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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 [54] had the largest ratio of [1.84614999999999996]

# 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 3 3 1.00 6 0.500
2 A 4 4 1.00 8 0.500
3 A 5 4 0.89 8 0.500
4 A 7 7 1.11 8 0.875
5 A 5 4 0.85 8 0.500
6 A 10 10 1.15 8 1.250
7 A 8 8 1.05 10 0.800
8 A 6 6 1.00 10 0.600
9 A 6 6 1.00 10 0.600
10 A 4 4 1.00 10 0.400
11 A 4 4 1.00 10 0.400
12 A 6 6 1.00 10 0.600
13 A 6 6 1.00 10 0.600
14 A 8 8 1.01 10 0.800
15 A 8 8 1.05 12 0.667
16 A 6 6 1.00 12 0.500
17 A 6 6 1.00 12 0.500
18 A 4 4 1.00 12 0.333
19 A 4 4 1.00 12 0.333
20 A 6 6 1.00 12 0.500
21 A 6 6 1.00 12 0.500
22 A 8 8 1.03 12 0.667
23 A 6 6 1.05 14 0.429
24 A 4 4 1.00 14 0.286
25 A 4 4 1.00 14 0.286
26 A 2 2 1.00 14 0.143
27 A 2 2 1.00 14 0.143
28 A 4 4 1.00 14 0.286
29 A 4 4 1.00 14 0.286
30 A 6 6 1.01 14 0.429
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 10 0.200
38 A 2 2 1.00 12 0.167
39 A 2 2 1.00 12 0.167
40 A 16 15 1.15 13 1.154
41 A 8 8 1.11 13 0.615
42 A 10 10 1.36 13 0.769
43 A 6 6 1.29 11 0.545
44 A 9 9 1.26 11 0.818
45 A 16 15 1.30 13 1.154
46 A 21 20 1.22 13 1.538
47 A 16 15 1.26 13 1.154
48 A 9 9 1.09 13 0.692
49 A 16 16 1.36 13 1.231
50 A 9 9 1.34 13 0.692
51 A 6 6 1.32 11 0.545
52 A 12 12 1.50 11 1.091
53 A 21 20 1.12 13 1.538
54 A 25 24 1.28 13 1.846
55 A 19 18 1.38 13 1.385
56 A 2 2 1.00 14 0.143
57 A 4 4 1.00 14 0.286
58 A 6 6 1.06 14 0.429
59 A 8 8 1.09 14 0.571
60 A 2 2 1.00 14 0.143
61 A 4 4 1.00 14 0.286
62 A 6 6 1.06 14 0.429
63 A 8 8 1.09 14 0.571
64 A 7 6 1.14 16 0.375
65 A 7 6 1.14 16 0.375
66 A 6 6 1.04 17 0.353
67 A 4 4 1.00 17 0.235
68 A 2 2 1.00 17 0.118
69 A 4 3 1.00 17 0.176
70 A 6 5 1.00 17 0.294
71 A 8 7 1.04 17 0.412
72 C 17 16 1.28 13 1.231
73 C 13 12 1.29 13 0.923
74 C 13 12 1.26 13 0.923
75 C 8 7 1.30 11 0.636
76 C 11 10 1.26 11 0.909
77 C 15 14 1.27 13 1.077
78 C 19 18 1.40 13 1.385
79 C 21 20 1.30 13 1.538
80 C 17 16 1.16 13 1.231
81 C 13 12 1.27 13 0.923
82 A 11 10 1.34 13 0.769
83 C 10 9 1.23 11 0.818
84 C 15 14 1.44 11 1.273
85 C 18 17 1.25 13 1.308
86 C 23 22 1.24 13 1.692
87 C 24 23 1.15 13 1.769
88 A 5 4 0.68 14 0.286
89 A 8 7 0.80 14 0.500
90 A 11 10 0.89 14 0.714
91 A 14 13 0.94 14 0.929
