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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 [38] had the largest ratio of [.200000000000000011]

# 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 36 0.139
2 A 3 3 1.00 30 0.100
3 A 3 3 1.00 36 0.083
4 A 5 4 1.00 38 0.105
5 A 4 4 1.00 38 0.105
6 A 5 5 1.00 38 0.132
7 A 6 5 1.00 38 0.132
8 A 7 5 1.00 38 0.132
9 A 6 6 1.00 38 0.158
10 A 4 4 1.00 32 0.125
11 A 4 4 1.00 38 0.105
12 A 5 4 1.00 40 0.100
13 A 5 4 1.00 40 0.100
14 A 5 5 1.00 40 0.125
15 A 6 6 1.00 40 0.150
16 A 7 6 1.00 40 0.150
17 A 5 4 1.00 32 0.125
18 A 5 4 1.00 38 0.105
19 A 6 5 1.00 40 0.125
20 A 6 5 1.00 40 0.125
21 A 6 5 1.00 40 0.125
22 A 6 6 1.00 40 0.150
23 A 7 7 1.00 40 0.175
24 A 8 7 1.00 40 0.175
25 A 7 7 1.00 40 0.175
26 A 6 6 1.00 38 0.158
27 A 6 4 1.00 32 0.125
28 A 3 3 1.00 38 0.079
29 A 4 4 1.00 40 0.100
30 A 5 5 1.00 40 0.125
31 A 6 6 1.00 40 0.150
32 A 7 7 1.00 40 0.175
33 A 6 6 1.00 38 0.158
34 A 3 3 1.00 32 0.094
35 A 4 4 1.00 38 0.105
36 A 5 5 1.00 40 0.125
37 A 6 6 1.00 40 0.150
38 A 8 8 1.00 40 0.200
39 A 7 7 1.00 40 0.175
40 A 5 5 1.00 38 0.132
41 A 4 4 1.00 32 0.125
42 A 5 4 1.00 38 0.105
43 A 6 6 1.00 40 0.150
44 A 7 6 1.00 40 0.150
45 A 7 5 1.00 39 0.128
46 A 7 5 1.00 39 0.128
47 A 7 5 1.00 41 0.122
48 A 7 5 1.00 41 0.122
49 A 13 7 1.00 43 0.163
50 A 6 5 1.00 43 0.116
51 A 5 5 1.00 43 0.116
52 A 4 4 1.00 41 0.098
53 A 3 3 1.00 31 0.097
54 A 5 5 0.99 43 0.116
55 A 5 5 1.00 43 0.116
56 A 4 4 1.00 43 0.093
57 A 7 6 1.00 45 0.133
58 A 6 6 1.00 45 0.133
59 A 5 5 0.99 43 0.116
60 A 4 4 1.00 33 0.121
61 A 6 6 0.99 45 0.133
62 A 6 6 1.00 45 0.133
63 A 6 6 1.00 45 0.133
64 A 7 6 1.00 45 0.133
65 A 6 5 0.99 43 0.116
66 A 5 4 1.00 33 0.121
67 A 7 6 1.00 45 0.133
68 A 7 7 1.00 45 0.156
69 A 7 6 1.00 45 0.133
70 A 7 6 1.00 45 0.133
71 A 6 6 1.00 45 0.133
72 A 5 5 1.00 43 0.116
73 A 4 4 1.00 33 0.121
74 A 3 2 0.99 45 0.044
75 A 4 3 1.00 45 0.067
76 A 5 3 1.00 45 0.067
77 A 7 7 1.00 45 0.156
78 A 6 6 1.00 45 0.133
79 A 5 5 0.99 43 0.116
80 A 3 3 1.00 33 0.091
81 A 4 3 1.00 45 0.067
82 A 5 3 1.00 45 0.067
83 A 6 3 1.00 45 0.067
84 A 7 6 1.00 45 0.133
85 A 6 6 1.00 45 0.133
