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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 [104] had the largest ratio of [.586207000000000034]

# 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 27 0.074
2 A 2 2 1.00 27 0.074
3 A 2 2 1.00 25 0.080
4 A 2 2 1.00 20 0.100
5 A 5 4 0.85 27 0.148
6 A 5 4 1.18 27 0.148
7 A 5 4 1.15 27 0.148
8 A 5 4 0.90 27 0.148
9 A 6 5 0.79 27 0.185
10 A 2 2 1.00 29 0.069
11 A 2 2 1.00 29 0.069
12 A 2 2 1.00 27 0.074
13 A 2 2 1.00 22 0.091
14 A 7 6 0.99 29 0.207
15 A 7 6 1.18 29 0.207
16 A 7 6 1.24 29 0.207
17 A 7 6 1.21 29 0.207
18 A 7 6 0.92 29 0.207
19 A 9 8 1.08 25 0.320
20 A 7 6 1.03 25 0.240
21 A 5 4 0.89 23 0.174
22 A 5 4 1.02 18 0.222
23 A 6 5 1.06 25 0.200
24 A 6 5 1.10 25 0.200
25 A 8 7 1.14 25 0.280
26 A 9 8 1.08 25 0.320
27 A 7 6 1.03 25 0.240
28 A 5 4 0.89 23 0.174
29 A 5 4 1.02 18 0.222
30 A 7 6 1.06 25 0.240
31 A 7 6 1.09 25 0.240
32 A 9 8 1.15 25 0.320
33 F 0 0 N/A 0.000 N/A
34 F 0 0 N/A 0.000 N/A
35 A 5 4 0.86 27 0.148
36 A 5 4 0.97 22 0.182
37 A 6 5 1.07 29 0.172
38 A 6 5 1.09 29 0.172
39 A 8 7 1.12 29 0.241
40 A 10 9 1.12 29 0.310
41 A 12 11 1.10 29 0.379
42 A 9 8 1.36 29 0.276
43 A 7 6 1.19 29 0.207
44 A 5 4 1.17 27 0.148
45 A 5 4 1.25 22 0.182
46 A 6 5 1.09 29 0.172
47 A 8 7 1.10 29 0.241
48 A 10 9 1.07 29 0.310
49 A 13 12 1.08 29 0.414
50 A 15 14 1.06 29 0.483
51 A 9 8 1.42 29 0.276
52 A 7 6 1.23 29 0.207
53 A 5 4 1.17 27 0.148
54 A 5 4 0.99 22 0.182
55 A 8 7 1.12 29 0.241
56 A 11 10 1.12 29 0.345
57 A 11 10 1.07 29 0.345
58 A 13 12 1.07 29 0.414
59 A 15 14 1.06 29 0.483
60 A 2 2 1.00 27 0.074
61 A 2 2 1.00 27 0.074
62 A 2 2 1.00 25 0.080
63 A 2 2 1.00 20 0.100
64 A 6 5 0.83 27 0.185
65 A 6 5 0.99 27 0.185
66 A 6 5 1.13 27 0.185
67 A 6 5 0.94 27 0.185
68 A 6 5 0.78 27 0.185
69 A 2 2 1.00 29 0.069
70 A 2 2 1.00 29 0.069
71 A 2 2 1.00 27 0.074
72 A 2 2 1.00 22 0.091
73 A 8 7 0.95 29 0.241
74 A 9 8 1.00 29 0.276
75 A 8 7 1.11 29 0.241
76 A 8 7 1.18 29 0.241
77 A 8 7 0.95 29 0.241
78 F 0 0 N/A 0.000 N/A
79 F 0 0 N/A 0.000 N/A
80 A 6 5 0.83 27 0.185
81 A 6 5 0.95 22 0.227
82 A 8 7 1.12 29 0.241
83 A 8 7 1.09 29 0.241
84 A 8 7 1.09 29 0.241
85 A 10 9 1.11 29 0.310
86 A 12 11 1.09 29 0.379
87 A 10 9 1.19 29 0.310
88 A 8 7 1.01 29 0.241
89 A 6 5 0.98 27 0.185
90 A 6 5 1.12 22 0.227
91 A 8 7 1.08 29 0.241
92 A 9 8 1.10 29 0.276
93 A 12 11 1.08 29 0.379
94 A 12 11 1.07 29 0.379
95 A 15 14 1.06 29 0.483
96 A 10 9 1.27 29 0.310
97 A 8 7 1.11 29 0.241
98 A 6 5 1.14 27 0.185
99 A 6 5 1.09 22 0.227
100 A 8 7 1.10 29 0.241
101 A 10 9 1.08 29 0.310
102 A 12 11 1.07 29 0.379
103 A 15 14 1.05 29 0.483
104 A 18 17 1.05 29 0.586
105 A 2 2 1.00 27 0.074
106 A 2 2 1.00 27 0.074
107 A 2 2 1.00 25 0.080
108 A 2 2 1.00 20 0.100
109 A 4 3 0.92 27 0.111
110 A 4 3 1.15 27 0.111
111 A 4 3 1.05 27 0.111
112 A 5 4 0.90 27 0.148
113 A 6 5 0.79 27 0.185
114 A 2 2 1.00 29 0.069
115 A 2 2 1.00 29 0.069
116 A 2 2 1.00 27 0.074
117 A 2 2 1.00 22 0.091
118 A 6 5 1.05 29 0.172
119 A 7 6 1.24 29 0.207
