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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 [16] 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 12 12 1.10 14 0.857
2 A 9 9 1.08 14 0.643
3 A 7 7 1.04 14 0.500
4 A 4 4 1.00 12 0.333
5 A 5 5 1.00 14 0.357
6 A 7 7 1.06 14 0.500
7 A 10 10 1.01 14 0.714
8 A 9 9 1.03 16 0.562
9 A 6 6 0.96 16 0.375
10 A 6 6 1.02 16 0.375
11 A 3 3 1.00 14 0.214
12 A 3 3 1.00 16 0.188
13 A 8 8 1.05 16 0.500
14 A 6 6 1.30 16 0.375
15 A 11 11 1.00 16 0.688
16 A 25 24 1.34 16 1.500
17 A 16 16 1.25 16 1.000
18 A 12 11 1.10 16 0.688
19 A 6 6 1.00 14 0.429
20 A 3 3 1.00 16 0.188
21 A 3 3 1.02 16 0.188
22 A 9 9 1.32 16 0.562
23 A 7 6 1.10 14 0.429
24 A 6 5 1.07 14 0.357
25 A 5 4 1.00 12 0.333
26 N/A 2 0 1.00 14 0.000
27 N/A 2 0 1.00 14 0.000
28 A 10 9 1.33 16 0.562
29 A 9 8 1.28 16 0.500
30 A 5 5 1.07 14 0.357
31 N/A 2 0 1.00 16 0.000
32 N/A 2 0 1.00 16 0.000
33 A 11 10 1.07 16 0.625
34 A 9 8 1.08 16 0.500
35 A 7 6 1.01 14 0.429
36 N/A 2 0 1.00 16 0.000
37 N/A 2 0 1.00 16 0.000
38 A 15 14 1.05 16 0.875
39 A 13 12 1.02 16 0.750
40 A 10 9 1.04 16 0.562
41 A 8 7 1.00 16 0.438
42 A 10 9 1.04 16 0.562
43 A 13 12 1.04 16 0.750
44 A 15 14 1.07 16 0.875
45 A 6 6 1.03 18 0.333
46 A 6 6 1.03 18 0.333
47 A 3 3 1.00 18 0.167
48 A 3 3 1.00 18 0.167
49 A 11 10 1.04 18 0.556
50 A 6 6 1.25 18 0.333
51 A 14 13 1.03 18 0.722
52 A 9 9 1.20 18 0.500
53 A 19 18 1.41 18 1.000
54 A 17 16 1.42 18 0.889
55 A 3 3 1.00 18 0.167
56 A 3 3 1.00 18 0.167
57 A 3 3 1.06 18 0.167
58 A 12 11 1.52 18 0.611
59 A 14 13 1.42 18 0.722
60 A 9 8 1.03 12 0.667
61 A 6 5 1.00 12 0.417
62 A 4 3 1.00 12 0.250
63 A 6 5 1.00 12 0.417
64 A 9 8 1.05 12 0.667
65 N/A 2 0 1.00 16 0.000
66 N/A 2 0 1.00 16 0.000
67 A 1 1 1.00 25 0.040
68 A 1 1 1.00 29 0.034
69 A 1 1 1.00 28 0.036
70 A 1 1 1.00 28 0.036
71 N/A 2 0 1.00 18 0.000
72 A 3 3 1.00 16 0.188
73 A 3 3 1.00 16 0.188
74 A 3 3 1.00 14 0.214
75 N/A 2 0 1.00 14 0.000
76 N/A 2 0 1.00 16 0.000
77 A 3 3 1.00 12 0.250
78 A 3 3 1.00 12 0.250
79 A 3 3 1.00 12 0.250
80 A 3 3 1.00 10 0.300
81 A 3 3 1.00 12 0.250
82 A 3 3 1.00 12 0.250
83 A 3 3 1.00 12 0.250
84 A 3 3 1.00 14 0.214
85 A 3 3 1.00 14 0.214
86 A 3 3 1.00 14 0.214
87 A 3 3 1.00 12 0.250
