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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 [1.25000000000000000]

# 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 5 5 1.00 4 1.250
2 A 3 3 1.00 11 0.273
3 A 3 3 1.00 11 0.273
4 A 2 2 1.00 2 1.000
5 A 1 1 1.00 7 0.143
6 A 4 3 1.00 7 0.429
7 A 1 1 1.00 11 0.091
8 A 1 1 1.00 6 0.167
9 A 5 4 1.00 7 0.571
10 A 4 3 1.00 4 0.750
11 A 2 2 1.00 6 0.333
12 A 1 1 1.00 6 0.167
13 A 1 1 1.00 16 0.062
14 A 2 2 1.00 7 0.286
15 A 1 1 1.00 14 0.071
16 A 4 3 1.00 5 0.600
17 A 1 1 1.00 7 0.143
18 A 1 1 1.00 11 0.091
19 A 3 2 1.00 11 0.182
20 A 1 1 1.00 5 0.200
21 A 2 2 1.00 6 0.333
22 A 2 2 1.00 9 0.222
23 A 5 4 0.90 14 0.286
24 A 2 2 1.00 9 0.222
25 A 3 3 1.00 7 0.429
26 A 3 2 1.00 15 0.133
27 A 3 2 1.00 17 0.118
28 A 4 3 1.00 13 0.231
29 A 1 1 1.00 5 0.200
30 A 6 5 0.90 8 0.625
31 A 9 8 1.12 11 0.727
32 A 2 2 1.00 12 0.167
33 A 7 6 0.95 6 1.000
34 A 2 2 1.00 9 0.222
35 A 5 4 1.12 13 0.308
36 A 5 4 1.00 15 0.267
37 A 3 3 1.00 15 0.200
38 A 7 6 1.13 13 0.462
39 A 3 3 1.00 15 0.200
40 A 6 5 1.00 29 0.172
41 A 3 3 1.00 4 0.750
42 A 8 7 1.16 19 0.368
43 A 2 2 1.00 6 0.333
44 A 2 2 1.00 5 0.400
45 A 1 1 1.00 10 0.100
46 A 2 2 1.00 13 0.154
47 A 1 1 1.00 5 0.200
48 A 1 1 1.00 7 0.143
49 A 8 7 1.10 9 0.778
50 A 9 8 1.68 7 1.143
51 A 1 1 1.00 27 0.037
52 A 1 1 1.00 4 0.250
53 A 5 4 1.08 6 0.667
54 A 2 2 1.00 10 0.200
55 A 2 2 1.00 9 0.222
56 A 3 2 1.00 12 0.167
57 A 1 1 1.00 4 0.250
58 A 2 2 1.00 7 0.286
59 A 2 2 1.00 11 0.182
60 A 2 2 1.00 9 0.222
61 A 5 5 1.00 4 1.250
62 A 7 6 0.95 6 1.000
63 A 5 5 1.00 4 1.250
64 A 2 2 1.00 6 0.333
65 A 4 3 1.00 9 0.333
66 A 3 2 1.00 12 0.167
67 A 3 2 1.00 20 0.100
68 A 4 4 1.00 10 0.400
69 A 8 7 1.00 30 0.233
70 B 8 7 2.88 39 0.179
71 B 6 6 2.75 48 0.125
72 B 5 5 2.75 31 0.161
73 A 3 3 1.00 15 0.200
74 A 5 5 1.00 4 1.250
75 A 2 2 1.00 11 0.182
76 A 2 2 1.00 13 0.154
77 A 2 2 1.00 33 0.061
78 A 1 1 1.00 7 0.143
79 A 3 3 1.00 8 0.375
80 A 3 2 1.00 9 0.222
81 A 4 3 0.88 11 0.273
82 A 5 5 1.00 8 0.625
83 A 3 3 1.00 15 0.200
84 A 3 3 1.00 16 0.188
85 A 1 1 1.00 6 0.167
86 A 1 1 1.00 3 0.333
87 A 5 4 0.89 17 0.235
88 A 3 3 1.00 4 0.750
89 A 2 2 1.00 11 0.182
90 A 4 3 1.09 14 0.214
91 A 4 3 1.00 7 0.429
92 A 3 2 1.00 11 0.182
93 A 4 3 1.00 13 0.231
94 A 2 2 1.00 8 0.250
95 A 4 3 1.00 7 0.429
96 A 1 1 1.00 4 0.250
97 A 4 3 1.00 5 0.600
98 A 4 3 1.17 17 0.176
99 A 4 3 1.00 16 0.188
100 A 3 3 1.00 15 0.200
101 A 4 3 0.90 15 0.200
102 A 3 3 1.21 8 0.375
103 A 1 1 1.00 20 0.050
104 A 1 1 1.00 25 0.040
105 A 1 1 1.00 26 0.038
106 A 1 1 1.00 31 0.032
107 A 1 1 1.00 24 0.042
108 A 1 1 1.00 29 0.034
109 A 1 1 1.00 18 0.056
110 A 1 1 1.00 23 0.043
111 A 1 1 1.00 24 0.042
112 A 1 1 1.00 29 0.034
113 A 1 1 1.00 27 0.037

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