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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 [10] had the largest ratio of [1.33299999999999996]

# 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 5 2 1.00 11 0.182
2 A 4 3 1.00 9 0.333
3 A 2 1 1.52 13 0.077
4 A 4 3 1.00 8 0.375
5 A 2 2 1.00 5 0.400
6 A 4 4 1.00 9 0.444
7 A 4 3 1.00 9 0.333
8 A 3 3 1.00 13 0.231
9 A 4 4 1.00 11 0.364
10 A 11 8 1.38 6 1.333
11 A 8 4 1.00 12 0.333
12 A 4 3 1.00 21 0.143
13 A 3 2 1.00 8 0.250
14 A 3 2 1.59 17 0.118
15 A 2 2 1.00 7 0.286
16 A 3 2 1.00 12 0.167
17 A 1 1 1.00 7 0.143
18 A 1 1 1.00 13 0.077
19 A 2 2 1.00 17 0.118
20 F 0 0 N/A 0.000 N/A
21 A 3 3 1.00 14 0.214
22 A 2 2 1.00 9 0.222
23 A 4 2 1.00 11 0.182
24 A 5 4 0.96 17 0.235
25 A 2 1 1.00 19 0.053
26 A 4 2 1.00 9 0.222
27 A 3 3 1.00 14 0.214
28 A 2 1 1.00 11 0.091
29 A 4 3 1.00 27 0.111
30 A 2 2 1.00 4 0.500
31 A 3 2 1.00 9 0.222
32 A 3 3 1.00 11 0.273
33 A 4 2 1.00 4 0.500
34 A 3 3 1.00 12 0.250
35 A 1 1 1.00 3 0.333
36 A 1 1 1.00 2 0.500
37 A 2 1 1.00 15 0.067
38 A 1 1 1.00 13 0.077
39 A 6 2 1.00 11 0.182
40 A 4 2 1.00 8 0.250
41 A 4 4 2.00 7 0.571
42 A 4 4 1.00 15 0.267
43 A 3 3 1.00 12 0.250
44 A 3 2 1.00 8 0.250
45 A 3 3 1.21 13 0.231
46 B 102 2 66.75 9 0.222
47 A 3 3 1.00 9 0.333
48 A 3 2 1.00 34 0.059
49 A 3 3 1.00 15 0.200
50 A 3 2 1.00 9 0.222
51 A 1 1 1.00 8 0.125
52 A 3 2 1.60 21 0.095
53 A 3 2 1.00 15 0.133
54 A 2 2 1.00 11 0.182
55 A 2 2 1.00 14 0.143
56 A 1 1 1.00 4 0.250
57 A 1 1 1.00 6 0.167
58 A 7 6 1.00 23 0.261
59 A 4 4 1.00 21 0.190
60 A 2 1 1.00 34 0.029
61 A 4 3 1.00 12 0.250
62 A 5 5 1.00 9 0.556
63 A 2 2 1.00 15 0.133
64 A 2 1 1.00 9 0.111
65 A 2 0 1.00 7 0.000
66 A 4 4 1.00 15 0.267
67 A 2 2 1.00 11 0.182
68 A 3 3 1.00 9 0.333
69 A 2 2 1.00 9 0.222
70 A 2 2 1.62 11 0.182
71 A 2 2 1.00 6 0.333
72 A 3 2 1.00 13 0.154
73 A 5 4 1.00 10 0.400
74 A 3 3 1.00 11 0.273
75 A 3 1 1.00 11 0.091
76 A 1 1 1.00 3 0.333
77 F 0 0 N/A 0.000 N/A
78 B 1 0 2.09 13 0.000
79 A 2 2 1.00 11 0.182
80 A 2 1 1.00 15 0.067
81 A 3 3 1.00 13 0.231
82 A 2 1 1.00 27 0.037
83 A 1 1 1.00 2 0.500
84 A 4 4 2.00 11 0.364
85 A 3 3 1.71 9 0.333
86 A 3 3 1.00 15 0.200
87 A 2 2 1.00 4 0.500
88 A 5 3 1.73 7 0.429
89 A 3 3 1.00 5 0.600
90 A 4 2 1.00 9 0.222
91 A 3 2 1.00 11 0.182
92 A 2 2 1.00 10 0.200
93 A 4 5 1.00 6 0.833
94 A 2 2 1.00 11 0.182
95 A 2 2 1.00 11 0.182
96 A 3 2 1.00 9 0.222
97 A 1 1 1.00 8 0.125
98 A 3 3 1.00 13 0.231
99 A 1 1 1.00 4 0.250
100 A 4 3 1.00 6 0.500
101 A 1 1 1.00 16 0.062
102 A 4 3 1.00 13 0.231
103 A 1 1 1.00 9 0.111
104 A 2 1 1.00 6 0.167
105 A 2 1 1.00 9 0.111
