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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 [51] had the largest ratio of [1.30000000000000004]

# 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 6 0.333
2 A 3 3 1.00 8 0.375
3 A 4 3 1.00 8 0.375
4 A 5 5 1.11 8 0.625
5 A 4 3 0.93 8 0.375
6 A 7 7 1.15 8 0.875
7 A 4 3 0.85 8 0.375
8 A 9 9 1.17 8 1.125
9 A 6 6 1.08 10 0.600
10 A 4 4 1.00 10 0.400
11 A 4 4 1.00 10 0.400
12 A 2 2 1.00 10 0.200
13 A 2 2 1.00 10 0.200
14 A 4 4 1.00 10 0.400
15 A 4 4 1.00 10 0.400
16 A 6 6 1.02 10 0.600
17 A 8 8 1.06 12 0.667
18 A 6 6 1.00 12 0.500
19 A 6 6 1.00 12 0.500
20 A 4 4 1.00 12 0.333
21 A 4 4 1.00 12 0.333
22 A 6 6 1.00 12 0.500
23 A 6 6 1.00 12 0.500
24 A 8 8 1.04 12 0.667
25 A 2 2 1.00 10 0.200
26 A 2 2 1.00 10 0.200
27 A 2 2 1.00 10 0.200
28 A 2 2 1.00 10 0.200
29 A 2 2 1.00 10 0.200
30 A 2 2 1.00 10 0.200
31 A 2 2 1.00 12 0.167
32 A 2 2 1.00 12 0.167
33 A 2 2 1.00 12 0.167
34 A 2 2 1.00 12 0.167
35 A 2 2 1.00 12 0.167
36 A 2 2 1.00 12 0.167
37 A 2 2 1.00 8 0.250
38 A 2 2 1.00 10 0.200
39 A 8 8 1.06 10 0.800
40 A 6 6 1.00 10 0.600
41 A 4 4 1.00 10 0.400
42 A 4 4 1.00 10 0.400
43 A 6 6 1.00 10 0.600
44 A 8 8 1.13 10 0.800
45 A 12 12 0.81 10 1.200
46 A 8 8 0.88 10 0.800
47 A 6 6 0.93 10 0.600
48 A 6 6 0.88 10 0.600
49 A 8 8 0.86 10 0.800
50 A 12 12 0.78 10 1.200
51 A 13 13 0.70 10 1.300
52 A 9 9 0.77 10 0.900
53 A 5 5 0.81 10 0.500
54 A 6 5 1.00 10 0.500
55 A 6 5 0.60 10 0.500
56 A 6 5 0.48 10 0.500
57 A 4 4 1.00 12 0.333
58 A 4 4 1.00 14 0.286
59 A 4 4 1.00 14 0.286
60 A 4 4 1.19 14 0.286
61 A 4 4 1.00 14 0.286
62 A 4 4 1.00 14 0.286
63 A 4 4 1.00 14 0.286
64 A 4 4 1.00 14 0.286
65 A 4 4 1.00 14 0.286
66 A 11 11 1.15 21 0.524
67 A 9 9 1.11 21 0.429
68 A 9 9 1.14 21 0.429
69 A 7 7 1.07 21 0.333
70 A 7 7 1.10 19 0.368
71 A 4 4 1.00 12 0.333
72 A 5 5 1.00 19 0.263
73 A 7 7 1.14 21 0.333
74 A 7 7 1.09 21 0.333
75 A 9 9 1.14 21 0.429
76 A 9 9 1.14 21 0.429
77 A 11 11 1.17 21 0.524
78 A 11 11 1.13 21 0.524
79 A 9 9 1.14 21 0.429
80 A 9 9 1.10 21 0.429
81 A 7 7 1.10 19 0.368
82 A 6 6 1.00 12 0.500
83 A 5 5 1.00 19 0.263
84 A 5 5 1.00 21 0.238
85 A 7 7 1.09 21 0.333
86 A 7 7 1.06 21 0.333
87 A 9 9 1.10 21 0.429
88 A 9 9 1.12 21 0.429
89 A 11 11 1.14 21 0.524
90 A 11 11 1.14 21 0.524
91 A 9 9 1.10 21 0.429
92 A 9 9 1.11 19 0.474
93 A 6 6 1.00 12 0.500
94 A 7 7 1.00 19 0.368
95 A 5 5 1.00 21 0.238
96 A 5 5 1.00 21 0.238
