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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 [320] had the largest ratio of [1.50000000000000000]

# 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 1 1 1.00 6 0.167
2 A 2 2 1.00 8 0.250
3 A 2 1 1.00 8 0.125
4 A 3 2 1.00 8 0.250
5 A 2 1 1.00 8 0.125
6 A 4 2 1.00 8 0.250
7 A 4 3 1.00 10 0.300
8 A 3 3 1.00 10 0.300
9 A 3 3 1.00 10 0.300
10 A 2 2 1.00 10 0.200
11 A 2 2 1.00 10 0.200
12 A 3 3 1.00 10 0.300
13 A 3 3 1.00 10 0.300
14 A 4 3 1.00 10 0.300
15 A 4 3 1.00 12 0.250
16 A 3 3 1.00 12 0.250
17 A 3 3 1.00 12 0.250
18 A 2 2 1.00 12 0.167
19 A 2 2 1.00 12 0.167
20 A 3 3 1.00 12 0.250
21 A 3 3 1.00 12 0.250
22 A 4 3 1.00 12 0.250
23 A 3 2 1.00 14 0.143
24 A 2 2 1.00 14 0.143
25 A 2 2 1.00 14 0.143
26 A 1 1 1.00 14 0.071
27 A 1 1 1.00 14 0.071
28 A 2 2 1.00 14 0.143
29 A 2 2 1.00 14 0.143
30 A 3 2 1.00 14 0.143
31 A 1 1 1.00 12 0.083
32 A 1 1 1.00 12 0.083
33 A 1 1 1.00 12 0.083
34 A 1 1 1.00 12 0.083
35 A 1 1 1.00 12 0.083
36 A 1 1 1.00 12 0.083
37 A 1 1 1.00 10 0.100
38 A 1 1 1.00 12 0.083
39 A 1 1 1.00 12 0.083
40 A 6 5 1.00 13 0.385
41 A 2 2 1.00 13 0.154
42 A 3 3 1.00 13 0.231
43 A 2 2 1.00 11 0.182
44 A 3 3 1.00 11 0.273
45 A 5 5 1.00 13 0.385
46 A 6 6 1.00 13 0.462
47 A 6 5 1.00 13 0.385
48 A 3 3 1.00 13 0.231
49 A 6 6 1.00 13 0.462
50 A 3 3 1.00 13 0.231
51 A 2 2 1.00 11 0.182
52 A 4 4 1.00 11 0.364
53 A 6 6 1.00 13 0.462
54 A 7 7 1.00 13 0.538
55 A 7 6 1.00 13 0.462
56 A 1 1 1.00 14 0.071
57 A 2 2 1.00 14 0.143
58 A 3 2 1.00 14 0.143
59 A 4 2 1.00 14 0.143
60 A 1 1 1.00 14 0.071
61 A 2 2 1.00 14 0.143
62 A 3 2 1.00 14 0.143
63 A 4 2 1.00 14 0.143
64 A 3 3 1.00 16 0.188
65 A 3 3 1.00 16 0.188
66 A 3 2 1.00 17 0.118
67 A 2 2 1.00 17 0.118
68 A 1 1 1.00 17 0.059
69 A 2 2 1.00 17 0.118
70 A 3 3 1.00 17 0.176
71 A 4 3 1.00 17 0.176
72 A 7 7 1.00 13 0.538
73 A 6 6 1.00 13 0.462
74 A 6 6 1.00 13 0.462
75 A 4 4 1.00 11 0.364
76 A 5 5 1.00 11 0.454
77 A 7 7 1.00 13 0.538
78 A 7 7 1.00 13 0.538
79 A 8 7 1.00 13 0.538
80 A 7 7 1.00 13 0.538
81 A 6 6 1.00 13 0.462
82 A 5 5 1.00 13 0.385
83 A 5 5 1.00 11 0.454
84 A 6 6 1.00 11 0.546
85 A 7 7 1.00 13 0.538
86 A 8 7 1.00 13 0.538
87 A 9 7 1.00 13 0.538
88 A 4 3 1.00 14 0.214
89 A 6 5 1.00 14 0.357
90 A 7 6 1.00 14 0.429
