[prev] [prev-tail] [tail] [up]

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 [30] 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 2 2 1.00 6 0.333
2 A 3 3 1.00 8 0.375
3 A 4 4 1.00 8 0.500
4 A 5 5 1.00 8 0.625
5 A 6 6 1.00 8 0.750
6 A 7 7 1.00 8 0.875
7 A 8 8 1.00 8 1.000
8 A 9 9 1.00 8 1.125
9 A 16 15 1.29 12 1.250
10 A 14 13 1.26 12 1.083
11 A 14 13 1.30 12 1.083
12 A 12 11 1.27 12 0.917
13 A 12 11 1.32 12 0.917
14 A 14 13 1.26 12 1.083
15 A 14 13 1.29 12 1.083
16 A 16 15 1.26 12 1.250
17 A 14 13 0.89 12 1.083
18 A 12 11 0.88 12 0.917
19 A 12 11 0.85 12 0.917
20 A 12 11 0.85 12 0.917
21 A 12 11 0.88 12 0.917
22 A 14 13 0.89 12 1.083
23 A 4 3 1.00 10 0.300
24 A 8 8 0.68 14 0.571
25 A 6 6 0.80 14 0.429
26 A 4 4 1.00 14 0.286
27 A 5 5 1.06 14 0.357
28 A 9 9 0.82 14 0.643
29 A 13 13 0.72 14 0.929
30 A 22 21 0.78 14 1.500
31 A 18 17 0.89 14 1.214
32 A 16 15 0.92 14 1.071
33 A 16 15 0.93 14 1.071
34 A 18 17 0.86 14 1.214
35 A 22 21 0.78 14 1.500
36 A 13 13 0.55 14 0.929
37 A 9 9 0.62 14 0.643
38 A 5 5 0.74 14 0.357
39 A 5 5 0.75 14 0.357
40 A 9 9 0.60 14 0.643
41 A 13 13 0.55 14 0.929
42 A 6 5 1.00 12 0.417
43 A 6 5 1.00 12 0.417
44 A 6 5 1.00 12 0.417
45 A 6 5 1.00 12 0.417
46 A 6 5 1.00 14 0.357
47 A 6 5 1.00 14 0.357
48 A 6 5 1.25 14 0.357
49 A 6 5 1.00 14 0.357
50 A 6 5 1.00 14 0.357
51 A 6 5 1.00 14 0.357
52 A 4 4 1.00 14 0.286
53 A 6 5 1.00 14 0.357
54 A 14 13 1.23 21 0.619
55 A 13 12 1.22 21 0.571
56 A 4 3 1.00 21 0.143
57 A 5 4 0.95 21 0.190
58 A 5 4 0.92 21 0.190
59 A 10 10 1.03 21 0.476
60 A 8 8 1.00 19 0.421
61 A 6 6 1.00 19 0.316
62 A 8 8 1.00 21 0.381
63 A 10 10 1.05 21 0.476
64 A 15 14 1.24 21 0.667
65 A 14 13 1.23 21 0.619
66 A 4 3 1.00 21 0.143
67 A 5 4 0.95 21 0.190
68 A 5 4 0.92 21 0.190
69 A 10 10 1.01 21 0.476
70 A 8 8 1.00 19 0.421
71 A 8 8 1.00 19 0.421
72 A 10 10 1.35 21 0.476
73 A 15 14 1.22 21 0.667
74 A 14 13 1.21 21 0.619
75 A 4 3 1.00 21 0.143
76 A 5 4 0.95 21 0.190
77 A 5 4 0.92 21 0.190
78 A 12 12 1.04 21 0.571
79 A 10 10 1.01 19 0.526
80 A 8 8 1.00 19 0.421
81 A 8 8 1.00 21 0.381
82 A 10 10 1.01 21 0.476
83 A 12 12 1.04 21 0.571
84 A 14 13 1.26 21 0.619
85 A 13 12 1.25 21 0.571
86 A 4 3 1.00 21 0.143
87 A 5 4 0.95 21 0.190
88 A 5 4 0.92 21 0.190
89 A 10 10 1.05 21 0.476
90 A 8 8 1.00 21 0.381
91 A 6 6 1.00 19 0.316
92 A 8 8 1.51 19 0.421
93 A 10 10 1.36 21 0.476
94 A 14 13 1.26 21 0.619
95 A 13 12 1.25 21 0.571
