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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 [305] had the largest ratio of [3.42857000000000012]

# 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 3 3 1.00 11 0.273
2 A 7 6 1.12 9 0.667
3 A 2 2 1.52 13 0.154
4 A 4 4 0.96 8 0.500
5 A 2 2 1.00 5 0.400
6 A 5 4 1.25 9 0.444
7 A 6 5 1.00 9 0.556
8 A 4 3 1.00 13 0.231
9 A 5 4 1.31 11 0.364
10 A 12 11 1.55 6 1.833
11 A 2 2 1.00 12 0.167
12 A 6 5 1.19 21 0.238
13 A 2 2 1.00 8 0.250
14 A 4 3 1.72 17 0.176
15 A 2 2 1.00 7 0.286
16 A 2 2 1.00 12 0.167
17 A 1 1 1.00 7 0.143
18 A 2 2 1.00 13 0.154
19 A 3 2 1.00 17 0.118
20 C 5 4 3.96 7 0.571
21 A 4 3 1.00 14 0.214
22 A 2 2 1.00 9 0.222
23 A 1 1 1.00 11 0.091
24 A 6 5 1.00 17 0.294
25 A 2 2 1.00 19 0.105
26 A 1 1 1.00 9 0.111
27 A 4 3 1.00 14 0.214
28 A 2 2 1.00 11 0.182
29 A 3 3 1.00 27 0.111
30 A 5 4 1.00 4 1.000
31 A 5 4 1.00 9 0.444
32 A 6 6 1.00 11 0.545
33 A 7 7 1.29 4 1.750
34 A 3 3 1.00 12 0.250
35 A 1 1 1.00 3 0.333
36 A 2 2 1.00 2 1.000
37 A 4 3 0.46 15 0.200
38 A 1 1 1.00 13 0.077
39 A 3 3 1.00 11 0.273
40 A 1 1 1.00 8 0.125
41 B 5 4 2.38 7 0.571
42 A 5 4 1.00 15 0.267
43 A 4 3 1.00 12 0.250
44 A 2 2 1.00 8 0.250
45 A 4 3 1.28 13 0.231
46 B 3 3 66.75 9 0.333
47 A 4 3 1.00 9 0.333
48 A 4 4 1.00 34 0.118
49 A 4 3 1.50 15 0.200
50 A 5 4 0.90 9 0.444
51 A 1 1 1.00 8 0.125
52 B 5 4 2.55 21 0.190
53 A 4 3 1.07 15 0.200
54 A 2 2 1.00 11 0.182
55 A 3 2 1.70 14 0.143
56 A 1 1 1.00 4 0.250
57 A 2 2 1.00 6 0.333
58 A 11 10 1.09 23 0.435
59 A 6 5 1.00 21 0.238
60 A 4 4 1.00 34 0.118
61 A 1 1 1.00 12 0.083
62 A 7 6 1.12 9 0.667
63 A 2 2 1.00 15 0.133
64 A 2 2 1.00 9 0.222
65 A 4 3 1.00 7 0.429
66 A 5 4 1.12 15 0.267
67 A 3 2 1.00 11 0.182
68 A 4 3 1.00 9 0.333
69 A 3 2 1.00 9 0.222
70 A 3 3 1.62 11 0.273
71 A 4 4 1.00 6 0.667
72 A 4 3 1.15 13 0.231
73 A 2 2 1.00 10 0.200
74 A 6 6 1.00 11 0.545
75 A 1 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 A 2 2 1.00 13 0.154
79 A 2 2 1.00 11 0.182
80 A 1 1 1.00 15 0.067
81 A 6 6 1.00 13 0.462
82 A 2 2 1.00 27 0.074
83 A 1 1 1.00 2 0.500
84 B 5 4 3.17 11 0.364
85 B 5 5 2.07 9 0.556
86 A 5 4 1.00 15 0.267
87 A 3 3 1.00 4 0.750
88 A 6 5 1.90 7 0.714
89 A 6 5 1.00 5 1.000
90 A 1 1 1.00 9 0.111
91 A 4 3 0.89 11 0.273
92 A 3 2 1.00 10 0.200
93 A 8 7 1.00 6 1.167
94 A 3 2 1.00 11 0.182
95 A 2 2 1.00 11 0.182
96 A 6 5 1.00 9 0.556
97 A 2 2 1.00 8 0.250
98 A 4 3 1.00 13 0.231
99 A 1 1 1.00 4 0.250
100 A 9 8 1.06 6 1.333
101 A 1 1 1.00 16 0.062
102 A 5 4 1.09 13 0.308
103 A 2 2 1.00 9 0.222
104 A 1 1 1.00 6 0.167
