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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 [281] had the largest ratio of [2.33333000000000013]

# 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 7 6 1.14 23 0.261
2 A 6 5 1.14 23 0.217
3 A 5 4 1.13 21 0.190
4 C 12 11 0.78 23 0.478
5 A 2 2 1.00 23 0.087
6 A 3 3 1.01 23 0.130
7 A 4 4 1.05 23 0.174
8 A 5 5 1.07 23 0.217
9 A 5 4 0.98 23 0.174
10 A 5 4 1.02 23 0.174
11 A 5 4 1.06 23 0.174
12 A 2 2 1.00 19 0.105
13 A 5 4 1.00 23 0.174
14 A 6 5 0.95 23 0.217
15 A 7 6 1.00 23 0.261
16 A 7 6 1.09 25 0.240
17 A 6 5 1.08 25 0.200
18 A 5 4 1.06 25 0.160
19 A 4 3 1.00 25 0.120
20 A 5 4 1.03 25 0.160
21 A 6 5 1.05 25 0.200
22 A 7 6 1.06 25 0.240
23 A 9 8 1.07 25 0.320
24 A 8 7 1.06 25 0.280
25 A 7 6 1.07 25 0.240
26 A 8 7 1.03 25 0.280
27 A 9 8 1.04 25 0.320
28 A 5 4 0.82 12 0.333
29 A 5 4 0.81 14 0.286
30 N/A 1 0 1.00 40 0.000
31 A 7 6 0.98 40 0.150
32 A 6 5 1.01 40 0.125
33 A 3 2 0.94 38 0.053
34 N/A 1 0 1.00 40 0.000
35 N/A 1 0 1.00 40 0.000
36 A 2 2 1.00 11 0.182
37 A 2 2 1.00 11 0.182
38 A 2 2 1.00 9 0.222
39 A 3 2 1.00 7 0.286
40 A 2 2 1.00 11 0.182
41 A 2 2 1.00 11 0.182
42 A 2 2 1.00 11 0.182
43 A 2 2 1.00 11 0.182
44 A 3 3 0.93 13 0.231
45 A 3 3 1.07 13 0.231
46 A 3 3 1.07 13 0.231
47 A 4 3 1.00 11 0.273
48 A 3 2 1.00 9 0.222
49 A 3 3 1.02 13 0.231
50 A 3 3 1.00 13 0.231
51 A 3 3 1.00 13 0.231
52 A 1 1 1.00 13 0.077
53 A 2 2 1.52 13 0.154
54 A 4 4 0.86 13 0.308
55 A 4 4 1.10 13 0.308
56 A 5 4 1.15 13 0.308
57 A 4 3 1.00 11 0.273
58 A 3 2 1.00 9 0.222
59 A 4 4 1.03 13 0.308
60 A 4 4 1.00 13 0.308
61 A 4 4 1.02 13 0.308
62 A 4 4 1.00 13 0.308
63 A 1 1 1.00 13 0.077
64 A 2 2 1.00 13 0.154
65 A 5 5 0.81 13 0.385
66 A 5 5 1.11 13 0.385
67 A 5 5 1.11 13 0.385
68 A 5 5 1.11 13 0.385
69 A 6 5 1.22 13 0.385
70 A 5 4 1.15 13 0.308
71 A 4 3 1.00 11 0.273
72 A 3 2 1.00 9 0.222
73 A 5 5 1.03 13 0.385
74 A 5 5 1.02 13 0.385
75 A 5 5 1.01 13 0.385
76 A 5 5 1.08 13 0.385
77 A 5 5 1.00 13 0.385
78 A 1 1 1.00 13 0.077
79 A 2 2 1.00 13 0.154
80 A 3 3 1.18 13 0.231
81 B 4 4 2.10 13 0.308
82 A 5 5 1.11 13 0.385
83 A 5 5 1.11 13 0.385
84 A 4 3 1.00 11 0.273
85 A 1 1 1.00 13 0.077
86 A 6 5 1.07 13 0.385
87 A 5 4 1.05 13 0.308
