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2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. 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 given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [16] had the largest ratio of [20]

# 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 6 6 1.00 10 0.600
2 A 5 5 1.00 10 0.500
3 A 4 4 1.00 8 0.500
4 A 0 0 0.00 0 0.000
5 A 0 0 0.00 0 0.000
6 A 7 7 1.00 12 0.583
7 A 6 6 1.00 12 0.500
8 A 3 3 1.00 10 0.300
9 A 0 0 0.00 0 0.000
10 A 0 0 0.00 0 0.000
11 A 13 10 1.00 12 0.833
12 A 9 8 1.00 12 0.667
13 A 7 7 1.00 10 0.700
14 A 0 0 0.00 0 0.000
15 A 0 0 0.00 0 0.000
16 A 5 3 1.00 20 0.150
17 A 4 3 1.00 20 0.150
18 A 3 3 1.00 18 0.167
19 A 7 4 1.00 20 0.200
20 A 7 4 1.00 20 0.200
21 A 8 5 1.00 20 0.250
22 A 10 3 1.00 20 0.150
23 A 8 3 1.00 20 0.150
24 A 7 3 1.00 18 0.167
25 A 21 5 1.00 20 0.250
26 A 24 7 1.00 20 0.350
27 A 14 3 1.00 20 0.150
28 A 11 3 1.00 20 0.150
29 A 11 3 1.00 18 0.167
30 A 53 7 1.00 20 0.350
31 A 60 9 1.00 20 0.450
32 A 0 0 0.00 0 0.000
33 A 0 0 0.00 0 0.000
34 A 2 2 1.00 20 0.100
35 A 4 2 1.00 20 0.100
36 A 5 2 1.00 20 0.100
37 A 8 7 1.00 18 0.389
38 A 7 6 1.00 18 0.333
39 A 6 5 1.00 16 0.312
40 A 0 0 0.00 0 0.000
41 A 0 0 0.00 0 0.000
42 A 15 9 1.00 20 0.450
43 A 13 10 1.00 20 0.500
44 A 9 7 1.00 18 0.389
45 A 0 0 0.00 0 0.000
46 A 0 0 0.00 0 0.000
47 A 28 11 1.00 20 0.550
48 A 22 11 1.00 20 0.550
49 A 16 9 1.00 18 0.500
50 A 0 0 0.00 0 0.000
51 A 0 0 0.00 0 0.000
52 A 6 6 1.00 20 0.300
53 A 5 5 1.00 20 0.250
54 A 4 4 1.00 18 0.222
55 A 0 0 0.00 0 0.000
56 A 0 0 0.00 0 0.000
57 A 28 10 1.00 20 0.500
58 A 24 11 1.00 20 0.550
59 A 5 5 1.00 18 0.278
60 A 0 0 0.00 0 0.000
61 A 0 0 0.00 0 0.000

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