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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 [30] 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 C 7 6 1.18 12 0.500
2 A 4 4 1.12 12 0.333
3 A 5 4 1.00 10 0.400
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 12 11 1.10 12 0.917
8 A 6 5 1.08 14 0.357
9 A 2 2 1.00 14 0.143
10 A 6 5 1.13 12 0.417
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 C 11 10 1.19 14 0.714
16 A 2 2 1.00 14 0.143
17 A 6 5 0.70 12 0.417
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 A 6 5 0.52 12 0.417
23 N/A 1 0 1.00 16 0.000
24 A 2 2 1.00 16 0.125
25 A 2 2 1.00 16 0.125
26 A 2 2 1.00 14 0.143
27 N/A 2 0 1.00 14 0.000
28 A 5 4 1.00 12 0.333
29 C 18 17 1.15 12 1.417
30 C 16 15 1.18 10 1.500
31 C 12 11 1.27 8 1.375
32 A 3 3 1.00 12 0.250
33 A 5 4 1.00 12 0.333
34 C 7 6 1.31 12 0.500
35 C 11 10 1.28 12 0.833
36 C 13 12 1.40 12 1.000
37 C 6 5 1.21 16 0.312
38 A 6 5 1.21 16 0.312
39 C 6 5 1.33 14 0.357
40 N/A 2 0 1.00 14 0.000
41 A 8 7 1.10 12 0.583
42 C 16 15 1.21 12 1.250
43 A 7 6 1.08 12 0.500
44 C 12 11 1.10 10 1.100
45 A 6 5 1.06 8 0.625
46 A 3 3 1.00 12 0.250
47 A 5 4 1.00 12 0.333
48 A 5 4 1.00 12 0.333
49 A 6 5 1.11 12 0.417
50 C 7 6 1.18 12 0.500
51 A 7 6 1.17 12 0.500
52 C 11 10 1.30 12 0.833
53 A 4 3 1.12 16 0.188
54 A 4 3 1.20 16 0.188
55 A 4 3 1.21 14 0.214
56 N/A 2 0 1.00 14 0.000
57 A 5 4 1.00 12 0.333
58 A 2 2 1.00 12 0.167
59 A 2 2 1.00 10 0.200
60 A 2 2 1.00 8 0.250
61 A 3 3 1.00 12 0.250
62 A 2 2 1.00 12 0.167
63 A 2 2 1.00 12 0.167
64 A 2 2 1.00 14 0.143
65 A 2 2 1.00 12 0.167
66 A 2 2 1.00 10 0.200
67 A 2 2 1.00 14 0.143
68 A 2 2 1.00 14 0.143
69 A 2 2 1.00 14 0.143
70 A 2 2 1.00 12 0.167
71 A 2 2 1.00 10 0.200
72 A 2 2 1.00 14 0.143
73 A 2 2 1.00 14 0.143
74 N/A 1 0 1.00 18 0.000
75 N/A 1 0 1.00 20 0.000
76 A 5 4 1.00 20 0.200
77 N/A 2 0 1.00 22 0.000
78 A 7 6 1.00 22 0.273
79 N/A 2 0 1.00 24 0.000
80 A 2 2 1.00 16 0.125
81 A 2 2 1.00 16 0.125
82 A 2 2 1.00 14 0.143
83 N/A 2 0 1.00 16 0.000
84 C 12 11 1.09 16 0.688
85 A 2 2 0.99 18 0.111
86 A 2 2 0.99 18 0.111
87 A 5 4 0.99 18 0.222
88 A 4 3 0.88 12 0.250
89 A 5 4 0.91 10 0.400
90 A 5 4 0.95 8 0.500
91 N/A 4 0 1.00 12 0.000
92 N/A 3 0 1.00 12 0.000
93 A 5 4 0.90 18 0.222
94 A 6 5 0.92 16 0.312
95 C 8 7 1.09 14 0.500
96 A 6 5 1.13 18 0.278
97 A 6 5 1.05 18 0.278
98 A 6 5 0.91 18 0.278
99 A 6 5 0.91 16 0.312
100 C 12 11 1.08 14 0.786
101 A 6 5 1.08 18 0.278
102 A 6 5 1.01 18 0.278

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