106 A 2 2 1.00 2 1.000
107 A 2 1 1.00 9 0.111
108 A 3 3 1.00 4 0.750
109 A 3 2 1.00 10 0.200
110 A 13 8 1.47 18 0.444
111 A 3 3 1.00 4 0.750
112 A 4 4 1.00 13 0.308
113 A 2 2 1.00 8 0.250
114 A 3 2 1.00 19 0.105
115 A 3 3 1.00 12 0.250
116 A 3 2 1.00 15 0.133
117 A 1 1 1.50 6 0.167
118 B 7 2 5.80 11 0.182
119 B 2 1 2.31 11 0.091
120 A 2 2 1.00 12 0.167
121 A 1 1 1.00 2 0.500
122 A 2 2 1.00 7 0.286
123 A 2 2 1.00 6 0.333
124 A 5 5 1.00 12 0.417
125 A 1 1 1.00 3 0.333
126 A 2 1 1.27 12 0.083
127 A 3 2 1.00 9 0.222
128 A 3 3 1.00 11 0.273
129 A 1 1 1.00 9 0.111
130 A 3 1 1.00 14 0.071
131 A 5 5 1.00 10 0.500
132 A 6 3 1.00 11 0.273
133 A 3 2 1.00 15 0.133
134 A 3 2 1.00 4 0.500
135 A 3 2 1.00 7 0.286
136 A 1 1 1.00 14 0.071
137 A 1 1 1.00 2 0.500
138 A 1 0 1.00 7 0.000
139 A 1 1 1.00 6 0.167
140 F 0 0 N/A 0.000 N/A
141 A 2 1 1.00 11 0.091
142 A 3 3 1.00 8 0.375
143 A 5 4 1.00 10 0.400
144 A 1 1 1.00 2 0.500
145 A 1 1 1.00 11 0.091
146 A 2 2 1.00 11 0.182
147 F 0 0 N/A 0.000 N/A
148 A 3 1 1.00 25 0.040
149 A 3 3 1.00 9 0.333
150 A 11 4 1.00 21 0.190
151 A 3 2 1.00 13 0.154
152 A 3 3 1.00 12 0.250
153 A 4 3 1.00 11 0.273
154 A 2 1 1.00 6 0.167
155 A 5 4 1.00 15 0.267
156 A 1 1 1.50 6 0.167
157 A 1 1 1.00 13 0.077
158 A 1 1 1.00 6 0.167
159 A 1 1 1.00 2 0.500
160 A 2 2 1.00 9 0.222
161 A 3 3 1.00 13 0.231
162 A 4 4 1.00 11 0.364
163 A 2 2 1.00 2 1.000
164 A 2 2 1.00 12 0.167
165 A 3 3 1.00 6 0.500
166 A 3 3 1.00 7 0.429
167 A 1 1 1.00 12 0.083
168 A 3 3 1.00 11 0.273
169 A 3 3 1.00 8 0.375
170 A 1 1 1.00 8 0.125
171 A 3 2 1.00 9 0.222
172 A 7 3 1.00 18 0.167
173 A 5 5 1.00 25 0.200
174 A 1 1 1.00 10 0.100
175 A 4 3 1.00 13 0.231
176 A 2 2 1.00 11 0.182
177 A 1 1 1.00 4 0.250
178 A 2 1 1.00 7 0.143
179 A 2 2 1.00 11 0.182
180 F 0 0 N/A 0.000 N/A
181 A 1 1 1.00 15 0.067
182 A 3 3 1.00 10 0.300
183 A 1 1 1.00 6 0.167
184 A 3 3 1.00 13 0.231
185 A 1 1 1.00 10 0.100
186 A 2 2 1.00 4 0.500
187 A 6 4 1.71 25 0.160
188 A 4 4 1.00 13 0.308
189 A 2 2 1.00 13 0.154
190 A 1 1 1.00 9 0.111
191 A 2 2 1.00 15 0.133
192 A 2 2 1.00 14 0.143
193 A 2 2 1.00 5 0.400
194 N/A 0 0 1.00 3 0.000
195 A 1 1 1.00 13 0.077
196 B 5 2 2.50 17 0.118
197 A 1 1 1.00 9 0.111
198 A 2 2 1.08 4 0.500
199 A 6 4 1.00 21 0.190
200 A 3 2 1.00 10 0.200
201 A 2 2 1.00 13 0.154
202 A 3 3 1.00 6 0.500
203 A 3 3 1.00 11 0.273
204 A 5 2 1.00 11 0.182
205 A 1 1 1.48 9 0.111
206 A 1 1 1.00 1 1.000
207 B 14 5 24.00 21 0.238
208 A 1 1 1.00 20 0.050
209 A 3 3 1.00 11 0.273
210 A 2 2 1.00 9 0.222
211 F 0 0 N/A 0.000 N/A
212 A 3 2 1.00 18 0.111
213 A 1 1 1.00 9 0.111
214 A 2 4 2.00 12 0.333
215 A 4 4 1.00 7 0.571
