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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 [54] had the largest ratio of [1.75000000000000000]

# 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 0.94 12 0.500
2 A 4 4 1.02 12 0.333
3 A 4 3 1.00 10 0.300
4 A 3 3 1.00 8 0.375
5 A 3 3 1.00 12 0.250
6 A 4 4 1.08 12 0.333
7 A 10 9 0.95 12 0.750
8 A 5 4 1.08 14 0.286
9 A 2 2 1.00 14 0.143
10 A 5 4 1.13 12 0.333
11 A 2 2 1.00 10 0.200
12 A 2 2 1.00 14 0.143
13 A 6 6 1.11 14 0.429
14 A 2 2 1.00 14 0.143
15 A 9 8 1.04 14 0.571
16 A 2 2 1.00 14 0.143
17 A 5 4 0.76 12 0.333
18 A 2 2 1.00 10 0.200
19 A 2 2 1.00 14 0.143
20 A 3 3 1.02 14 0.214
21 A 2 2 1.00 14 0.143
22 A 5 4 0.55 12 0.333
23 A 3 3 1.02 14 0.214
24 A 3 3 1.02 14 0.214
25 A 2 2 1.00 14 0.143
26 A 2 2 1.00 14 0.143
27 A 3 3 1.06 14 0.214
28 A 3 3 1.04 14 0.214
29 A 4 3 1.02 16 0.188
30 A 4 3 1.02 16 0.188
31 A 4 3 1.02 16 0.188
32 A 4 3 1.06 16 0.188
33 A 4 3 1.09 16 0.188
34 A 7 6 1.05 16 0.375
35 A 10 9 1.03 8 1.125
36 A 3 3 1.00 12 0.250
37 A 4 3 1.00 12 0.250
38 A 7 6 1.00 12 0.500
39 A 9 8 1.11 12 0.667
40 A 6 5 1.10 8 0.625
41 A 3 3 1.00 12 0.250
42 A 5 4 1.00 12 0.333
43 A 4 3 1.00 12 0.250
44 A 6 5 1.02 12 0.417
45 A 5 4 1.47 14 0.286
46 A 4 3 1.00 12 0.250
47 A 7 6 0.95 6 1.000
48 A 5 4 1.14 8 0.500
49 A 27 26 1.14 16 1.625
50 A 19 18 1.10 16 1.125
51 A 12 11 1.03 16 0.688
52 A 14 13 1.11 16 0.812
53 A 22 21 1.07 16 1.312
54 A 29 28 1.09 16 1.750
55 A 14 13 1.06 18 0.722
56 A 11 10 1.04 18 0.556
57 A 5 4 1.07 18 0.222
58 A 8 7 1.30 18 0.389
59 A 18 17 1.03 18 0.944
60 A 17 16 1.11 18 0.889
61 A 13 12 1.16 8 1.500
62 A 4 3 1.00 12 0.250
63 N/A 1 0 1.00 18 0.000
64 N/A 1 0 1.00 20 0.000
65 A 5 4 1.00 20 0.200
66 N/A 2 0 1.00 22 0.000
67 A 7 6 1.00 22 0.273
68 N/A 2 0 1.00 24 0.000
69 A 3 3 1.00 12 0.250
70 A 2 2 1.00 14 0.143
71 A 2 2 1.00 14 0.143
72 A 2 2 1.00 14 0.143
73 A 2 2 1.00 8 0.250
74 A 2 2 1.00 10 0.200
75 A 2 2 1.00 10 0.200
76 A 2 2 1.00 12 0.167
77 A 2 2 1.00 14 0.143
78 A 2 2 1.00 14 0.143
79 A 10 9 0.89 16 0.562
80 A 2 2 1.00 18 0.111
81 A 2 2 1.00 18 0.111
82 A 12 11 0.83 16 0.688
83 A 2 2 1.00 18 0.111
84 A 2 2 1.00 18 0.111
85 A 3 2 0.92 12 0.167
86 A 3 2 0.96 10 0.200
87 A 1 1 1.00 8 0.125
88 N/A 1 0 1.00 12 0.000
89 N/A 1 0 1.00 12 0.000
90 A 3 2 1.01 18 0.111
91 A 3 2 1.02 16 0.125
92 A 7 6 0.94 14 0.429
93 A 3 2 1.19 18 0.111
94 A 6 5 1.05 18 0.278
95 A 3 2 1.01 18 0.111
96 A 3 2 1.02 16 0.125
97 A 9 8 1.00 14 0.571
98 A 3 2 1.12 18 0.111
99 A 6 5 1.01 18 0.278

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