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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 [1.41667000000000010]

# 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 11 10 1.10 10 1.000
2 A 8 7 1.08 10 0.700
3 A 9 8 1.04 8 1.000
4 A 4 3 0.91 6 0.500
5 A 9 8 1.04 10 0.800
6 A 6 5 1.03 10 0.500
7 A 8 7 1.06 10 0.700
8 A 9 8 1.13 10 0.800
9 A 11 10 1.19 10 1.000
10 A 7 6 0.92 12 0.500
11 A 6 5 0.96 12 0.417
12 A 7 6 0.95 10 0.600
13 A 5 4 1.04 8 0.500
14 A 10 9 1.10 12 0.750
15 A 13 12 0.90 12 1.000
16 A 18 17 1.03 12 1.417
17 A 8 7 0.90 12 0.583
18 A 9 8 0.94 10 0.800
19 A 6 5 0.94 8 0.625
20 A 11 10 1.09 12 0.833
21 A 14 13 0.94 12 1.083
22 A 6 5 0.87 12 0.417
23 A 7 6 0.93 10 0.600
24 A 5 4 1.00 8 0.500
25 N/A 5 0 1.00 12 0.000
26 A 5 4 1.71 12 0.333
27 A 6 5 1.49 10 0.500
28 A 6 5 0.95 8 0.625
29 N/A 5 0 1.00 12 0.000
30 A 5 4 1.31 12 0.333
31 A 6 5 1.24 10 0.500
32 A 7 6 0.92 8 0.750
33 N/A 5 0 1.00 12 0.000
34 A 8 7 1.06 18 0.389
35 A 9 8 1.11 16 0.500
36 A 13 12 0.97 14 0.857
37 A 9 8 1.13 16 0.500
38 A 13 12 0.94 14 0.857
39 A 9 8 1.17 16 0.500
40 A 15 14 0.94 14 1.000
41 A 15 14 0.94 14 1.000
42 A 8 7 0.98 18 0.389
43 A 9 8 0.99 16 0.500
44 A 11 10 1.01 14 0.714
45 A 6 5 0.95 16 0.312
46 A 13 12 1.00 14 0.857
47 A 6 5 0.94 16 0.312
48 A 13 12 0.99 14 0.857
49 A 6 5 0.94 16 0.312
50 A 15 14 1.02 14 1.000
51 N/A 3 0 1.00 16 0.000
52 A 6 5 0.97 16 0.312
53 A 7 6 0.97 14 0.429
54 A 7 6 1.02 12 0.500
55 N/A 5 0 1.00 16 0.000
56 A 7 6 0.79 21 0.286
57 A 7 6 0.92 21 0.286
58 A 7 6 0.84 21 0.286
59 A 6 5 0.96 19 0.263
60 A 1 1 1.00 10 0.100
61 A 11 10 0.97 21 0.476
62 A 7 6 0.86 21 0.286
63 A 5 4 0.92 21 0.190
64 A 8 7 0.83 21 0.333
65 A 6 5 0.93 21 0.238
66 A 9 8 0.84 21 0.381
67 A 10 9 0.87 23 0.391
68 A 9 8 0.88 23 0.348
69 A 8 7 0.89 23 0.304
70 A 7 6 0.93 21 0.286
71 A 5 4 1.03 12 0.333
72 A 12 11 0.98 23 0.478
73 A 9 8 0.79 23 0.348
74 A 6 5 0.87 23 0.217
75 A 11 10 0.80 23 0.435
76 A 16 15 1.03 23 0.652
77 A 14 13 1.03 23 0.565
78 A 11 10 0.94 23 0.435
79 A 9 8 0.93 21 0.381
80 A 5 4 0.96 12 0.333
81 A 13 12 0.97 23 0.522
82 A 10 9 0.82 23 0.391
83 A 13 12 0.93 23 0.522
84 A 15 14 0.82 23 0.609
85 A 13 12 1.08 23 0.522
