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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 [340] had the largest ratio of [.666667000000000010]

# 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 17 0.118
2 A 2 2 1.00 17 0.118
3 A 2 2 1.00 17 0.118
4 A 2 2 1.00 15 0.133
5 A 2 2 1.00 17 0.118
6 A 2 2 1.00 17 0.118
7 A 3 3 1.00 17 0.176
8 A 2 2 1.00 19 0.105
9 A 2 2 1.00 19 0.105
10 A 2 2 1.00 17 0.118
11 A 2 2 1.00 19 0.105
12 A 2 2 1.00 19 0.105
13 A 3 3 1.11 19 0.158
14 A 2 2 1.00 19 0.105
15 A 2 2 1.00 19 0.105
16 A 2 2 1.00 17 0.118
17 A 2 2 1.00 19 0.105
18 A 2 2 1.00 19 0.105
19 A 2 2 1.00 19 0.105
20 A 2 2 1.00 19 0.105
21 A 2 2 1.00 19 0.105
22 A 2 2 1.00 19 0.105
23 A 2 2 1.00 17 0.118
24 A 2 2 1.00 19 0.105
25 A 3 3 1.17 19 0.158
26 A 4 4 1.24 19 0.211
27 A 2 2 1.00 19 0.105
28 A 2 2 1.00 19 0.105
29 A 2 2 1.00 19 0.105
30 A 2 2 1.00 19 0.105
31 A 2 2 1.00 17 0.118
32 A 4 4 1.16 19 0.211
33 A 6 6 1.14 19 0.316
34 A 7 7 1.20 19 0.368
35 A 2 2 1.00 19 0.105
36 A 2 2 1.00 19 0.105
37 A 2 2 1.00 19 0.105
38 A 3 3 1.11 19 0.158
39 A 3 3 1.00 17 0.176
40 A 6 6 1.22 19 0.316
41 A 8 8 1.19 19 0.421
42 A 10 10 1.18 19 0.526
43 A 3 3 1.00 15 0.200
44 A 5 5 1.11 15 0.333
45 A 7 6 0.93 21 0.286
46 A 6 5 0.94 21 0.238
47 A 5 4 0.95 19 0.211
48 A 4 3 1.00 11 0.273
49 A 6 5 1.00 21 0.238
50 A 4 3 1.00 21 0.143
51 A 5 4 0.99 21 0.190
52 A 8 7 1.12 21 0.333
53 A 8 7 0.85 21 0.333
54 A 7 6 0.83 21 0.286
55 A 6 5 0.89 19 0.263
56 A 5 4 1.05 11 0.364
57 A 8 7 1.05 21 0.333
58 A 7 6 1.08 21 0.286
59 A 5 4 1.05 21 0.190
60 A 6 5 0.93 21 0.238
61 A 9 8 1.10 21 0.381
62 A 9 8 0.74 21 0.381
63 A 8 7 0.77 21 0.333
64 A 7 6 0.85 19 0.316
65 A 6 5 1.07 11 0.455
66 A 10 9 1.08 21 0.429
67 A 9 8 1.04 21 0.381
68 A 9 8 1.12 21 0.381
69 A 6 5 1.08 21 0.238
70 A 7 6 0.89 21 0.286
71 A 5 4 1.00 19 0.211
72 A 6 5 1.00 17 0.294
73 A 6 5 1.00 21 0.238
74 A 6 5 1.09 21 0.238
75 A 5 4 1.07 21 0.190
76 A 4 3 1.00 19 0.158
77 A 3 2 1.00 11 0.182
78 A 3 2 1.00 21 0.095
79 A 4 3 1.00 21 0.143
80 A 6 5 1.11 21 0.238
81 A 8 7 1.05 21 0.333
82 A 7 6 1.05 21 0.286
83 A 6 5 1.22 21 0.238
84 A 4 3 1.00 19 0.158
85 A 1 1 1.00 11 0.091
