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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 [3] 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 7 6 0.93 10 0.600
2 A 6 5 1.01 10 0.500
3 A 7 6 1.00 8 0.750
4 A 4 3 0.94 6 0.500
5 A 8 7 1.00 10 0.700
6 A 8 7 0.98 10 0.700
7 A 6 5 1.07 10 0.500
8 A 7 6 1.05 10 0.600
9 A 6 5 0.83 14 0.357
10 A 5 4 1.00 12 0.333
11 A 4 3 0.96 14 0.214
12 A 7 6 0.96 14 0.429
13 A 5 4 1.11 12 0.333
14 A 5 4 0.96 19 0.211
15 N/A 1 0 1.00 18 0.000
16 A 6 5 0.99 18 0.278
17 A 6 5 1.06 18 0.278
18 A 6 5 1.10 16 0.312
19 A 1 1 1.00 10 0.100
20 A 7 6 1.11 18 0.333
21 A 10 9 0.97 18 0.500
22 A 6 6 1.07 18 0.333
23 A 5 4 1.00 20 0.200
24 A 5 4 1.03 18 0.222
25 A 7 6 1.00 12 0.500
26 A 4 3 1.10 20 0.150
27 A 7 6 1.22 20 0.300
28 A 5 4 0.98 20 0.200
29 A 5 4 0.99 18 0.222
30 A 7 6 0.99 12 0.500
31 A 4 3 1.10 20 0.150
32 A 7 6 1.83 20 0.300
33 A 5 4 1.33 18 0.222
34 N/A 3 0 1.00 20 0.000
35 N/A 3 0 1.00 20 0.000
36 B 13 12 2.57 16 0.750
37 B 8 7 2.26 16 0.438
38 A 7 6 1.12 14 0.429
39 A 7 7 1.42 16 0.438
40 A 7 7 1.66 16 0.438
41 F 0 0 N/A 0.000 N/A
42 A 5 4 1.63 18 0.222
43 A 5 4 1.62 18 0.222
44 A 2 2 1.07 23 0.087
45 A 3 2 0.96 28 0.071
46 A 4 3 0.72 33 0.091
47 N/A 3 0 1.00 28 0.000
48 N/A 3 0 1.00 33 0.000
49 B 2 2 2.34 25 0.080
50 A 5 4 0.95 35 0.114
51 A 6 5 0.77 40 0.125
52 N/A 3 0 1.00 35 0.000
53 N/A 3 0 1.00 40 0.000

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