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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 [300] had the largest ratio of [3]

# 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 3 0.333
2 A 1 1 1.00 3 0.333
3 A 1 1 1.00 3 0.333
4 A 1 1 1.00 3 0.333
5 A 2 2 1.00 2 1.000
6 A 2 2 1.00 2 1.000
7 A 4 3 1.00 4 0.750
8 A 4 3 1.00 4 0.750
9 A 4 3 1.00 5 0.600
10 A 5 4 1.00 5 0.800
11 A 3 3 1.00 2 1.500
12 A 2 2 1.00 2 1.000
13 A 2 2 1.00 2 1.000
14 A 3 3 1.00 2 1.500
15 A 4 4 1.00 4 1.000
16 A 1 1 1.00 2 0.500
17 A 3 3 1.11 7 0.429
18 A 1 1 1.00 6 0.167
19 A 2 2 1.00 2 1.000
20 A 2 2 1.00 7 0.286
21 A 5 5 1.00 4 1.250
22 A 4 4 1.00 6 0.667
23 A 1 1 1.00 4 0.250
24 A 7 7 1.17 8 0.875
25 A 7 7 1.00 8 0.875
26 A 2 2 1.13 4 0.500
27 A 2 2 1.00 2 1.000
28 A 4 4 1.22 6 0.667
29 A 5 5 1.00 6 0.833
30 A 1 1 1.00 6 0.167
31 A 4 4 1.15 7 0.571
32 A 1 1 1.00 10 0.100
33 A 1 1 1.00 10 0.100
34 C 5 5 2.00 4 1.250
35 A 6 6 1.00 6 1.000
36 A 2 2 1.00 7 0.286
37 A 1 1 1.00 8 0.125
38 A 5 5 1.00 6 0.833
39 A 3 3 1.12 9 0.333
40 A 2 2 1.00 2 1.000
41 A 5 5 1.00 6 0.833
42 A 2 2 1.00 9 0.222
43 A 2 2 1.00 9 0.222
44 A 3 3 1.00 6 0.500
45 A 2 2 1.00 9 0.222
46 A 2 2 1.00 9 0.222
47 A 2 2 1.00 5 0.400
48 A 1 1 1.00 3 0.333
49 A 4 3 1.04 7 0.429
50 A 1 1 1.00 6 0.167
51 A 1 1 1.00 3 0.333
52 A 6 5 1.00 6 0.833
53 A 7 6 0.85 8 0.750
54 A 3 3 1.32 9 0.333
55 A 3 3 0.95 4 0.750
56 A 5 5 1.00 6 0.833
57 A 1 1 1.00 8 0.125
58 A 3 3 1.00 6 0.500
59 A 3 3 1.00 4 0.750
60 A 5 5 1.21 4 1.250
61 A 4 3 1.00 4 0.750
62 A 5 4 1.00 9 0.444
63 A 5 4 1.00 9 0.444
64 A 7 7 1.28 9 0.778
65 A 5 5 1.21 9 0.556
66 A 2 2 1.00 10 0.200
67 A 2 2 1.00 11 0.182
68 A 6 5 1.16 9 0.556
69 A 7 7 1.29 4 1.750
70 A 7 7 1.29 4 1.750
71 A 7 7 1.22 13 0.538
72 A 4 3 1.00 4 0.750
73 A 9 9 1.33 9 1.000
74 A 5 4 1.00 11 0.364
75 A 5 4 1.00 11 0.364
76 A 5 4 1.47 14 0.286
77 A 5 4 0.95 8 0.500
78 A 5 4 1.00 7 0.571
79 A 7 6 0.82 9 0.667
80 A 4 3 1.00 9 0.333
81 A 2 2 1.00 8 0.250
82 A 3 3 1.00 4 0.750
83 A 5 5 1.00 4 1.250
84 A 4 3 1.00 4 0.750
85 A 4 3 1.00 4 0.750
86 A 4 3 1.00 9 0.333
87 A 5 4 1.00 9 0.444
88 A 4 3 1.00 7 0.429
89 A 6 5 1.00 9 0.556
90 A 6 6 1.00 4 1.500
91 A 7 7 1.00 4 1.750
92 A 5 4 1.00 7 0.571
93 A 5 4 1.00 9 0.444
94 A 4 3 1.00 7 0.429
