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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 [24] had the largest ratio of [.550000000000000044]

# 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 18 0.111
2 A 2 2 1.00 18 0.111
3 A 2 2 1.00 15 0.133
4 A 2 2 1.00 18 0.111
5 A 2 2 1.00 18 0.111
6 A 2 2 1.00 20 0.100
7 A 2 2 1.00 20 0.100
8 A 2 2 1.00 17 0.118
9 A 2 2 1.00 20 0.100
10 A 2 2 1.00 20 0.100
11 A 11 10 1.30 20 0.500
12 A 10 9 1.33 20 0.450
13 A 10 9 1.34 17 0.529
14 A 10 9 1.34 20 0.450
15 A 10 9 1.33 20 0.450
16 A 11 10 1.30 20 0.500
17 A 3 3 1.19 20 0.150
18 A 11 10 1.34 20 0.500
19 A 11 10 1.38 20 0.500
20 A 10 9 1.32 20 0.450
21 A 10 9 1.33 17 0.529
22 A 11 10 1.35 20 0.500
23 A 11 10 1.36 20 0.500
24 A 12 11 1.31 20 0.550
25 A 4 4 0.99 22 0.182
26 A 3 3 0.99 22 0.136
27 A 2 2 1.00 19 0.105
28 A 2 2 1.00 22 0.091
29 A 3 3 0.99 22 0.136
30 A 4 4 0.99 22 0.182
31 A 6 6 0.96 22 0.273
32 A 5 5 0.95 22 0.227
33 A 5 5 0.96 22 0.227
34 A 6 6 0.93 22 0.273
35 A 4 4 1.00 22 0.182
36 A 3 3 1.01 22 0.136
37 A 2 2 1.00 19 0.105
38 A 3 3 0.99 22 0.136
39 A 4 4 0.99 22 0.182
40 A 7 7 0.96 22 0.318
41 A 6 6 0.96 22 0.273
42 A 5 5 0.96 22 0.227
43 A 6 6 0.94 22 0.273
44 A 7 7 0.94 22 0.318
45 A 5 5 0.99 22 0.227
46 A 4 4 0.99 22 0.182
47 A 3 3 1.03 22 0.136
48 A 3 3 1.00 19 0.158
49 A 4 4 0.98 22 0.182
50 A 5 5 0.99 22 0.227
51 A 7 7 0.96 22 0.318
52 A 6 6 0.97 22 0.273
53 A 6 6 0.97 22 0.273
54 A 7 7 0.94 22 0.318
55 A 8 8 0.94 22 0.364
56 A 6 6 0.98 22 0.273
57 A 5 5 1.00 22 0.227
58 A 4 4 1.03 22 0.182
59 A 4 4 1.02 22 0.182
60 A 4 4 0.98 19 0.211
61 A 5 5 0.99 22 0.227
62 A 6 6 0.98 22 0.273
63 A 9 9 0.96 22 0.409
64 A 8 8 0.96 22 0.364
65 A 7 7 0.96 22 0.318
66 A 7 7 0.95 22 0.318
67 A 7 7 0.94 22 0.318
68 A 8 8 0.94 22 0.364
69 A 9 9 0.94 22 0.409
70 A 4 3 1.04 22 0.136
71 A 4 3 1.05 22 0.136
72 A 4 3 1.09 22 0.136
73 A 9 8 1.08 22 0.364
74 A 9 8 0.99 22 0.364
75 A 7 6 0.98 22 0.273
76 A 6 5 0.99 19 0.263
77 A 6 5 1.01 22 0.227
78 A 2 2 1.00 22 0.091
79 A 3 3 0.99 22 0.136
80 A 4 4 0.97 22 0.182
81 A 8 7 0.97 22 0.318
82 A 7 6 0.97 22 0.273
83 A 7 6 0.95 22 0.273
84 A 7 6 0.93 22 0.273
85 A 7 6 0.96 22 0.273
86 A 6 5 0.96 20 0.250
87 A 6 5 0.97 22 0.227
88 A 7 6 0.96 22 0.273
89 A 4 3 1.05 22 0.136
90 A 4 3 1.06 22 0.136
91 A 4 3 1.12 22 0.136
92 A 7 6 1.16 22 0.273
93 A 7 6 1.04 22 0.273
94 A 6 5 0.99 22 0.227
95 A 6 5 1.01 22 0.227
96 A 2 2 1.00 22 0.091
97 A 3 3 0.99 22 0.136
98 A 4 4 0.97 22 0.182