86 A 14 13 1.00 23 0.565
87 A 10 9 0.94 21 0.429
88 A 7 6 0.97 12 0.500
89 A 14 13 1.00 23 0.565
90 A 11 10 0.84 23 0.435
91 A 14 13 0.96 23 0.565
92 A 15 14 0.83 23 0.609
93 A 7 6 0.94 12 0.500
94 A 6 5 0.79 23 0.217
95 A 7 6 0.82 23 0.261
96 A 6 5 0.82 23 0.217
97 A 13 12 0.88 21 0.571
98 A 9 8 0.91 12 0.667
99 N/A 4 0 1.00 23 0.000
100 A 5 4 0.81 23 0.174
101 A 5 4 0.84 23 0.174
102 A 5 4 0.84 23 0.174
103 A 10 9 0.92 21 0.429
104 A 11 10 0.95 12 0.833
105 N/A 4 0 1.00 23 0.000
106 A 8 7 1.20 23 0.304
107 A 16 15 1.12 23 0.652
108 A 15 14 1.08 23 0.609
109 A 16 15 0.94 21 0.714
110 A 11 10 0.93 12 0.833
111 N/A 4 0 1.00 23 0.000
112 A 7 6 1.16 23 0.261
113 A 13 12 1.06 23 0.522
114 A 16 15 1.07 23 0.652
115 A 13 12 0.93 21 0.571
116 A 13 12 0.99 12 1.000
117 N/A 4 0 1.00 23 0.000
118 A 13 12 1.01 12 1.000
119 A 8 7 0.92 25 0.280
120 A 9 8 0.93 25 0.320
121 A 8 7 0.95 23 0.304
122 A 13 12 0.97 14 0.857
123 N/A 4 0 1.00 25 0.000
124 A 23 22 1.19 25 0.880
125 A 18 17 1.22 25 0.680
126 A 18 17 0.96 23 0.739
127 A 13 12 0.94 14 0.857
128 N/A 4 0 1.00 25 0.000
129 A 13 12 1.16 25 0.480
130 A 20 19 1.17 25 0.760
131 A 11 10 0.95 23 0.435
132 A 15 14 0.94 14 1.000
133 N/A 4 0 1.00 25 0.000
134 F 0 0 N/A 0.000 N/A
135 A 21 20 0.96 23 0.870
136 A 15 14 0.94 14 1.000
137 N/A 4 0 1.00 25 0.000
138 A 6 5 0.93 25 0.200
139 A 7 6 0.94 25 0.240
140 A 6 5 0.94 25 0.200
141 A 15 14 0.98 23 0.609
142 A 11 10 1.01 14 0.714
143 N/A 4 0 1.00 25 0.000
144 A 5 4 0.93 25 0.160
145 A 5 4 0.97 25 0.160
146 A 5 4 0.98 25 0.160
147 A 12 11 0.98 23 0.478
148 A 13 12 1.00 14 0.857
149 N/A 4 0 1.00 25 0.000
150 A 18 17 1.24 25 0.680
151 A 17 16 1.30 25 0.640
152 A 18 17 0.96 23 0.739
153 A 13 12 0.99 14 0.857
154 N/A 4 0 1.00 25 0.000
155 A 15 14 1.20 25 0.560
156 A 18 17 1.22 25 0.680
157 A 15 14 0.98 23 0.609
158 A 15 14 1.02 14 1.000
159 N/A 4 0 1.00 25 0.000
160 A 7 6 1.04 23 0.261
161 A 6 5 1.03 23 0.217
162 A 5 4 0.97 23 0.174
163 A 6 5 1.02 23 0.217
164 A 7 6 1.04 23 0.261
165 A 8 7 0.95 23 0.304
166 A 7 6 0.92 23 0.261
167 A 6 5 0.86 23 0.217
168 A 7 6 0.89 23 0.261
169 A 8 7 0.94 23 0.304
170 A 4 3 1.01 25 0.120
171 A 4 3 1.01 25 0.120
172 A 4 3 1.01 25 0.120
