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2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. 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 given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [343] had the largest ratio of [40]

# 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 8 5 1.00 12 0.417
2 A 10 6 1.00 14 0.429
3 A 12 7 1.00 14 0.500
4 A 5 5 1.00 16 0.312
5 A 4 4 1.00 16 0.250
6 A 4 4 1.00 14 0.286
7 A 3 2 1.00 8 0.250
8 A 8 5 1.00 16 0.312
9 A 3 3 1.00 16 0.188
10 A 4 4 1.00 16 0.250
11 A 5 5 1.00 16 0.312
12 A 18 7 1.00 18 0.389
13 A 13 7 1.00 18 0.389
14 A 9 7 1.00 16 0.438
15 A 3 3 1.00 10 0.300
16 A 10 6 1.00 18 0.333
17 A 10 7 1.00 18 0.389
18 A 13 10 1.00 18 0.556
19 A 27 7 1.00 18 0.389
20 A 17 6 1.00 18 0.333
21 A 11 7 1.00 16 0.438
22 A 4 4 1.00 10 0.400
23 A 0 0 0.00 0 0.000
24 A 0 0 0.00 0 0.000
25 A 19 7 1.00 18 0.389
26 A 11 7 1.00 16 0.438
27 A 5 5 1.00 10 0.500
28 A 0 0 0.00 0 0.000
29 A 0 0 0.00 0 0.000
30 A 0 0 0.00 0 0.000
31 A 3 3 1.00 16 0.188
32 A 0 0 0.00 0 0.000
33 A 0 0 0.00 0 0.000
34 A 16 12 1.00 30 0.400
35 A 13 8 1.00 30 0.267
36 A 8 6 1.00 28 0.214
37 A 22 20 1.00 30 0.667
38 A 35 22 1.00 30 0.733
39 A 24 17 1.00 30 0.567
40 A 20 12 1.00 30 0.400
41 A 12 9 1.00 28 0.321
42 A 29 24 1.00 30 0.800
43 A 30 18 1.00 30 0.600
44 A 26 15 1.00 30 0.500
45 A 14 10 1.00 28 0.357
46 A 37 29 1.00 30 0.967
47 A 13 7 1.00 30 0.233
48 A 9 7 1.00 30 0.233
49 A 6 5 1.00 28 0.179
50 A 1 1 1.00 23 0.043
51 A 10 7 1.00 30 0.233
52 A 13 10 1.00 30 0.333
53 A 0 0 0.00 0 0.000
54 A 13 9 1.00 34 0.265
55 A 11 8 1.00 32 0.250
56 A 9 7 1.00 24 0.292
57 A 0 0 0.00 0 0.000
58 A 6 6 1.00 10 0.600
59 A 5 5 1.00 10 0.500
60 A 5 5 1.00 8 0.625
61 A 3 3 1.00 6 0.500
62 A 9 6 1.00 10 0.600
63 A 4 4 1.00 10 0.400
64 A 5 5 1.00 10 0.500
65 A 6 6 1.00 10 0.600
66 A 7 7 1.00 10 0.700
67 A 19 8 1.00 12 0.667
68 A 14 8 1.00 12 0.667
69 A 10 8 1.00 10 0.800
70 A 4 4 1.00 8 0.500
71 A 11 7 1.00 12 0.583
72 A 11 8 1.00 12 0.667
73 A 14 11 1.00 12 0.917
74 A 40 16 1.00 12 1.333
75 A 18 11 1.00 12 0.917
76 A 12 10 1.00 10 1.000
77 A 5 4 1.00 8 0.500
78 A 13 8 1.00 12 0.667
79 A 13 9 1.00 12 0.750
80 A 21 13 1.00 12 1.083
81 A 14 8 1.00 12 0.667
82 A 10 8 1.00 10 0.800
83 A 3 3 1.00 8 0.375
84 A 0 0 0.00 0 0.000
85 A 12 7 1.00 12 0.583
86 A 8 7 1.00 10 0.700