96 A 4 3 1.00 21 0.143
97 A 5 4 0.95 21 0.190
98 A 5 4 0.92 21 0.190
99 A 10 10 1.01 21 0.476
100 A 8 8 1.43 19 0.421
101 A 8 8 1.00 19 0.421
102 A 10 10 1.03 21 0.476
103 A 14 13 1.29 21 0.619
104 A 13 12 1.29 21 0.571
105 A 4 3 1.00 21 0.143
106 A 5 4 0.95 21 0.190
107 A 5 4 0.92 21 0.190
108 A 12 12 1.04 21 0.571
109 A 10 10 1.03 21 0.476
110 A 8 8 1.00 21 0.381
111 A 8 8 1.00 19 0.421
112 A 10 10 1.31 19 0.526
113 A 12 12 1.26 21 0.571
114 A 4 4 1.00 25 0.160
115 A 6 6 1.00 25 0.240
116 A 2 2 1.00 25 0.080
117 A 4 4 1.00 25 0.160
118 A 10 9 0.68 25 0.360
119 A 6 6 1.00 25 0.240
120 A 8 8 0.98 25 0.320
121 A 4 4 1.00 25 0.160
122 A 6 6 1.00 25 0.240
123 A 2 2 1.00 25 0.080
124 A 6 6 1.00 25 0.240
125 A 12 11 0.76 25 0.440
126 A 8 8 1.04 25 0.320
127 A 4 4 1.00 25 0.160
128 A 6 6 1.00 25 0.240
129 A 2 2 1.00 25 0.080
130 A 4 4 1.00 25 0.160
131 A 10 9 0.69 25 0.360
132 A 6 6 1.00 25 0.240
133 A 12 11 0.76 25 0.440
134 A 8 8 1.05 25 0.320
135 A 6 6 1.04 25 0.240
136 A 2 2 1.00 25 0.080
137 A 12 11 0.76 25 0.440
138 A 12 11 0.75 25 0.440
139 A 10 10 1.04 25 0.400
140 A 8 8 1.02 25 0.320
141 A 6 6 1.00 25 0.240
142 A 6 6 1.00 25 0.240
143 A 8 8 0.98 25 0.320
144 A 10 10 1.02 25 0.400
145 A 4 4 1.00 25 0.160
146 A 4 4 1.00 25 0.160
147 A 4 4 1.00 25 0.160
148 A 4 4 1.00 25 0.160
149 A 4 4 1.00 25 0.160
150 A 4 4 1.00 25 0.160
151 A 4 4 1.00 25 0.160
152 A 4 4 1.00 25 0.160
153 A 4 4 1.00 25 0.160
154 A 4 4 1.00 25 0.160
155 A 4 4 1.00 25 0.160
156 A 4 4 1.00 25 0.160
157 A 4 4 1.00 25 0.160
158 A 4 4 1.00 25 0.160
159 A 4 4 1.00 25 0.160
160 A 4 4 1.00 25 0.160
161 A 4 3 1.00 19 0.158
162 A 4 3 1.00 17 0.176
163 A 4 3 1.00 17 0.176
164 A 5 4 0.96 19 0.211
165 A 5 4 0.93 19 0.211
166 A 4 4 1.00 19 0.211
167 A 4 4 1.00 19 0.211
168 A 4 4 1.00 19 0.211
169 A 4 4 1.00 19 0.211
170 A 4 4 1.00 23 0.174
171 A 4 4 1.00 23 0.174
172 A 4 4 1.00 23 0.174
173 A 4 4 1.00 23 0.174
174 A 4 4 1.00 21 0.190
175 A 4 3 1.00 19 0.158
176 A 4 3 1.00 19 0.158
177 A 4 3 1.00 19 0.158
178 A 5 4 0.96 19 0.211
179 A 5 4 0.94 19 0.211
180 A 4 4 1.00 19 0.211
181 A 4 4 1.00 17 0.235
182 A 4 4 1.00 17 0.235
183 A 4 4 1.00 19 0.211
184 A 4 4 1.00 19 0.211
185 A 4 4 1.00 23 0.174
186 A 4 4 1.00 23 0.174
187 A 4 4 1.00 23 0.174
188 A 4 4 1.00 23 0.174
189 A 4 4 1.00 21 0.190
190 A 5 4 1.00 21 0.190
191 A 17 16 1.30 21 0.762
192 A 16 15 1.32 21 0.714
193 A 15 14 1.30 21 0.667
194 A 14 13 1.33 19 0.684