173 A 4 3 1.01 25 0.120
174 A 4 3 0.99 25 0.120
175 A 4 3 0.99 25 0.120
176 A 4 3 0.98 25 0.120
177 A 4 3 1.01 25 0.120
178 A 4 3 1.01 25 0.120
179 N/A 4 0 1.00 25 0.000
180 N/A 4 0 1.00 25 0.000
181 N/A 4 0 1.00 25 0.000
182 N/A 4 0 1.00 25 0.000
183 N/A 4 0 1.00 23 0.000
184 N/A 4 0 1.00 23 0.000
185 A 4 3 0.96 23 0.130
186 A 4 3 0.98 21 0.143
187 N/A 3 0 1.00 23 0.000
188 A 8 7 0.93 33 0.212
189 A 7 6 0.95 33 0.182
190 A 5 4 0.92 31 0.129
191 A 6 5 0.94 33 0.152
192 A 8 7 0.95 33 0.212
193 A 6 5 0.96 33 0.152
194 A 11 10 0.90 33 0.303
195 A 16 15 1.25 33 0.455
196 A 12 11 1.20 33 0.333
197 A 8 7 1.03 31 0.226
198 A 6 5 0.89 33 0.152
199 A 6 5 1.00 33 0.152
200 A 11 10 1.27 33 0.303
201 A 17 16 1.12 33 0.485
202 A 3 2 1.00 33 0.061
203 A 3 2 1.00 33 0.061
204 A 3 2 1.00 31 0.065
205 A 3 2 1.00 33 0.061
206 A 3 2 1.00 33 0.061
207 A 3 2 1.00 33 0.061
208 A 10 9 1.03 33 0.273
209 A 9 8 1.00 33 0.242
210 A 4 3 0.96 31 0.097
211 N/A 3 0 1.00 33 0.000
212 N/A 4 0 1.00 33 0.000
213 A 3 2 1.00 23 0.087
214 A 3 2 1.00 36 0.056
215 A 6 5 1.02 14 0.357
216 A 7 6 1.15 14 0.429
217 A 6 5 1.05 14 0.357
218 A 6 5 1.09 14 0.357
219 A 3 2 0.89 12 0.167
220 A 2 2 1.00 14 0.143
221 A 6 5 1.00 14 0.357
222 A 3 3 1.00 14 0.214
223 A 7 6 1.00 14 0.429
224 A 4 4 1.06 14 0.286
225 A 8 7 1.04 14 0.500
226 A 5 5 1.09 14 0.357
227 A 5 5 1.14 14 0.357
228 A 7 7 1.08 14 0.500
229 A 4 4 1.08 14 0.286
230 A 1 1 1.00 10 0.100
231 A 3 3 1.00 14 0.214
232 A 7 7 1.02 14 0.500
233 A 4 4 1.07 14 0.286
234 A 8 8 1.06 14 0.571
235 A 9 8 1.15 10 0.800
236 A 9 8 1.17 10 0.800
237 A 8 7 1.13 8 0.875
238 A 7 6 1.05 6 1.000
239 A 9 8 1.23 10 0.800
240 A 3 3 1.00 10 0.300
241 A 4 4 1.10 10 0.400
242 A 5 5 1.15 10 0.500
243 A 6 6 1.17 10 0.600
244 A 9 8 1.04 14 0.571
245 A 5 5 1.06 14 0.357
246 A 8 7 1.00 14 0.500
247 A 4 4 1.00 12 0.333
248 A 1 1 1.00 10 0.100
249 A 2 2 1.00 14 0.143
250 A 3 2 1.00 14 0.143
251 A 7 6 1.09 14 0.429
252 A 7 6 1.05 14 0.429
253 A 8 7 1.15 14 0.500
254 A 3 3 1.00 14 0.214
255 A 3 3 1.00 14 0.214
256 A 3 3 1.00 12 0.250
257 A 1 1 1.00 10 0.100
258 A 2 2 1.00 14 0.143
259 A 3 3 1.00 14 0.214
260 A 3 3 1.01 14 0.214
261 A 9 8 1.19 16 0.500