88 A 3 3 1.00 14 0.214
89 A 3 3 1.00 14 0.214
90 A 3 3 1.00 14 0.214
91 A 1 1 1.00 28 0.036
92 A 1 1 1.00 32 0.031
93 A 1 1 1.00 28 0.036
94 A 1 1 1.00 28 0.036
95 A 3 3 1.00 18 0.167
96 A 3 3 1.00 18 0.167
97 A 3 3 1.00 16 0.188
98 A 3 3 1.00 18 0.167
99 A 3 3 1.00 18 0.167
100 A 3 3 1.00 18 0.167
101 A 3 3 0.95 20 0.150
102 A 3 3 1.00 20 0.150
103 A 3 3 0.83 18 0.167
104 A 5 5 0.96 20 0.250
105 A 5 5 1.02 20 0.250
106 A 15 15 1.39 20 0.750
107 A 12 11 1.18 20 0.550
108 A 11 10 1.14 20 0.500
109 A 7 7 1.05 18 0.389
110 N/A 2 0 1.00 20 0.000
111 N/A 2 0 1.00 20 0.000
112 A 15 14 1.06 20 0.700
113 A 15 14 1.02 20 0.700
114 A 9 9 0.99 18 0.500
115 N/A 2 0 1.00 20 0.000
116 N/A 2 0 1.00 20 0.000
117 A 13 12 1.04 21 0.571
118 A 12 11 1.04 21 0.524
119 A 7 7 1.03 19 0.368
120 N/A 2 0 1.00 21 0.000
121 N/A 2 0 1.00 21 0.000
122 A 11 11 1.21 18 0.611
123 A 9 9 1.15 18 0.500
124 A 6 6 1.40 16 0.375
125 A 7 7 0.69 18 0.389
126 A 9 9 0.79 18 0.500
127 A 12 12 0.75 18 0.667
128 A 18 18 1.08 18 1.000
129 A 14 13 0.91 18 0.722
130 A 8 8 0.98 16 0.500
131 A 5 5 0.56 18 0.278
132 A 5 5 0.58 18 0.278
133 A 11 11 0.75 18 0.611
134 A 9 8 0.61 18 0.444
135 A 8 7 0.61 18 0.389
136 A 7 6 0.64 16 0.375
137 N/A 2 0 1.00 18 0.000
138 N/A 2 0 1.00 18 0.000
139 A 13 12 0.61 18 0.667
140 A 11 10 0.65 18 0.556
141 A 9 8 0.76 16 0.500
142 N/A 2 0 1.00 18 0.000
143 N/A 2 0 1.00 18 0.000
144 N/A 2 0 1.00 18 0.000
145 N/A 2 0 1.00 20 0.000
146 A 5 5 0.96 20 0.250
147 A 5 5 0.98 20 0.250
148 A 3 3 1.00 18 0.167
149 N/A 2 0 1.00 20 0.000
150 N/A 2 0 1.00 20 0.000
151 A 3 3 1.00 18 0.167
152 A 3 3 1.00 18 0.167
153 A 3 3 1.00 16 0.188
154 A 3 3 1.00 18 0.167
155 A 3 3 1.00 18 0.167
156 A 3 3 1.00 18 0.167
157 A 3 3 0.95 20 0.150
158 A 3 3 1.00 20 0.150
159 A 3 3 0.97 18 0.167
160 A 3 3 1.00 20 0.150
161 A 3 3 1.00 20 0.150
162 A 3 3 1.00 20 0.150
163 A 10 9 0.94 20 0.450
164 A 9 8 0.95 20 0.400
165 A 8 7 1.01 18 0.389
166 N/A 2 0 1.00 20 0.000
167 N/A 2 0 1.00 20 0.000
168 A 17 16 0.93 20 0.800
169 A 15 14 0.94 20 0.700
170 A 12 11 1.04 18 0.611
171 N/A 2 0 1.00 20 0.000
172 N/A 2 0 1.00 20 0.000
173 N/A 2 0 1.00 20 0.000
174 A 3 3 1.00 20 0.150
175 A 3 3 1.00 20 0.150
176 A 3 3 1.00 18 0.167