87 A 4 4 1.00 8 0.500
88 A 0 0 0.00 0 0.000
89 A 24 12 1.00 12 1.000
90 A 14 12 1.00 10 1.200
91 A 5 5 1.00 8 0.625
92 A 0 0 0.00 0 0.000
93 A 0 0 0.00 0 0.000
94 A 22 9 1.00 16 0.562
95 A 14 9 1.00 14 0.643
96 A 5 4 1.00 12 0.333
97 A 0 0 0.00 0 0.000
98 A 23 12 1.00 18 0.667
99 A 14 10 1.00 16 0.625
100 A 8 7 1.00 14 0.500
101 A 16 10 1.00 16 0.625
102 A 9 8 1.00 14 0.571
103 A 18 10 1.00 16 0.625
104 A 10 8 1.00 14 0.571
105 A 20 9 1.00 18 0.500
106 A 12 8 1.00 16 0.500
107 A 7 6 1.00 14 0.429
108 A 16 10 1.00 16 0.625
109 A 8 7 1.00 14 0.500
110 A 22 15 1.00 16 0.938
111 A 9 8 1.00 14 0.571
112 A 21 13 1.00 16 0.812
113 A 10 8 1.00 14 0.571
114 A 3 3 1.00 21 0.143
115 A 6 5 1.00 21 0.238
116 A 6 5 1.00 21 0.238
117 A 6 5 1.00 21 0.238
118 A 5 5 1.00 19 0.263
119 A 4 3 1.00 10 0.300
120 A 7 7 1.00 21 0.333
121 A 6 6 1.00 21 0.286
122 A 4 4 1.00 21 0.190
123 A 7 7 1.00 21 0.333
124 A 5 5 1.00 21 0.238
125 A 8 7 1.00 21 0.333
126 A 3 3 1.00 23 0.130
127 A 9 7 1.00 23 0.304
128 A 8 6 1.00 23 0.261
129 A 7 7 1.00 23 0.304
130 A 6 6 1.00 21 0.286
131 A 4 4 1.00 12 0.333
132 A 8 8 1.00 23 0.348
133 A 9 7 1.00 23 0.304
134 A 5 5 1.00 23 0.217
135 A 11 9 1.00 23 0.391
136 A 0 0 0.00 0 0.000
137 A 17 9 1.00 23 0.391
138 A 13 7 1.00 23 0.304
139 A 12 9 1.00 23 0.391
140 A 8 7 1.00 21 0.333
141 A 6 4 1.00 12 0.333
142 A 9 9 1.00 23 0.391
143 A 11 8 1.00 23 0.348
144 A 9 9 1.00 23 0.391
145 A 16 12 1.00 23 0.522
146 A 0 0 0.00 0 0.000
147 A 16 6 1.00 23 0.261
148 A 13 8 1.00 23 0.348
149 A 9 6 1.00 21 0.286
150 A 6 4 1.00 12 0.333
151 A 10 9 1.00 23 0.391
152 A 13 9 1.00 23 0.391
153 A 10 10 1.00 23 0.435
154 A 21 12 1.00 23 0.522
155 A 0 0 0.00 0 0.000
156 A 14 7 1.00 23 0.304
157 A 11 7 1.00 23 0.304
158 A 11 7 1.00 23 0.304
159 A 8 7 1.00 21 0.333
160 A 5 5 1.00 12 0.417
161 A 0 0 0.00 0 0.000
162 A 13 6 1.00 23 0.261
163 A 10 6 1.00 23 0.261
164 A 10 6 1.00 23 0.261
165 A 6 6 1.00 21 0.286
166 A 6 6 1.00 12 0.500
167 A 0 0 0.00 0 0.000
168 A 26 9 1.00 23 0.391
169 A 20 9 1.00 23 0.391
170 A 18 10 1.00 23 0.435
171 A 11 10 1.00 21 0.476
172 A 7 7 1.00 12 0.583
173 A 0 0 0.00 0 0.000
174 A 24 8 1.00 23 0.348
175 A 17 8 1.00 23 0.348
176 A 18 10 1.00 23 0.435
177 A 9 9 1.00 21 0.429
178 A 8 7 1.00 12 0.583
179 A 0 0 0.00 0 0.000
180 A 21 9 1.00 25 0.360
181 A 16 9 1.00 25 0.360
