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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 [224] had the largest ratio of [.789474000000000009]

# 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 1.19 22 0.091
2 A 2 2 1.28 22 0.091
3 C 4 4 0.92 20 0.200
4 A 1 1 1.00 9 0.111
5 N/A 1 0 1.00 22 0.000
6 N/A 1 0 1.00 22 0.000
7 A 2 2 1.00 23 0.087
8 A 2 2 0.96 20 0.100
9 A 2 2 0.96 20 0.100
10 A 2 2 0.97 18 0.111
11 A 2 2 0.99 17 0.118
12 A 2 2 1.00 20 0.100
13 A 2 2 0.93 20 0.100
14 A 2 2 0.96 20 0.100
15 A 2 2 0.95 20 0.100
16 A 2 2 0.90 22 0.091
17 A 2 2 0.90 22 0.091
18 A 2 2 0.92 20 0.100
19 A 2 2 0.87 19 0.105
20 A 3 3 0.96 22 0.136
21 A 2 2 0.98 22 0.091
22 A 2 2 0.95 22 0.091
23 A 2 2 0.93 22 0.091
24 A 2 2 0.94 22 0.091
25 A 2 2 0.93 20 0.100
26 A 2 2 0.93 19 0.105
27 A 4 4 0.95 22 0.182
28 A 2 2 0.98 22 0.091
29 A 2 2 0.95 22 0.091
30 A 2 2 0.97 26 0.077
31 A 2 2 0.99 24 0.083
32 A 2 2 1.00 26 0.077
33 A 2 2 0.96 26 0.077
34 A 2 2 0.97 26 0.077
35 A 2 2 0.97 23 0.087
36 A 2 2 0.98 26 0.077
37 A 2 2 0.98 26 0.077
38 A 2 2 0.92 28 0.071
39 A 2 2 0.94 26 0.077
40 A 3 3 0.97 28 0.107
41 A 2 2 0.99 28 0.071
42 C 2 2 1.12 28 0.071
43 C 3 3 1.15 25 0.120
44 C 2 2 1.14 28 0.071
45 C 2 2 1.11 28 0.071
46 A 2 2 0.95 28 0.071
47 A 2 2 0.96 26 0.077
48 A 4 4 1.00 28 0.143
49 A 2 2 0.98 28 0.071
50 C 3 3 1.16 25 0.120
51 C 2 2 1.16 28 0.071
52 A 2 2 0.96 28 0.071
53 A 2 2 0.96 26 0.077
54 A 2 2 0.98 25 0.080
55 A 2 2 1.00 28 0.071
56 A 2 2 0.96 28 0.071
57 A 2 2 0.97 28 0.071
58 A 2 2 0.96 28 0.071
59 A 2 2 0.92 30 0.067
60 A 2 2 0.92 28 0.071
61 A 2 2 0.93 27 0.074
62 A 3 3 0.99 30 0.100
63 A 2 2 1.06 30 0.067
64 A 2 2 1.02 30 0.067
65 A 2 2 0.94 28 0.071
66 A 2 2 0.94 27 0.074
67 A 4 4 0.98 30 0.133
68 A 2 2 1.05 30 0.067
69 A 2 2 1.02 30 0.067
70 A 5 5 1.02 28 0.179
71 A 4 4 1.02 28 0.143
72 A 3 3 1.01 28 0.107
73 A 2 2 1.00 26 0.077
74 N/A 1 0 1.00 28 0.000
75 N/A 1 0 1.00 28 0.000
76 A 2 2 0.96 24 0.083
77 A 2 2 0.96 24 0.083
78 A 2 2 0.97 22 0.091
79 A 2 2 0.95 21 0.095
80 A 4 4 1.12 24 0.167
81 A 2 2 0.96 24 0.083
82 A 2 2 0.96 24 0.083
83 A 2 2 0.96 24 0.083