177 N/A 2 0 1.00 20 0.000
178 N/A 2 0 1.00 20 0.000
179 A 14 13 1.18 26 0.500
180 A 13 12 1.14 26 0.462
181 A 9 9 1.07 24 0.375
182 A 4 4 1.00 19 0.211
183 N/A 1 0 1.00 26 0.000
184 N/A 1 0 1.00 26 0.000
185 A 24 23 1.11 28 0.821
186 A 21 20 1.08 28 0.714
187 A 14 14 1.02 26 0.538
188 A 7 7 0.93 21 0.333
189 N/A 1 0 1.00 28 0.000
190 N/A 1 0 1.00 28 0.000
191 A 31 30 1.07 28 1.071
192 A 28 27 1.10 28 0.964
193 A 18 18 1.09 26 0.692
194 A 4 4 1.00 21 0.190
195 N/A 1 0 1.00 28 0.000
196 N/A 1 0 1.00 28 0.000
197 A 18 17 1.09 26 0.654
198 A 16 15 1.06 26 0.577
199 A 12 11 1.01 24 0.458
200 A 5 5 1.00 19 0.263
201 N/A 1 0 1.00 26 0.000
202 N/A 1 0 1.00 26 0.000
203 A 27 26 1.16 28 0.929
204 A 25 24 1.15 28 0.857
205 A 18 17 1.01 26 0.654
206 A 10 9 1.02 21 0.429
207 N/A 1 0 1.00 28 0.000
208 N/A 1 0 1.00 28 0.000
209 F 0 0 N/A 0.000 N/A
210 F 0 0 N/A 0.000 N/A
211 A 25 24 1.32 26 0.923
212 A 12 11 1.01 21 0.524
213 N/A 1 0 1.00 28 0.000
214 N/A 1 0 1.00 28 0.000
215 N/A 1 0 1.00 28 0.000
216 N/A 1 0 1.00 26 0.000
217 N/A 2 0 1.00 20 0.000
218 N/A 1 0 1.00 26 0.000
219 N/A 1 0 1.00 28 0.000
220 A 12 11 0.89 26 0.423
221 A 11 10 0.90 26 0.385
222 A 10 9 0.97 24 0.375
223 A 7 6 1.11 19 0.316
224 A 22 21 0.89 28 0.750
225 A 19 18 0.90 28 0.643
226 A 15 14 0.96 26 0.538
227 A 11 10 1.12 21 0.476
228 A 29 28 0.89 28 1.000
229 A 26 25 0.91 28 0.893
230 A 19 18 0.95 26 0.692
231 A 11 10 1.16 21 0.476
232 A 13 12 0.92 26 0.462
233 A 13 12 0.92 26 0.462
234 A 12 11 0.96 24 0.458
235 A 8 7 1.09 19 0.368
236 A 23 22 0.95 28 0.786
237 A 22 21 0.95 28 0.750
238 A 18 17 0.96 26 0.654
239 A 12 11 1.13 21 0.524
240 N/A 1 0 1.00 28 0.000
241 N/A 1 0 1.00 26 0.000
242 N/A 2 0 1.00 20 0.000
243 N/A 1 0 1.00 26 0.000
244 N/A 1 0 1.00 28 0.000
245 A 2 2 1.00 24 0.083
246 A 2 2 1.00 26 0.077
247 A 2 2 1.00 26 0.077
248 A 2 2 1.00 24 0.083
249 A 2 2 1.00 26 0.077
250 A 2 2 1.00 26 0.077
251 A 7 6 1.03 26 0.231
252 A 6 5 1.03 26 0.192
253 A 5 4 1.03 24 0.167
254 A 4 3 1.12 19 0.158
255 N/A 1 0 1.00 26 0.000
256 N/A 1 0 1.00 26 0.000
257 A 11 11 1.01 28 0.393
258 A 9 9 1.00 28 0.321
259 A 6 6 1.00 26 0.231
260 A 3 3 1.00 21 0.143
261 A 7 7 0.97 28 0.250
262 A 9 9 1.02 28 0.321
