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2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. 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 given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [207] had the largest ratio of [.4231]

Table 2.1:Rubi specific breakdown of results for each integral
# 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 2 1.00 22 0.091
2 A 4 3 1.00 20 0.150
3 A 3 2 1.00 19 0.105
4 A 4 3 1.00 22 0.136
5 A 3 2 1.00 22 0.091
6 A 4 3 1.00 22 0.136
7 A 3 2 1.00 22 0.091
8 A 4 3 1.00 22 0.136
9 A 3 2 1.00 22 0.091
10 A 4 3 1.00 22 0.136
11 A 3 2 1.00 22 0.091
12 A 3 2 1.00 21 0.095
13 A 4 3 1.00 24 0.125
14 A 3 2 1.00 24 0.083
15 A 4 3 1.00 24 0.125
16 A 3 2 1.00 24 0.083
17 A 5 4 1.00 24 0.167
18 A 3 2 1.00 24 0.083
19 A 4 3 1.00 24 0.125
20 A 3 2 1.00 24 0.083
21 A 4 3 1.00 24 0.125
22 A 3 2 1.00 24 0.083
23 A 4 3 1.00 24 0.125
24 A 3 2 1.00 24 0.083
25 A 3 2 1.00 24 0.083
26 A 4 3 1.00 24 0.125
27 A 3 2 1.00 24 0.083
28 A 4 3 1.00 24 0.125
29 A 3 2 1.00 24 0.083
30 A 5 4 1.00 24 0.167
31 A 3 2 1.00 24 0.083
32 A 4 3 1.00 24 0.125
33 A 3 2 1.00 24 0.083
34 A 4 3 1.00 24 0.125
35 A 3 2 1.00 24 0.083
36 A 4 3 1.00 24 0.125
37 A 3 2 1.00 24 0.083
38 A 5 4 1.00 24 0.167
39 A 3 2 1.00 24 0.083
40 A 4 4 1.00 24 0.167
41 A 5 4 1.00 24 0.167
42 A 4 3 1.00 24 0.125
43 A 5 4 1.00 24 0.167
44 A 4 3 1.00 24 0.125
45 A 5 4 1.00 24 0.167
46 A 4 3 1.00 24 0.125
47 A 4 4 1.00 24 0.167
48 A 4 3 1.00 24 0.125
49 A 3 3 1.00 24 0.125
50 A 4 3 1.00 22 0.136
51 A 3 3 1.00 21 0.143
52 A 3 3 1.00 22 0.136
53 A 4 3 1.00 24 0.125
54 A 4 4 1.00 24 0.167
55 A 4 3 1.00 24 0.125
56 A 5 4 1.00 24 0.167
57 A 4 3 1.00 24 0.125
58 A 5 4 1.00 24 0.167
59 A 4 3 1.00 24 0.125
60 A 5 4 1.00 24 0.167
61 A 4 3 1.00 24 0.125
62 A 5 4 1.00 24 0.167
63 A 4 3 1.00 24 0.125
64 A 4 4 1.00 24 0.167
65 A 4 3 1.00 24 0.125
66 A 3 3 1.00 24 0.125
67 A 4 3 1.00 24 0.125
68 A 4 4 1.00 24 0.167
69 A 4 3 1.00 22 0.136
70 A 5 4 1.00 21 0.190
71 A 4 3 1.00 24 0.125
72 A 5 4 1.00 24 0.167
73 A 6 5 1.00 24 0.208
74 A 4 3 1.00 24 0.125
75 A 6 5 1.00 24 0.208
76 A 4 3 1.00 24 0.125
77 A 5 5 1.00 24 0.208
78 A 4 3 1.00 24 0.125
79 A 4 4 1.00 24 0.167
80 A 3 3 1.00 24 0.125
81 A 4 4 1.00 24 0.167
82 A 4 3 1.00 24 0.125
83 A 5 4 1.00 24 0.167
84 A 4 3 1.00 24 0.125
85 A 6 5 1.00 24 0.208
86 A 4 3 1.00 22 0.136
87 A 6 5 1.00 21 0.238
88 A 4 3 1.00 24 0.125
89 A 8 7 1.00 26 0.269
90 A 7 7 1.00 26 0.269
91 A 5 5 1.00 26 0.192
92 A 5 5 1.00 24 0.208
93 A 5 5 1.00 26 0.192
94 A 5 5 1.00 26 0.192
95 A 5 5 1.00 26 0.192
96 A 3 3 1.00 26 0.115
97 A 4 4 1.00 26 0.154
98 A 5 4 1.00 26 0.154
99 A 6 4 1.00 26 0.154
100 A 4 3 1.00 26 0.115
101 A 3 3 1.00 26 0.115
102 A 2 2 1.00 23 0.087
103 A 4 4 1.00 26 0.154
104 A 4 4 1.00 26 0.154
105 A 4 4 1.00 26 0.154
106 A 8 7 1.00 26 0.269
107 A 6 5 1.00 26 0.192
108 A 6 5 1.00 24 0.208
109 A 6 6 1.00 26 0.231
110 A 6 6 1.00 26 0.231
111 A 6 5 1.00 26 0.192