88 A 4 3 1.00 11 0.273
89 A 3 2 1.00 9 0.222
90 A 5 4 1.00 13 0.308
91 A 6 5 1.25 13 0.385
92 A 7 6 1.32 13 0.462
93 A 2 2 1.00 13 0.154
94 A 7 6 1.12 13 0.462
95 A 6 5 1.09 13 0.385
96 A 5 4 1.08 13 0.308
97 A 4 3 1.00 11 0.273
98 A 3 2 1.00 9 0.222
99 A 6 5 1.26 13 0.385
100 A 7 6 1.32 13 0.462
101 A 8 7 1.31 13 0.538
102 A 3 3 1.03 13 0.231
103 A 7 6 1.16 13 0.462
104 A 6 5 1.14 13 0.385
105 A 5 4 1.11 13 0.308
106 A 4 3 1.00 11 0.273
107 A 3 2 1.00 9 0.222
108 A 7 6 1.38 13 0.462
109 A 8 7 1.38 13 0.538
110 A 9 8 1.36 13 0.615
111 A 7 6 1.24 15 0.400
112 A 6 5 1.18 15 0.333
113 A 5 4 1.14 15 0.267
114 A 4 3 1.00 13 0.231
115 A 3 2 1.00 11 0.182
116 A 2 2 1.00 15 0.133
117 A 2 2 1.00 15 0.133
118 A 4 4 0.99 15 0.267
119 A 6 6 1.09 15 0.400
120 A 7 6 1.24 15 0.400
121 A 6 5 1.20 15 0.333
122 A 5 4 1.14 15 0.267
123 A 4 3 1.00 13 0.231
124 A 3 2 1.00 11 0.182
125 A 3 3 1.03 15 0.200
126 A 3 3 1.05 15 0.200
127 A 3 3 0.98 15 0.200
128 A 5 5 1.01 15 0.333
129 A 7 6 1.24 15 0.400
130 A 6 5 1.20 15 0.333
131 A 5 4 1.14 15 0.267
132 A 4 3 1.00 13 0.231
133 A 3 2 1.00 11 0.182
134 A 4 4 1.03 15 0.267
135 A 4 4 1.05 15 0.267
136 A 4 4 0.99 15 0.267
137 A 4 4 1.01 15 0.267
138 A 6 6 1.03 15 0.400
139 A 8 8 1.10 15 0.533
140 A 7 6 1.20 15 0.400
141 A 6 5 1.21 15 0.333
142 A 5 4 1.11 15 0.267
143 A 4 3 1.00 13 0.231
144 A 3 2 1.00 11 0.182
145 A 1 1 1.00 15 0.067
146 A 3 3 1.06 15 0.200
147 A 5 5 1.09 15 0.333
148 A 7 7 1.15 15 0.467
149 A 7 6 1.23 15 0.400
150 A 6 5 1.19 15 0.333
151 A 5 4 1.11 15 0.267
152 A 4 3 1.00 13 0.231
153 A 3 2 1.00 11 0.182
154 A 2 2 1.00 15 0.133
155 A 4 4 1.19 15 0.267
156 A 6 6 1.15 15 0.400
157 A 8 8 1.19 15 0.533
158 A 7 6 1.18 15 0.400
159 A 6 5 1.16 15 0.333
160 A 5 4 1.07 15 0.267
161 A 4 3 1.00 13 0.231
162 A 3 2 1.00 11 0.182
163 A 3 3 1.17 15 0.200
164 A 5 5 1.26 15 0.333
165 A 7 7 1.20 15 0.467
166 A 9 9 1.22 15 0.600
167 A 2 2 1.00 13 0.154
168 A 2 2 1.00 13 0.154
169 A 2 2 1.00 13 0.154
170 A 2 2 1.00 13 0.154
171 A 2 2 1.00 13 0.154
172 A 2 2 1.00 13 0.154
173 A 2 2 1.00 13 0.154
174 A 2 2 1.00 13 0.154
175 A 3 3 1.06 15 0.200
176 A 3 3 1.06 15 0.200
177 A 3 3 1.06 15 0.200
178 A 3 3 1.06 15 0.200
179 A 3 3 1.02 15 0.200
180 A 3 3 1.02 15 0.200