95 A 6 5 1.00 9 0.556
96 A 4 3 1.00 7 0.429
97 A 4 4 1.00 7 0.571
98 A 3 3 1.00 4 0.750
99 A 7 7 1.00 4 1.750
100 A 5 4 1.00 9 0.444
101 A 7 6 1.00 9 0.667
102 A 2 2 1.00 2 1.000
103 A 4 4 1.00 4 1.000
104 A 6 5 1.00 5 1.000
105 A 4 3 1.00 4 0.750
106 A 2 2 1.00 9 0.222
107 A 2 2 1.00 7 0.286
108 A 2 2 1.00 9 0.222
109 A 2 2 1.00 9 0.222
110 A 4 3 1.00 7 0.429
111 A 3 3 1.00 11 0.273
112 B 4 3 2.20 13 0.231
113 A 3 3 1.00 10 0.300
114 A 5 4 1.00 7 0.571
115 A 7 6 0.82 9 0.667
116 A 4 3 1.00 7 0.429
117 A 6 5 1.00 9 0.556
118 A 2 2 1.00 15 0.133
119 A 1 1 1.00 13 0.077
120 A 1 1 1.00 11 0.091
121 A 3 2 1.00 13 0.154
122 A 4 3 1.13 15 0.200
123 A 4 3 1.00 16 0.188
124 A 1 1 1.00 15 0.067
125 A 4 3 1.13 15 0.200
126 A 1 1 1.00 13 0.077
127 A 1 1 1.00 13 0.077
128 A 2 2 1.00 11 0.182
129 A 4 3 1.16 13 0.231
130 A 1 1 1.00 9 0.111
131 A 2 2 1.00 9 0.222
132 A 5 4 1.11 13 0.308
133 A 1 1 1.00 17 0.059
134 A 5 4 1.20 15 0.267
135 A 1 1 1.00 15 0.067
136 A 4 3 1.00 17 0.176
137 A 2 2 1.00 15 0.133
138 A 4 3 1.00 13 0.231
139 A 1 1 1.00 11 0.091
140 A 4 3 1.13 15 0.200
141 A 3 3 1.11 15 0.200
142 A 2 2 1.00 12 0.167
143 A 1 1 1.00 11 0.091
144 A 4 3 1.12 13 0.231
145 A 3 2 1.25 12 0.167
146 A 3 2 1.00 14 0.143
147 A 5 4 1.11 17 0.235
148 A 4 3 1.00 10 0.300
149 A 2 2 1.00 14 0.143
150 A 4 3 1.00 17 0.176
151 A 5 4 1.20 11 0.364
152 A 3 2 1.00 11 0.182
153 A 2 2 1.00 12 0.167
154 A 3 3 1.00 11 0.273
155 A 3 3 1.00 25 0.120
156 A 2 2 1.00 29 0.069
157 A 3 3 1.00 20 0.150
158 A 2 2 1.00 23 0.087
159 A 2 2 1.00 32 0.062
160 A 4 4 1.00 26 0.154
161 A 2 2 1.00 7 0.286
162 A 2 2 1.00 11 0.182
163 A 3 3 1.11 14 0.214
164 A 2 2 1.00 23 0.087
165 A 3 3 1.00 22 0.136
166 A 3 3 1.00 11 0.273
167 A 3 3 1.00 26 0.115
168 A 5 4 1.73 16 0.250
169 A 2 2 1.00 25 0.080
170 A 2 2 1.00 23 0.087
171 A 2 2 1.00 26 0.077
172 A 3 3 1.14 11 0.273
173 A 6 6 1.07 20 0.300
174 A 3 3 1.00 23 0.130
175 A 10 9 1.10 11 0.818
176 A 2 2 1.00 9 0.222
177 A 2 2 1.00 7 0.286
178 A 2 2 1.00 16 0.125
179 A 2 2 1.00 11 0.182
180 A 2 2 1.00 13 0.154
181 A 2 2 1.00 11 0.182
182 A 3 3 1.00 15 0.200
183 A 2 2 1.00 20 0.100
184 A 2 2 1.00 11 0.182
185 A 2 2 1.00 16 0.125
186 A 3 3 1.00 25 0.120
187 A 3 3 1.00 12 0.250
188 A 2 2 1.00 11 0.182
189 A 2 2 1.00 14 0.143
