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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 [76] had the largest ratio of [1.28570999999999991]

# 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 2 2 1.00 12 0.167
3 A 1 1 1.00 10 0.100
4 A 2 2 1.00 12 0.167
5 A 4 4 0.98 12 0.333
6 A 6 6 1.05 12 0.500
7 A 3 3 1.00 13 0.231
8 A 2 2 1.00 13 0.154
9 A 1 1 1.00 11 0.091
10 A 2 2 1.00 13 0.154
11 A 4 4 0.98 13 0.308
12 A 6 6 1.05 13 0.462
13 A 8 8 1.07 14 0.571
14 A 6 6 1.04 14 0.429
15 A 4 4 1.00 14 0.286
16 A 2 2 1.00 14 0.143
17 A 4 3 1.00 14 0.214
18 A 6 5 1.00 14 0.357
19 A 8 7 1.05 14 0.500
20 A 8 8 1.07 15 0.533
21 A 6 6 1.04 15 0.400
22 A 4 4 1.00 15 0.267
23 A 2 2 1.00 15 0.133
24 A 4 3 1.00 15 0.200
25 A 6 5 1.00 15 0.333
26 A 8 7 1.05 15 0.467
27 A 8 8 1.06 16 0.500
28 A 6 6 1.04 16 0.375
29 A 4 4 1.00 16 0.250
30 A 2 2 1.00 16 0.125
31 A 4 3 1.00 16 0.188
32 A 6 5 1.00 16 0.312
33 A 8 7 1.04 16 0.438
34 A 4 4 1.00 14 0.286
35 A 4 4 1.00 14 0.286
36 A 4 4 1.00 14 0.286
37 A 4 4 1.00 14 0.286
38 A 4 4 1.00 14 0.286
39 A 4 4 1.00 14 0.286
40 A 4 4 1.00 12 0.333
41 A 4 4 1.00 13 0.308
42 A 2 2 1.00 12 0.167
43 A 2 2 1.00 12 0.167
44 A 2 2 1.00 12 0.167
45 A 5 5 1.09 12 0.417
46 A 8 8 1.12 12 0.667
47 A 11 11 1.14 12 0.917
48 A 2 2 1.00 12 0.167
49 A 5 5 1.09 12 0.417
50 A 8 8 1.12 12 0.667
51 A 11 11 1.14 12 0.917
52 A 2 2 1.00 12 0.167
53 A 5 5 1.09 12 0.417
54 A 7 7 1.12 12 0.583
55 A 11 11 1.14 12 0.917
56 A 2 2 1.00 12 0.167
57 A 5 5 1.09 12 0.417
58 A 7 7 1.12 12 0.583
59 A 11 11 1.14 12 0.917
60 A 5 4 0.67 12 0.333
61 A 8 7 0.80 12 0.583
62 A 11 10 0.88 12 0.833
63 A 14 13 0.94 12 1.083
64 A 5 4 0.68 12 0.333
65 A 8 7 0.80 12 0.583
66 A 11 10 0.89 12 0.833
67 A 14 13 0.94 12 1.083
68 A 5 4 0.68 12 0.333
69 A 8 7 0.80 12 0.583
70 A 10 9 0.89 12 0.750
71 A 14 13 0.94 12 1.083
72 A 5 4 0.67 12 0.333
73 A 8 7 0.80 12 0.583
74 A 10 9 0.88 12 0.750
75 A 14 13 0.94 12 1.083
76 A 18 18 1.04 14 1.286
77 A 15 15 1.03 14 1.071
78 A 12 12 1.01 14 0.857
79 A 4 4 1.00 14 0.286
80 A 4 4 1.00 14 0.286
81 A 7 7 1.00 14 0.500
82 A 15 15 1.04 14 1.071
83 A 18 18 1.09 14 1.286
84 A 5 4 1.03 14 0.286
85 A 5 4 1.00 14 0.286
86 A 5 4 1.00 14 0.286
87 A 5 4 1.00 14 0.286
88 A 5 4 1.00 14 0.286
89 A 5 4 1.05 14 0.286
90 A 5 4 1.00 12 0.333
91 A 4 3 1.00 12 0.250
92 A 4 3 1.00 12 0.250
93 A 4 3 0.89 12 0.250
94 A 4 3 1.03 12 0.250
95 A 4 3 1.00 12 0.250
96 A 4 3 1.00 12 0.250
97 A 5 4 1.02 12 0.333
98 A 6 5 1.12 12 0.417

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