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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 [286] had the largest ratio of [1.44443999999999995]

# 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 14 0.214
2 A 3 3 1.00 14 0.214
3 A 3 3 1.00 12 0.250
4 A 1 1 1.00 9 0.111
5 A 3 3 1.00 12 0.250
6 A 3 3 1.00 14 0.214
7 A 3 3 1.00 14 0.214
8 A 8 8 1.01 16 0.500
9 A 7 6 1.00 16 0.375
10 A 4 4 1.00 14 0.286
11 A 4 3 1.00 11 0.273
12 A 6 6 1.00 14 0.429
13 A 7 6 1.00 16 0.375
14 A 11 10 0.96 16 0.625
15 B 3 3 2.64 16 0.188
16 A 9 9 1.17 16 0.562
17 A 6 5 1.00 14 0.357
18 A 2 2 1.00 11 0.182
19 A 7 6 1.00 14 0.429
20 A 5 4 1.00 16 0.250
21 A 15 14 1.32 16 0.875
22 A 12 12 1.23 16 0.750
23 B 3 3 3.26 16 0.188
24 A 4 3 1.27 14 0.214
25 A 6 5 1.00 11 0.455
26 A 5 4 1.00 14 0.286
27 A 17 16 1.16 16 1.000
28 A 5 4 1.00 16 0.250
29 A 2 2 1.00 33 0.061
30 A 3 3 1.00 26 0.115
31 A 3 3 1.00 26 0.115
32 A 3 3 1.00 26 0.115
33 A 3 3 1.00 26 0.115
34 A 3 3 1.00 24 0.125
35 A 1 1 1.00 17 0.059
36 A 3 3 1.00 24 0.125
37 A 3 3 1.00 26 0.115
38 A 3 3 1.00 26 0.115
39 A 3 3 1.00 26 0.115
40 A 3 3 1.00 26 0.115
41 A 3 3 1.00 26 0.115
42 A 3 3 1.00 26 0.115
43 A 3 3 1.00 28 0.107
44 A 3 3 1.00 28 0.107
45 A 3 3 1.00 28 0.107
46 A 3 3 1.00 28 0.107
47 A 3 3 1.00 26 0.115
48 A 3 3 1.00 19 0.158
49 A 3 3 1.00 26 0.115
50 A 6 6 1.00 28 0.214
51 A 3 3 1.00 28 0.107
52 A 4 3 1.00 28 0.107
53 A 3 3 1.00 28 0.107
54 A 5 4 0.91 28 0.143
55 A 3 3 1.00 28 0.107
56 A 5 4 0.90 28 0.143
57 A 3 3 1.00 28 0.107
58 A 3 3 1.00 28 0.107
59 A 3 3 1.00 28 0.107
60 A 3 3 1.00 28 0.107
61 A 7 6 1.22 26 0.231
62 A 4 3 0.97 19 0.158
63 A 7 6 1.14 26 0.231
64 A 3 3 1.00 28 0.107
65 A 8 8 1.00 28 0.286
66 A 3 3 1.00 28 0.107
67 A 4 3 1.00 28 0.107
68 A 3 3 1.00 28 0.107
69 A 5 4 0.90 28 0.143
70 A 3 3 1.00 28 0.107
71 A 5 4 0.90 28 0.143
72 A 3 3 1.00 28 0.107
73 A 5 4 0.89 28 0.143
74 A 3 3 1.00 28 0.107
75 A 3 3 1.00 28 0.107
76 A 3 3 1.00 28 0.107
77 A 3 3 1.00 28 0.107
78 A 3 3 1.00 26 0.115
79 A 5 5 1.03 19 0.263
80 A 3 3 1.00 26 0.115
81 A 7 6 1.08 28 0.214
82 A 3 3 1.00 28 0.107
83 A 10 10 1.00 28 0.357
84 A 3 3 1.00 28 0.107
85 A 4 3 1.00 28 0.107
86 A 3 3 1.00 28 0.107
87 A 5 4 0.90 28 0.143
88 A 3 3 1.00 28 0.107
89 A 5 4 0.90 28 0.143
90 A 3 3 1.00 28 0.107
91 A 5 4 0.90 28 0.143
92 A 3 3 1.00 28 0.107
93 A 3 3 1.00 28 0.107
94 A 3 3 1.00 28 0.107
95 A 3 3 1.00 28 0.107
96 A 8 7 1.16 26 0.269
97 A 5 4 0.95 19 0.211