120 A 7 6 1.22 29 0.207
121 A 7 6 1.17 29 0.207
122 A 8 7 0.93 29 0.241
123 F 0 0 N/A 0.000 N/A
124 F 0 0 N/A 0.000 N/A
125 A 4 3 0.92 27 0.111
126 A 4 3 1.00 22 0.136
127 A 4 3 1.00 29 0.103
128 A 6 5 1.16 29 0.172
129 A 8 7 1.15 29 0.241
130 A 10 9 1.13 29 0.310
131 A 12 11 1.11 29 0.379
132 A 8 7 1.44 29 0.241
133 A 6 5 1.24 29 0.172
134 A 4 3 1.14 27 0.111
135 A 4 3 1.00 22 0.136
136 A 6 5 1.16 29 0.172
137 A 7 6 1.16 29 0.207
138 A 9 8 1.13 29 0.276
139 A 12 11 1.10 29 0.379
140 A 13 12 1.08 29 0.414
141 A 8 7 1.47 29 0.241
142 A 6 5 1.22 29 0.172
143 A 4 3 1.06 27 0.111
144 A 5 4 0.97 22 0.182
145 A 8 7 1.15 29 0.241
146 A 9 8 1.12 29 0.276
147 A 11 10 1.09 29 0.345
148 A 13 12 1.08 29 0.414
149 A 15 14 1.06 29 0.483
150 A 2 2 1.00 27 0.074
151 A 2 2 1.00 27 0.074
152 A 2 2 1.00 25 0.080
153 A 2 2 1.00 20 0.100
154 A 4 3 1.11 27 0.111
155 A 4 3 1.27 27 0.111
156 A 5 4 1.08 27 0.148
157 A 6 5 0.92 27 0.185
158 A 7 6 0.82 27 0.222
159 A 2 2 1.00 29 0.069
160 A 2 2 1.00 29 0.069
161 A 2 2 1.00 27 0.074
162 A 2 2 1.00 22 0.091
163 A 6 5 1.29 29 0.172
164 A 6 5 1.51 29 0.172
165 A 6 5 1.52 29 0.172
166 A 7 6 1.17 29 0.207
167 A 8 7 0.94 29 0.241
168 A 8 7 1.49 29 0.241
169 A 6 5 1.29 29 0.172
170 A 4 3 1.11 27 0.111
171 A 4 3 1.00 22 0.136
172 A 6 5 1.22 29 0.172
173 A 8 7 1.20 29 0.241
174 A 10 9 1.15 29 0.310
175 A 12 11 1.12 29 0.379
176 A 14 13 1.10 29 0.448
177 A 8 7 1.78 29 0.241
178 A 6 5 1.45 29 0.172
179 A 4 3 1.25 27 0.111
180 A 5 4 1.11 22 0.182
181 A 8 7 1.20 29 0.241
182 A 9 8 1.14 29 0.276
183 A 11 10 1.10 29 0.345
184 A 14 13 1.08 29 0.448
185 A 16 15 1.07 29 0.517
186 A 8 7 1.66 29 0.241
187 A 6 5 1.45 29 0.172
188 A 5 4 1.05 27 0.148
189 A 6 5 1.04 22 0.227
190 A 10 9 1.14 29 0.310
191 A 11 10 1.09 29 0.345
192 A 14 13 1.07 29 0.448
193 A 16 15 1.06 29 0.517
194 A 18 17 1.05 29 0.586
195 A 11 10 1.17 31 0.323
196 A 11 10 1.07 31 0.323
197 A 7 6 0.59 29 0.207
198 A 6 5 0.64 29 0.172
199 A 5 4 0.73 29 0.138
200 A 5 4 1.09 29 0.138
201 A 5 4 1.07 29 0.138
202 A 5 4 1.01 29 0.138
203 A 2 2 1.06 29 0.069
204 A 3 3 0.89 29 0.103
205 A 4 4 0.79 29 0.138
206 A 6 6 1.00 33 0.182
207 A 5 5 0.92 31 0.161
208 A 5 5 1.00 32 0.156
209 A 5 5 1.00 32 0.156
210 A 5 5 1.01 33 0.152
211 A 3 3 0.96 45 0.067
212 A 5 5 1.07 39 0.128
213 A 4 4 1.00 38 0.105
214 A 8 7 0.97 29 0.241
215 A 7 6 0.93 29 0.207
216 A 6 5 0.82 29 0.172
217 A 7 6 0.91 29 0.207
218 A 8 7 0.93 29 0.241
219 A 8 7 0.97 29 0.241
220 A 7 6 0.93 29 0.207
221 A 6 5 0.83 29 0.172
222 A 7 6 0.92 29 0.207
223 A 8 7 0.94 29 0.241
224 A 8 7 0.80 29 0.241
225 A 1 1 1.00 30 0.033
226 A 2 2 1.00 26 0.077
227 A 2 2 0.70 35 0.057
228 A 2 2 1.00 34 0.059
229 A 3 3 0.92 21 0.143
230 A 3 3 0.98 25 0.120
231 A 4 4 0.98 29 0.138
232 A 4 4 1.00 33 0.121
233 A 4 4 1.00 34 0.118
234 A 5 5 1.00 34 0.147
235 A 3 3 1.00 34 0.088
236 A 4 4 1.03 34 0.118
237 C 8 7 1.22 35 0.200
238 A 5 4 1.00 38 0.105
239 C 8 7 0.92 38 0.184

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