91 A 8 6 1.00 14 0.429
92 A 1 1 1.00 14 0.071
93 A 3 3 1.00 14 0.214
94 A 4 4 1.00 14 0.286
95 A 5 4 1.00 14 0.286
96 A 4 3 1.00 12 0.250
97 A 3 3 1.00 12 0.250
98 A 2 2 1.00 12 0.167
99 A 1 1 1.00 12 0.083
100 A 2 1 1.00 10 0.100
101 A 3 3 1.00 12 0.250
102 A 5 5 1.00 12 0.417
103 A 6 6 1.00 12 0.500
104 A 7 6 1.00 12 0.500
105 A 7 7 1.00 10 0.700
106 A 6 6 1.00 10 0.600
107 A 2 2 1.00 10 0.200
108 A 2 2 1.00 10 0.200
109 A 4 4 1.00 10 0.400
110 A 7 7 1.00 10 0.700
111 A 5 5 1.00 13 0.385
112 A 4 3 1.00 20 0.150
113 A 3 3 1.00 20 0.150
114 A 2 2 1.00 20 0.100
115 A 2 2 1.00 15 0.133
116 A 2 2 1.00 15 0.133
117 A 3 3 1.00 15 0.200
118 A 4 3 1.00 15 0.200
119 A 2 2 1.00 17 0.118
120 A 2 2 1.00 17 0.118
121 A 3 3 1.00 17 0.176
122 A 4 3 1.00 17 0.176
123 A 3 3 1.00 20 0.150
124 A 3 3 1.00 20 0.150
125 A 4 4 1.00 20 0.200
126 A 8 6 1.00 17 0.353
127 A 7 6 1.00 17 0.353
128 A 6 6 1.00 17 0.353
129 A 4 4 1.00 15 0.267
130 A 5 5 1.00 15 0.333
131 A 6 5 1.00 15 0.333
132 A 7 5 1.00 15 0.333
133 A 4 4 1.00 20 0.200
134 A 2 2 1.00 20 0.100
135 A 2 2 1.00 16 0.125
136 A 2 2 1.00 13 0.154
137 A 5 5 1.00 17 0.294
138 A 6 6 1.00 17 0.353
139 A 7 6 1.00 17 0.353
140 A 4 3 1.00 10 0.300
141 A 3 3 1.00 10 0.300
142 A 2 2 1.00 10 0.200
143 A 2 2 1.00 10 0.200
144 A 3 3 1.00 10 0.300
145 A 4 3 1.00 10 0.300
146 A 7 4 1.00 10 0.400
147 A 5 4 1.00 10 0.400
148 A 4 4 1.00 10 0.400
149 A 4 4 1.00 10 0.400
150 A 5 4 1.00 10 0.400
151 A 7 4 1.00 10 0.400
152 A 7 3 1.00 10 0.300
153 A 5 3 1.00 10 0.300
154 A 3 3 1.00 10 0.300
155 A 3 3 1.00 10 0.300
156 A 3 2 1.00 10 0.200
157 A 3 2 1.00 10 0.200
158 A 5 3 1.00 13 0.231
159 A 3 2 1.00 13 0.154
160 A 4 3 1.00 13 0.231
161 A 3 2 1.00 13 0.154
162 A 3 3 1.00 13 0.231
163 A 2 1 1.00 13 0.077
164 A 2 2 1.00 13 0.154
165 A 2 2 1.00 11 0.182
166 A 4 3 1.00 11 0.273
167 A 3 3 1.00 13 0.231
168 A 4 3 1.00 13 0.231
169 A 3 2 1.00 13 0.154
170 A 4 3 1.00 13 0.231
171 A 4 4 1.00 13 0.308
172 A 2 2 1.00 13 0.154
173 A 3 3 1.00 13 0.231
174 A 3 2 1.00 13 0.154
175 A 2 2 1.00 13 0.154
176 A 2 2 1.00 11 0.182
177 A 4 3 1.00 11 0.273
178 A 4 3 1.00 13 0.231
179 A 4 3 1.00 13 0.231
180 A 4 2 1.00 13 0.154
181 A 3 2 1.00 15 0.133
182 A 1 1 1.00 15 0.067
183 A 2 2 1.00 13 0.154
184 A 3 2 1.00 15 0.133