181 A 3 3 0.98 15 0.200
182 A 3 3 1.06 15 0.200
183 A 4 4 1.09 15 0.267
184 A 4 4 1.09 15 0.267
185 A 4 4 1.09 15 0.267
186 A 4 4 1.06 15 0.267
187 A 4 4 1.09 15 0.267
188 A 4 4 1.06 15 0.267
189 A 4 4 1.03 15 0.267
190 A 4 4 1.03 15 0.267
191 A 5 5 1.08 15 0.333
192 A 4 4 1.07 15 0.267
193 A 3 3 1.06 15 0.200
194 A 2 2 1.00 15 0.133
195 A 1 1 1.00 15 0.067
196 A 2 2 1.00 15 0.133
197 A 3 3 1.17 15 0.200
198 A 4 4 1.25 15 0.267
199 A 5 5 1.12 15 0.333
200 A 4 4 1.12 15 0.267
201 A 3 3 1.10 15 0.200
202 A 2 2 1.00 15 0.133
203 A 3 3 1.06 15 0.200
204 A 4 4 1.21 15 0.267
205 A 5 5 1.29 15 0.333
206 A 6 6 1.33 15 0.400
207 A 5 5 1.11 15 0.333
208 A 4 4 1.09 15 0.267
209 A 3 3 1.04 15 0.200
210 A 4 4 1.06 15 0.267
211 A 5 5 1.14 15 0.333
212 A 6 6 1.23 15 0.400
213 A 7 7 1.28 15 0.467
214 A 8 8 1.32 15 0.533
215 A 4 4 1.02 17 0.235
216 A 3 3 0.97 17 0.176
217 A 2 2 1.00 17 0.118
218 A 2 2 1.00 17 0.118
219 A 1 1 1.00 17 0.059
220 A 2 2 1.00 17 0.118
221 A 3 3 1.16 17 0.176
222 A 4 4 1.24 17 0.235
223 A 5 5 1.03 17 0.294
224 A 4 4 1.00 17 0.235
225 A 3 3 0.98 17 0.176
226 A 3 3 1.02 17 0.176
227 A 3 3 1.03 17 0.176
228 A 1 1 1.00 17 0.059
229 A 2 2 1.00 17 0.118
230 A 3 3 1.16 17 0.176
231 A 4 4 1.24 17 0.235
232 A 5 5 1.02 17 0.294
233 A 4 4 1.01 17 0.235
234 A 4 4 1.00 17 0.235
235 A 4 4 1.03 17 0.235
236 A 4 4 1.02 17 0.235
237 A 1 1 1.00 17 0.059
238 A 2 2 1.00 17 0.118
239 A 3 3 1.16 17 0.176
240 A 4 4 1.24 17 0.235
241 A 4 4 1.04 17 0.235
242 A 3 3 1.00 17 0.176
243 A 2 2 1.00 17 0.118
244 A 1 1 1.00 17 0.059
245 A 1 1 1.00 17 0.059
246 A 2 2 1.00 17 0.118
247 A 3 3 1.16 17 0.176
248 A 4 4 1.24 17 0.235
249 A 5 5 1.07 17 0.294
250 A 4 4 1.05 17 0.235
251 A 3 3 1.05 17 0.176
252 A 2 2 1.00 17 0.118
253 A 1 1 1.00 17 0.059
254 A 2 2 1.00 17 0.118
255 A 3 3 1.13 17 0.176
256 A 4 4 1.22 17 0.235
257 A 5 5 1.08 17 0.294
258 A 4 4 1.09 17 0.235
259 A 3 3 1.07 17 0.176
260 A 1 1 1.00 17 0.059
261 A 2 2 1.00 17 0.118
262 A 3 3 1.16 17 0.176
263 A 4 4 1.21 17 0.235
264 A 5 5 1.25 17 0.294
265 A 1 1 1.00 13 0.077
266 A 7 6 0.91 13 0.462
267 A 6 5 0.96 13 0.385
268 A 5 4 1.00 13 0.308
269 A 4 3 1.00 11 0.273
270 A 3 2 1.00 9 0.222
271 A 1 1 1.00 13 0.077
272 A 2 2 1.00 13 0.154