195 A 12 11 1.28 12 0.917
196 A 15 14 1.34 19 0.737
197 A 15 14 1.26 21 0.667
198 A 17 16 1.31 21 0.762
199 A 18 17 1.29 21 0.810
200 A 15 14 1.32 21 0.667
201 A 16 15 1.28 21 0.714
202 A 13 12 1.33 21 0.571
203 A 14 13 1.29 19 0.684
204 A 14 13 1.31 12 1.083
205 A 15 14 1.29 19 0.737
206 A 17 16 1.31 21 0.762
207 A 18 17 1.31 21 0.810
208 A 15 14 1.34 21 0.667
209 A 16 15 1.29 19 0.789
210 A 12 11 1.31 12 0.917
211 A 13 12 1.27 19 0.632
212 A 15 14 1.31 21 0.667
213 A 15 14 1.26 21 0.667
214 A 17 16 1.30 21 0.762
215 A 16 15 1.34 19 0.789
216 A 14 13 1.25 12 1.083
217 A 13 12 1.31 19 0.632
218 A 13 12 1.29 21 0.571
219 A 15 14 1.31 21 0.667
220 A 15 14 1.26 21 0.667
221 A 17 16 1.29 21 0.762
222 A 6 5 1.00 17 0.294
223 A 6 5 1.00 19 0.263
224 A 6 5 1.00 19 0.263
225 A 6 5 1.00 21 0.238
226 A 5 4 0.93 21 0.190
227 A 5 4 0.96 21 0.190
228 A 4 3 1.00 21 0.143
229 A 12 11 1.27 12 0.917
230 A 14 13 1.33 21 0.619
231 A 10 10 1.01 21 0.476
232 A 8 8 1.00 19 0.421
233 A 6 6 1.00 19 0.316
234 A 8 8 1.00 21 0.381
235 A 10 10 1.05 21 0.476
236 A 5 4 0.93 21 0.190
237 A 5 4 0.96 21 0.190
238 A 4 3 1.00 21 0.143
239 A 14 13 1.30 12 1.083
240 A 14 13 1.35 21 0.619
241 A 12 12 1.10 21 0.571
242 A 10 10 1.06 21 0.476
243 A 8 8 1.00 19 0.421
244 A 8 8 1.00 19 0.421
245 A 10 10 1.04 21 0.476
246 A 12 12 1.08 21 0.571
247 A 5 4 0.93 21 0.190
248 A 5 4 0.96 21 0.190
249 A 4 3 1.00 21 0.143
250 A 14 13 1.26 12 1.083
251 A 14 13 1.35 21 0.619
252 A 15 14 1.34 21 0.667
253 A 10 10 1.05 21 0.476
254 A 8 8 1.00 21 0.381
255 A 6 6 1.00 19 0.316
256 A 8 8 1.00 19 0.421
257 A 10 10 1.02 21 0.476
258 A 5 4 0.92 21 0.190
259 A 5 4 0.95 21 0.190
260 A 4 3 1.00 21 0.143
261 A 14 13 1.26 12 1.083
262 A 15 14 1.29 21 0.667
263 A 12 12 1.03 21 0.571
264 A 10 10 1.03 21 0.476
265 A 8 8 1.00 19 0.421
266 A 8 8 1.00 19 0.421
267 A 10 10 1.03 21 0.476
268 A 12 12 1.06 21 0.571
269 A 8 8 1.00 19 0.421
270 A 10 10 1.04 21 0.476
271 A 4 4 1.00 19 0.211
272 A 4 4 1.00 19 0.211
273 A 4 4 1.00 19 0.211
274 A 4 4 1.00 19 0.211
275 A 4 4 1.00 19 0.211
276 A 4 4 1.00 19 0.211
277 A 4 4 1.00 19 0.211
278 A 4 4 1.00 19 0.211
279 A 4 4 1.00 19 0.211
280 A 4 4 1.00 19 0.211
281 A 2 2 1.00 21 0.095
282 A 2 2 1.00 21 0.095
283 A 2 2 1.00 21 0.095
284 A 2 2 1.00 21 0.095
285 A 2 2 1.00 21 0.095
286 A 2 2 1.00 21 0.095
287 A 2 2 1.00 21 0.095
288 A 2 2 1.00 21 0.095
289 A 2 2 1.00 21 0.095
290 A 2 2 1.00 21 0.095
