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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 [39] had the largest ratio of [.692300000000000026]

# 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 5 1.00 13 0.385
2 A 6 6 1.00 13 0.462
3 A 4 4 1.00 13 0.308
4 A 3 3 1.00 13 0.231
5 A 1 1 1.00 11 0.091
6 A 2 2 1.00 12 0.167
7 A 4 4 1.00 11 0.364
8 A 5 5 1.00 13 0.385
9 A 6 5 1.00 13 0.385
10 A 7 5 1.00 13 0.385
11 A 3 3 1.00 12 0.250
12 A 4 4 1.00 12 0.333
13 A 5 5 1.00 10 0.500
14 A 4 4 1.00 10 0.400
15 A 2 2 1.00 10 0.200
16 A 5 4 1.00 10 0.400
17 A 6 5 1.00 10 0.500
18 A 7 6 1.00 10 0.600
19 A 2 2 1.00 25 0.080
20 A 2 2 1.00 28 0.071
21 A 4 4 1.00 25 0.160
22 A 3 3 1.00 25 0.120
23 A 4 4 1.00 25 0.160
24 A 6 6 1.00 25 0.240
25 A 5 5 1.00 25 0.200
26 A 6 6 1.00 25 0.240
27 A 7 6 1.00 25 0.240
28 A 2 2 1.00 23 0.087
29 A 3 3 1.00 24 0.125
30 A 5 5 1.00 21 0.238
31 A 4 4 1.00 21 0.190
32 A 3 3 1.00 19 0.158
33 A 3 3 1.00 12 0.250
34 A 3 3 1.00 19 0.158
35 A 3 3 1.00 21 0.143
36 A 6 5 1.00 12 0.417
37 A 5 4 1.00 12 0.333
38 A 4 4 1.00 12 0.333
39 A 9 9 1.00 13 0.692
40 A 8 8 1.00 13 0.615
41 A 7 7 1.00 13 0.538
42 A 6 6 1.00 13 0.462
43 A 4 4 1.00 11 0.364
44 A 4 4 1.00 12 0.333
45 A 6 6 1.00 11 0.546
46 A 7 7 1.00 13 0.538
47 A 8 7 1.00 13 0.538
48 A 9 7 1.00 13 0.538
49 A 6 6 1.00 12 0.500
50 A 7 7 1.00 12 0.583
51 A 8 7 1.00 12 0.583
52 A 2 2 1.00 12 0.167
53 A 5 4 1.00 12 0.333
54 A 8 5 1.00 21 0.238
55 A 7 4 1.00 21 0.190
56 A 3 3 1.00 19 0.158
57 N/A 0 0 1.00 12 0.000
58 N/A 0 0 1.00 19 0.000
59 N/A 0 0 1.00 21 0.000

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