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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 [19] had the largest ratio of [.750000000000000000]

# 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 2 2 1.00 16 0.125
2 A 2 2 1.00 16 0.125
3 A 2 2 1.00 14 0.143
4 N/A 2 0 1.00 16 0.000
5 N/A 2 0 1.00 16 0.000
6 N/A 2 0 1.00 16 0.000
7 N/A 2 0 1.00 16 0.000
8 N/A 2 0 1.00 16 0.000
9 N/A 2 0 1.00 16 0.000
10 A 5 4 0.98 18 0.222
11 A 5 4 0.99 18 0.222
12 A 8 7 0.98 16 0.438
13 N/A 1 0 1.00 18 0.000
14 N/A 1 0 1.00 18 0.000
15 N/A 1 0 1.00 18 0.000
16 N/A 1 0 1.00 18 0.000
17 N/A 1 0 1.00 18 0.000
18 N/A 1 0 1.00 18 0.000
19 A 10 9 1.16 12 0.750
20 A 5 4 1.00 18 0.222
21 A 5 4 0.98 18 0.222
22 A 7 6 1.02 16 0.375
23 N/A 1 0 1.00 18 0.000
24 N/A 1 0 1.00 18 0.000
25 N/A 1 0 1.00 18 0.000
26 N/A 1 0 1.00 18 0.000
27 N/A 1 0 1.00 18 0.000
28 N/A 1 0 1.00 18 0.000
29 A 5 4 1.00 18 0.222
30 A 5 4 0.98 18 0.222
31 A 12 11 1.19 16 0.688
32 N/A 1 0 1.00 18 0.000
33 N/A 1 0 1.00 18 0.000
34 N/A 1 0 1.00 18 0.000
35 N/A 1 0 1.00 18 0.000
36 N/A 1 0 1.00 18 0.000
37 N/A 1 0 1.00 18 0.000
38 A 5 4 1.00 10 0.400
39 A 2 2 1.00 18 0.111
40 A 2 2 1.00 18 0.111
41 A 2 2 1.00 16 0.125
42 N/A 2 0 1.00 18 0.000
43 N/A 2 0 1.00 18 0.000
44 A 5 4 1.01 20 0.200
45 A 5 4 1.00 20 0.200
46 A 5 4 1.01 18 0.222
47 N/A 1 0 1.00 20 0.000
48 N/A 1 0 1.00 20 0.000
49 A 5 4 1.00 20 0.200
50 A 5 4 1.00 20 0.200
51 A 5 4 1.00 18 0.222
52 N/A 1 0 1.00 20 0.000
53 N/A 1 0 1.00 20 0.000
54 A 5 4 1.00 20 0.200
55 A 5 4 1.00 20 0.200
56 A 5 4 1.00 18 0.222
57 N/A 1 0 1.00 20 0.000
58 N/A 1 0 1.00 20 0.000
59 A 2 2 1.00 20 0.100
60 A 2 2 1.00 20 0.100
61 A 2 2 1.00 20 0.100
62 N/A 2 0 1.00 20 0.000
63 N/A 2 0 1.00 20 0.000
64 A 5 4 1.00 22 0.182
65 A 5 4 1.00 22 0.182
66 A 8 7 1.00 22 0.318
67 N/A 1 0 1.00 22 0.000
68 N/A 1 0 1.00 22 0.000
69 A 5 4 1.00 22 0.182
70 A 5 4 1.00 22 0.182
71 A 7 6 1.01 22 0.273
72 N/A 1 0 1.00 22 0.000
73 N/A 1 0 1.00 22 0.000
74 A 5 4 1.00 22 0.182
75 A 5 4 1.00 22 0.182
76 A 12 11 1.20 22 0.500
77 N/A 1 0 1.00 22 0.000
78 N/A 1 0 1.00 22 0.000
79 N/A 2 0 1.00 20 0.000
80 A 2 2 1.00 20 0.100
81 A 2 2 1.00 22 0.091
82 A 2 2 1.00 22 0.091
83 A 9 8 0.71 22 0.364
84 A 6 5 0.65 24 0.208
85 A 6 5 0.65 24 0.208
86 A 8 7 0.92 22 0.318
87 A 6 5 0.82 24 0.208
88 A 6 5 0.82 24 0.208
89 A 13 12 1.01 22 0.545
90 A 6 5 0.79 24 0.208
91 A 6 5 0.79 24 0.208

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