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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 [9] had the largest ratio of [1.30000000000000004]

# 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 C 9 9 1.19 10 0.900
2 C 7 7 1.24 10 0.700
3 C 5 5 1.34 10 0.500
4 C 3 3 1.18 10 0.300
5 A 4 3 0.75 6 0.500
6 A 8 7 1.92 10 0.700
7 A 10 9 1.54 10 0.900
8 A 12 11 1.37 10 1.100
9 A 14 13 1.28 10 1.300
10 A 8 8 0.84 10 0.800
11 A 6 6 0.78 10 0.600
12 A 4 4 0.72 8 0.500
13 A 6 6 1.00 10 0.600
14 C 5 5 2.43 10 0.500
15 C 7 7 1.76 10 0.700
16 C 9 9 1.51 10 0.900
17 A 13 12 1.35 12 1.000
18 B 12 11 2.19 12 0.917
19 A 8 7 1.21 12 0.583
20 A 11 10 1.36 10 1.000
21 A 7 6 1.44 8 0.750
22 A 6 5 1.24 12 0.417
23 A 5 4 1.05 12 0.333
24 A 6 5 0.96 12 0.417
25 A 6 5 0.94 12 0.417
26 A 7 6 0.93 12 0.500
27 A 6 5 0.92 12 0.417
28 A 13 12 1.49 12 1.000
29 A 10 9 1.26 12 0.750
30 B 9 8 2.29 12 0.667
31 A 7 6 1.30 10 0.600
32 A 7 6 1.43 8 0.750
33 A 6 5 1.13 12 0.417
34 A 6 5 1.10 12 0.417
35 A 5 4 0.97 12 0.333
36 A 7 6 0.94 12 0.500
37 A 6 5 0.94 12 0.417
38 A 7 6 0.93 12 0.500
39 A 6 5 0.93 12 0.417
40 F 0 0 N/A 0.000 N/A
41 F 0 0 N/A 0.000 N/A
42 C 4 4 91.00 10 0.400
43 F 0 0 N/A 0.000 N/A
44 F 0 0 N/A 0.000 N/A
45 A 7 6 0.83 12 0.500
46 C 4 4 1.61 12 0.333
47 A 6 5 0.80 12 0.417
48 A 7 6 1.11 10 0.600
49 A 6 5 0.97 12 0.417
50 A 8 7 1.76 12 0.583
51 C 5 5 2.34 12 0.417
52 A 9 8 1.35 12 0.667
53 C 6 6 1.65 12 0.500
54 A 10 9 1.20 12 0.750
55 A 5 5 0.63 12 0.417
56 A 7 7 0.47 12 0.583
57 A 4 4 0.67 12 0.333
58 A 8 8 0.58 8 1.000
59 A 5 5 0.90 12 0.417
60 A 4 4 1.33 12 0.333
61 A 4 4 1.33 12 0.333
62 A 4 4 1.17 10 0.400
63 A 6 5 1.47 12 0.417
64 A 6 5 1.45 12 0.417
65 A 4 4 1.36 12 0.333
66 A 4 4 1.40 10 0.400
67 A 4 4 0.96 8 0.500
68 A 7 6 0.89 12 0.500
69 A 4 4 1.29 12 0.333
70 A 4 4 1.48 12 0.333
71 A 5 5 0.86 24 0.208
72 A 9 8 1.02 22 0.364
73 A 8 8 0.89 22 0.364
74 A 4 4 1.00 22 0.182
75 A 5 5 1.16 20 0.250
76 A 9 8 1.36 19 0.421
77 A 5 5 1.10 22 0.227
78 A 11 10 1.33 22 0.455
79 A 8 8 1.28 22 0.364
80 B 2 2 2.17 25 0.080

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