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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 [48] had the largest ratio of [.555599999999999983]

# 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 18 0.111
2 A 2 2 1.00 18 0.111
3 A 2 2 1.00 18 0.111
4 A 1 1 1.00 16 0.062
5 A 1 1 1.00 16 0.062
6 A 1 1 1.00 18 0.056
7 A 2 2 1.00 18 0.111
8 A 2 2 1.00 18 0.111
9 A 3 2 1.00 8 0.250
10 A 2 2 1.00 18 0.111
11 A 2 2 1.00 18 0.111
12 A 2 2 1.00 18 0.111
13 A 1 1 1.00 16 0.062
14 A 1 1 1.00 16 0.062
15 A 1 1 1.00 18 0.056
16 A 2 2 1.00 18 0.111
17 A 2 2 1.00 18 0.111
18 A 3 2 1.00 8 0.250
19 A 6 3 1.00 18 0.167
20 A 5 3 1.00 18 0.167
21 A 4 3 1.00 16 0.188
22 A 4 3 1.00 16 0.188
23 A 5 3 1.00 18 0.167
24 A 6 3 1.00 18 0.167
25 A 5 4 1.00 27 0.148
26 A 2 2 1.00 18 0.111
27 A 2 2 1.00 18 0.111
28 F 0 0 N/A 0.000 N/A
29 N/A 0 0 1.00 21 0.000
30 N/A 0 0 1.00 23 0.000
31 A 11 5 1.00 44 0.114
32 F 0 0 N/A 0.000 N/A
33 A 7 4 1.00 43 0.093
34 B 14 6 19.24 35 0.171
35 A 1 1 1.00 30 0.033
36 A 6 3 1.00 38 0.079
37 A 10 4 1.00 38 0.105
38 A 3 3 1.00 20 0.150
39 A 4 2 1.00 22 0.091
40 A 4 2 1.00 22 0.091
41 A 4 2 1.00 22 0.091
42 A 4 3 1.00 24 0.125
43 A 5 2 1.00 24 0.083
44 A 4 2 1.00 22 0.091
45 A 5 2 1.00 24 0.083
46 A 4 2 1.00 24 0.083
47 A 4 3 1.00 7 0.429
48 A 11 5 1.00 9 0.556
49 A 4 3 1.00 7 0.429
50 A 11 5 1.00 9 0.556
51 A 4 3 1.00 19 0.158
52 A 3 1 1.00 15 0.067
53 A 5 4 1.00 26 0.154
54 A 5 4 1.00 27 0.148
55 A 5 4 1.00 26 0.154
56 A 5 4 1.00 27 0.148
57 A 6 3 1.00 10 0.300
58 A 6 3 1.00 10 0.300
59 A 6 3 1.00 12 0.250
60 A 6 3 1.00 12 0.250
61 A 2 2 1.00 15 0.133
62 A 2 2 1.00 8 0.250
63 A 3 3 1.00 12 0.250
64 A 2 2 1.00 8 0.250
65 A 2 2 1.00 12 0.167
66 A 2 2 1.00 12 0.167
67 A 3 3 1.00 10 0.300
68 A 4 3 1.00 26 0.115
69 A 2 2 1.00 8 0.250
70 A 2 2 1.00 8 0.250
71 A 3 3 1.00 12 0.250
72 A 3 3 1.00 10 0.300
73 A 1 1 1.00 10 0.100
74 A 6 4 1.00 12 0.333
75 A 6 4 1.00 15 0.267
76 A 6 3 1.00 12 0.250
77 A 4 2 1.00 14 0.143
78 A 6 3 1.00 17 0.176
79 A 8 5 1.00 16 0.312
80 A 9 6 1.00 18 0.333
81 A 14 5 1.00 18 0.278
82 A 8 5 1.00 19 0.263
83 A 9 6 1.00 21 0.286
84 A 14 5 1.00 21 0.238
85 A 8 4 1.00 16 0.250
86 A 9 4 1.00 18 0.222
87 A 14 4 1.00 18 0.222
88 A 6 4 1.00 18 0.222
89 A 7 4 1.00 20 0.200
90 A 10 4 1.00 20 0.200
91 A 8 5 1.00 21 0.238
92 A 9 5 1.00 23 0.217
93 A 14 5 1.00 23 0.217
94 A 8 4 1.00 19 0.210
95 A 10 4 1.00 21 0.190
96 A 14 4 1.00 21 0.190
97 A 8 5 1.00 21 0.238
98 A 10 5 1.00 23 0.217
99 A 14 5 1.00 23 0.217
100 A 8 5 1.00 24 0.208
101 A 10 5 1.00 26 0.192
102 A 14 5 1.00 26 0.192
103 A 8 5 1.00 24 0.208
104 A 1 1 1.00 10 0.100
105 A 6 4 1.00 12 0.333
106 A 6 4 1.00 15 0.267
107 A 6 3 1.00 12 0.250
108 A 4 2 1.00 14 0.143
109 A 6 3 1.00 17 0.176
110 A 8 5 1.00 16 0.312
111 A 9 6 1.00 18 0.333
112 A 14 5 1.00 18 0.278
113 A 8 5 1.00 19 0.263
114 A 9 6 1.00 21 0.286
115 A 14 5 1.00 21 0.238
116 A 8 4 1.00 16 0.250
117 A 9 4 1.00 18 0.222
118 A 14 4 1.00 18 0.222
119 A 6 4 1.00 18 0.222
120 A 7 4 1.00 20 0.200
121 A 10 4 1.00 20 0.200
122 A 8 5 1.00 21 0.238
123 A 9 5 1.00 23 0.217
124 A 14 5 1.00 23 0.217
125 A 8 4 1.00 19 0.210
126 A 10 4 1.00 21 0.190
127 A 14 4 1.00 21 0.190
128 A 8 5 1.00 21 0.238
129 A 10 5 1.00 23 0.217
130 A 14 5 1.00 23 0.217
131 A 8 5 1.00 24 0.208
132 A 10 5 1.00 26 0.192
133 A 14 5 1.00 26 0.192
134 A 8 5 1.00 24 0.208
135 A 8 6 1.00 22 0.273
136 A 6 5 1.00 20 0.250
137 A 2 2 1.00 22 0.091
138 A 3 3 1.00 22 0.136
139 A 8 6 1.00 22 0.273
140 A 6 5 1.00 20 0.250
141 A 2 2 1.00 22 0.091
142 A 3 3 1.00 22 0.136

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