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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 [25] had the largest ratio of [1.50000000000000000]

# 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 8 7 0.97 12 0.583
2 A 4 4 1.12 12 0.333
3 A 4 3 1.00 10 0.300
4 A 3 3 1.00 8 0.375
5 A 3 3 1.00 12 0.250
6 A 4 4 1.06 12 0.333
7 C 13 12 1.14 12 1.000
8 A 5 4 1.08 14 0.286
9 A 2 2 1.00 14 0.143
10 A 5 4 1.13 12 0.333
11 A 2 2 1.00 10 0.200
12 A 2 2 1.00 14 0.143
13 A 6 6 1.05 14 0.429
14 A 2 2 1.00 14 0.143
15 A 10 9 1.05 14 0.643
16 A 2 2 1.00 14 0.143
17 C 5 4 0.88 12 0.333
18 A 2 2 1.00 10 0.200
19 A 2 2 1.00 14 0.143
20 A 3 3 1.06 14 0.214
21 A 2 2 1.00 14 0.143
22 C 5 4 0.61 12 0.333
23 A 4 3 1.00 8 0.375
24 A 4 3 1.00 8 0.375
25 C 13 12 1.24 8 1.500
26 A 3 3 1.00 12 0.250
27 A 4 3 1.00 12 0.250
28 A 8 7 1.00 12 0.583
29 C 10 9 1.26 12 0.750
30 A 6 5 1.06 8 0.625
31 A 3 3 1.00 12 0.250
32 A 5 4 1.00 12 0.333
33 A 4 3 1.00 12 0.250
34 A 6 5 1.11 12 0.417
35 A 2 2 1.00 8 0.250
36 A 3 3 1.00 12 0.250
37 A 2 2 1.00 10 0.200
38 A 2 2 1.00 14 0.143
39 A 2 2 1.00 10 0.200
40 A 2 2 1.00 14 0.143
41 N/A 1 0 1.00 18 0.000
42 N/A 1 0 1.00 20 0.000
43 A 5 4 1.00 20 0.200
44 N/A 2 0 1.00 22 0.000
45 A 7 6 1.00 22 0.273
46 N/A 2 0 1.00 24 0.000
47 A 2 2 1.00 12 0.167
48 A 2 2 1.00 14 0.143
49 A 2 2 1.00 14 0.143
50 C 13 12 1.11 16 0.750
51 A 2 2 1.00 18 0.111
52 A 2 2 1.00 18 0.111
53 A 5 4 0.99 18 0.222
54 A 4 3 0.88 12 0.250
55 A 5 4 0.91 10 0.400
56 A 5 4 0.95 8 0.500
57 N/A 4 0 1.00 12 0.000
58 N/A 3 0 1.00 12 0.000
59 A 5 4 0.90 18 0.222
60 A 6 5 0.92 16 0.312
61 A 9 8 0.96 14 0.571
62 A 6 5 1.15 18 0.278
63 A 6 5 1.07 18 0.278
64 A 6 5 0.91 18 0.278
65 A 6 5 0.91 16 0.312
66 C 11 10 1.08 14 0.714
67 A 6 5 1.09 18 0.278
68 A 6 5 1.02 18 0.278

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