185 A 1 1 1.00 15 0.067
186 A 2 2 1.00 13 0.154
187 A 3 2 1.00 13 0.154
188 A 7 6 1.00 13 0.462
189 A 3 2 1.00 13 0.154
190 A 6 6 1.00 13 0.462
191 A 3 2 1.00 13 0.154
192 A 5 5 1.00 13 0.385
193 A 2 2 1.00 11 0.182
194 A 6 6 1.00 11 0.546
195 A 5 5 1.00 13 0.385
196 A 7 6 1.00 13 0.462
197 A 6 6 1.00 13 0.462
198 A 8 7 1.00 13 0.538
199 A 7 6 1.00 13 0.462
200 A 6 6 1.00 13 0.462
201 A 3 2 1.00 13 0.154
202 A 5 5 1.00 13 0.385
203 A 2 2 1.00 11 0.182
204 A 7 6 1.00 11 0.546
205 A 6 6 1.00 13 0.462
206 A 7 6 1.00 13 0.462
207 A 7 6 1.00 13 0.462
208 A 6 5 1.00 13 0.385
209 A 6 5 1.00 13 0.385
210 A 5 4 1.00 13 0.308
211 A 5 5 1.00 11 0.454
212 A 4 4 1.00 11 0.364
213 A 4 4 1.00 13 0.308
214 A 5 4 1.00 13 0.308
215 A 5 5 1.00 13 0.385
216 A 5 4 1.00 13 0.308
217 A 6 5 1.00 13 0.385
218 A 10 6 1.00 13 0.462
219 A 4 3 1.00 13 0.231
220 A 10 5 1.00 13 0.385
221 A 4 3 1.00 11 0.273
222 A 3 2 1.00 11 0.182
223 A 7 5 1.00 13 0.385
224 A 3 2 1.00 13 0.154
225 A 9 6 1.00 13 0.462
226 A 3 2 1.00 13 0.154
227 A 11 5 1.00 13 0.385
228 A 13 9 1.00 13 0.692
229 A 7 6 1.00 13 0.462
230 A 8 7 1.00 13 0.538
231 A 6 5 1.00 11 0.454
232 A 4 4 1.00 11 0.364
233 A 7 7 1.00 13 0.538
234 A 3 2 1.00 13 0.154
235 A 7 7 1.00 13 0.538
236 A 16 9 1.00 13 0.692
237 A 7 6 1.00 13 0.462
238 A 13 9 1.00 13 0.692
239 A 6 5 1.00 11 0.454
240 A 3 2 1.00 11 0.182
241 A 8 7 1.00 13 0.538
242 A 3 2 1.00 13 0.154
243 A 8 7 1.00 13 0.538
244 A 4 4 1.00 13 0.308
245 A 3 3 1.00 13 0.231
246 A 7 6 1.00 15 0.400
247 A 5 4 1.00 15 0.267
248 A 5 4 1.00 17 0.235
249 A 11 9 1.00 15 0.600
250 A 9 8 1.00 15 0.533
251 A 12 11 1.00 15 0.733
252 A 6 6 1.00 15 0.400
253 A 7 7 1.00 31 0.226
254 A 8 8 1.00 31 0.258
255 A 9 8 1.00 31 0.258
256 A 10 8 1.00 31 0.258
257 A 13 8 1.00 14 0.571
258 A 11 7 1.00 14 0.500
259 A 9 6 1.00 12 0.500
260 A 13 5 1.00 20 0.250
261 A 5 3 1.00 36 0.083
262 A 4 3 1.00 36 0.083
263 A 2 2 1.00 34 0.059
264 N/A 0 0 1.00 34 0.000
265 N/A 0 0 1.00 36 0.000
266 A 1 1 1.00 11 0.091
267 A 2 2 1.00 13 0.154
268 A 2 2 1.00 13 0.154
269 A 3 2 1.00 13 0.154
270 A 1 1 1.01 15 0.067
271 A 2 2 1.02 17 0.118
272 A 2 2 1.00 17 0.118
273 A 3 2 1.00 17 0.118
274 A 2 1 1.00 15 0.067
275 A 3 2 1.00 17 0.118
276 A 3 1 1.00 17 0.059
277 A 4 2 1.00 17 0.118
278 A 3 1 1.00 17 0.059
