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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 [107] had the largest ratio of [.727272999999999947]

# 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 2 2 1.00 9 0.222
2 A 2 2 1.00 9 0.222
3 A 2 2 1.00 9 0.222
4 A 2 2 1.00 9 0.222
5 A 1 1 1.00 7 0.143
6 A 1 1 1.00 9 0.111
7 A 2 2 1.00 9 0.222
8 A 3 3 1.13 9 0.333
9 A 4 4 1.20 9 0.444
10 A 2 2 1.00 10 0.200
11 A 2 2 1.00 10 0.200
12 A 2 2 1.00 10 0.200
13 A 1 1 1.00 8 0.125
14 A 1 1 1.00 10 0.100
15 A 2 2 1.00 10 0.200
16 A 3 3 1.12 10 0.300
17 A 4 4 1.20 10 0.400
18 A 2 2 1.00 7 0.286
19 A 1 1 1.00 9 0.111
20 A 1 1 1.00 9 0.111
21 A 2 2 1.00 7 0.286
22 A 1 1 1.00 10 0.100
23 A 1 1 1.00 18 0.056
24 A 1 1 1.00 14 0.071
25 A 1 1 1.00 15 0.067
26 A 1 1 1.00 20 0.050
27 A 2 2 1.00 11 0.182
28 A 1 1 1.00 17 0.059
29 A 1 1 1.00 57 0.018
30 A 1 1 1.26 81 0.012
31 A 3 3 1.15 27 0.111
32 A 2 2 1.06 24 0.083
33 A 1 1 1.29 22 0.045
34 A 3 3 1.15 27 0.111
35 A 2 2 1.06 24 0.083
36 A 1 1 1.29 22 0.045
37 A 6 5 1.07 11 0.455
38 A 5 4 1.05 11 0.364
39 A 4 3 1.00 11 0.273
40 A 3 2 1.00 11 0.182
41 A 1 1 1.00 11 0.091
42 A 2 2 1.00 11 0.182
43 A 3 3 1.14 11 0.273
44 A 4 4 1.21 11 0.364
45 A 3 2 1.00 11 0.182
46 A 3 2 1.00 12 0.167
47 A 3 2 1.00 13 0.154
48 A 3 2 1.00 14 0.143
49 A 2 2 1.00 11 0.182
50 A 2 2 1.00 11 0.182
51 A 4 3 1.00 11 0.273
52 A 4 3 1.00 11 0.273
53 A 1 1 1.00 11 0.091
54 A 1 1 1.00 11 0.091
55 A 3 2 1.00 11 0.182
56 A 3 2 1.00 11 0.182
57 A 1 1 1.00 11 0.091
58 A 1 1 1.00 12 0.083
59 A 3 2 1.00 11 0.182
60 A 3 2 1.00 12 0.167
61 A 1 1 1.00 11 0.091
62 A 1 1 1.00 12 0.083
63 A 3 2 1.00 13 0.154
64 A 3 2 1.00 14 0.143
65 A 3 2 1.00 13 0.154
66 A 5 4 1.01 11 0.364
67 A 4 3 1.00 11 0.273
68 A 3 2 1.00 11 0.182
69 A 4 3 1.00 11 0.273
70 A 5 4 1.03 11 0.364
71 A 7 6 1.08 11 0.545
72 A 6 5 1.08 11 0.455
73 A 5 4 1.09 11 0.364
74 A 6 5 1.08 11 0.455
75 A 7 6 1.09 11 0.545
76 A 4 4 1.05 11 0.364
77 A 4 4 1.04 11 0.364
78 A 3 3 1.00 11 0.273
79 A 3 3 1.06 11 0.273
80 A 2 2 1.00 11 0.182
81 A 2 2 1.00 11 0.182
82 A 3 3 1.00 11 0.273
83 A 3 3 1.00 11 0.273
84 A 4 4 1.05 12 0.333
85 A 3 3 1.00 12 0.250
86 A 3 3 1.00 12 0.250
87 A 2 2 1.00 12 0.167
88 A 2 2 1.00 12 0.167
89 A 3 3 1.00 12 0.250
90 A 3 3 1.00 12 0.250
91 A 4 4 1.04 12 0.333
92 A 1 1 1.00 18 0.056
93 A 1 1 1.00 19 0.053
94 A 2 2 1.00 11 0.182
95 A 2 2 1.00 11 0.182
96 A 2 2 1.00 11 0.182
97 A 2 2 1.00 11 0.182
98 A 2 2 1.00 11 0.182
99 A 2 2 1.00 11 0.182
100 A 2 2 1.00 11 0.182
101 A 2 2 1.00 11 0.182
102 A 6 5 1.32 11 0.455
103 A 5 4 1.32 11 0.364
104 A 4 3 1.32 11 0.273
105 A 5 4 1.32 11 0.364
106 A 6 5 1.33 11 0.455
107 A 9 8 1.24 11 0.727
108 A 8 7 1.24 11 0.636
109 A 7 6 1.24 11 0.545
110 A 6 5 1.18 11 0.455
111 A 7 6 1.17 11 0.545
112 A 2 2 1.00 11 0.182
113 A 2 2 1.00 11 0.182
114 A 2 2 1.00 11 0.182
115 A 2 2 1.00 11 0.182
116 A 2 2 1.00 11 0.182
117 A 2 2 1.00 11 0.182
118 A 2 2 1.00 11 0.182
119 A 2 2 1.00 11 0.182
120 A 2 2 1.00 11 0.182
121 A 2 2 1.00 11 0.182
122 A 2 2 1.00 11 0.182
123 A 2 2 1.00 11 0.182
124 C 2 2 0.10 13 0.154
125 C 2 2 0.10 13 0.154
126 C 2 2 0.11 13 0.154
127 C 2 2 0.11 13 0.154
128 C 2 2 0.11 13 0.154
129 C 2 2 0.11 13 0.154
130 C 2 2 0.05 13 0.154
131 C 2 2 0.05 13 0.154
132 C 2 2 0.05 13 0.154
133 C 2 2 0.06 13 0.154
134 C 2 2 0.06 13 0.154
135 A 1 1 1.00 11 0.091
136 A 2 2 1.00 11 0.182

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