97 A 7 7 1.06 21 0.333
98 A 7 7 1.06 21 0.333
99 A 9 9 1.08 21 0.429
100 A 9 9 1.12 21 0.429
101 A 11 11 1.12 21 0.524
102 A 8 8 1.06 12 0.667
103 A 11 11 1.14 21 0.524
104 A 9 9 1.08 21 0.429
105 A 9 9 1.11 21 0.429
106 A 7 7 1.03 21 0.333
107 A 7 7 1.07 21 0.333
108 A 5 5 1.00 19 0.263
109 A 4 4 1.00 12 0.333
110 A 7 7 1.08 19 0.368
111 A 7 7 1.13 21 0.333
112 A 9 9 1.11 21 0.429
113 A 9 9 1.18 21 0.429
114 A 11 11 1.15 21 0.524
115 A 11 11 1.11 21 0.524
116 A 9 9 1.08 21 0.429
117 A 9 9 1.08 21 0.429
118 A 7 7 1.03 21 0.333
119 A 7 7 1.03 21 0.333
120 A 5 5 1.00 21 0.238
121 A 5 5 1.00 19 0.263
122 A 6 6 1.00 12 0.500
123 A 7 7 1.07 19 0.368
124 A 9 9 1.10 21 0.429
125 A 9 9 1.15 21 0.429
126 A 11 11 1.14 21 0.524
127 A 11 11 1.11 21 0.524
128 A 9 9 1.08 21 0.429
129 A 9 9 1.08 21 0.429
130 A 7 7 1.03 21 0.333
131 A 7 7 1.03 21 0.333
132 A 5 5 1.00 21 0.238
133 A 5 5 1.00 21 0.238
134 A 7 7 1.06 19 0.368
135 A 6 6 1.00 12 0.500
136 A 9 9 1.09 19 0.474
137 A 9 9 1.14 21 0.429
138 A 11 11 1.15 21 0.524
139 A 8 8 1.04 12 0.667
140 A 6 6 0.76 23 0.261
141 A 5 4 0.69 23 0.174
142 A 4 4 0.76 23 0.174
143 A 3 3 1.00 23 0.130
144 A 2 2 1.00 23 0.087
145 A 3 3 1.00 23 0.130
146 A 5 4 1.00 23 0.174
147 A 5 5 0.79 23 0.217
148 A 5 4 0.69 23 0.174
149 A 7 7 0.78 23 0.304
150 A 6 6 0.74 23 0.261
151 A 5 4 0.68 23 0.174
152 A 4 4 0.75 23 0.174
153 A 3 3 1.00 23 0.130
154 A 2 2 1.00 23 0.087
155 A 3 3 1.00 23 0.130
156 A 5 4 1.00 23 0.174
157 A 5 5 0.78 23 0.217
158 A 5 4 0.68 23 0.174
159 A 7 7 0.76 23 0.304
160 A 5 4 0.54 23 0.174
161 A 6 6 0.72 23 0.261
162 A 5 4 0.67 23 0.174
163 A 4 4 0.74 23 0.174
164 A 3 3 1.00 23 0.130
165 A 2 2 1.00 23 0.087
166 A 3 3 1.00 23 0.130
167 A 5 4 1.00 23 0.174
168 A 5 5 0.77 23 0.217
169 A 5 4 0.67 23 0.174
170 A 7 7 0.74 23 0.304
171 A 5 4 0.56 23 0.174
172 A 6 6 0.76 23 0.261
173 A 5 4 0.69 23 0.174
174 A 4 4 0.76 23 0.174
175 A 3 3 1.00 23 0.130
176 A 2 2 1.00 23 0.087
177 A 3 3 1.00 23 0.130
178 A 5 4 1.00 23 0.174
179 A 5 5 0.79 23 0.217
180 A 5 4 0.69 23 0.174
181 A 7 7 0.78 23 0.304
182 A 6 6 0.72 23 0.261
183 A 5 4 0.67 23 0.174
184 A 4 4 0.74 23 0.174
185 A 3 3 1.00 23 0.130
186 A 2 2 1.00 23 0.087
187 A 3 3 1.00 23 0.130
188 A 5 4 1.00 23 0.174
189 A 5 5 0.77 23 0.217
190 A 5 4 0.67 23 0.174
191 A 7 7 0.74 23 0.304
192 A 6 6 0.72 23 0.261
193 A 5 4 0.67 23 0.174
194 A 4 4 0.74 23 0.174
195 A 3 3 1.00 23 0.130
196 A 2 2 1.00 23 0.087