92 A 2 2 1.00 14 0.143
93 A 5 5 1.08 14 0.357
94 A 8 8 1.11 14 0.571
95 A 11 11 1.12 14 0.786
96 A 8 8 1.07 12 0.667
97 A 6 6 1.06 12 0.500
98 A 4 4 1.03 12 0.333
99 A 2 2 1.00 12 0.167
100 A 1 1 1.00 10 0.100
101 A 5 4 0.95 12 0.333
102 A 9 8 0.97 12 0.667
103 A 12 11 1.08 12 0.917
104 A 14 13 1.14 12 1.083
105 A 15 15 1.03 10 1.500
106 A 12 12 1.01 10 1.200
107 A 4 4 1.00 10 0.400
108 A 4 4 1.00 10 0.400
109 A 7 7 1.00 10 0.700
110 A 15 15 1.04 10 1.500
111 A 10 10 1.00 13 0.769
112 A 8 8 0.97 20 0.400
113 A 6 6 1.00 20 0.300
114 A 4 4 1.08 20 0.200
115 A 4 4 1.09 15 0.267
116 A 4 4 1.09 15 0.267
117 A 6 6 0.97 15 0.400
118 A 8 8 0.98 15 0.533
119 A 4 4 1.04 17 0.235
120 A 4 4 1.08 17 0.235
121 A 6 6 0.97 17 0.353
122 A 8 8 0.98 17 0.471
123 A 6 5 1.02 20 0.250
124 A 6 5 1.00 20 0.250
125 A 8 7 1.00 20 0.350
126 A 18 18 1.04 17 1.059
127 A 15 15 1.03 17 0.882
128 A 12 12 1.01 17 0.706
129 A 7 6 1.09 15 0.400
130 A 9 8 1.07 15 0.533
131 A 12 11 1.13 15 0.733
132 A 14 13 1.17 15 0.867
133 A 7 6 1.08 20 0.300
134 A 2 2 1.00 20 0.100
135 A 3 3 1.00 16 0.188
136 A 4 4 1.06 13 0.308
137 A 9 9 1.00 17 0.529
138 A 12 12 1.05 17 0.706
139 A 15 15 1.03 17 0.882
140 A 9 9 1.06 10 0.900
141 A 7 7 1.00 10 0.700
142 A 5 5 1.00 10 0.500
143 A 5 5 1.00 10 0.500
144 A 7 7 1.00 10 0.700
145 A 9 9 1.13 10 0.900
146 A 14 14 0.90 10 1.400
147 A 10 10 1.02 10 1.000
148 A 8 8 1.08 10 0.800
149 A 8 8 1.05 10 0.800
150 A 10 10 1.00 10 1.000
151 A 14 14 0.87 10 1.400
152 A 18 18 0.70 10 1.800
153 A 12 12 0.78 10 1.200
154 A 6 6 0.83 10 0.600
155 A 7 6 1.00 10 0.600
156 C 7 6 0.71 10 0.600
157 C 7 6 0.58 10 0.600
158 A 9 9 1.14 13 0.692
159 A 5 4 1.00 13 0.308
160 A 7 7 1.11 13 0.538
161 A 5 4 1.00 13 0.308
162 A 5 5 1.04 13 0.385
163 A 4 3 0.93 13 0.231
164 A 3 3 1.00 13 0.231
165 A 4 3 1.00 11 0.273
166 A 5 4 1.00 11 0.364
167 A 6 5 1.00 13 0.385
168 A 5 4 1.00 13 0.308
169 A 6 5 1.08 13 0.385
170 A 5 4 1.00 13 0.308
171 A 7 7 1.25 13 0.538
172 A 4 3 1.00 13 0.231
173 A 5 5 1.03 13 0.385
174 A 5 4 1.00 13 0.308
175 A 3 3 1.00 13 0.231
176 A 4 3 1.00 11 0.273
177 A 5 4 1.00 11 0.364
178 A 8 7 1.30 13 0.538
179 A 5 4 1.00 13 0.308
180 A 8 7 1.33 13 0.538
181 A 5 4 1.00 15 0.267
182 A 2 2 1.00 15 0.133
183 A 4 3 1.00 13 0.231
184 A 5 4 1.08 15 0.267