86 A 4 3 1.00 21 0.143
87 A 6 5 1.07 21 0.238
88 A 8 7 1.11 21 0.333
89 A 8 7 1.07 21 0.333
90 A 7 6 1.09 21 0.286
91 A 5 4 1.10 21 0.190
92 A 2 2 1.00 19 0.105
93 A 2 2 1.00 11 0.182
94 A 7 6 1.14 21 0.286
95 A 8 7 1.13 21 0.333
96 A 11 10 1.13 21 0.476
97 A 5 5 0.83 21 0.238
98 A 4 4 0.86 21 0.190
99 A 3 3 0.97 19 0.158
100 A 2 2 1.00 11 0.182
101 A 4 3 1.00 21 0.143
102 A 4 3 1.00 21 0.143
103 A 5 4 0.99 21 0.190
104 A 6 5 0.93 21 0.238
105 A 2 2 1.00 26 0.077
106 A 3 2 1.00 19 0.105
107 A 3 2 1.00 21 0.095
108 A 2 2 1.00 15 0.133
109 A 11 10 1.08 24 0.417
110 A 9 8 1.08 24 0.333
111 A 7 6 1.08 22 0.273
112 A 7 6 1.09 24 0.250
113 A 7 6 1.08 24 0.250
114 A 11 10 1.07 24 0.417
115 A 13 12 1.08 24 0.500
116 A 12 11 1.09 24 0.458
117 A 10 9 1.09 24 0.375
118 A 8 7 1.09 22 0.318
119 A 9 8 1.08 24 0.333
120 A 9 8 1.08 24 0.333
121 A 11 10 1.08 24 0.417
122 A 12 11 1.08 24 0.458
123 A 10 9 1.08 24 0.375
124 A 8 7 1.08 24 0.292
125 A 6 5 1.08 22 0.227
126 A 1 1 1.00 24 0.042
127 A 9 8 1.07 24 0.333
128 A 11 10 1.08 24 0.417
129 A 10 9 1.08 24 0.375
130 A 8 7 1.08 24 0.292
131 A 6 5 1.09 22 0.227
132 A 9 8 1.07 24 0.333
133 A 11 10 1.07 24 0.417
134 A 13 12 1.08 24 0.500
135 A 12 11 1.08 24 0.458
136 A 8 7 1.09 24 0.292
137 A 3 3 1.00 24 0.125
138 A 7 6 1.09 22 0.273
139 A 11 10 1.08 24 0.417
140 A 13 12 1.09 24 0.500
141 A 1 1 1.00 26 0.038
142 A 1 1 1.00 24 0.042
143 A 1 1 1.00 23 0.043
144 A 1 1 1.00 24 0.042
145 A 1 1 1.00 22 0.045
146 A 1 1 1.00 19 0.053
147 A 1 1 1.00 19 0.053
148 A 1 1 1.00 24 0.042
149 A 1 1 1.00 22 0.045
150 A 1 1 1.00 27 0.037
151 A 1 1 1.00 28 0.036
152 A 1 1 1.00 29 0.034
153 A 1 1 1.00 30 0.033
154 A 1 1 1.00 26 0.038
155 A 1 1 1.00 26 0.038
156 A 1 1 1.00 23 0.043
157 A 1 1 1.00 23 0.043
158 A 1 1 1.00 23 0.043
159 A 1 1 1.00 23 0.043
160 A 1 1 1.00 17 0.059
161 A 1 1 1.00 21 0.048
162 A 1 1 1.00 21 0.048
163 A 3 3 0.73 29 0.103
164 A 3 3 0.78 29 0.103
165 A 3 3 0.76 29 0.103
166 A 8 8 0.95 23 0.348
167 A 6 6 0.97 23 0.261
168 A 4 4 1.01 23 0.174
169 A 1 1 1.00 23 0.043
170 A 5 5 1.01 23 0.217
171 A 7 7 1.07 23 0.304
172 A 9 9 0.96 23 0.391
173 A 7 7 0.93 23 0.304
174 A 5 5 0.97 23 0.217