182 A 16 9 1.00 25 0.360
183 A 11 9 1.00 23 0.391
184 A 8 7 1.00 14 0.500
185 A 0 0 0.00 0 0.000
186 A 43 12 1.00 25 0.480
187 A 27 11 1.00 25 0.440
188 A 24 12 1.00 25 0.480
189 A 13 11 1.00 23 0.478
190 A 9 8 1.00 14 0.571
191 A 0 0 0.00 0 0.000
192 A 46 12 1.00 25 0.480
193 A 29 11 1.00 25 0.440
194 A 26 12 1.00 25 0.480
195 A 14 11 1.00 23 0.478
196 A 10 8 1.00 14 0.571
197 A 0 0 0.00 0 0.000
198 A 77 13 1.00 25 0.520
199 A 42 11 1.00 25 0.440
200 A 35 13 1.00 25 0.520
201 A 16 11 1.00 23 0.478
202 A 11 8 1.00 14 0.571
203 A 0 0 0.00 0 0.000
204 A 20 8 1.00 25 0.320
205 A 15 8 1.00 25 0.320
206 A 15 8 1.00 25 0.320
207 A 10 8 1.00 23 0.348
208 A 7 6 1.00 14 0.429
209 A 0 0 0.00 0 0.000
210 A 19 7 1.00 25 0.280
211 A 14 7 1.00 25 0.280
212 A 14 7 1.00 25 0.280
213 A 8 7 1.00 23 0.304
214 A 8 7 1.00 14 0.500
215 A 0 0 0.00 0 0.000
216 A 36 10 1.00 25 0.400
217 A 26 10 1.00 25 0.400
218 A 24 11 1.00 25 0.440
219 A 13 11 1.00 23 0.478
220 A 9 8 1.00 14 0.571
221 A 0 0 0.00 0 0.000
222 A 34 9 1.00 25 0.360
223 A 23 9 1.00 25 0.360
224 A 24 11 1.00 25 0.440
225 A 11 10 1.00 23 0.435
226 A 10 8 1.00 14 0.571
227 A 0 0 0.00 0 0.000
228 A 8 7 1.00 23 0.304
229 A 6 5 1.00 23 0.217
230 A 7 7 1.00 23 0.304
231 A 5 5 1.00 23 0.217
232 A 6 6 1.00 23 0.261
233 A 4 4 1.00 23 0.174
234 A 7 7 1.00 23 0.304
235 A 5 5 1.00 23 0.217
236 A 3 3 1.00 25 0.120
237 A 3 3 1.00 25 0.120
238 A 3 3 1.00 25 0.120
239 A 3 3 1.00 25 0.120
240 A 3 3 1.00 25 0.120
241 A 3 3 1.00 25 0.120
242 A 3 3 1.00 25 0.120
243 A 3 3 1.00 25 0.120
244 A 0 0 0.00 0 0.000
245 A 0 0 0.00 0 0.000
246 A 0 0 0.00 0 0.000
247 A 0 0 0.00 0 0.000
248 A 0 0 0.00 0 0.000
249 A 0 0 0.00 0 0.000
250 A 0 0 0.00 0 0.000
251 A 0 0 0.00 0 0.000
252 A 0 0 0.00 0 0.000
253 A 0 0 0.00 0 0.000
254 A 0 0 0.00 0 0.000
255 A 0 0 0.00 0 0.000
256 A 0 0 0.00 0 0.000
257 A 0 0 0.00 0 0.000
258 A 0 0 0.00 0 0.000
259 A 0 0 0.00 0 0.000
260 A 7 6 1.00 30 0.200
261 A 6 6 1.00 30 0.200
262 A 4 4 1.00 28 0.143
263 A 5 4 1.00 30 0.133
264 A 6 6 1.00 30 0.200
265 A 4 4 0.97 30 0.133
266 A 15 9 1.00 30 0.300
267 A 11 9 1.00 30 0.300
268 A 7 6 1.00 28 0.214
269 A 6 4 1.00 30 0.133
270 A 7 5 1.00 30 0.167
271 A 11 8 1.00 30 0.267
272 A 2 2 1.00 30 0.067
273 A 2 2 1.00 30 0.067
274 A 2 2 1.00 28 0.071
275 A 2 2 1.00 30 0.067
276 A 2 2 1.00 30 0.067