263 A 18 18 0.98 28 0.643
264 A 12 12 0.91 28 0.429
265 A 10 10 1.00 26 0.385
266 A 4 3 0.72 21 0.143
267 A 13 13 0.96 28 0.464
268 A 18 18 1.01 28 0.643
269 A 21 20 0.99 26 0.769
270 A 16 15 0.99 26 0.577
271 A 12 11 0.95 24 0.458
272 A 5 4 1.05 19 0.211
273 N/A 1 0 1.00 26 0.000
274 N/A 1 0 1.00 26 0.000
275 A 22 21 1.00 28 0.750
276 A 21 20 0.95 28 0.714
277 A 13 13 0.97 26 0.500
278 A 6 5 1.00 21 0.238
279 N/A 1 0 1.00 28 0.000
280 N/A 1 0 1.00 28 0.000
281 F 0 0 N/A 0.000 N/A
282 A 23 22 0.98 28 0.786
283 A 14 13 0.93 26 0.500
284 A 5 4 1.04 21 0.190
285 N/A 1 0 1.00 28 0.000
286 N/A 1 0 1.00 28 0.000
287 A 6 6 0.98 28 0.214
288 A 10 10 1.01 28 0.357
289 A 5 5 1.00 28 0.179
290 N/A 1 0 1.00 26 0.000
291 N/A 2 0 1.00 20 0.000
292 N/A 1 0 1.00 26 0.000
293 N/A 1 0 1.00 28 0.000
294 A 7 6 1.01 26 0.231
295 A 6 5 1.01 26 0.192
296 A 5 4 1.00 24 0.167
297 A 4 3 1.00 19 0.158
298 A 20 19 0.93 28 0.679
299 A 17 16 0.95 28 0.571
300 A 13 12 1.01 26 0.462
301 A 9 8 1.16 21 0.381
302 A 25 24 0.91 28 0.857
303 A 18 17 0.88 28 0.607
304 A 15 14 0.91 26 0.538
305 A 5 4 0.89 21 0.190
306 A 10 9 0.87 26 0.346
307 A 9 8 0.89 26 0.308
308 A 8 7 0.93 24 0.292
309 A 5 4 1.07 19 0.211
310 A 13 12 0.84 28 0.429
311 A 12 11 0.85 28 0.393
312 A 11 10 0.93 26 0.385
313 A 8 7 1.07 21 0.333
314 N/A 1 0 1.00 28 0.000
315 N/A 1 0 1.00 26 0.000
316 N/A 2 0 1.00 20 0.000
317 N/A 1 0 1.00 26 0.000
318 N/A 1 0 1.00 28 0.000
319 A 6 5 1.08 24 0.208
320 A 9 8 0.97 26 0.308
321 A 10 9 0.91 26 0.346
322 A 10 9 1.10 24 0.375
323 A 13 12 0.99 26 0.462
324 A 16 15 0.89 26 0.577
325 F 0 0 N/A 0.000 N/A
326 A 29 28 1.13 32 0.875
327 A 22 21 1.16 30 0.700
328 A 10 9 1.16 25 0.360
329 F 0 0 N/A 0.000 N/A
330 A 30 29 1.24 34 0.853
331 A 27 26 1.22 32 0.812
332 A 6 5 0.97 27 0.185
333 F 0 0 N/A 0.000 N/A
334 F 0 0 N/A 0.000 N/A
335 F 0 0 N/A 0.000 N/A
336 A 11 10 1.11 27 0.370
337 F 0 0 N/A 0.000 N/A
338 F 0 0 N/A 0.000 N/A
339 F 0 0 N/A 0.000 N/A
340 A 6 5 1.00 27 0.185
341 F 0 0 N/A 0.000 N/A
342 F 0 0 N/A 0.000 N/A
343 F 0 0 N/A 0.000 N/A
344 A 10 9 1.18 29 0.310
345 F 0 0 N/A 0.000 N/A
346 F 0 0 N/A 0.000 N/A
347 F 0 0 N/A 0.000 N/A
348 A 6 5 0.94 29 0.172

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