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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 [1] had the largest ratio of [1]

# 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 11 10 1.11 10 1.000
2 A 8 7 1.08 10 0.700
3 A 9 8 1.06 8 1.000
4 A 4 3 0.94 6 0.500
5 A 9 8 1.00 10 0.800
6 A 6 5 1.06 10 0.500
7 A 8 7 1.06 10 0.700
8 A 9 8 1.13 10 0.800
9 A 6 5 0.96 8 0.625
10 A 5 4 1.11 8 0.500
11 A 5 4 1.00 8 0.500
12 A 6 5 0.95 8 0.625
13 A 7 6 0.89 8 0.750
14 A 9 8 0.95 10 0.800
15 A 8 7 0.94 10 0.700
16 A 7 6 0.96 10 0.600
17 A 6 5 1.00 10 0.500
18 A 7 6 0.97 10 0.600
19 A 8 7 0.96 10 0.700
20 A 12 11 1.02 14 0.786
21 A 11 10 1.01 15 0.667
22 A 9 8 0.97 19 0.421
23 A 3 3 1.00 14 0.214
24 A 6 5 1.12 10 0.500
25 A 4 4 1.11 10 0.400
26 A 4 3 0.97 8 0.375
27 A 6 6 1.07 6 1.000
28 A 7 6 1.15 10 0.600
29 A 3 3 1.00 10 0.300
30 A 7 6 1.02 10 0.600
31 A 3 3 1.00 8 0.375
32 A 6 5 1.00 6 0.833
33 A 7 6 1.12 10 0.600
34 A 3 3 1.00 10 0.300
35 A 6 5 1.12 10 0.500
36 A 6 5 1.07 10 0.500
37 A 9 8 1.17 10 0.800
38 A 8 7 1.13 8 0.875
39 A 7 6 1.08 6 1.000
40 A 7 6 1.23 10 0.600
41 A 3 3 1.00 10 0.300
42 A 4 4 1.10 10 0.400
43 A 5 5 1.15 10 0.500
44 A 6 6 1.17 10 0.600
45 A 4 3 1.04 12 0.250
46 A 7 6 1.06 10 0.600
47 A 7 6 1.15 10 0.600
48 A 5 4 0.79 12 0.333
49 A 5 4 0.81 14 0.286
50 A 3 3 1.00 14 0.214
51 A 2 2 0.97 14 0.143
52 A 2 2 1.00 14 0.143
53 A 1 1 1.00 12 0.083
54 A 1 1 1.00 14 0.071
55 A 1 1 1.00 14 0.071
56 A 2 2 1.01 14 0.143
57 A 3 3 1.00 14 0.214
58 A 2 2 0.97 14 0.143
59 A 2 2 1.00 14 0.143
60 A 1 1 1.00 12 0.083
61 A 1 1 1.00 14 0.071
62 A 1 1 1.00 14 0.071
63 A 2 2 1.02 14 0.143
64 A 2 2 1.01 16 0.125
65 A 2 2 1.03 16 0.125
66 A 1 1 1.00 16 0.062
67 A 1 1 1.00 16 0.062
68 A 1 1 1.00 16 0.062
69 A 2 2 1.02 16 0.125
70 A 2 2 1.00 16 0.125
71 A 2 2 1.01 16 0.125
72 A 2 2 1.03 16 0.125
73 A 1 1 1.00 16 0.062
74 A 1 1 1.00 16 0.062
75 A 1 1 1.00 16 0.062
76 A 2 2 1.02 16 0.125
77 A 2 2 1.00 16 0.125
78 N/A 1 0 1.00 40 0.000
79 A 10 9 1.02 40 0.225
80 A 9 8 1.03 40 0.200
81 A 8 7 1.01 38 0.184
82 N/A 1 0 1.00 40 0.000
83 N/A 1 0 1.00 40 0.000
84 A 8 7 1.02 10 0.700
85 A 5 4 0.91 10 0.400
86 A 5 4 0.93 10 0.400
87 A 6 5 1.02 8 0.625
88 A 3 2 1.08 6 0.333
89 A 5 4 1.00 10 0.400
90 A 5 4 1.01 10 0.400
91 A 7 6 1.02 10 0.600
92 A 5 4 1.00 19 0.211
93 A 4 3 1.00 17 0.176
94 A 3 2 1.00 26 0.077
95 A 3 2 1.00 26 0.077

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