291 A 12 11 0.73 25 0.440
292 A 8 8 1.00 25 0.320
293 A 10 9 0.67 25 0.360
294 A 6 6 1.00 25 0.240
295 A 2 2 1.00 25 0.080
296 A 8 8 1.00 25 0.320
297 A 4 4 1.00 25 0.160
298 A 10 10 1.04 25 0.400
299 A 10 10 1.01 25 0.400
300 A 12 11 0.74 25 0.440
301 A 8 8 1.00 25 0.320
302 A 11 10 0.64 25 0.400
303 A 8 8 1.00 25 0.320
304 A 2 2 1.00 25 0.080
305 A 10 10 1.05 25 0.400
306 A 6 6 1.12 25 0.240
307 A 14 13 0.82 25 0.520
308 A 10 10 1.02 25 0.400
309 A 12 11 0.74 25 0.440
310 A 8 8 1.00 25 0.320
311 A 12 11 0.74 25 0.440
312 A 8 8 1.00 25 0.320
313 A 2 2 1.00 25 0.080
314 A 10 10 1.05 25 0.400
315 A 12 11 0.73 25 0.440
316 A 8 8 1.00 25 0.320
317 A 10 9 0.67 25 0.360
318 A 6 6 1.00 25 0.240
319 A 2 2 1.00 25 0.080
320 A 8 8 1.00 25 0.320
321 A 4 4 1.00 25 0.160
322 A 12 11 0.75 25 0.440
323 A 8 8 1.00 25 0.320
324 A 2 2 1.00 25 0.080
325 A 8 8 1.00 25 0.320
326 A 4 4 0.93 25 0.160
327 A 10 10 1.02 25 0.400
328 A 12 11 0.76 25 0.440
329 A 8 8 1.00 25 0.320
330 A 2 2 1.00 25 0.080
331 A 8 8 1.00 25 0.320
332 A 4 4 1.00 25 0.160
333 A 10 10 1.02 25 0.400
334 A 6 6 1.08 25 0.240
335 A 2 2 1.00 25 0.080
336 A 2 2 1.00 25 0.080
337 A 2 2 1.00 25 0.080
338 A 2 2 1.00 25 0.080
339 A 2 2 1.00 25 0.080
340 A 2 2 1.00 25 0.080
341 A 2 2 1.00 25 0.080
342 A 2 2 1.00 25 0.080
343 A 2 2 1.00 25 0.080
344 A 2 2 1.00 25 0.080
345 A 2 2 1.00 25 0.080
346 A 2 2 1.00 25 0.080
347 A 2 2 1.00 25 0.080
348 A 2 2 1.00 25 0.080
349 A 2 2 1.00 25 0.080
350 A 2 2 1.00 25 0.080
351 A 5 4 0.99 19 0.211
352 A 6 5 1.05 19 0.263
353 A 4 3 1.00 17 0.176
354 A 5 4 1.00 17 0.235
355 A 4 3 1.00 19 0.158
356 A 5 4 1.00 19 0.211
357 A 2 2 1.00 19 0.105
358 A 2 2 1.00 19 0.105
359 A 2 2 1.00 19 0.105
360 A 2 2 1.00 19 0.105
361 A 2 2 1.00 19 0.105
362 A 2 2 1.00 21 0.095
363 A 5 4 0.93 19 0.211
364 A 5 4 0.96 19 0.211
365 A 4 3 1.00 19 0.158
366 A 4 3 1.00 10 0.300
367 A 4 3 1.00 19 0.158
368 A 4 3 1.00 19 0.158
369 A 2 2 1.00 19 0.105
370 A 2 2 1.00 19 0.105
371 A 2 2 1.00 17 0.118
372 A 2 2 1.00 17 0.118
373 A 2 2 1.00 19 0.105
374 A 5 4 1.00 19 0.211
375 A 6 5 1.00 17 0.294
376 A 5 4 1.00 17 0.235
377 A 7 6 1.07 19 0.316
378 A 6 5 0.97 19 0.263
379 A 2 2 1.00 19 0.105
380 A 2 2 1.00 19 0.105
381 A 2 2 1.00 19 0.105
382 A 2 2 1.00 19 0.105
383 A 6 6 1.00 23 0.261
384 A 6 6 1.00 23 0.261
385 A 6 6 1.00 23 0.261
386 A 6 6 1.00 23 0.261
387 A 6 6 1.00 21 0.286

[prev] [prev-tail] [front] [up]