273 A 3 3 0.97 13 0.231
274 A 2 2 1.00 11 0.182
275 A 2 2 1.00 11 0.182
276 A 2 2 1.00 9 0.222
277 A 3 2 1.00 7 0.286
278 A 2 2 1.00 11 0.182
279 A 2 2 1.00 11 0.182
280 A 2 2 1.00 11 0.182
281 C 8 7 1.48 3 2.333
282 C 9 8 1.35 5 1.600
283 C 10 9 1.29 7 1.286
284 A 7 6 1.29 15 0.400
285 A 6 5 1.32 13 0.385
286 A 5 4 1.38 11 0.364
287 N/A 1 0 1.00 15 0.000
288 A 9 8 1.28 16 0.500
289 A 8 7 1.29 16 0.438
290 A 7 6 1.30 14 0.429
291 A 6 5 1.30 12 0.417
292 N/A 1 0 1.00 16 0.000
293 A 9 8 1.30 19 0.421
294 A 8 7 1.31 19 0.368
295 A 7 6 1.33 17 0.353
296 A 6 5 1.36 15 0.333
297 N/A 1 0 1.00 19 0.000
298 A 7 6 1.29 15 0.400
299 A 6 5 1.31 13 0.385
300 A 5 4 1.38 11 0.364
301 N/A 1 0 1.00 15 0.000
302 A 9 8 1.28 16 0.500
303 A 8 7 1.29 16 0.438
304 A 7 6 1.28 14 0.429
305 A 6 5 1.29 12 0.417
306 N/A 1 0 1.00 16 0.000
307 A 9 8 1.30 19 0.421
308 A 8 7 1.31 19 0.368
309 A 7 6 1.31 17 0.353
310 A 6 5 1.34 15 0.333
311 N/A 1 0 1.00 19 0.000
312 A 9 8 1.18 15 0.533
313 A 8 7 1.16 15 0.467
314 A 7 6 1.12 13 0.462
315 A 6 5 1.09 7 0.714
316 N/A 1 0 1.00 15 0.000
317 A 7 6 1.32 15 0.400
318 A 6 5 1.36 13 0.385
319 A 5 4 1.48 11 0.364
320 N/A 1 0 1.00 15 0.000
321 A 8 7 1.28 20 0.350
322 A 7 6 1.29 18 0.333
323 A 6 5 1.32 16 0.312
324 N/A 1 0 1.00 20 0.000
325 A 8 7 1.30 21 0.333
326 A 7 6 1.31 19 0.316
327 A 6 5 1.36 17 0.294
328 N/A 1 0 1.00 21 0.000
329 A 9 8 1.18 15 0.533
330 A 8 7 1.16 15 0.467
331 A 7 6 1.12 13 0.462
332 A 6 5 1.09 7 0.714
333 N/A 1 0 1.00 15 0.000
334 A 7 6 1.31 15 0.400
335 A 6 5 1.34 13 0.385
336 A 5 4 1.46 11 0.364
337 N/A 1 0 1.00 15 0.000
338 A 8 7 1.30 20 0.350
339 A 7 6 1.30 18 0.333
340 A 6 5 1.35 16 0.312
341 N/A 1 0 1.00 20 0.000
342 A 8 7 1.28 21 0.333
343 A 7 6 1.27 19 0.316
344 A 6 5 1.31 17 0.294
345 N/A 1 0 1.00 21 0.000
346 A 3 2 1.00 4 0.500
347 A 5 4 0.98 6 0.667
348 A 6 5 1.21 8 0.625
349 A 3 2 0.94 8 0.250
350 A 5 4 1.00 10 0.400
351 A 6 5 1.17 12 0.417
352 A 9 8 0.89 12 0.667
353 A 6 5 1.00 14 0.357
354 A 7 6 1.09 16 0.375
355 A 8 7 0.81 20 0.350
356 A 7 6 0.94 20 0.300
357 A 4 3 0.91 20 0.150
358 A 4 3 0.91 20 0.150
359 A 7 6 0.94 20 0.300
360 A 9 8 0.85 20 0.400
361 A 2 2 1.24 24 0.083

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