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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 [26] had the largest ratio of [1.25000000000000000]

# 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 1.10 8 0.750
2 A 5 5 1.08 8 0.625
3 A 4 4 1.00 6 0.667
4 A 1 1 1.00 4 0.250
5 A 2 2 1.00 8 0.250
6 A 4 4 1.00 8 0.500
7 A 5 5 1.06 8 0.625
8 A 6 6 1.10 8 0.750
9 A 11 11 1.24 10 1.100
10 A 7 7 1.08 8 0.875
11 A 4 4 1.06 6 0.667
12 N/A 1 0 1.00 10 0.000
13 N/A 1 0 1.00 10 0.000
14 N/A 1 0 1.00 12 0.000
15 N/A 1 0 1.00 12 0.000
16 A 4 4 1.00 10 0.400
17 N/A 1 0 1.00 12 0.000
18 N/A 1 0 1.00 12 0.000
19 A 3 3 0.90 10 0.300
20 A 3 3 0.91 10 0.300
21 A 3 3 0.95 8 0.375
22 A 1 1 1.00 6 0.167
23 N/A 1 0 1.00 10 0.000
24 A 3 3 1.03 10 0.300
25 A 3 3 0.87 10 0.300
26 A 15 15 1.41 12 1.250
27 A 9 9 1.16 10 0.900
28 A 3 3 1.04 8 0.375
29 N/A 1 0 1.00 12 0.000
30 N/A 1 0 1.00 12 0.000
31 N/A 1 0 1.00 12 0.000
32 N/A 1 0 1.00 10 0.000
33 N/A 3 0 1.00 8 0.000
34 N/A 1 0 1.00 12 0.000
35 N/A 1 0 1.00 12 0.000
36 N/A 1 0 1.00 16 0.000
37 N/A 1 0 1.00 16 0.000
38 N/A 2 0 1.00 14 0.000
39 N/A 1 0 1.00 16 0.000
40 N/A 1 0 1.00 16 0.000
41 A 4 3 1.24 17 0.176
42 A 4 3 1.24 15 0.200
43 A 5 4 1.26 13 0.308
44 A 4 3 0.80 17 0.176
45 A 4 3 1.00 17 0.176
46 A 4 3 1.00 17 0.176
47 A 4 3 1.16 19 0.158
48 A 10 10 1.30 13 0.769
49 A 5 5 1.00 13 0.385
50 A 1 1 1.00 13 0.077
51 A 3 3 1.00 10 0.300
52 A 6 6 1.12 11 0.545
53 A 10 10 1.35 13 0.769
54 A 15 15 1.69 13 1.154
55 A 11 11 1.03 17 0.647
56 A 8 8 1.06 17 0.471
57 A 5 5 1.09 15 0.333
58 A 2 2 1.00 14 0.143
59 N/A 1 0 1.00 17 0.000
60 N/A 4 0 1.00 17 0.000
61 N/A 5 0 1.00 17 0.000
62 A 4 3 1.00 8 0.375
63 A 4 3 1.00 6 0.500
64 A 1 1 1.00 4 0.250
65 A 1 1 1.00 8 0.125
66 A 4 3 1.00 8 0.375
67 A 4 3 1.00 8 0.375
68 A 4 3 1.00 10 0.300
69 A 3 3 1.03 10 0.300
70 A 3 3 1.02 8 0.375
71 A 1 1 1.00 6 0.167
72 N/A 1 0 1.00 10 0.000
73 N/A 2 0 1.00 10 0.000
74 N/A 2 0 1.00 12 0.000

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