112 A 6 6 1.00 26 0.231
113 A 6 5 1.00 26 0.192
114 A 3 3 1.00 26 0.115
115 A 4 4 1.00 26 0.154
116 A 5 4 1.00 26 0.154
117 A 6 4 1.00 26 0.154
118 A 7 4 1.00 26 0.154
119 A 5 4 1.00 26 0.154
120 A 4 4 1.00 26 0.154
121 A 3 3 1.00 23 0.130
122 A 2 2 1.00 26 0.077
123 A 5 4 1.00 26 0.154
124 A 5 4 1.00 26 0.154
125 A 5 5 1.00 26 0.192
126 A 5 4 1.00 26 0.154
127 A 6 5 1.00 26 0.192
128 A 7 5 1.00 26 0.192
129 A 8 5 1.00 26 0.192
130 A 7 6 1.00 26 0.231
131 A 6 6 1.00 26 0.231
132 A 4 4 1.00 26 0.154
133 A 4 4 1.00 24 0.167
134 A 4 4 1.00 26 0.154
135 A 3 3 1.00 26 0.115
136 A 4 4 1.00 26 0.154
137 A 5 4 1.00 26 0.154
138 A 6 4 1.00 26 0.154
139 A 4 3 1.00 26 0.115
140 A 3 3 1.00 26 0.115
141 A 2 2 1.00 26 0.077
142 A 3 3 1.00 23 0.130
143 A 3 3 1.00 26 0.115
144 A 4 4 1.00 26 0.154
145 A 7 6 1.00 26 0.231
146 A 6 6 1.00 26 0.231
147 A 5 5 1.00 26 0.192
148 A 4 4 1.00 26 0.154
149 A 2 2 1.00 24 0.083
150 A 3 3 1.00 26 0.115
151 A 4 4 1.00 26 0.154
152 A 5 4 1.00 26 0.154
153 A 4 3 1.00 26 0.115
154 A 3 3 1.00 26 0.115
155 A 2 2 1.00 26 0.077
156 A 3 3 1.00 26 0.115
157 A 5 5 1.00 23 0.217
158 A 5 5 1.00 26 0.192
159 A 3 2 1.00 24 0.083
160 A 3 2 1.00 24 0.083
161 A 3 2 1.00 24 0.083
162 A 3 2 1.00 24 0.083
163 A 3 2 1.00 24 0.083
164 A 3 2 1.00 24 0.083
165 A 3 2 1.00 24 0.083
166 A 3 2 1.00 24 0.083
167 A 3 2 1.00 26 0.077
168 A 3 2 1.00 26 0.077
169 A 3 2 1.00 26 0.077
170 A 3 2 1.00 26 0.077
171 A 3 2 1.00 26 0.077
172 A 3 2 1.00 26 0.077
173 A 3 2 1.00 26 0.077
174 A 3 2 1.00 26 0.077
175 A 3 2 1.00 26 0.077
176 A 3 2 1.00 26 0.077
177 A 3 2 1.00 26 0.077
178 A 3 2 1.00 26 0.077
179 A 3 2 1.00 26 0.077
180 A 3 2 1.00 26 0.077
181 A 3 2 1.00 26 0.077
182 A 3 2 1.00 26 0.077
183 A 14 10 1.00 26 0.385
184 A 14 10 1.00 26 0.385
185 A 13 10 1.00 26 0.385
186 A 13 10 1.00 26 0.385
187 A 12 9 1.00 26 0.346
188 A 12 9 1.00 26 0.346
189 A 12 9 1.00 26 0.346
190 A 12 9 1.00 26 0.346
191 A 13 10 1.00 26 0.385
192 A 13 10 1.00 26 0.385
193 A 14 10 1.00 26 0.385
194 A 14 10 1.00 26 0.385
195 A 15 10 1.00 26 0.385
196 A 14 10 1.00 26 0.385
197 A 14 10 1.00 26 0.385
198 A 13 10 1.00 26 0.385
199 A 13 10 1.00 26 0.385
200 A 12 9 1.00 26 0.346
201 A 12 9 1.00 26 0.346
202 A 13 10 1.00 26 0.385
203 A 13 10 1.00 26 0.385
204 A 14 10 1.00 26 0.385
205 A 14 10 1.00 26 0.385
206 A 15 10 1.00 26 0.385
207 A 15 11 1.00 26 0.423
208 A 14 11 1.00 26 0.423
209 A 14 11 1.00 26 0.423
210 A 13 10 1.00 26 0.385
211 A 13 10 1.00 26 0.385
212 A 13 10 1.00 26 0.385
213 A 13 10 1.00 26 0.385
214 A 14 11 1.00 26 0.423
215 A 14 11 1.00 26 0.423
216 A 15 11 1.00 26 0.423
217 A 15 11 1.00 26 0.423
218 A 16 11 1.00 26 0.423
219 A 16 11 1.00 26 0.423
220 A 3 2 1.00 24 0.083
221 A 3 2 1.00 24 0.083
222 A 3 2 1.00 22 0.091
223 A 2 2 1.00 32 0.062
224 A 4 3 1.00 19 0.158
225 A 4 3 1.00 15 0.200
226 A 4 3 1.00 19 0.158
227 A 3 2 1.00 17 0.118
228 A 2 2 1.00 39 0.051

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