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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 [.515152000000000054]

# 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 3 3 1.00 32 0.094
2 A 3 3 1.00 32 0.094
3 A 3 3 1.00 30 0.100
4 A 7 7 0.90 24 0.292
5 A 3 3 1.00 30 0.100
6 A 5 5 0.83 32 0.156
7 A 3 3 1.00 32 0.094
8 A 11 10 1.05 32 0.312
9 A 3 3 1.00 32 0.094
10 A 3 3 1.00 32 0.094
11 A 3 3 1.00 32 0.094
12 A 12 12 1.45 34 0.353
13 A 9 8 1.00 34 0.235
14 A 13 12 1.06 34 0.353
15 A 8 7 1.00 40 0.175
16 A 4 3 1.00 40 0.075
17 A 8 7 1.00 40 0.175
18 A 8 7 1.00 40 0.175
19 A 5 5 1.04 36 0.139
20 A 12 11 1.03 36 0.306
21 A 12 11 1.04 36 0.306
22 A 6 5 1.00 36 0.139
23 A 7 6 1.00 33 0.182
24 A 12 11 1.07 33 0.333
25 A 8 7 1.00 39 0.179
26 A 4 3 1.00 39 0.077
27 A 8 7 1.00 39 0.179
28 A 8 7 1.00 39 0.179
29 A 17 17 1.15 33 0.515
30 A 17 17 1.07 33 0.515
31 A 5 5 1.00 39 0.128
32 A 2 2 1.00 39 0.051
33 A 5 5 1.00 39 0.128
34 A 5 5 1.00 39 0.128
35 A 8 7 1.00 35 0.200
36 A 4 3 1.00 35 0.086
37 A 8 7 1.00 35 0.200
38 A 8 7 1.00 35 0.200
39 A 10 9 1.24 33 0.273
40 A 6 6 1.00 33 0.182
41 A 6 6 1.00 33 0.182
42 A 5 5 1.00 39 0.128
43 A 5 5 1.00 39 0.128
44 A 2 2 1.00 39 0.051
45 A 5 5 1.00 39 0.128
46 A 5 5 1.00 39 0.128
47 A 2 2 1.00 39 0.051
48 A 5 5 1.00 35 0.143
49 A 2 2 1.00 35 0.057
50 A 5 5 1.00 35 0.143
51 A 6 5 1.00 38 0.132

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