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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 [29] had the largest ratio of [1]

# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\)
1 A 1 1 1.00 6 0.167
2 A 2 2 1.00 8 0.250
3 A 2 2 1.00 8 0.250
4 A 3 2 1.00 8 0.250
5 A 3 2 1.00 8 0.250
6 A 4 2 1.00 8 0.250
7 A 4 2 1.00 8 0.250
8 A 5 2 1.00 8 0.250
9 A 13 9 1.00 12 0.750
10 A 12 9 1.00 12 0.750
11 A 12 9 1.00 12 0.750
12 A 11 8 1.00 12 0.667
13 A 11 8 1.00 12 0.667
14 A 12 9 1.00 12 0.750
15 A 12 9 1.00 12 0.750
16 A 13 9 1.00 12 0.750
17 A 13 9 1.00 12 0.750
18 A 12 8 1.00 12 0.667
19 A 9 9 1.00 12 0.750
20 A 9 9 1.00 12 0.750
21 A 12 8 1.00 12 0.667
22 A 13 9 1.00 12 0.750
23 A 2 2 1.00 8 0.250
24 A 2 2 1.00 10 0.200
25 A 3 3 1.00 10 0.300
26 A 2 2 1.00 10 0.200
27 A 2 2 1.00 10 0.200
28 A 3 3 1.00 10 0.300
29 A 14 10 1.00 10 1.000
30 A 13 10 1.00 10 1.000
31 A 13 10 1.00 10 1.000
32 A 14 10 1.00 10 1.000
33 A 5 3 1.00 10 0.300
34 A 3 3 1.00 10 0.300
35 A 3 3 1.00 10 0.300
36 A 5 3 1.00 10 0.300
37 A 3 3 1.00 12 0.250
38 A 3 3 1.00 14 0.214
39 A 2 2 1.00 21 0.095
40 A 2 2 1.00 21 0.095
41 A 3 3 1.00 21 0.143
42 A 3 3 1.00 21 0.143
43 A 3 2 1.00 19 0.105
44 A 3 2 1.00 19 0.105
45 A 2 2 1.00 19 0.105
46 A 2 2 1.00 19 0.105
47 A 2 2 1.00 19 0.105
48 A 1 1 1.00 19 0.053
49 A 1 1 1.00 17 0.059
50 A 1 1 1.00 17 0.059
51 A 1 1 1.00 19 0.053
52 A 1 1 1.00 21 0.048

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