216 A 2 2 1.00 9 0.222
217 A 2 2 1.00 12 0.167
218 A 3 3 1.00 11 0.273
219 A 4 3 1.00 15 0.200
220 A 2 1 1.00 21 0.048
221 A 3 3 1.00 6 0.500
222 A 1 1 1.00 18 0.056
223 A 2 2 1.00 6 0.333
224 A 4 3 1.00 8 0.375
225 N/A 0 0 1.00 9 0.000
226 N/A 0 0 1.00 14 0.000
227 A 2 1 1.00 9 0.111
228 A 5 5 1.73 15 0.333
229 A 5 4 1.00 12 0.333
230 A 2 2 1.00 11 0.182
231 A 3 3 1.00 11 0.273
232 A 1 1 1.00 11 0.091
233 A 8 4 1.00 9 0.444
234 A 2 2 1.50 12 0.167
235 A 5 2 1.00 19 0.105
236 N/A 0 0 1.00 5 0.000
237 A 3 3 1.00 8 0.375
238 A 2 2 1.00 11 0.182
239 A 2 2 1.00 4 0.500
240 A 6 3 1.00 17 0.176
241 A 3 2 1.00 13 0.154
242 B 5 4 8.04 23 0.174
243 F 0 0 N/A 0.000 N/A
244 B 9 3 2.75 19 0.158
245 F 0 0 N/A 0.000 N/A
246 C 11 5 14.00 37 0.135
247 A 2 2 1.00 11 0.182
248 A 2 2 1.00 8 0.250
249 A 4 4 1.00 8 0.500
250 F 0 0 N/A 0.000 N/A
251 A 2 1 1.00 14 0.071
252 A 6 4 1.00 22 0.182
253 A 3 2 1.47 9 0.222
254 B 6 6 3.12 11 0.546
255 A 3 2 1.00 9 0.222
256 A 3 3 1.00 9 0.333
257 F 0 0 N/A 0.000 N/A
258 C 7 5 9.00 19 0.263
259 A 5 5 1.00 12 0.417
260 A 29 4 1.00 13 0.308
261 A 1 1 1.00 21 0.048
262 A 6 3 1.00 34 0.088
263 A 1 1 1.00 7 0.143
264 A 25 5 1.00 20 0.250
265 F 0 0 N/A 0.000 N/A
266 B 3 3 2.21 22 0.136
267 A 2 1 1.00 13 0.077
268 A 3 2 1.79 6 0.333
269 A 4 3 1.00 19 0.158
270 A 2 2 1.00 12 0.167
271 A 8 7 1.00 16 0.438
272 B 53 5 2.11 11 0.454
273 A 4 3 1.00 29 0.103
274 A 3 2 1.00 7 0.286
275 F 0 0 N/A 0.000 N/A
276 B 4 3 3.12 39 0.077
277 F 0 0 N/A 0.000 N/A
278 A 3 2 1.00 15 0.133
279 A 1 1 1.00 1 1.000
280 A 1 1 1.00 2 0.500
281 A 4 4 1.00 19 0.210
282 A 2 1 1.00 29 0.034
283 A 3 2 1.00 17 0.118
284 A 6 4 2.00 13 0.308
285 A 13 4 1.00 25 0.160
286 A 1 1 1.00 13 0.077
287 B 8 4 3.00 43 0.093
288 C 12 3 50.00 19 0.158
289 A 1 1 1.00 11 0.091
290 A 7 6 1.00 31 0.194
291 A 4 3 1.00 15 0.200
292 A 3 2 1.89 17 0.118
293 F 0 0 N/A 0.000 N/A
294 C 4 5 9.67 16 0.312
295 A 1 0 1.00 20 0.000
296 A 2 1 1.00 17 0.059
297 A 4 4 1.00 4 1.000
298 F 0 0 N/A 0.000 N/A
299 A 2 2 1.00 13 0.154
300 A 3 2 1.00 6 0.333
301 A 4 3 1.00 17 0.176
302 A 8 4 1.00 25 0.160
303 A 3 4 1.00 8 0.500
304 A 1 1 1.00 40 0.025
305 A 13 4 1.26 7 0.571
306 A 3 2 1.00 18 0.111
307 F 0 0 N/A 0.000 N/A
308 A 1 1 1.00 16 0.062
309 A 3 2 1.00 13 0.154
310 A 2 2 1.00 8 0.250
311 A 3 2 1.00 4 0.500
312 A 4 4 1.00 9 0.444
313 F 0 0 N/A 0.000 N/A
314 A 3 2 1.00 25 0.080
315 A 4 2 1.31 17 0.118
316 A 3 1 1.00 17 0.059
317 F 0 0 N/A 0.000 N/A
318 A 6 5 1.00 14 0.357
319 A 10 4 1.22 47 0.085
320 F 0 0 N/A 0.000 N/A
321 A 4 3 1.00 16 0.188

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