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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 [79] had the largest ratio of [1]

# 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 3 3 1.00 23 0.130
2 A 5 4 1.00 23 0.174
3 A 5 4 1.00 23 0.174
4 F 0 0 N/A 0.000 N/A
5 A 4 3 1.01 23 0.130
6 A 9 8 1.17 19 0.421
7 A 3 3 1.18 23 0.130
8 A 3 3 1.00 23 0.130
9 A 3 3 1.00 23 0.130
10 A 2 2 1.00 17 0.118
11 A 2 2 1.00 17 0.118
12 A 2 2 1.00 17 0.118
13 A 2 2 1.00 15 0.133
14 A 10 9 0.91 17 0.529
15 A 10 9 0.93 17 0.529
16 A 11 10 0.93 17 0.588
17 A 2 2 1.00 19 0.105
18 A 2 2 1.00 19 0.105
19 A 2 2 1.00 17 0.118
20 A 2 2 1.00 19 0.105
21 A 2 2 1.00 19 0.105
22 A 11 10 0.87 19 0.526
23 A 2 2 1.00 19 0.105
24 A 2 2 1.00 19 0.105
25 A 2 2 1.00 17 0.118
26 A 2 2 1.00 19 0.105
27 A 2 2 1.00 19 0.105
28 A 2 2 1.00 19 0.105
29 A 2 2 1.00 19 0.105
30 A 2 2 1.00 19 0.105
31 A 2 2 1.00 19 0.105
32 A 10 9 0.90 17 0.529
33 A 10 9 0.86 19 0.474
34 A 11 10 0.89 19 0.526
35 A 2 2 1.00 19 0.105
36 A 2 2 1.00 19 0.105
37 A 2 2 1.00 19 0.105
38 A 2 2 1.00 19 0.105
39 A 10 9 0.93 17 0.529
40 A 12 11 0.88 19 0.579
41 A 14 13 0.89 19 0.684
42 A 5 5 0.99 21 0.238
43 A 3 3 0.99 19 0.158
44 A 2 2 1.00 21 0.095
45 A 2 2 1.00 21 0.095
46 A 4 4 1.04 21 0.190
47 A 2 2 1.00 19 0.105
48 A 1 1 1.00 11 0.091
49 C 2 2 0.08 21 0.095
50 A 2 2 1.00 21 0.095
51 A 2 2 1.00 21 0.095
52 A 4 4 1.07 21 0.190
53 A 2 2 1.00 19 0.105
54 A 2 2 1.00 11 0.182
55 A 2 2 1.00 21 0.095
56 A 2 2 1.00 21 0.095
57 A 3 3 1.00 23 0.130
58 A 3 3 1.00 23 0.130
59 A 3 3 1.00 23 0.130
60 A 3 3 1.00 23 0.130
61 A 3 3 1.00 23 0.130
62 A 3 3 1.00 23 0.130
63 A 3 3 1.00 23 0.130
64 A 3 3 1.00 23 0.130
65 A 3 3 1.00 23 0.130
66 A 3 3 1.00 23 0.130
67 A 3 3 1.02 20 0.150
68 A 2 2 1.01 20 0.100
69 A 2 2 1.00 20 0.100
70 A 2 2 1.31 20 0.100
71 A 3 3 1.09 20 0.150
72 A 4 4 1.18 20 0.200
73 A 5 5 1.23 20 0.250
74 A 22 21 1.20 22 0.955
75 A 20 19 1.16 22 0.864
76 A 11 10 1.03 22 0.455
77 A 14 13 1.03 22 0.591
78 A 20 19 1.14 22 0.864
79 A 23 22 1.16 22 1.000
80 A 5 5 1.07 22 0.227
81 A 4 4 1.06 22 0.182
82 A 5 5 1.08 22 0.227
83 A 4 4 1.18 22 0.182
84 A 3 3 1.53 22 0.136
85 A 4 4 1.64 22 0.182
86 A 6 6 1.27 22 0.273
87 A 7 7 1.30 22 0.318
88 A 5 5 1.11 22 0.227
89 A 5 5 1.04 22 0.227
90 A 5 5 1.04 22 0.227
91 A 4 4 0.90 22 0.182
92 A 4 4 0.91 22 0.182
93 A 4 4 0.90 22 0.182
94 A 5 5 1.14 22 0.227