98 A 9 8 1.11 26 0.308
99 A 3 3 1.00 28 0.107
100 A 7 6 1.02 28 0.214
101 A 3 3 1.00 28 0.107
102 A 12 12 1.00 28 0.429
103 A 3 3 1.00 28 0.107
104 A 4 3 1.00 28 0.107
105 A 3 3 1.00 28 0.107
106 A 5 4 0.90 28 0.143
107 A 3 3 1.00 28 0.107
108 A 5 4 0.90 28 0.143
109 A 3 3 1.00 28 0.107
110 A 14 14 0.97 28 0.500
111 A 11 10 1.00 28 0.357
112 A 8 8 1.01 28 0.286
113 A 7 6 1.00 28 0.214
114 A 4 4 1.00 26 0.154
115 A 4 3 1.00 19 0.158
116 A 5 5 1.00 26 0.192
117 A 7 6 1.00 28 0.214
118 A 10 9 0.98 28 0.321
119 A 11 10 0.98 28 0.357
120 A 13 12 0.92 28 0.429
121 A 15 14 0.94 28 0.500
122 A 7 6 1.19 28 0.214
123 A 5 4 1.61 28 0.143
124 A 8 8 1.13 28 0.286
125 A 6 5 1.00 26 0.192
126 A 2 2 1.00 19 0.105
127 A 7 6 1.00 26 0.231
128 A 5 4 0.93 28 0.143
129 A 15 14 1.27 28 0.500
130 A 5 4 0.91 28 0.143
131 B 5 4 2.21 28 0.143
132 A 10 10 1.18 28 0.357
133 A 9 8 1.98 28 0.286
134 A 4 3 1.36 26 0.115
135 A 6 5 1.00 19 0.263
136 A 5 4 0.94 26 0.154
137 A 17 16 1.14 28 0.571
138 A 5 4 0.91 28 0.143
139 A 27 26 1.82 28 0.929
140 A 5 4 0.91 28 0.143
141 A 12 12 1.20 28 0.429
142 B 11 10 2.49 28 0.357
143 A 4 3 1.00 28 0.107
144 A 9 8 1.07 26 0.308
145 A 4 4 1.00 19 0.211
146 A 13 12 1.02 26 0.462
147 A 5 4 0.93 28 0.143
148 A 31 30 1.96 28 1.071
149 A 5 4 0.93 28 0.143
150 A 5 5 1.03 31 0.161
151 A 5 5 1.06 31 0.161
152 A 5 5 1.04 31 0.161
153 A 5 5 1.08 31 0.161
154 A 3 3 1.00 29 0.103
155 A 2 2 1.00 22 0.091
156 A 5 5 1.17 29 0.172
157 A 5 5 1.10 31 0.161
158 A 5 5 1.12 31 0.161
159 A 5 5 1.05 31 0.161
160 A 5 5 1.08 31 0.161
161 A 5 5 1.04 31 0.161
162 A 5 5 1.06 31 0.161
163 A 5 5 1.08 31 0.161
164 A 7 6 0.87 31 0.194
165 A 5 5 1.07 31 0.161
166 A 5 5 1.04 31 0.161
167 A 5 5 1.12 29 0.172
168 A 2 2 1.00 22 0.091
169 A 5 5 1.09 29 0.172
170 A 7 6 0.75 31 0.194
171 A 5 5 1.09 31 0.161
172 A 6 5 1.00 31 0.161
173 A 5 5 1.06 31 0.161
174 A 7 6 0.79 31 0.194
175 A 7 6 0.85 31 0.194
176 A 5 5 1.11 31 0.161
177 A 7 7 1.07 31 0.226
178 A 5 5 1.11 31 0.161
179 A 5 4 1.00 29 0.138
180 A 2 2 1.00 22 0.091
181 A 7 6 0.80 29 0.207
182 A 5 5 1.10 31 0.161
183 A 7 6 0.76 31 0.194
184 A 5 5 1.09 31 0.161
185 A 6 5 1.00 31 0.161
186 A 5 5 1.09 31 0.161
187 A 2 2 1.00 33 0.061
188 A 6 5 1.00 7 0.714
189 A 7 6 1.00 10 0.600
190 A 5 5 1.00 10 0.500
191 A 6 6 1.00 10 0.600
192 A 7 7 1.00 10 0.700
193 A 4 4 1.00 10 0.400
194 A 8 7 1.00 10 0.700
195 A 6 5 1.00 9 0.556
196 A 8 7 1.00 12 0.583
197 A 5 5 1.00 12 0.417