185 A 2 2 1.00 15 0.133
186 A 4 3 1.00 13 0.231
187 A 6 5 1.00 13 0.385
188 A 16 15 1.17 13 1.154
189 A 5 4 0.99 13 0.308
190 A 13 12 1.16 13 0.923
191 A 6 5 1.00 13 0.385
192 A 10 9 1.19 13 0.692
193 A 4 3 1.00 11 0.273
194 A 8 7 1.23 11 0.636
195 A 9 8 1.08 13 0.615
196 A 7 6 1.55 13 0.462
197 A 11 10 1.16 13 0.769
198 A 10 9 1.59 13 0.692
199 A 14 13 1.21 13 1.000
200 C 14 13 1.24 13 1.000
201 A 6 5 0.92 13 0.385
202 C 11 10 1.29 13 0.769
203 A 4 3 1.00 11 0.273
204 A 7 6 1.30 11 0.545
205 A 11 10 1.17 13 0.769
206 A 7 6 1.32 13 0.462
207 A 14 13 1.19 13 1.000
208 A 11 10 1.00 13 0.769
209 A 17 16 1.14 13 1.231
210 A 14 13 1.30 13 1.000
211 A 15 14 1.00 11 1.273
212 A 8 7 1.21 11 0.636
213 A 13 12 1.17 13 0.923
214 A 12 11 1.00 13 0.846
215 A 13 12 1.35 13 0.923
216 A 13 12 1.39 13 0.923
217 A 21 20 1.36 13 1.538
218 A 3 3 1.00 13 0.231
219 A 7 6 1.00 13 0.462
220 A 5 5 1.00 13 0.385
221 A 7 6 1.06 11 0.545
222 A 7 6 1.24 11 0.545
223 A 5 5 1.00 13 0.385
224 A 7 6 1.21 13 0.462
225 A 5 5 1.00 13 0.385
226 A 7 6 1.00 13 0.462
227 A 5 5 1.00 13 0.385
228 A 23 22 1.04 13 1.692
229 A 9 8 1.39 13 0.615
230 A 14 13 1.07 13 1.000
231 A 10 9 1.12 11 0.818
232 A 7 6 1.10 11 0.545
233 C 18 17 1.32 13 1.308
234 A 7 6 1.04 13 0.462
235 C 18 17 1.19 13 1.308
236 A 3 3 1.00 13 0.231
237 A 8 7 1.31 13 0.538
238 A 4 4 1.00 13 0.308
239 A 9 8 1.28 11 0.727
240 A 6 5 1.06 11 0.455
241 C 22 21 1.58 13 1.615
242 A 7 6 1.03 13 0.462
243 C 22 21 1.25 13 1.615
244 A 7 6 1.00 13 0.462
245 A 6 5 1.00 13 0.385
246 A 3 3 1.00 15 0.200
247 A 3 3 1.00 15 0.200
248 A 3 3 1.00 17 0.176
249 A 3 3 1.00 15 0.200
250 A 3 3 1.00 15 0.200
251 A 5 5 1.00 15 0.333
252 C 15 14 1.22 15 0.933
253 A 11 10 0.98 31 0.323
254 A 13 12 0.98 31 0.387
255 A 16 15 1.06 31 0.484
256 A 18 17 1.10 31 0.548
257 A 11 10 0.89 14 0.714
258 A 10 9 0.93 14 0.643
259 A 9 8 0.99 12 0.667
260 A 2 2 1.00 20 0.100
261 C 6 5 1.09 36 0.139
262 A 6 5 0.98 36 0.139
263 A 5 4 1.00 34 0.118
264 N/A 5 0 1.00 34 0.000
265 N/A 5 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 0.96 13 0.154
269 A 3 3 0.93 13 0.231
270 A 1 1 1.01 15 0.067
271 A 2 2 1.02 17 0.118
272 A 2 2 0.93 17 0.118
273 A 3 3 0.89 17 0.176
274 A 5 4 1.00 15 0.267
275 A 6 5 1.13 17 0.294
