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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 [7] had the largest ratio of [1.87500000000000000]

# 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 1.18 6 0.500
2 A 3 3 1.00 8 0.375
3 A 7 7 1.07 8 0.875
4 A 5 5 1.00 8 0.625
5 A 11 11 1.05 8 1.375
6 A 7 7 1.00 8 0.875
7 A 15 15 1.03 8 1.875
8 A 9 9 1.00 8 1.125
9 A 16 15 0.98 12 1.250
10 A 14 13 0.93 12 1.083
11 A 14 13 0.96 12 1.083
12 A 12 11 0.91 12 0.917
13 A 12 11 0.94 12 0.917
14 A 14 13 0.93 12 1.083
15 A 14 13 0.96 12 1.083
16 A 16 15 0.96 12 1.250
17 A 14 13 0.90 12 1.083
18 A 12 11 0.87 12 0.917
19 A 12 11 0.85 12 0.917
20 A 12 11 0.85 12 0.917
21 A 12 11 0.87 12 0.917
22 A 14 13 0.90 12 1.083
23 A 4 3 1.00 8 0.375
24 A 4 3 1.00 10 0.300
25 A 9 9 0.75 10 0.900
26 A 5 5 1.00 10 0.500
27 A 4 4 1.00 10 0.400
28 A 6 6 0.72 10 0.600
29 A 18 17 0.74 10 1.700
30 A 16 15 0.77 10 1.500
31 A 16 15 0.77 10 1.500
32 A 18 17 0.71 10 1.700
33 A 9 9 0.57 10 0.900
34 A 5 5 0.72 10 0.500
35 A 5 5 0.68 10 0.500
36 A 9 9 0.52 10 0.900
37 A 6 5 1.00 12 0.417
38 A 6 5 1.00 14 0.357
39 A 4 4 1.00 21 0.190
40 A 4 4 1.00 21 0.190
41 A 5 4 1.00 21 0.190
42 A 6 6 1.00 21 0.286
43 A 5 4 0.93 19 0.211
44 A 5 4 0.96 19 0.211
45 A 4 3 1.00 19 0.158
46 A 4 3 1.00 19 0.158
47 A 4 3 1.00 19 0.158
48 A 2 2 1.00 19 0.105
49 A 2 2 1.00 17 0.118
50 A 2 2 1.00 17 0.118
51 A 2 2 1.00 19 0.105
52 A 2 2 1.00 21 0.095

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