198 A 6 6 1.00 12 0.500
199 A 7 7 1.00 12 0.583
200 A 4 4 1.00 12 0.333
201 A 8 7 1.15 12 0.583
202 A 8 7 1.00 20 0.350
203 A 5 5 1.00 10 0.500
204 A 8 7 1.00 10 0.700
205 A 7 7 1.00 10 0.700
206 A 6 6 1.00 10 0.600
207 A 9 8 1.00 10 0.800
208 A 4 4 1.00 10 0.400
209 A 5 5 1.00 12 0.417
210 A 9 8 1.00 12 0.667
211 A 7 7 1.00 12 0.583
212 A 6 6 1.00 12 0.500
213 A 9 8 1.15 12 0.667
214 A 4 4 1.00 12 0.333
215 A 6 5 1.00 15 0.333
216 A 5 4 0.63 22 0.182
217 A 4 3 1.00 22 0.136
218 A 6 5 0.93 22 0.227
219 A 4 3 1.00 22 0.136
220 A 5 4 1.00 22 0.182
221 A 4 3 0.46 22 0.136
222 A 6 5 1.00 17 0.294
223 A 5 4 1.43 24 0.167
224 A 4 3 1.67 24 0.125
225 A 5 4 1.18 24 0.167
226 A 4 3 1.00 24 0.125
227 A 4 3 1.40 24 0.125
228 A 4 3 1.00 24 0.125
229 A 7 6 1.00 26 0.231
230 A 9 8 1.00 26 0.308
231 A 8 7 1.32 24 0.292
232 A 1 1 1.00 17 0.059
233 A 8 7 1.00 24 0.292
234 A 8 7 1.00 26 0.269
235 A 7 6 1.00 26 0.231
236 A 12 12 1.10 28 0.429
237 A 9 9 0.98 28 0.321
238 A 16 16 1.03 26 0.615
239 A 5 5 1.00 19 0.263
240 A 15 15 1.01 26 0.577
241 A 16 16 1.00 28 0.571
242 A 19 18 1.09 28 0.643
243 A 7 6 0.87 28 0.214
244 A 9 8 1.01 28 0.286
245 A 9 8 0.99 26 0.308
246 A 8 7 0.89 19 0.368
247 A 9 8 0.93 26 0.308
248 A 9 8 1.00 28 0.286
249 A 9 8 1.00 28 0.286
250 A 10 9 0.97 28 0.321
251 A 12 11 1.05 28 0.393
252 A 8 7 1.00 26 0.269
253 A 11 10 1.03 19 0.526
254 A 7 6 1.07 26 0.231
255 A 10 9 1.07 28 0.321
256 A 8 7 1.06 28 0.250
257 A 6 6 1.00 28 0.214
258 A 5 5 1.00 28 0.179
259 A 6 6 1.00 26 0.231
260 A 5 5 1.00 19 0.263
261 A 13 12 1.18 26 0.462
262 A 12 11 1.20 28 0.393
263 A 6 6 1.00 28 0.214
264 A 10 9 1.09 28 0.321
265 A 11 10 1.10 28 0.357
266 A 10 9 1.12 26 0.346
267 A 9 8 1.12 19 0.421
268 A 10 9 1.08 26 0.346
269 A 12 11 1.08 28 0.393
270 A 7 6 0.93 28 0.214
271 A 8 7 1.00 28 0.250
272 A 15 15 1.01 28 0.536
273 A 7 6 1.00 26 0.231
274 A 7 6 1.00 28 0.214
275 A 8 7 1.00 16 0.438
276 A 11 10 1.00 18 0.556
277 A 13 12 1.01 18 0.667
278 A 11 10 0.98 18 0.556
279 A 14 13 1.03 20 0.650
280 A 19 18 0.93 20 0.900
281 A 13 12 1.00 18 0.667
282 A 19 18 0.93 20 0.900
283 A 22 21 0.96 20 1.050
284 A 9 9 1.67 16 0.562
285 B 19 18 2.08 18 1.000
286 B 27 26 2.29 18 1.444
287 B 19 18 2.09 18 1.000
288 B 22 21 2.56 20 1.050
289 F 0 0 N/A 0.000 N/A
290 B 26 25 2.29 18 1.389
291 F 0 0 N/A 0.000 N/A
292 F 0 0 N/A 0.000 N/A
293 A 3 3 1.00 14 0.214
294 A 3 3 1.00 14 0.214

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