277 A 2 2 1.00 30 0.067
278 A 8 8 1.00 30 0.267
279 A 7 7 1.00 30 0.233
280 A 3 3 1.00 28 0.107
281 A 0 0 0.00 0 0.000
282 A 0 0 0.00 0 0.000
283 A 5 5 1.00 10 0.500
284 A 4 4 1.00 10 0.400
285 A 3 3 1.00 8 0.375
286 A 5 5 1.00 6 0.833
287 A 5 5 1.00 10 0.500
288 A 3 3 1.00 10 0.300
289 A 5 5 1.00 10 0.500
290 A 6 6 1.00 10 0.600
291 A 5 5 1.00 10 0.500
292 A 7 5 1.00 10 0.500
293 A 6 5 1.00 8 0.625
294 A 6 6 1.00 6 1.000
295 A 5 5 1.00 10 0.500
296 A 3 3 1.00 10 0.300
297 A 4 4 1.00 10 0.400
298 A 5 4 1.00 10 0.400
299 A 6 4 1.00 10 0.400
300 A 6 6 1.00 10 0.600
301 A 3 3 1.00 8 0.375
302 A 5 5 1.00 6 0.833
303 A 5 5 1.00 10 0.500
304 A 3 3 1.00 10 0.300
305 A 5 5 1.00 10 0.500
306 A 5 4 1.00 10 0.400
307 A 3 3 1.00 10 0.300
308 A 3 3 1.00 10 0.300
309 A 3 3 1.00 8 0.375
310 A 3 3 1.00 6 0.500
311 A 5 5 1.00 10 0.500
312 A 3 3 1.00 10 0.300
313 A 3 3 1.00 10 0.300
314 A 3 2 1.00 20 0.100
315 A 5 4 1.00 20 0.200
316 A 2 2 1.00 20 0.100
317 A 4 3 1.00 18 0.167
318 A 1 1 1.00 20 0.050
319 A 1 1 1.00 20 0.050
320 A 2 2 1.00 20 0.100
321 A 3 2 1.00 20 0.100
322 A 5 4 1.00 20 0.200
323 A 2 2 1.00 20 0.100
324 A 4 3 1.00 18 0.167
325 A 1 1 1.00 20 0.050
326 A 1 1 1.00 20 0.050
327 A 2 2 1.00 20 0.100
328 A 2 2 1.00 22 0.091
329 A 2 2 1.00 22 0.091
330 A 1 1 1.00 22 0.045
331 A 1 1 1.00 22 0.045
332 A 1 1 1.00 22 0.045
333 A 2 2 1.00 22 0.091
334 A 2 2 1.00 22 0.091
335 A 2 2 1.00 22 0.091
336 A 2 2 1.00 22 0.091
337 A 1 1 1.00 22 0.045
338 A 1 1 1.00 22 0.045
339 A 1 1 1.00 22 0.045
340 A 2 2 1.00 22 0.091
341 A 2 2 1.00 22 0.091
342 A 0 0 0.00 0 0.000
343 A 8 8 1.00 40 0.200
344 A 7 7 1.00 40 0.175
345 A 6 7 1.00 38 0.184
346 A 0 0 0.00 0 0.000
347 A 0 0 0.00 0 0.000
348 A 6 6 1.00 10 0.600
349 A 5 4 1.00 12 0.333
350 A 5 4 1.00 12 0.333
351 A 5 4 1.00 10 0.400
352 A 5 4 1.00 8 0.500
353 A 9 8 1.00 12 0.667
354 A 9 8 1.00 12 0.667
355 A 6 5 1.00 12 0.417
356 A 7 6 1.00 12 0.500
357 A 8 7 1.00 12 0.583
358 A 37 8 1.00 14 0.571
359 A 27 8 1.00 14 0.571
360 A 17 8 1.00 12 0.667
361 A 7 4 1.00 10 0.400
362 A 0 0 0.00 0 0.000
363 A 0 0 0.00 0 0.000
364 A 7 7 1.00 19 0.368
365 A 2 2 1.00 15 0.133
366 A 4 4 1.00 12 0.333
367 A 4 4 1.00 14 0.286
368 A 6 6 1.00 10 0.600
369 F 0 0 N/A 0. N/A
370 A 2 2 1.00 26 0.077
371 A 2 2 1.00 26 0.077

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