99 A 6 5 0.99 22 0.227
100 A 5 4 1.00 20 0.200
101 A 5 4 1.00 22 0.182
102 A 6 5 0.96 22 0.227
103 A 7 6 0.99 22 0.273
104 A 6 5 1.00 19 0.263
105 A 6 5 1.00 22 0.227
106 A 7 6 0.99 22 0.273
107 A 4 3 1.04 22 0.136
108 A 4 3 1.07 22 0.136
109 A 4 3 1.09 22 0.136
110 A 9 8 1.12 22 0.364
111 A 10 9 0.99 22 0.409
112 A 7 6 0.94 22 0.273
113 A 6 5 1.05 19 0.263
114 A 2 2 1.00 22 0.091
115 A 3 3 0.98 22 0.136
116 A 4 4 0.97 22 0.182
117 A 7 6 0.99 22 0.273
118 A 6 5 1.00 22 0.227
119 A 6 5 1.00 22 0.227
120 A 7 6 0.96 22 0.273
121 A 6 5 0.96 22 0.227
122 A 5 4 1.00 20 0.200
123 A 5 4 1.00 22 0.182
124 A 6 5 0.96 22 0.227
125 A 4 3 1.04 22 0.136
126 A 4 3 1.07 22 0.136
127 A 4 3 1.12 22 0.136
128 A 7 6 1.16 22 0.273
129 A 8 7 1.03 22 0.318
130 A 7 6 1.10 22 0.273
131 A 6 5 1.04 22 0.227
132 A 2 2 1.00 22 0.091
133 A 3 3 0.98 22 0.136
134 A 4 4 0.97 22 0.182
135 A 7 6 1.08 22 0.273
136 A 6 5 1.11 22 0.227
137 A 5 4 1.00 20 0.200
138 A 6 5 0.99 22 0.227
139 A 7 6 0.96 22 0.273
140 A 8 7 1.08 22 0.318
141 A 7 6 1.12 22 0.273
142 A 6 5 1.00 19 0.263
143 A 7 6 0.98 22 0.273
144 A 8 7 0.97 22 0.318
145 A 4 3 1.05 22 0.136
146 A 4 3 1.06 22 0.136
147 A 4 3 1.09 22 0.136
148 A 10 9 1.14 22 0.409
149 A 11 10 0.97 22 0.455
150 A 8 7 1.07 22 0.318
151 A 7 6 1.07 22 0.273
152 A 2 2 0.77 19 0.105
153 A 3 3 0.99 22 0.136
154 A 4 4 0.96 22 0.182
155 A 8 7 1.09 22 0.318
156 A 7 6 1.11 22 0.273
157 A 6 5 1.00 22 0.227
158 A 7 6 0.98 22 0.273
159 A 8 7 0.95 22 0.318
160 A 7 6 1.05 22 0.273
161 A 6 5 1.10 22 0.227
162 A 5 4 1.00 20 0.200
163 A 6 5 0.99 22 0.227
164 A 7 6 0.96 22 0.273
165 A 9 8 1.05 22 0.364
166 A 8 7 1.09 22 0.318
167 A 2 2 1.00 22 0.091
168 A 3 3 0.97 19 0.158
169 A 4 4 0.96 22 0.182
170 A 5 5 0.93 22 0.227
171 A 9 8 1.07 22 0.364
172 A 8 7 1.08 22 0.318
173 A 7 6 1.02 22 0.273
174 A 7 6 1.00 22 0.273
175 A 8 7 0.97 22 0.318
176 A 9 8 0.96 22 0.364
177 A 10 9 1.03 22 0.409
178 A 9 8 1.10 22 0.364
179 A 2 2 1.00 22 0.091
180 A 3 3 0.97 22 0.136
181 A 4 4 0.95 19 0.211
182 A 5 5 0.98 22 0.227
183 A 6 6 0.94 22 0.273
184 A 10 9 1.05 22 0.409
185 A 9 8 1.06 22 0.364
186 A 8 7 1.01 22 0.318
187 A 8 7 0.99 22 0.318
188 A 8 7 0.97 22 0.318
189 A 9 8 0.97 22 0.364
190 A 10 9 0.96 22 0.409
191 A 3 3 1.02 22 0.136
192 A 4 3 1.09 26 0.115
193 A 1 1 1.00 34 0.029
194 A 4 3 0.97 22 0.136
195 A 4 3 0.94 22 0.136
196 A 4 3 0.98 22 0.136
197 A 4 3 0.98 22 0.136
198 A 4 3 1.02 22 0.136
199 A 4 3 0.99 22 0.136
200 A 7 6 1.18 22 0.273