84 A 2 2 1.00 26 0.077
85 A 2 2 1.00 24 0.083
86 A 3 3 1.03 23 0.130
87 A 5 5 1.07 26 0.192
88 A 2 2 0.96 26 0.077
89 A 2 2 0.93 26 0.077
90 A 2 2 0.96 26 0.077
91 A 2 2 1.00 24 0.083
92 A 3 3 1.01 23 0.130
93 A 6 6 1.04 26 0.231
94 A 2 2 0.96 26 0.077
95 A 2 2 0.94 26 0.077
96 A 2 2 0.97 26 0.077
97 A 2 2 0.98 24 0.083
98 A 4 4 1.12 26 0.154
99 A 2 2 0.96 26 0.077
100 A 2 2 0.96 26 0.077
101 A 2 2 0.97 26 0.077
102 A 2 2 0.97 23 0.087
103 A 2 2 0.98 26 0.077
104 A 2 2 0.98 26 0.077
105 A 2 2 0.97 26 0.077
106 A 2 2 1.03 26 0.077
107 A 5 5 1.10 28 0.179
108 A 2 2 0.97 28 0.071
109 A 2 2 0.94 28 0.071
110 C 2 2 1.09 28 0.071
111 C 3 3 1.12 25 0.120
112 C 2 2 1.11 28 0.071
113 C 2 2 1.08 28 0.071
114 A 2 2 1.01 26 0.077
115 A 6 6 1.07 28 0.214
116 A 2 2 0.96 28 0.071
117 C 2 2 1.10 28 0.071
118 C 3 3 1.13 25 0.120
119 C 2 2 1.13 28 0.071
120 C 2 2 1.10 28 0.071
121 A 2 2 0.96 28 0.071
122 A 2 2 0.97 26 0.077
123 A 2 2 0.97 25 0.080
124 A 4 4 1.11 28 0.143
125 A 2 2 0.96 28 0.071
126 A 2 2 0.96 28 0.071
127 A 2 2 0.96 28 0.071
128 A 2 2 1.02 28 0.071
129 A 2 2 1.05 26 0.077
130 A 2 2 1.12 25 0.080
131 A 5 5 1.10 28 0.179
132 A 2 2 1.22 28 0.071
133 A 2 2 1.14 28 0.071
134 A 2 2 1.03 26 0.077
135 A 2 2 1.06 25 0.080
136 A 6 6 1.07 28 0.214
137 A 2 2 1.16 28 0.071
138 A 2 2 1.11 28 0.071
139 A 2 2 0.96 30 0.067
140 A 2 2 0.97 30 0.067
141 A 2 2 0.96 30 0.067
142 A 2 2 0.96 30 0.067
143 A 2 2 0.96 30 0.067
144 N/A 1 0 1.00 28 0.000
145 A 6 6 1.10 28 0.214
146 A 5 5 1.13 28 0.179
147 A 4 4 1.17 26 0.154
148 N/A 1 0 1.00 28 0.000
149 N/A 1 0 1.00 28 0.000
150 N/A 1 0 1.00 26 0.000
151 N/A 1 0 1.00 24 0.000
152 N/A 1 0 1.00 23 0.000
153 A 4 4 1.17 26 0.154
154 N/A 1 0 1.00 26 0.000
155 N/A 1 0 1.00 26 0.000
156 A 2 2 0.98 32 0.062
157 A 2 2 0.98 32 0.062
158 A 2 2 0.96 30 0.067
159 A 2 2 0.98 32 0.062
160 A 2 2 0.98 32 0.062
161 A 2 2 0.98 32 0.062
162 A 3 3 1.04 24 0.125
163 A 3 3 1.04 22 0.136
164 A 2 2 0.97 21 0.095
165 A 5 4 1.00 24 0.167
166 A 3 3 1.00 24 0.125
167 A 3 3 1.04 24 0.125
168 A 3 3 1.04 24 0.125
169 A 4 4 0.95 26 0.154
170 A 4 4 0.94 24 0.167