95 A 4 4 1.09 21 0.190
96 A 3 3 1.00 19 0.158
97 A 2 2 1.00 21 0.095
98 A 2 2 1.00 21 0.095
99 A 3 3 0.96 21 0.143
100 A 2 2 0.96 19 0.105
101 A 1 1 1.00 21 0.048
102 A 2 2 0.99 21 0.095
103 A 5 5 1.13 21 0.238
104 A 4 4 1.10 21 0.190
105 A 2 2 1.04 19 0.105
106 A 2 2 1.06 21 0.095
107 A 4 4 1.01 21 0.190
108 A 4 4 0.87 19 0.211
109 A 3 3 0.91 19 0.158
110 A 2 2 0.96 19 0.105
111 A 2 2 1.04 19 0.105
112 A 2 2 0.77 19 0.105
113 A 3 3 0.97 19 0.158
114 A 4 4 0.95 19 0.211
115 A 5 5 0.94 19 0.263
116 A 3 3 1.00 19 0.158
117 A 3 3 1.00 19 0.158
118 A 3 3 1.00 19 0.158
119 A 3 3 1.00 19 0.158
120 A 3 3 1.19 19 0.158
121 A 3 3 1.12 19 0.158
122 A 5 5 0.80 21 0.238
123 A 4 4 0.88 21 0.190
124 A 3 3 0.96 21 0.143
125 A 4 4 1.10 21 0.190
126 A 3 3 1.12 21 0.143
127 A 3 3 0.72 21 0.143
128 A 4 4 0.93 21 0.190
129 A 5 5 0.90 21 0.238
130 A 6 6 0.83 21 0.286
131 A 4 4 1.09 21 0.190
132 A 4 4 1.08 21 0.190
133 A 4 4 1.09 21 0.190
134 A 4 4 1.08 21 0.190
135 A 4 4 1.11 21 0.190
136 A 4 4 1.15 21 0.190
137 A 4 4 0.65 21 0.190
138 A 7 7 0.99 21 0.333
139 A 5 5 1.01 21 0.238
140 A 3 3 1.02 21 0.143
141 A 1 1 1.00 21 0.048
142 A 2 2 1.06 21 0.095
143 A 5 5 1.10 21 0.238
144 A 7 7 1.15 21 0.333
145 A 2 2 1.00 21 0.095
146 A 2 2 1.00 21 0.095
147 A 2 2 1.00 21 0.095
148 A 2 2 1.00 21 0.095
149 A 2 2 1.00 21 0.095
150 A 6 6 0.97 21 0.286
151 A 4 4 1.00 21 0.190
152 A 2 2 1.02 21 0.095
153 A 2 2 0.99 21 0.095
154 A 4 4 1.01 21 0.190
155 A 6 6 1.04 21 0.286
156 A 2 2 1.00 21 0.095
157 A 2 2 1.00 21 0.095
158 A 2 2 1.00 21 0.095
159 A 2 2 1.00 21 0.095
160 A 2 2 1.00 21 0.095
161 A 10 10 0.93 21 0.476
162 A 8 8 0.94 21 0.381
163 A 6 6 0.96 21 0.286
164 A 3 3 1.02 21 0.143
165 A 3 3 0.98 21 0.143
166 A 4 4 0.96 21 0.190
167 A 6 6 1.01 21 0.286
168 A 9 9 1.05 21 0.429
169 A 2 2 1.00 21 0.095
170 A 2 2 1.00 21 0.095
171 A 2 2 1.00 21 0.095
172 A 2 2 1.00 21 0.095
173 A 2 2 1.00 21 0.095
174 A 3 3 1.85 23 0.130
175 A 2 2 1.40 23 0.087
176 A 2 2 1.40 23 0.087
177 A 1 1 1.00 23 0.043
178 A 1 1 1.01 23 0.043
179 A 1 1 1.01 23 0.043
180 A 2 2 1.41 23 0.087
181 A 2 2 1.41 23 0.087
182 A 3 3 1.86 23 0.130
183 A 3 3 1.00 19 0.158
184 A 7 7 1.02 19 0.368
185 A 5 5 1.01 19 0.263
186 A 3 3 1.00 17 0.176
187 A 2 2 1.00 19 0.105
188 A 2 2 1.00 19 0.105
189 A 2 2 1.00 19 0.105
190 A 1 1 1.00 50 0.020

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