262 A 9 8 1.18 16 0.500
263 A 3 2 0.91 14 0.143
264 A 2 2 1.00 16 0.125
265 A 6 5 1.00 16 0.312
266 A 7 6 0.99 16 0.375
267 A 10 9 1.05 16 0.562
268 A 10 10 0.86 16 0.625
269 A 7 7 0.81 16 0.438
270 A 1 1 1.00 12 0.083
271 A 4 4 1.00 16 0.250
272 A 9 9 1.18 16 0.562
273 A 11 11 0.85 16 0.688
274 A 5 4 0.74 12 0.333
275 A 5 4 0.79 14 0.286
276 A 3 3 1.00 14 0.214
277 A 2 2 0.97 14 0.143
278 A 2 2 1.00 14 0.143
279 A 1 1 1.00 12 0.083
280 A 1 1 1.00 14 0.071
281 A 1 1 1.00 14 0.071
282 A 2 2 1.04 14 0.143
283 A 3 3 1.00 16 0.188
284 A 2 2 0.98 16 0.125
285 A 2 2 1.00 16 0.125
286 A 1 1 1.00 14 0.071
287 A 1 1 1.00 16 0.062
288 A 1 1 1.00 16 0.062
289 A 2 2 1.03 16 0.125
290 A 2 2 1.00 8 0.250
291 A 2 2 1.00 10 0.200
292 A 2 2 1.00 16 0.125
293 A 2 2 1.02 16 0.125
294 A 1 1 1.00 16 0.062
295 A 1 1 1.00 16 0.062
296 A 1 1 1.00 16 0.062
297 A 2 2 1.02 16 0.125
298 A 2 2 1.00 16 0.125
299 A 2 2 1.00 18 0.111
300 A 2 2 1.02 18 0.111
301 A 1 1 1.00 18 0.056
302 A 1 1 1.00 18 0.056
303 A 1 1 1.00 18 0.056
304 A 2 2 1.01 18 0.111
305 A 2 2 1.00 18 0.111
306 N/A 1 0 1.00 40 0.000
307 A 12 11 1.03 40 0.275
308 A 11 10 1.03 40 0.250
309 A 10 9 1.02 38 0.237
310 N/A 1 0 1.00 40 0.000
311 N/A 1 0 1.00 40 0.000
312 A 4 3 1.00 8 0.375
313 A 10 9 1.01 10 0.900
314 A 5 4 0.90 10 0.400
315 A 5 4 0.91 10 0.400
316 A 6 5 1.02 8 0.625
317 A 3 2 1.05 6 0.333
318 A 5 4 1.00 10 0.400
319 A 5 4 1.00 10 0.400
320 A 5 4 0.92 12 0.333
321 A 5 4 0.94 12 0.333
322 A 5 4 0.96 10 0.400
323 A 4 3 0.97 8 0.375
324 N/A 4 0 1.00 12 0.000
325 N/A 4 0 1.00 12 0.000
326 A 7 6 0.90 12 0.500
327 A 6 5 0.90 12 0.417
328 A 7 6 0.93 10 0.600
329 A 3 2 0.96 8 0.250
330 N/A 6 0 1.00 12 0.000
331 N/A 5 0 1.00 12 0.000
332 A 7 6 0.92 14 0.429
333 A 6 5 0.92 14 0.357
334 A 7 6 0.94 12 0.500
335 A 4 3 0.97 10 0.300
336 N/A 6 0 1.00 14 0.000
337 N/A 5 0 1.00 14 0.000
338 A 8 7 1.03 21 0.333
339 A 7 6 1.02 21 0.286
340 A 6 5 0.98 21 0.238
341 A 5 4 1.00 21 0.190
342 A 5 4 1.00 21 0.190
343 A 6 5 0.99 21 0.238
344 A 7 6 1.02 10 0.600
345 F 0 0 N/A 0.000 N/A
346 A 3 2 1.00 26 0.077
347 A 3 2 1.00 26 0.077
348 A 1 1 1.00 28 0.036
349 F 0 0 N/A 0.000 N/A

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