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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 [74] had the largest ratio of [.500000000000000000]

# 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 16 0.125
3 A 2 2 1.00 18 0.111
4 A 2 2 1.00 18 0.111
5 A 2 2 1.00 14 0.143
6 A 2 2 1.00 14 0.143
7 A 2 2 1.00 14 0.143
8 A 1 1 1.00 14 0.071
9 A 2 2 1.00 14 0.143
10 A 2 2 1.00 14 0.143
11 A 2 2 1.00 14 0.143
12 A 2 2 1.00 14 0.143
13 A 2 2 1.00 14 0.143
14 A 2 2 1.00 14 0.143
15 A 2 2 1.12 18 0.111
16 A 2 2 1.13 21 0.095
17 A 2 2 1.18 21 0.095
18 A 1 1 1.00 19 0.053
19 A 2 2 1.42 21 0.095
20 A 2 2 1.31 21 0.095
21 A 2 2 1.12 21 0.095
22 A 2 2 1.09 21 0.095
23 A 2 2 1.09 12 0.167
24 A 2 2 1.12 12 0.167
25 A 1 1 1.00 10 0.100
26 A 2 2 1.62 12 0.167
27 A 2 2 1.32 12 0.167
28 A 2 2 1.04 12 0.167
29 A 2 2 1.09 12 0.167
30 A 2 2 1.12 12 0.167
31 A 1 1 1.00 10 0.100
32 A 2 2 1.10 12 0.167
33 A 2 2 1.05 12 0.167
34 A 2 2 1.03 12 0.167
35 A 2 2 1.00 12 0.167
36 A 2 2 1.00 12 0.167
37 A 2 2 1.00 12 0.167
38 A 1 1 1.00 10 0.100
39 A 2 2 2.00 12 0.167
40 A 3 3 1.49 12 0.250
41 A 4 4 1.41 12 0.333
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 1 1 1.00 10 0.100
46 B 2 2 2.37 12 0.167
47 A 3 3 1.60 12 0.250
48 A 4 4 1.48 12 0.333
49 B 2 2 2.29 10 0.200
50 B 2 2 2.83 10 0.200
51 A 2 2 1.91 30 0.067
52 B 2 2 2.03 31 0.065
53 A 2 2 1.11 12 0.167
54 A 3 3 1.11 22 0.136
55 A 5 4 1.12 12 0.333
56 A 4 3 1.07 12 0.250
57 A 3 2 1.14 12 0.167
58 A 1 1 1.00 12 0.083
59 A 2 2 1.00 12 0.167
60 A 3 3 1.08 12 0.250
61 A 6 5 1.11 12 0.417
62 A 5 4 1.07 12 0.333
63 A 4 3 1.00 12 0.250
64 A 3 2 1.00 12 0.167
65 A 1 1 1.00 12 0.083
66 A 2 2 1.00 12 0.167
67 A 3 3 1.08 12 0.250
68 A 4 4 1.12 12 0.333
69 A 5 4 1.86 12 0.333
70 B 4 3 2.04 12 0.250
71 B 3 2 2.60 12 0.167
72 B 4 3 2.04 12 0.250
73 A 5 4 1.86 12 0.333
74 B 7 6 3.59 12 0.500
75 B 6 5 4.30 12 0.417
76 B 5 4 6.07 12 0.333
77 B 6 5 4.51 12 0.417
78 B 7 6 3.54 12 0.500
79 A 1 1 1.00 10 0.100
80 A 1 1 1.00 21 0.048
81 A 2 2 1.00 12 0.167
82 A 2 2 1.00 12 0.167
83 A 2 2 1.00 12 0.167
84 A 1 1 1.00 10 0.100
85 A 3 2 1.00 12 0.167
86 A 4 3 1.00 12 0.250
87 A 5 4 1.11 12 0.333
88 A 2 2 1.04 23 0.087
89 A 2 2 1.04 23 0.087
90 A 2 2 1.04 23 0.087
91 A 2 2 1.04 23 0.087
92 A 3 2 1.00 10 0.200
93 A 3 2 1.17 12 0.167
94 A 3 2 1.33 15 0.133
95 A 3 2 1.00 12 0.167
96 A 3 2 1.00 12 0.167
97 A 3 2 1.00 12 0.167
98 A 3 2 1.00 12 0.167
99 A 3 2 1.00 12 0.167
100 A 3 2 1.17 13 0.154
101 A 3 2 1.16 14 0.143
102 A 4 3 1.07 12 0.250
103 A 4 3 1.00 12 0.250
104 A 4 3 1.08 13 0.231
105 A 4 3 1.07 14 0.214
106 A 3 2 1.23 40 0.050
107 A 3 2 1.41 14 0.143
108 A 3 2 1.30 16 0.125
109 A 4 3 1.06 15 0.200
110 A 4 3 1.05 16 0.188
111 A 4 3 1.00 14 0.214
112 A 4 3 1.20 14 0.214
113 A 4 3 1.04 14 0.214
114 A 4 3 1.07 14 0.214
115 A 4 3 1.07 14 0.214
116 A 4 3 1.09 14 0.214
117 A 4 3 1.00 14 0.214
118 A 4 3 1.00 14 0.214
119 A 4 3 1.00 14 0.214
120 A 4 3 1.09 14 0.214
121 A 4 3 1.00 14 0.214
122 A 3 2 1.00 14 0.143
123 A 3 2 1.40 14 0.143
124 A 3 2 1.00 14 0.143
125 A 3 2 1.17 14 0.143
126 A 3 2 1.16 14 0.143
127 A 3 2 1.13 14 0.143
128 A 3 2 1.00 14 0.143
129 A 3 2 1.00 14 0.143
130 A 3 2 1.00 14 0.143
131 A 3 2 1.13 14 0.143
132 A 3 2 1.00 14 0.143
133 A 3 2 1.00 27 0.074
134 A 3 2 1.00 30 0.067
135 A 3 2 1.00 28 0.071
136 A 1 1 1.00 12 0.083
137 A 1 1 1.00 14 0.071
138 A 2 2 1.00 14 0.143
139 B 6 5 8.76 14 0.357
140 B 7 6 17.48 14 0.429
141 B 5 4 7.52 14 0.286
142 B 6 5 16.43 14 0.357
143 B 4 3 6.38 14 0.214
144 B 7 6 17.48 14 0.429
145 B 5 4 6.06 14 0.286
146 B 6 5 12.03 14 0.357
147 B 4 3 5.57 14 0.214
148 B 5 4 11.98 14 0.286
149 B 3 2 5.31 14 0.143
150 B 6 5 12.35 14 0.357
151 A 1 1 1.44 12 0.083
152 A 3 2 1.08 12 0.167
153 A 3 2 1.00 12 0.167
154 A 3 2 1.08 12 0.167
155 A 3 2 1.43 12 0.167
156 A 1 1 1.00 10 0.100
157 A 1 1 1.00 7 0.143
158 A 3 2 1.06 12 0.167
159 A 3 2 1.06 12 0.167
160 A 3 2 1.05 12 0.167
161 A 3 2 1.00 12 0.167
162 A 3 2 1.05 12 0.167
163 A 5 4 1.06 15 0.267
164 A 4 3 1.14 15 0.200
165 A 3 2 1.13 14 0.143
166 A 4 3 1.13 13 0.231
167 A 7 6 1.95 19 0.316
168 B 6 5 6.07 15 0.333
169 B 6 5 2.72 19 0.263
170 B 4 3 2.60 15 0.200

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