279 A 4 3 1.00 19 0.158
280 A 4 3 1.00 19 0.158
281 A 3 2 1.00 19 0.105
282 A 3 2 1.00 19 0.105
283 A 4 3 1.00 19 0.158
284 A 4 3 1.00 19 0.158
285 A 8 8 1.00 18 0.444
286 A 6 6 1.00 18 0.333
287 A 3 3 1.00 18 0.167
288 A 4 4 1.00 18 0.222
289 A 4 4 1.00 10 0.400
290 A 5 5 1.00 12 0.417
291 A 6 4 1.00 12 0.333
292 A 5 5 1.00 11 0.454
293 A 6 6 1.00 13 0.462
294 A 9 5 1.00 13 0.385
295 A 5 5 1.00 14 0.357
296 A 6 6 1.00 16 0.375
297 A 9 5 1.00 16 0.312
298 A 6 6 1.00 17 0.353
299 A 7 7 1.00 19 0.368
300 A 10 6 1.00 19 0.316
301 A 4 3 1.00 16 0.188
302 A 5 4 1.00 16 0.250
303 A 4 3 1.00 16 0.188
304 A 4 3 1.00 14 0.214
305 A 3 3 1.00 14 0.214
306 A 4 4 1.00 16 0.250
307 A 3 3 1.00 16 0.188
308 A 6 5 1.00 16 0.312
309 A 5 4 1.00 16 0.250
310 A 4 3 1.00 10 0.300
311 A 4 3 1.00 8 0.375
312 A 5 5 1.00 8 0.625
313 A 6 6 1.00 10 0.600
314 A 4 3 1.00 10 0.300
315 A 4 3 1.00 8 0.375
316 A 9 9 1.00 8 1.125
317 A 13 9 1.00 10 0.900
318 A 4 3 1.00 10 0.300
319 A 4 3 1.00 8 0.375
320 A 15 12 1.00 8 1.500
321 A 16 13 1.00 10 1.300
322 A 2 2 1.00 18 0.111
323 A 2 2 1.00 18 0.111
324 A 1 1 1.00 16 0.062
325 A 1 1 1.00 16 0.062
326 A 1 1 1.00 18 0.056
327 A 2 2 1.00 18 0.111
328 A 2 2 1.00 18 0.111
329 A 6 5 1.00 25 0.200
330 A 6 5 1.00 25 0.200
331 A 5 4 1.00 25 0.160
332 A 4 4 1.00 25 0.160
333 A 4 4 1.00 25 0.160
334 A 6 5 1.00 25 0.200
335 A 6 5 1.00 25 0.200
336 A 1 1 1.00 10 0.100
337 A 6 4 1.00 12 0.333
338 A 6 4 1.00 15 0.267
339 A 6 3 1.00 12 0.250
340 A 4 2 1.00 14 0.143
341 A 6 3 1.00 17 0.176
342 A 8 5 1.00 16 0.312
343 A 9 6 1.00 18 0.333
344 A 14 5 1.00 18 0.278
345 A 8 5 1.00 19 0.263
346 A 9 6 1.00 21 0.286
347 A 14 5 1.00 21 0.238
348 A 8 4 1.00 16 0.250
349 A 9 4 1.00 18 0.222
350 A 14 4 1.00 18 0.222
351 A 6 4 1.00 18 0.222
352 A 7 4 1.00 20 0.200
353 A 10 4 1.00 20 0.200
354 A 8 5 1.00 21 0.238
355 A 9 5 1.00 23 0.217
356 A 14 5 1.00 23 0.217
357 A 8 4 1.00 19 0.210
358 A 10 4 1.00 21 0.190
359 A 14 4 1.00 21 0.190
360 A 8 5 1.00 21 0.238
361 A 10 5 1.00 23 0.217
362 A 14 5 1.00 23 0.217
363 A 8 5 1.00 24 0.208
364 A 10 5 1.00 26 0.192
365 A 14 5 1.00 26 0.192
366 A 6 5 1.00 6 0.833
367 A 9 6 1.00 6 1.000
368 A 8 4 1.00 16 0.250
369 A 8 4 1.00 19 0.210

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