175 A 6 6 0.97 23 0.261
176 A 4 4 1.02 23 0.174
177 A 7 7 1.03 23 0.304
178 A 6 6 0.98 23 0.261
179 A 3 3 1.00 23 0.130
180 A 2 2 0.95 23 0.087
181 A 4 4 1.05 23 0.174
182 A 5 5 1.00 23 0.217
183 A 4 4 1.00 21 0.190
184 A 1 1 1.00 23 0.043
185 A 1 1 1.00 23 0.043
186 A 1 1 1.00 23 0.043
187 A 1 1 1.00 21 0.048
188 A 1 1 1.00 21 0.048
189 A 1 1 1.00 21 0.048
190 A 1 1 1.00 23 0.043
191 A 4 4 1.00 21 0.190
192 A 3 3 1.00 23 0.130
193 A 3 3 1.00 23 0.130
194 A 3 3 1.00 23 0.130
195 A 4 4 1.00 21 0.190
196 A 4 4 1.00 21 0.190
197 A 4 4 1.02 23 0.174
198 A 2 2 1.00 23 0.087
199 A 10 10 0.98 23 0.435
200 A 8 8 0.97 23 0.348
201 A 6 6 1.00 23 0.261
202 A 4 4 1.05 23 0.174
203 A 1 1 1.00 23 0.043
204 A 6 6 0.95 23 0.261
205 A 5 5 1.05 23 0.217
206 A 7 7 1.09 23 0.304
207 A 10 10 0.94 23 0.435
208 A 8 8 0.95 23 0.348
209 A 6 6 1.00 23 0.261
210 A 1 1 1.00 23 0.043
211 A 6 6 1.35 23 0.261
212 A 5 5 1.05 23 0.217
213 A 8 8 1.07 23 0.348
214 A 1 1 1.00 23 0.043
215 A 3 3 1.00 24 0.125
216 A 3 3 1.00 24 0.125
217 A 3 3 1.00 25 0.120
218 A 1 1 1.00 23 0.043
219 A 1 1 1.00 23 0.043
220 A 1 1 1.00 23 0.043
221 A 2 2 1.00 23 0.087
222 A 1 1 1.00 21 0.048
223 A 1 1 1.00 23 0.043
224 A 2 2 1.00 23 0.087
225 A 1 1 1.00 23 0.043
226 A 1 1 1.00 23 0.043
227 A 1 1 1.00 23 0.043
228 A 1 1 1.00 21 0.048
229 A 1 1 1.00 21 0.048
230 A 1 1 1.00 21 0.048
231 A 2 2 1.00 21 0.095
232 A 1 1 1.00 19 0.053
233 A 1 1 1.00 21 0.048
234 A 2 2 1.00 21 0.095
235 A 1 1 1.00 21 0.048
236 A 1 1 1.00 21 0.048
237 A 1 1 1.00 21 0.048
238 A 2 2 1.00 21 0.095
239 A 3 3 1.00 21 0.143
240 A 2 2 1.00 21 0.095
241 A 1 1 1.00 21 0.048
242 A 2 2 1.00 19 0.105
243 A 1 1 1.00 21 0.048
244 A 2 2 1.00 21 0.095
245 A 2 2 1.00 21 0.095
246 A 3 3 1.00 21 0.143
247 A 2 2 1.00 21 0.095
248 A 1 1 1.00 23 0.043
249 A 1 1 1.00 23 0.043
250 A 1 1 1.00 23 0.043
251 A 2 2 1.04 23 0.087
252 A 1 1 1.00 21 0.048
253 A 2 2 1.00 23 0.087
254 A 2 2 0.71 23 0.087
255 A 2 2 1.00 23 0.087
256 A 3 3 1.00 23 0.130
257 A 2 2 1.00 23 0.087
258 A 3 3 1.00 24 0.125
259 A 3 3 1.00 27 0.111
260 A 3 3 1.00 25 0.120
261 A 3 3 1.00 28 0.107
262 A 3 3 1.00 25 0.120
263 A 3 3 1.00 26 0.115
