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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 0.98 10 0.600
2 A 6 5 1.05 10 0.500
3 A 7 6 1.09 8 0.750
4 A 4 3 0.94 6 0.500
5 A 8 7 1.00 10 0.700
6 A 6 5 1.05 10 0.500
7 A 5 4 1.03 10 0.400
8 A 6 5 0.93 12 0.417
9 A 5 4 0.95 12 0.333
10 A 6 5 0.93 10 0.500
11 A 7 6 0.94 8 0.750
12 A 5 4 1.00 12 0.333
13 A 8 7 1.02 12 0.583
14 A 7 6 0.94 12 0.500
15 A 5 4 1.00 12 0.333
16 A 6 5 0.76 14 0.357
17 A 3 2 0.94 14 0.143
18 A 7 6 0.94 14 0.429
19 A 4 3 1.16 12 0.250
20 A 4 3 0.94 19 0.158
21 A 6 5 0.99 18 0.278
22 A 6 5 1.07 18 0.278
23 A 6 5 1.09 16 0.312
24 A 1 1 1.00 10 0.100
25 A 7 6 1.14 18 0.333
26 A 4 4 1.06 18 0.222
27 A 4 4 1.02 18 0.222
28 A 5 4 1.00 20 0.200
29 A 5 4 1.05 18 0.222
30 A 7 6 0.96 12 0.500
31 A 4 3 1.13 20 0.150
32 A 7 6 1.22 20 0.300
33 A 5 4 0.98 20 0.200
34 A 5 4 0.99 18 0.222
35 A 7 6 0.98 12 0.500
36 A 4 3 1.12 20 0.150
37 A 7 6 1.71 20 0.300
38 A 5 4 1.37 18 0.222
39 N/A 3 0 1.00 20 0.000
40 N/A 3 0 1.00 20 0.000
41 B 13 12 2.79 16 0.750
42 B 8 7 2.47 16 0.438
43 A 7 6 1.15 14 0.429
44 A 7 7 1.49 16 0.438
45 A 7 7 1.57 16 0.438
46 A 5 4 1.00 18 0.222
47 A 5 4 1.02 18 0.222
48 F 0 0 N/A 0.000 N/A
49 A 2 2 1.08 23 0.087
50 B 2 2 2.46 25 0.080

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