2 |
1.01 |
16 |
0.125 |
| | | | | | |
65 |
A |
2 |
2 |
1.03 |
16 |
0.125 |
| | | | | | |
66 |
A |
1 |
1 |
1.00 |
16 |
0.062 |
| | | | | | |
67 |
A |
1 |
1 |
1.00 |
16 |
0.062 |
| | | | | | |
68 |
A |
1 |
1 |
1.00 |
16 |
0.062 |
| | | | | | |
69 |
A |
2 |
2 |
1.02 |
16 |
0.125 |
| | | | | | |
70 |
A |
2 |
2 |
1.00 |
16 |
0.125 |
| | | | | | |
71 |
A |
2 |
2 |
1.01 |
16 |
0.125 |
| | | | | | |
72 |
A |
2 |
2 |
1.03 |
16 |
0.125 |
| | | | | | |
73 |
A |
1 |
1 |
1.00 |
16 |
0.062 |
| | | | | | |
74 |
A |
1 |
1 |
1.00 |
16 |
0.062 |
| | | | | | |
75 |
A |
1 |
1 |
1.00 |
16 |
0.062 |
| | | | | | |
76 |
A |
2 |
2 |
1.02 |
16 |
0.125 |
| | | | | | |
77 |
A |
2 |
2 |
1.00 |
16 |
0.125 |
| | | | | | |
78 |
N/A |
1 |
0 |
1.00 |
40 |
0.000 |
| | | | | | |
79 |
A |
10 |
9 |
1.02 |
40 |
0.225 |
| | | | | | |
80 |
A |
9 |
8 |
1.03 |
40 |
0.200 |
| | | | | | |
81 |
A |
8 |
7 |
1.01 |
38 |
0.184 |
| | | | | | |
82 |
N/A |
1 |
0 |
1.00 |
40 |
0.000 |
| | | | | | |
83 |
N/A |
1 |
0 |
1.00 |
40 |
0.000 |
| | | | | | |
84 |
A |
8 |
7 |
1.02 |
10 |
0.700 |
| | | | | | |
85 |
A |
5 |
4 |
0.91 |
10 |
0.400 |
| | | | | | |
86 |
A |
5 |
4 |
0.93 |
10 |
0.400 |
| | | | | | |
87 |
A |
6 |
5 |
1.02 |
8 |
0.625 |
| | | | | | |
88 |
A |
3 |
2 |
1.08 |
6 |
0.333 |
| | | | | | |
89 |
A |
5 |
4 |
1.00 |
10 |
0.400 |
| | | | | | |
90 |
A |
5 |
4 |
1.01 |
10 |
0.400 |
| | | | | | |
91 |
A |
7 |
6 |
1.02 |
10 |
0.600 |
| | | | | | |
92 |
A |
5 |
4 |
1.00 |
19 |
0.211 |
| | | | | | |
93 |
A |
4 |
3 |
1.00 |
17 |
0.176 |
| | | | | | |
94 |
A |
3 |
2 |
1.00 |
26 |
0.077 |
| | | | | | |
95 |
A |
3 |
2 |
1.00 |
26 |
0.077 |
| | | | | | |
| | | | | | |