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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 [42] had the largest ratio of [.875000000000000000]

# 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 1.00 10 0.700
2 A 7 6 1.00 10 0.600
3 A 6 6 1.00 8 0.750
4 A 14 8 1.00 10 0.800
5 A 6 6 1.00 10 0.600
6 A 8 8 1.00 10 0.800
7 A 20 9 1.00 20 0.450
8 A 17 9 1.00 20 0.450
9 A 11 8 1.00 18 0.444
10 A 8 6 1.00 12 0.500
11 A 17 9 1.00 20 0.450
12 A 12 8 1.00 20 0.400
13 A 23 11 1.00 20 0.550
14 A 4 3 1.00 10 0.300
15 A 4 3 1.00 10 0.300
16 A 4 3 1.00 8 0.375
17 A 3 3 1.00 6 0.500
18 A 7 6 1.00 10 0.600
19 A 5 5 1.00 10 0.500
20 A 6 5 1.00 10 0.500
21 A 7 5 1.00 10 0.500
22 A 3 3 1.00 4 0.750
23 A 7 6 1.00 10 0.600
24 A 7 6 1.00 10 0.600
25 A 7 7 1.00 10 0.700
26 A 4 4 1.00 10 0.400
27 A 4 4 1.00 10 0.400
28 A 7 7 1.00 10 0.700
29 A 3 3 1.00 10 0.300
30 A 6 6 1.00 8 0.750
31 A 5 5 1.29 6 0.833
32 A 6 6 1.00 10 0.600
33 A 5 5 1.00 10 0.500
34 A 3 3 1.00 10 0.300
35 A 6 6 1.00 10 0.600
36 A 5 4 1.00 10 0.400
37 A 4 4 1.00 12 0.333
38 A 8 8 1.00 12 0.667
39 A 6 6 1.00 12 0.500
40 A 5 5 1.00 12 0.417
41 A 6 6 1.00 10 0.600
42 A 7 7 1.00 8 0.875
43 A 6 6 1.00 12 0.500
44 A 5 5 1.00 12 0.417
45 A 6 6 1.00 12 0.500
46 A 7 7 1.00 12 0.583
47 A 3 3 1.00 12 0.250
48 A 5 4 1.00 12 0.333
49 A 8 7 1.00 12 0.583
50 A 4 3 1.00 12 0.250
51 A 7 6 1.00 12 0.500
52 A 6 5 1.00 10 0.500
53 A 7 6 1.00 8 0.750
54 A 6 5 1.00 12 0.417
55 A 4 3 1.59 12 0.250
56 A 7 6 1.00 12 0.500
57 A 6 4 1.00 12 0.333
58 A 8 6 1.00 12 0.500
59 A 4 3 1.00 23 0.130
60 A 9 7 1.00 21 0.333
61 A 6 5 1.00 21 0.238
62 A 7 7 1.00 21 0.333
63 A 3 3 1.00 21 0.143
64 A 5 5 1.00 19 0.263
65 A 7 7 1.00 18 0.389
66 A 4 4 1.00 21 0.190
67 A 7 6 1.00 21 0.286
68 A 7 5 1.00 21 0.238
69 A 8 8 1.00 19 0.421
70 A 6 6 1.00 12 0.500
71 A 6 6 1.00 14 0.429

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