276 A 6 5 0.86 17 0.294
277 A 9 8 1.10 17 0.471
278 A 6 5 0.82 17 0.294
279 A 8 7 0.98 19 0.368
280 A 8 7 0.98 19 0.368
281 A 6 5 1.00 19 0.263
282 A 6 5 1.00 19 0.263
283 A 8 7 0.98 19 0.368
284 A 8 7 0.98 19 0.368
285 A 9 8 1.00 18 0.444
286 A 7 6 1.09 18 0.333
287 A 4 3 1.00 18 0.167
288 A 5 4 1.40 18 0.222
289 C 8 7 1.17 10 0.700
290 A 10 9 0.97 12 0.750
291 C 7 6 1.08 12 0.500
292 C 12 11 1.23 11 1.000
293 C 14 13 1.22 13 1.000
294 C 6 5 1.05 13 0.385
295 C 12 11 1.14 14 0.786
296 C 14 13 1.14 16 0.812
297 C 6 5 0.96 16 0.312
298 C 13 12 1.05 17 0.706
299 C 15 14 1.05 19 0.737
300 C 7 6 0.92 19 0.316
301 A 5 4 0.86 16 0.250
302 A 6 5 0.82 16 0.312
303 A 5 4 0.88 16 0.250
304 A 5 4 1.39 14 0.286
305 A 4 3 1.00 14 0.214
306 A 5 4 1.07 16 0.250
307 A 4 3 1.00 16 0.188
308 A 7 6 1.11 16 0.375
309 A 6 5 1.00 16 0.312
310 A 5 4 1.08 10 0.400
311 A 5 4 1.00 8 0.500
312 A 6 5 1.73 8 0.625
313 A 7 6 1.31 10 0.600
314 A 5 4 1.08 10 0.400
315 A 5 4 1.21 8 0.500
316 A 10 9 1.04 8 1.125
317 A 12 11 1.12 10 1.100
318 A 5 4 1.08 10 0.400
319 A 5 4 1.21 8 0.500
320 A 15 14 1.15 8 1.750
321 A 16 15 1.17 10 1.500
322 A 2 2 0.94 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 1.12 18 0.111
328 A 2 2 1.11 18 0.111
329 A 7 6 0.41 25 0.240
330 A 7 6 0.46 25 0.240
331 A 6 5 0.82 25 0.200
332 A 5 4 1.00 25 0.160
333 A 5 4 1.00 25 0.160
334 A 7 6 0.63 25 0.240
335 A 7 6 0.57 25 0.240
336 A 1 1 1.00 10 0.100
337 A 2 2 1.00 12 0.167
338 A 2 2 1.00 15 0.133
339 A 2 2 1.00 12 0.167
340 A 2 2 1.00 14 0.143
341 A 2 2 1.00 17 0.118
342 A 2 2 1.00 16 0.125
343 A 2 2 1.00 18 0.111
344 A 2 2 1.00 18 0.111
345 A 2 2 1.00 19 0.105
346 A 2 2 1.00 21 0.095
347 A 2 2 1.00 21 0.095
348 A 2 2 1.00 16 0.125
349 A 2 2 1.00 18 0.111
350 A 2 2 1.00 18 0.111
351 A 2 2 1.00 18 0.111
352 A 2 2 1.00 20 0.100
353 A 2 2 1.00 20 0.100
354 A 2 2 1.00 21 0.095
355 A 2 2 1.00 23 0.087
356 A 2 2 1.00 23 0.087
357 A 2 2 1.00 19 0.105
358 A 2 2 1.00 21 0.095
359 A 2 2 1.00 21 0.095
360 A 2 2 1.00 21 0.095
361 A 2 2 1.00 23 0.087
362 A 2 2 1.00 23 0.087
363 A 2 2 1.00 24 0.083
364 A 2 2 1.00 26 0.077
365 A 2 2 1.00 26 0.077
366 A 2 2 1.00 6 0.333
367 A 2 2 1.00 6 0.333
368 A 2 2 1.00 16 0.125
369 A 2 2 1.00 19 0.105

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