190 A 3 3 1.00 22 0.136
191 A 2 2 1.00 24 0.083
192 A 1 1 1.00 20 0.050
193 A 2 2 1.00 9 0.222
194 A 2 2 1.00 9 0.222
195 A 3 3 1.00 11 0.273
196 A 1 1 1.00 22 0.045
197 A 4 3 0.89 11 0.273
198 A 6 5 1.00 14 0.357
199 A 5 4 1.00 10 0.400
200 A 2 2 1.00 23 0.087
201 A 2 2 1.00 23 0.087
202 A 3 3 1.00 15 0.200
203 A 8 7 1.12 7 1.000
204 A 9 8 1.15 11 0.727
205 A 2 2 1.00 21 0.095
206 A 4 4 1.00 11 0.364
207 A 2 2 1.00 30 0.067
208 A 5 5 1.00 24 0.208
209 A 4 3 1.13 14 0.214
210 A 4 3 1.80 16 0.188
211 A 5 4 1.00 21 0.190
212 A 5 4 1.00 15 0.267
213 A 2 2 1.00 10 0.200
214 A 2 2 1.00 9 0.222
215 A 2 2 1.10 18 0.111
216 A 2 2 1.00 10 0.200
217 A 2 2 1.00 43 0.047
218 A 2 2 1.00 50 0.040
219 A 4 3 1.00 11 0.273
220 A 12 11 1.02 15 0.733
221 A 4 3 1.00 11 0.273
222 A 4 3 1.00 9 0.333
223 A 5 4 1.00 9 0.444
224 A 4 3 1.00 11 0.273
225 A 3 2 1.00 11 0.182
226 A 2 2 1.00 11 0.182
227 A 5 4 1.06 13 0.308
228 A 2 2 1.00 11 0.182
229 A 4 3 1.00 13 0.231
230 A 4 3 1.07 11 0.273
231 A 4 3 1.00 13 0.231
232 A 5 4 1.29 17 0.235
233 A 5 4 1.13 17 0.235
234 A 4 3 1.15 13 0.231
235 A 6 5 1.03 21 0.238
236 A 11 10 1.15 13 0.769
237 A 5 4 1.08 13 0.308
238 A 6 5 1.00 13 0.385
239 A 5 4 1.00 12 0.333
240 A 4 3 1.00 20 0.150
241 A 4 3 1.00 9 0.333
242 A 5 4 1.00 11 0.364
243 A 5 4 0.77 8 0.500
244 A 4 3 1.00 7 0.429
245 A 4 3 1.00 10 0.300
246 A 4 3 1.00 11 0.273
247 A 14 13 1.00 7 1.857
248 A 6 5 1.00 11 0.455
249 A 5 4 1.00 9 0.444
250 A 4 3 1.00 11 0.273
251 A 4 3 1.00 19 0.158
252 A 1 1 1.00 9 0.111
253 A 2 2 1.00 13 0.154
254 A 2 2 1.00 8 0.250
255 A 4 4 1.00 7 0.571
256 A 6 5 1.00 9 0.556
257 A 4 3 1.04 7 0.429
258 A 3 3 1.00 20 0.150
259 A 3 2 1.00 10 0.200
260 A 2 2 1.00 11 0.182
261 A 3 2 1.00 7 0.286
262 A 5 5 1.21 9 0.556
263 A 2 2 1.00 15 0.133
264 A 1 1 1.00 13 0.077
265 A 1 1 1.00 6 0.167
266 A 4 3 1.00 13 0.231
267 A 2 2 1.00 7 0.286
268 A 3 3 1.06 6 0.500
269 A 5 4 1.00 16 0.250
270 A 4 3 1.07 9 0.333
271 A 6 5 1.00 9 0.556
272 A 6 5 1.00 12 0.417
273 A 3 3 1.16 4 0.750
274 A 5 4 1.20 15 0.267
275 A 2 2 1.00 12 0.167
276 C 8 8 1.56 6 1.333
277 A 1 1 1.00 21 0.048
278 A 4 3 1.00 11 0.273
279 A 7 6 0.95 6 1.000
280 A 2 2 1.00 4 0.500
281 A 4 3 1.00 13 0.231
282 A 1 1 1.00 10 0.100
283 A 2 2 1.00 9 0.222