105 A 2 2 1.00 9 0.222
106 A 2 2 1.00 2 1.000
107 A 2 2 1.00 9 0.222
108 A 3 3 0.95 4 0.750
109 A 2 2 1.00 10 0.200
110 A 2 2 1.47 18 0.111
111 A 3 3 1.04 4 0.750
112 A 5 4 1.27 13 0.308
113 A 5 5 1.00 8 0.625
114 A 3 3 1.16 19 0.158
115 A 4 3 0.55 12 0.250
116 A 4 3 1.11 15 0.200
117 A 2 2 1.50 6 0.333
118 B 1 1 5.80 11 0.091
119 B 2 2 2.31 11 0.182
120 A 4 3 1.00 12 0.250
121 A 2 2 1.00 2 1.000
122 A 3 2 1.00 7 0.286
123 A 2 2 1.00 6 0.333
124 A 7 6 1.55 12 0.500
125 A 1 1 1.00 3 0.333
126 A 2 2 1.27 12 0.167
127 A 4 3 1.07 9 0.333
128 A 6 6 1.00 11 0.545
129 A 1 1 1.00 9 0.111
130 A 5 4 1.00 14 0.286
131 A 6 5 0.97 10 0.500
132 A 6 5 0.52 11 0.455
133 A 4 3 1.25 15 0.200
134 A 5 5 1.00 4 1.250
135 A 5 4 1.00 7 0.571
136 A 1 1 1.00 14 0.071
137 A 3 3 1.00 2 1.500
138 A 1 1 1.00 7 0.143
139 A 1 1 1.00 6 0.167
140 F 0 0 N/A 0.000 N/A
141 A 3 2 1.00 11 0.182
142 A 5 5 1.00 8 0.625
143 A 6 5 1.11 10 0.500
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 4 3 1.11 25 0.120
149 A 5 4 1.00 9 0.444
150 A 1 1 1.00 21 0.048
151 A 4 3 1.15 13 0.231
152 A 4 3 1.00 12 0.250
153 A 5 4 0.93 11 0.364
154 A 1 1 1.00 6 0.167
155 A 2 2 1.00 15 0.133
156 A 2 2 1.50 6 0.333
157 A 1 1 1.00 13 0.077
158 A 1 1 1.00 6 0.167
159 A 2 2 1.00 2 1.000
160 A 2 2 1.00 9 0.222
161 A 4 3 1.00 13 0.231
162 A 5 4 1.31 11 0.364
163 A 2 2 1.00 2 1.000
164 A 2 2 1.00 12 0.167
165 A 6 5 1.00 6 0.833
166 A 3 3 1.00 7 0.429
167 A 1 1 1.00 12 0.083
168 A 4 3 1.00 11 0.273
169 A 5 4 1.00 8 0.500
170 A 2 2 1.00 8 0.250
171 A 4 3 1.00 9 0.333
172 A 2 2 1.00 18 0.111
173 A 6 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 3 2 1.00 11 0.182
177 A 2 2 1.00 4 0.500
178 A 4 3 1.50 7 0.429
179 A 3 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 5 4 1.00 10 0.400
183 A 2 2 1.00 6 0.333
184 A 4 3 1.00 13 0.231
185 A 1 1 1.00 10 0.100
186 A 4 4 1.00 4 1.000
187 B 6 5 2.29 25 0.200
188 A 5 4 1.00 13 0.308
189 A 4 3 1.00 13 0.231
190 A 1 1 1.00 9 0.111
191 A 3 2 1.00 15 0.133
192 A 2 2 1.00 14 0.143
193 A 4 3 1.00 5 0.600
194 N/A 4 0 1.00 3 0.000
195 A 1 1 1.00 13 0.077
196 B 1 1 2.50 17 0.059
197 A 1 1 1.00 9 0.111
198 A 2 2 1.08 4 0.500
199 A 1 1 1.00 21 0.048
200 A 5 4 1.00 10 0.400
201 A 3 2 1.00 13 0.154
202 A 6 5 1.00 6 0.833
203 A 4 3 1.00 11 0.273
204 A 3 3 1.00 11 0.273
205 A 1 1 1.48 9 0.111
206 A 1 1 1.00 1 1.000
207 B 3 3 12.64 21 0.143
208 A 1 1 1.00 20 0.050
209 A 5 5 1.00 11 0.455
210 A 2 2 1.00 9 0.222
211 F 0 0 N/A 0.000 N/A
212 A 5 4 1.73 18 0.222
213 A 1 1 1.00 9 0.111
214 A 2 2 2.00 12 0.167
215 A 5 4 1.30 7 0.571
216 A 3 2 1.00 9 0.222