201 A 5 4 1.08 22 0.182
202 A 4 3 0.99 22 0.136
203 A 4 3 0.99 20 0.150
204 A 6 5 1.09 22 0.227
205 A 7 6 1.19 22 0.273
206 A 11 10 1.34 22 0.455
207 A 10 9 1.30 22 0.409
208 A 10 9 1.30 22 0.409
209 A 10 9 1.30 22 0.409
210 A 10 9 1.30 19 0.474
211 A 4 4 1.41 22 0.182
212 A 12 11 1.34 22 0.500
213 A 5 5 1.46 22 0.227
214 A 4 4 1.42 22 0.182
215 A 2 2 1.28 19 0.105
216 A 4 4 1.43 22 0.182
217 A 4 4 1.45 22 0.182
218 A 4 4 1.43 22 0.182
219 A 4 3 1.00 24 0.125
220 A 6 5 1.05 24 0.208
221 A 5 4 1.00 24 0.167
222 A 5 4 1.00 24 0.167
223 A 7 6 1.05 24 0.250
224 A 8 7 1.07 24 0.292
225 A 7 6 0.98 22 0.273
226 A 7 6 1.00 24 0.250
227 A 8 7 1.07 24 0.292
228 A 9 8 1.09 24 0.333
229 A 9 9 1.49 24 0.375
230 A 8 8 1.29 21 0.381
231 A 10 10 1.47 24 0.417
232 A 3 3 1.25 24 0.125
233 A 11 11 1.39 24 0.458
234 A 4 4 1.26 24 0.167
235 A 4 3 1.00 24 0.125
236 A 5 4 1.00 24 0.167
237 A 4 3 1.00 24 0.125
238 A 5 4 1.00 24 0.167
239 A 7 6 1.09 24 0.250
240 A 8 7 1.09 24 0.292
241 A 7 6 0.99 24 0.250
242 A 4 3 1.00 22 0.136
243 A 7 6 1.00 24 0.250
244 A 8 7 1.10 24 0.292
245 A 9 9 1.52 24 0.375
246 A 8 8 1.53 24 0.333
247 A 6 6 1.38 21 0.286
248 A 10 10 1.49 24 0.417
249 A 11 11 1.35 24 0.458
250 A 6 6 1.32 24 0.250
251 A 4 4 1.20 24 0.167
252 A 7 6 1.18 24 0.250
253 A 7 6 1.17 24 0.250
254 A 5 4 0.99 24 0.167
255 A 5 4 0.99 24 0.167
256 A 7 6 1.17 24 0.250
257 A 8 7 1.15 24 0.292
258 A 10 9 1.12 24 0.375
259 A 8 7 1.18 24 0.292
260 A 6 5 1.04 24 0.208
261 A 5 4 1.04 22 0.182
262 A 8 7 1.05 24 0.292
263 A 9 8 1.02 24 0.333
264 A 12 12 1.36 24 0.500
265 A 11 11 1.41 24 0.458
266 A 9 9 1.43 24 0.375
267 A 9 9 1.64 24 0.375
268 A 10 10 1.41 21 0.476
269 A 11 11 1.38 24 0.458
270 A 12 12 1.34 24 0.500
271 A 3 3 0.94 24 0.125
272 A 4 4 0.92 24 0.167
273 A 5 5 0.92 24 0.208
274 C 7 6 3.57 20 0.300
275 A 5 4 1.00 28 0.143
276 A 5 4 1.00 28 0.143
277 A 5 4 1.00 28 0.143
278 A 5 4 1.00 28 0.143
279 A 4 4 1.04 26 0.154
280 A 3 3 1.02 24 0.125
281 A 2 2 1.00 17 0.118
282 A 2 2 1.00 26 0.077
283 A 2 2 1.00 26 0.077
284 A 2 2 1.00 26 0.077
285 A 5 5 0.98 26 0.192
286 A 3 3 1.12 24 0.125
287 A 2 2 1.00 17 0.118
288 A 2 2 1.00 26 0.077
289 A 2 2 1.00 26 0.077
290 A 2 2 1.00 26 0.077
291 A 6 6 1.17 24 0.250
292 A 4 4 1.03 24 0.167
293 A 3 3 1.02 22 0.136
294 A 2 2 1.00 15 0.133
295 A 2 2 1.00 24 0.083
296 A 2 2 1.00 24 0.083
297 A 3 3 1.00 24 0.125
298 A 1 1 1.00 22 0.045
299 A 3 3 1.00 24 0.125

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