284 A 2 2 1.00 11 0.182
285 A 3 3 0.97 8 0.375
286 A 2 2 1.00 11 0.182
287 A 3 3 1.00 6 0.500
288 A 3 2 1.00 14 0.143
289 A 5 4 0.96 6 0.667
290 A 2 2 1.00 15 0.133
291 A 3 2 1.00 13 0.154
292 A 4 3 1.14 14 0.214
293 A 2 2 1.00 9 0.222
294 A 7 7 1.29 9 0.778
295 A 3 2 1.00 14 0.143
296 A 4 3 1.00 22 0.136
297 A 4 3 1.00 7 0.429
298 A 3 2 1.00 13 0.154
299 A 9 8 1.19 7 1.143
300 C 18 18 1.59 6 3.000
301 A 1 1 1.00 8 0.125
302 A 1 1 1.00 10 0.100
303 A 4 3 1.25 15 0.200
304 A 4 3 1.19 16 0.188
305 A 5 4 0.77 8 0.500
306 A 2 2 1.00 9 0.222
307 A 5 4 1.08 7 0.571
308 A 6 5 1.16 12 0.417
309 A 3 3 1.00 17 0.176
310 A 2 2 1.00 13 0.154
311 A 4 3 1.00 6 0.500
312 A 1 1 1.00 11 0.091
313 A 2 2 1.00 9 0.222
314 A 7 6 1.19 13 0.462
315 A 2 2 1.00 6 0.333
316 A 1 1 1.00 12 0.083
317 A 5 4 1.31 11 0.364
318 A 4 4 1.11 9 0.444
319 A 8 7 1.10 15 0.467
320 A 3 3 1.00 11 0.273
321 A 1 1 1.00 6 0.167
322 A 4 3 1.39 15 0.200
323 A 6 5 1.21 13 0.385
324 A 3 3 1.00 13 0.231
325 A 4 3 1.00 12 0.250
326 A 3 2 1.00 11 0.182
327 A 5 4 1.00 12 0.333
328 A 3 3 1.00 6 0.500
329 A 3 2 1.00 13 0.154
330 A 3 3 1.00 15 0.200
331 A 4 3 1.09 16 0.188
332 A 2 2 1.00 12 0.167
333 A 4 4 1.00 8 0.500
334 A 5 4 1.00 13 0.308
335 A 8 7 1.00 17 0.412
336 A 3 2 1.00 13 0.154
337 A 7 6 1.36 17 0.353
338 A 2 2 1.00 15 0.133
339 A 9 9 1.12 6 1.500
340 A 5 4 1.10 14 0.286
341 A 1 1 1.00 9 0.111
342 A 5 4 1.00 9 0.444
343 A 1 1 1.00 10 0.100
344 A 4 4 1.00 8 0.500
345 A 4 3 1.00 15 0.200
346 A 5 4 1.20 15 0.267
347 A 3 3 1.16 9 0.333
348 A 5 4 1.00 13 0.308
349 A 4 3 0.89 6 0.500
350 A 6 5 1.13 8 0.625
351 A 4 3 1.00 8 0.375
352 A 7 7 1.17 8 0.875
353 A 4 3 1.00 14 0.214
354 A 4 3 1.21 15 0.200
355 A 6 6 1.19 4 1.500
356 A 7 7 1.22 6 1.167
357 A 6 5 1.00 10 0.500
358 A 4 3 1.14 15 0.200
359 A 7 6 1.00 13 0.462
360 A 4 3 1.00 13 0.231
361 A 4 3 1.00 4 0.750
362 A 5 5 1.20 9 0.556
363 A 4 3 1.00 13 0.231
364 A 1 1 1.00 10 0.100
365 A 5 4 1.22 10 0.400
366 A 5 4 0.96 6 0.667
367 A 5 4 1.23 11 0.364
368 A 5 4 1.07 9 0.444
369 A 3 3 1.11 15 0.200
370 A 1 1 1.00 11 0.091
371 A 5 4 1.00 9 0.444
372 A 5 4 1.00 9 0.444
373 A 2 2 1.00 11 0.182
374 A 5 5 1.21 4 1.250
375 A 4 4 1.00 4 1.000
376 A 4 3 1.10 13 0.231

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