217 A 2 2 1.00 12 0.167
218 A 4 3 1.00 11 0.273
219 A 5 4 1.65 15 0.267
220 A 4 3 1.33 21 0.143
221 A 3 3 1.06 6 0.500
222 A 1 1 1.00 18 0.056
223 A 2 2 1.00 6 0.333
224 A 8 7 0.92 8 0.875
225 N/A 2 0 1.00 9 0.000
226 N/A 2 0 1.00 14 0.000
227 A 2 2 1.00 9 0.222
228 A 7 6 1.91 15 0.400
229 A 4 4 1.00 12 0.333
230 A 2 2 1.00 11 0.182
231 A 4 3 1.00 11 0.273
232 A 1 1 1.00 11 0.091
233 A 2 2 1.00 9 0.222
234 C 4 4 2.07 12 0.333
235 A 3 3 1.22 19 0.158
236 N/A 1 0 1.00 5 0.000
237 A 6 5 0.90 8 0.625
238 A 3 2 1.00 11 0.182
239 A 4 3 1.00 4 0.750
240 A 1 1 1.00 17 0.059
241 A 4 3 1.06 13 0.231
242 B 6 5 8.08 23 0.217
243 F 0 0 N/A 0.000 N/A
244 B 1 1 2.75 19 0.053
245 F 0 0 N/A 0.000 N/A
246 C 1 1 14.00 37 0.027
247 A 3 2 1.00 11 0.182
248 A 4 3 0.47 8 0.375
249 A 4 4 1.00 8 0.500
250 F 0 0 N/A 0.000 N/A
251 A 2 2 1.00 14 0.143
252 A 2 2 1.00 22 0.091
253 A 5 4 1.47 9 0.444
254 B 11 10 3.88 11 0.909
255 A 6 5 1.00 9 0.556
256 A 4 3 0.91 9 0.333
257 C 3 3 36.17 16 0.188
258 C 2 2 9.00 19 0.105
259 A 6 5 1.16 12 0.417
260 A 3 3 1.00 13 0.231
261 A 2 2 1.00 21 0.095
262 A 1 1 1.00 34 0.029
263 A 1 1 1.00 7 0.143
264 A 3 3 1.00 20 0.150
265 F 0 0 N/A 0.000 N/A
266 B 4 3 2.21 22 0.136
267 A 2 2 1.00 13 0.154
268 A 2 2 1.79 6 0.333
269 A 2 2 1.12 19 0.105
270 A 2 2 1.00 12 0.167
271 A 2 2 1.00 16 0.125
272 B 4 4 2.36 11 0.364
273 A 5 4 1.14 29 0.138
274 A 3 3 1.16 7 0.429
275 F 0 0 N/A 0.000 N/A
276 B 6 5 2.59 39 0.128
277 F 0 0 N/A 0.000 N/A
278 A 3 3 1.04 15 0.200
279 A 1 1 1.00 1 1.000
280 A 2 2 1.00 2 1.000
281 A 5 4 1.00 19 0.211
282 A 2 2 1.00 29 0.069
283 A 3 3 1.00 17 0.176
284 A 1 1 2.00 13 0.077
285 A 1 1 1.00 25 0.040
286 A 1 1 1.00 13 0.077
287 B 1 1 3.00 43 0.023
288 C 1 1 50.00 19 0.053
289 A 1 1 1.00 11 0.091
290 A 1 1 1.00 31 0.032
291 A 5 4 1.15 15 0.267
292 A 1 1 1.89 17 0.059
293 F 0 0 N/A 0.000 N/A
294 C 6 5 8.22 16 0.312
295 A 1 1 1.00 20 0.050
296 A 2 2 1.00 17 0.118
297 A 8 7 1.21 4 1.750
298 F 0 0 N/A 0.000 N/A
299 A 2 2 0.88 13 0.154
300 A 5 5 1.11 6 0.833
301 A 7 6 1.55 17 0.353
302 A 1 1 1.00 25 0.040
303 A 5 5 1.00 8 0.625
304 A 1 1 1.00 40 0.025
305 B 25 24 2.21 7 3.429
306 A 6 5 1.00 18 0.278
307 F 0 0 N/A 0.000 N/A
308 A 1 1 1.00 16 0.062
309 A 2 2 1.00 13 0.154
310 A 4 3 1.00 8 0.375
311 A 6 6 1.00 4 1.500
312 A 5 4 1.00 9 0.444
313 F 0 0 N/A 0.000 N/A
314 A 2 2 1.00 25 0.080
315 A 7 6 0.82 17 0.353
316 A 1 1 1.00 17 0.059
317 F 0 0 N/A 0.000 N/A
318 A 8 7 1.07 14 0.500
319 B 19 18 2.12 47 0.383
320 F 0 0 N/A 0.000 N/A
321 A 4 3 1.16 16 0.188

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