171 A 2 2 0.96 23 0.087
172 A 5 4 1.00 26 0.154
173 A 4 4 0.96 26 0.154
174 A 4 4 0.95 26 0.154
175 A 4 4 0.95 26 0.154
176 A 7 6 1.06 26 0.231
177 A 7 6 1.06 24 0.250
178 A 7 6 1.07 23 0.261
179 A 6 5 1.04 26 0.192
180 A 7 6 1.06 26 0.231
181 A 7 6 1.06 26 0.231
182 A 2 2 1.52 23 0.087
183 A 2 2 1.03 18 0.111
184 A 9 8 0.83 28 0.286
185 A 8 7 0.82 26 0.269
186 A 8 7 0.82 24 0.292
187 A 8 7 0.83 23 0.304
188 A 5 4 1.00 26 0.154
189 A 9 8 0.83 26 0.308
190 A 9 8 0.82 26 0.308
191 A 9 8 0.82 26 0.308
192 A 2 2 0.98 18 0.111
193 A 2 2 0.99 18 0.111
194 A 2 2 0.98 18 0.111
195 A 2 2 0.98 18 0.111
196 A 2 2 0.99 18 0.111
197 A 2 2 0.99 18 0.111
198 A 2 2 0.98 18 0.111
199 A 2 2 0.98 18 0.111
200 A 3 3 0.98 20 0.150
201 A 3 3 0.98 20 0.150
202 A 3 3 0.98 20 0.150
203 A 3 3 0.98 20 0.150
204 N/A 1 0 1.00 23 0.000
205 A 4 4 1.02 23 0.174
206 A 3 3 1.01 23 0.130
207 A 2 2 1.00 21 0.095
208 N/A 1 0 1.00 23 0.000
209 N/A 2 0 1.00 23 0.000
210 N/A 3 0 1.00 23 0.000
211 A 2 2 1.00 11 0.182
212 A 3 3 1.06 13 0.231
213 A 1 1 1.00 57 0.018
214 A 7 7 1.29 19 0.368
215 A 7 7 1.30 17 0.412
216 A 7 6 1.22 16 0.375
217 A 2 2 1.00 19 0.105
218 A 8 8 1.17 19 0.421
219 A 7 7 1.21 19 0.368
220 A 13 13 1.59 19 0.684
221 A 13 13 1.59 17 0.765
222 A 12 11 1.44 16 0.688
223 A 2 2 1.00 19 0.105
224 A 15 15 1.36 19 0.789
225 A 13 13 1.47 19 0.684
226 N/A 2 0 1.00 26 0.000
227 N/A 6 0 1.00 23 0.000
228 N/A 12 0 1.00 23 0.000
229 A 3 2 1.00 14 0.143
230 A 3 2 1.00 12 0.167
231 A 3 2 1.00 10 0.200
232 A 3 2 1.00 14 0.143
233 A 3 2 1.00 14 0.143
234 A 3 2 1.00 14 0.143
235 A 3 2 1.00 14 0.143
236 A 4 3 1.02 16 0.188
237 A 4 3 0.98 14 0.214
238 A 4 3 0.95 12 0.250
239 A 4 3 1.00 16 0.188
240 A 4 3 0.98 16 0.188
241 A 4 3 0.96 16 0.188
242 A 4 3 1.02 16 0.188
243 A 5 4 1.01 22 0.182
244 A 4 3 1.01 22 0.136
245 A 3 2 1.00 20 0.100
246 A 4 3 1.00 22 0.136
247 A 5 4 1.00 22 0.182
248 A 4 3 1.00 22 0.136
249 A 4 3 1.00 20 0.150
250 A 4 3 1.00 18 0.167
251 A 4 3 1.00 16 0.188
252 A 4 3 1.00 20 0.150
253 A 4 3 1.00 20 0.150
254 A 4 3 1.00 20 0.150
255 C 6 5 0.92 24 0.208

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