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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 [88] 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 3 3 1.00 12 0.250
2 A 4 4 1.00 12 0.333
3 A 2 2 1.00 10 0.200
4 A 3 3 1.00 8 0.375
5 A 3 3 1.00 12 0.250
6 A 4 4 1.00 12 0.333
7 A 5 5 1.00 12 0.417
8 A 3 3 1.00 14 0.214
9 A 6 5 1.00 14 0.357
10 A 3 3 1.00 12 0.250
11 A 5 4 1.00 10 0.400
12 A 5 4 1.00 14 0.286
13 A 6 6 1.00 14 0.429
14 A 7 6 1.00 14 0.429
15 A 4 4 1.00 14 0.286
16 A 10 5 1.00 14 0.357
17 A 3 2 1.00 12 0.167
18 A 8 4 1.00 10 0.400
19 A 8 4 1.00 14 0.286
20 A 9 5 1.00 14 0.357
21 A 12 6 1.00 14 0.429
22 A 3 2 1.00 12 0.167
23 N/A 0 0 1.00 16 0.000
24 A 8 3 1.00 16 0.188
25 A 5 3 1.00 16 0.188
26 A 3 2 1.00 14 0.143
27 N/A 0 0 1.00 14 0.000
28 A 2 2 1.00 12 0.167
29 A 7 5 1.00 12 0.417
30 A 6 5 1.00 10 0.500
31 A 5 5 1.00 8 0.625
32 A 3 3 1.00 12 0.250
33 A 2 2 1.00 12 0.167
34 A 3 3 1.00 12 0.250
35 A 4 3 1.00 12 0.250
36 A 5 3 1.00 12 0.250
37 A 9 4 1.00 16 0.250
38 A 6 4 1.00 16 0.250
39 A 4 3 1.00 14 0.214
40 N/A 0 0 1.00 14 0.000
41 A 7 6 1.00 12 0.500
42 A 6 5 1.00 12 0.417
43 A 6 6 1.00 12 0.500
44 A 5 5 1.00 10 0.500
45 A 5 5 1.00 8 0.625
46 A 3 3 1.00 12 0.250
47 A 4 4 1.00 12 0.333
48 A 2 2 1.00 12 0.167
49 A 5 5 1.00 12 0.417
50 A 3 3 1.00 12 0.250
51 A 6 6 1.00 12 0.500
52 A 4 3 1.00 12 0.250
53 A 9 4 1.00 16 0.250
54 A 6 4 1.00 16 0.250
55 A 4 3 1.00 14 0.214
56 N/A 0 0 1.00 14 0.000
57 A 2 2 1.00 12 0.167
58 A 3 2 1.00 12 0.167
59 A 3 2 1.00 10 0.200
60 A 3 2 1.00 8 0.250
61 A 3 3 1.00 12 0.250
62 A 3 2 1.00 12 0.167
63 A 3 2 1.00 12 0.167
64 A 5 3 1.00 14 0.214
65 A 5 3 1.00 12 0.250
66 A 5 3 1.00 10 0.300
67 A 5 4 1.00 14 0.286
68 A 5 3 1.00 14 0.214
69 A 8 3 1.00 14 0.214
70 A 8 3 1.00 12 0.250
71 A 8 3 1.00 10 0.300
72 A 8 4 1.00 14 0.286
73 A 8 3 1.00 14 0.214
74 N/A 0 0 1.00 18 0.000
75 N/A 0 0 1.00 20 0.000
76 A 3 3 1.00 20 0.150
77 N/A 0 0 1.00 22 0.000
78 A 5 5 1.00 22 0.227
79 N/A 0 0 1.00 24 0.000
80 A 8 3 1.00 16 0.188
81 A 5 3 1.00 16 0.188
82 A 3 2 1.00 14 0.143
83 N/A 0 0 1.00 16 0.000
84 A 5 5 1.00 16 0.312
85 A 7 6 1.00 18 0.333
86 A 12 6 1.00 18 0.333
87 A 4 4 1.00 18 0.222
88 A 12 9 1.00 12 0.750
89 A 8 7 1.00 10 0.700
90 A 4 4 1.00 8 0.500
91 N/A 0 0 1.00 12 0.000
92 N/A 0 0 1.00 12 0.000
93 A 16 4 1.00 18 0.222
94 A 10 4 1.00 16 0.250
95 A 4 4 1.00 14 0.286
96 A 10 5 1.00 18 0.278
97 A 11 6 1.00 18 0.333
98 A 23 6 1.00 18 0.333
99 A 13 5 1.00 16 0.312
100 A 5 4 1.00 14 0.286
101 A 13 5 1.00 18 0.278
102 A 14 6 1.00 18 0.333

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