197 A 3 3 1.00 23 0.130
198 A 5 4 1.00 23 0.174
199 A 5 5 0.77 23 0.217
200 A 5 4 0.67 23 0.174
201 A 7 7 0.74 23 0.304
202 A 3 3 1.00 21 0.143
203 A 3 3 1.00 21 0.143
204 A 3 3 1.00 19 0.158
205 A 2 2 1.00 12 0.167
206 A 3 3 1.00 19 0.158
207 A 3 3 1.00 21 0.143
208 A 3 3 1.00 21 0.143
209 A 3 3 1.00 21 0.143
210 A 3 3 1.00 21 0.143
211 A 3 3 1.00 19 0.158
212 A 2 2 1.00 12 0.167
213 A 3 3 1.00 19 0.158
214 A 3 3 1.00 21 0.143
215 A 3 3 1.00 21 0.143
216 A 3 3 1.00 21 0.143
217 A 3 3 1.00 21 0.143
218 A 3 3 1.00 19 0.158
219 A 2 2 1.00 12 0.167
220 A 3 3 1.00 19 0.158
221 A 3 3 1.00 21 0.143
222 A 3 3 1.00 21 0.143
223 A 3 3 1.00 21 0.143
224 A 3 3 1.00 21 0.143
225 A 3 3 1.00 19 0.158
226 A 2 2 1.00 12 0.167
227 A 3 3 1.00 19 0.158
228 A 3 3 1.00 21 0.143
229 A 3 3 1.00 21 0.143
230 A 3 3 1.00 21 0.143
231 A 3 3 1.00 21 0.143
232 A 3 3 1.00 19 0.158
233 A 2 2 1.00 12 0.167
234 A 3 3 1.00 19 0.158
235 A 3 3 1.00 21 0.143
236 A 3 3 1.00 21 0.143
237 A 3 3 1.00 21 0.143
238 A 3 3 1.00 21 0.143
239 A 3 3 1.00 19 0.158
240 A 2 2 1.00 12 0.167
241 A 3 3 1.00 19 0.158
242 A 3 3 1.00 21 0.143
243 A 3 3 1.00 21 0.143
244 A 3 3 1.00 21 0.143
245 A 3 3 1.00 19 0.158
246 A 3 3 1.00 17 0.176
247 A 2 2 1.00 10 0.200
248 A 3 3 1.00 17 0.176
249 A 3 3 1.00 19 0.158
250 A 3 3 1.00 19 0.158
251 A 3 3 1.00 19 0.158
252 A 3 3 1.00 21 0.143
253 A 3 3 1.00 21 0.143
254 A 3 3 1.00 21 0.143
255 A 3 3 1.00 21 0.143
256 A 3 3 1.00 21 0.143
257 A 3 3 1.00 21 0.143
258 A 3 3 1.00 21 0.143
259 A 3 3 1.00 21 0.143
260 A 4 4 1.00 21 0.190
261 A 4 3 1.00 17 0.176
262 A 4 3 1.00 17 0.176
263 A 6 6 1.00 19 0.316
264 A 6 6 1.00 19 0.316
265 A 6 5 1.00 11 0.455
266 A 6 5 0.97 19 0.263
267 A 6 5 0.97 19 0.263
268 A 8 8 1.05 19 0.421
269 A 8 8 1.05 19 0.421
270 A 4 3 1.00 9 0.333
271 A 8 7 1.12 17 0.412
272 A 8 7 1.16 17 0.412
273 A 6 6 1.00 19 0.316
274 A 6 6 1.00 19 0.316
275 A 8 7 1.11 19 0.368
276 A 8 7 1.11 19 0.368
277 A 8 8 0.99 19 0.421
278 A 8 8 1.00 19 0.421
279 A 4 4 1.00 21 0.190
280 A 4 4 1.00 21 0.190
281 A 4 4 1.00 21 0.190
282 A 4 4 1.00 21 0.190
283 A 4 4 1.00 21 0.190
284 A 4 4 1.00 17 0.235
285 A 4 4 1.00 19 0.211
286 A 4 4 1.00 19 0.211
287 A 4 4 1.00 21 0.190
288 A 4 4 0.97 23 0.174
289 A 4 4 1.00 23 0.174
290 A 4 4 1.00 23 0.174
291 A 4 4 1.00 23 0.174
292 A 4 4 1.00 23 0.174
293 A 4 4 1.00 23 0.174
294 A 4 4 1.00 23 0.174

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