264 A 3 3 1.00 26 0.115
265 A 3 3 1.00 27 0.111
266 A 4 4 1.05 23 0.174
267 A 4 4 1.05 26 0.154
268 A 4 4 1.04 26 0.154
269 A 4 4 1.05 29 0.138
270 A 7 7 1.00 24 0.292
271 A 7 7 1.00 25 0.280
272 A 7 7 1.00 27 0.259
273 A 7 7 1.00 28 0.250
274 A 3 3 1.00 24 0.125
275 A 3 3 1.00 27 0.111
276 A 3 3 1.00 25 0.120
277 A 3 3 1.00 28 0.107
278 A 3 3 1.00 25 0.120
279 A 3 3 1.00 26 0.115
280 A 3 3 1.00 26 0.115
281 A 3 3 1.00 27 0.111
282 A 4 4 1.01 23 0.174
283 A 4 4 1.01 26 0.154
284 A 4 4 1.01 26 0.154
285 A 4 4 1.01 29 0.138
286 A 7 7 1.00 24 0.292
287 A 7 7 1.00 25 0.280
288 A 7 7 1.00 27 0.259
289 A 7 7 1.00 28 0.250
290 A 1 1 1.00 23 0.043
291 A 2 2 1.00 23 0.087
292 A 1 1 1.00 21 0.048
293 A 1 1 1.00 23 0.043
294 A 4 4 1.00 28 0.143
295 A 4 4 1.05 23 0.174
296 A 1 1 1.00 23 0.043
297 A 1 1 1.00 59 0.017
298 A 1 1 1.00 59 0.017
299 A 4 4 1.13 59 0.068
300 A 3 3 1.00 59 0.051
301 C 1 1 0.37 21 0.048
302 A 2 2 1.00 26 0.077
303 A 1 1 1.00 41 0.024
304 A 1 1 1.00 21 0.048
305 A 1 1 1.00 21 0.048
306 A 1 1 1.00 21 0.048
307 A 1 1 1.00 23 0.043
308 A 1 1 1.00 23 0.043
309 A 1 1 1.00 23 0.043
310 A 1 1 1.00 23 0.043
311 A 1 1 1.00 25 0.040
312 A 1 1 1.00 21 0.048
313 A 1 1 1.00 21 0.048
314 A 1 1 1.00 21 0.048
315 A 1 1 1.00 23 0.043
316 A 1 1 1.00 25 0.040
317 A 1 1 1.00 25 0.040
318 A 1 1 1.00 25 0.040
319 A 1 1 1.00 27 0.037
320 A 1 1 1.00 19 0.053
321 A 13 12 1.01 21 0.571
322 A 13 12 1.02 21 0.571
323 A 8 7 1.02 21 0.333
324 A 9 8 1.08 21 0.381
325 A 4 3 0.95 21 0.143
326 A 6 5 0.95 21 0.238
327 A 7 6 1.01 21 0.286
328 A 10 9 0.97 21 0.429
329 A 12 11 1.28 21 0.524
330 A 13 12 1.06 21 0.571
331 A 10 9 0.93 21 0.429
332 A 11 10 1.01 21 0.476
333 A 10 9 0.93 21 0.429
334 A 11 10 0.90 21 0.476
335 A 10 9 0.90 21 0.429
336 A 11 10 0.91 21 0.476
337 A 12 11 1.16 21 0.524
338 A 13 12 0.97 21 0.571
339 A 14 13 1.22 21 0.619
340 A 15 14 1.01 21 0.667
341 A 3 3 1.00 19 0.158
342 A 7 7 0.97 19 0.368
343 A 5 5 0.99 19 0.263
344 A 3 3 0.91 17 0.176
345 A 2 2 1.00 9 0.222
346 A 2 2 1.00 19 0.105
347 A 2 2 1.00 19 0.105
348 A 2 2 1.00 19 0.105
349 A 1 1 1.00 50 0.020

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