86 A 4 4 0.99 43 0.093
87 A 4 4 1.00 33 0.121
88 A 5 3 1.00 45 0.067
89 A 6 3 1.00 45 0.067
90 A 12 8 1.00 47 0.170
91 A 11 8 1.00 47 0.170
92 A 10 7 1.00 45 0.156
93 A 9 6 1.00 35 0.171
94 A 12 7 1.00 47 0.149
95 A 12 7 1.00 47 0.149
96 A 13 8 1.00 47 0.170
97 A 13 8 1.00 47 0.170
98 A 12 8 1.00 47 0.170
99 A 11 7 1.00 45 0.156
100 A 10 6 1.00 35 0.171
101 A 13 7 1.00 47 0.149
102 A 13 8 1.00 47 0.170
103 A 13 7 1.00 47 0.149
104 A 13 8 1.00 47 0.170
105 A 12 7 0.99 45 0.156
106 A 11 6 1.00 35 0.171
107 A 14 7 1.00 47 0.149
108 A 14 8 1.00 47 0.170
109 A 14 8 1.00 47 0.170
110 A 11 7 1.00 47 0.149
111 A 10 7 1.00 47 0.149
112 A 9 6 1.00 45 0.133
113 A 8 5 1.00 35 0.143
114 A 11 6 1.00 47 0.128
115 A 12 7 1.00 47 0.149
116 A 11 8 1.00 47 0.170
117 A 10 7 1.00 47 0.149
118 A 9 6 1.00 45 0.133
119 A 8 5 1.00 35 0.143
120 A 12 7 1.00 47 0.149
121 A 13 7 1.00 47 0.149
122 A 11 7 1.00 47 0.149
123 A 10 7 1.00 47 0.149
124 A 9 6 0.99 45 0.133
125 A 9 6 1.00 35 0.171
126 A 13 7 1.00 47 0.149
127 A 14 7 1.00 47 0.149
128 A 16 8 1.00 49 0.163
129 A 15 8 1.00 49 0.163
130 A 14 8 1.01 49 0.163
131 A 13 8 1.00 49 0.163
132 A 13 8 1.00 49 0.163
133 A 9 6 1.00 49 0.122
134 A 10 6 1.00 49 0.122
135 A 16 8 1.00 49 0.163
136 A 15 8 1.00 49 0.163
137 A 14 8 1.00 49 0.163
138 A 14 9 1.00 49 0.184
139 A 14 8 1.00 49 0.163
140 A 10 6 1.00 49 0.122
141 A 16 8 1.00 49 0.163
142 A 15 8 1.00 49 0.163
143 A 15 9 1.00 49 0.184
144 A 15 9 1.00 49 0.184
145 A 15 8 1.00 49 0.163
146 A 11 6 1.00 49 0.122
147 A 15 8 1.00 49 0.163
148 A 14 8 1.00 49 0.163
149 A 13 8 1.00 49 0.163
150 A 12 7 1.00 49 0.143
151 A 8 5 1.00 49 0.102
152 A 9 5 1.00 49 0.102
153 A 15 9 1.00 49 0.184
154 A 14 9 1.00 49 0.184
155 A 13 8 1.00 49 0.163
156 A 8 5 1.00 49 0.102
157 A 9 5 1.00 49 0.102
158 A 10 5 1.00 49 0.102
159 A 15 9 1.00 49 0.184
160 A 14 8 1.00 49 0.163
161 A 9 6 1.00 49 0.122
162 A 9 5 1.00 49 0.102
163 A 10 5 1.00 49 0.102
164 A 9 6 1.00 45 0.133
165 A 9 6 0.98 45 0.133
166 A 8 6 0.99 45 0.133
167 A 7 5 1.00 43 0.116
168 A 6 4 1.00 33 0.121
169 A 8 5 1.00 45 0.111
170 A 9 6 1.00 45 0.133
171 A 10 6 1.00 45 0.133

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