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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 [207] had the largest ratio of [1.66700000000000004]

# 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 N/A 0 0 1.00 32 0.000
2 A 10 5 1.00 32 0.156
3 A 8 5 1.00 32 0.156
4 A 6 5 1.00 30 0.167
5 A 2 2 1.00 14 0.143
6 N/A 0 0 1.00 32 0.000
7 N/A 0 0 1.00 32 0.000
8 N/A 0 0 1.00 32 0.000
9 A 13 5 1.00 28 0.179
10 A 8 5 1.00 28 0.179
11 A 5 4 1.00 26 0.154
12 A 1 1 1.00 10 0.100
13 N/A 0 0 1.00 28 0.000
14 N/A 0 0 1.00 28 0.000
15 N/A 0 0 1.00 28 0.000
16 A 1 1 1.00 43 0.023
17 A 1 1 1.00 43 0.023
18 A 1 1 1.00 41 0.024
19 A 4 3 1.00 25 0.120
20 A 1 1 1.00 43 0.023
21 A 1 1 1.00 43 0.023
22 A 1 1 1.00 43 0.023
23 A 3 2 1.00 39 0.051
24 A 3 2 1.00 37 0.054
25 A 2 1 1.00 15 0.067
26 A 2 2 1.00 34 0.059
27 A 3 2 1.00 37 0.054
28 A 3 2 1.00 39 0.051
29 A 2 2 1.00 45 0.044
30 N/A 0 0 1.00 40 0.000
31 A 9 4 1.00 40 0.100
32 A 7 4 1.00 40 0.100
33 A 5 4 1.00 38 0.105
34 A 4 3 1.00 22 0.136
35 N/A 0 0 1.00 40 0.000
36 N/A 0 0 1.00 40 0.000
37 N/A 0 0 1.00 40 0.000
38 A 1 1 1.00 60 0.017
39 N/A 0 0 1.00 29 0.000
40 A 1 1 1.00 39 0.026
41 A 1 1 1.00 40 0.025
42 A 1 1 1.00 41 0.024
43 A 1 1 1.00 42 0.024
44 A 1 1 1.00 40 0.025
45 A 1 1 1.00 41 0.024
46 A 3 3 1.00 19 0.158
47 A 3 3 1.00 21 0.143
48 A 3 3 1.00 19 0.158
49 A 3 3 1.00 17 0.176
50 A 4 3 1.00 15 0.200
51 A 1 1 1.00 19 0.053
52 A 3 3 1.00 19 0.158
53 A 3 3 1.00 19 0.158
54 A 3 3 1.00 19 0.158
55 A 2 2 1.00 9 0.222
56 A 1 1 1.00 13 0.077
57 A 3 3 1.00 11 0.273
58 A 1 1 1.00 15 0.067
59 A 3 3 1.00 18 0.167
60 A 3 2 1.00 18 0.111
61 A 3 2 1.00 18 0.111
62 A 3 2 1.00 18 0.111
63 A 3 2 1.00 16 0.125
64 A 3 2 1.00 14 0.143
65 A 7 6 1.00 18 0.333
66 A 3 2 1.00 18 0.111
67 A 3 2 1.00 18 0.111
68 A 3 2 1.00 18 0.111
69 A 3 2 1.00 18 0.111
70 A 5 3 1.00 19 0.158
71 A 7 6 1.00 19 0.316
72 A 7 6 1.00 19 0.316
73 A 7 6 1.00 19 0.316
74 A 7 6 1.00 17 0.353
75 A 6 6 1.00 15 0.400
76 A 7 4 1.00 19 0.210
77 A 7 6 1.00 19 0.316
78 A 7 6 1.00 19 0.316
79 A 7 6 1.00 19 0.316
80 A 7 6 1.00 19 0.316
81 A 6 6 1.00 7 0.857
82 A 7 6 1.00 23 0.261
83 A 7 6 1.00 23 0.261
84 A 7 6 1.00 23 0.261
85 A 7 6 1.00 21 0.286
86 A 6 6 1.00 15 0.400
87 A 9 5 1.00 23 0.217
88 A 7 6 1.00 23 0.261
89 A 7 6 1.00 23 0.261
90 A 7 6 1.00 23 0.261
91 A 7 6 1.00 23 0.261
92 A 6 7 1.00 25 0.280
93 A 8 9 1.00 32 0.281
94 A 20 6 1.00 25 0.240
95 A 20 6 1.00 28 0.214
96 A 14 10 1.00 16 0.625
97 A 27 14 1.00 17 0.824
98 A 28 12 1.00 21 0.571
99 A 27 14 1.00 9 1.556
100 A 34 16 1.00 13 1.231
101 A 25 11 1.00 21 0.524
102 A 20 10 1.00 21 0.476
103 A 16 10 1.00 19 0.526
104 A 13 9 1.00 17 0.529
105 N/A 0 0 1.00 21 0.000
106 A 19 11 1.00 21 0.524
107 A 20 12 1.00 21 0.571
108 A 15 12 1.00 23 0.522
109 A 13 12 1.00 23 0.522
110 A 12 10 1.00 23 0.435
111 A 15 13 1.00 23 0.565
112 A 18 13 1.00 23 0.565
113 A 6 5 1.00 12 0.417
114 A 5 5 1.00 12 0.417
115 A 4 4 1.00 10 0.400
116 A 4 4 1.00 8 0.500
117 N/A 0 0 1.00 12 0.000
118 A 5 4 1.00 20 0.200
119 A 4 4 1.00 20 0.200
120 A 3 3 1.00 18 0.167
121 A 2 2 1.00 16 0.125
122 N/A 0 0 1.00 20 0.000
123 A 6 5 1.00 20 0.250
124 A 5 5 1.00 20 0.250
125 A 4 4 1.00 18 0.222
126 A 4 4 1.00 16 0.250
127 N/A 0 0 1.00 20 0.000
128 A 3 3 1.00 16 0.188
129 A 2 2 1.00 10 0.200
130 A 2 2 1.00 12 0.167
131 A 2 2 1.00 10 0.200
132 A 2 2 1.00 10 0.200
133 A 2 1 1.00 12 0.083
134 A 3 2 1.00 14 0.143
135 A 2 1 1.00 16 0.062
136 A 2 1 1.00 14 0.071
137 A 7 6 1.00 16 0.375
138 A 2 1 1.00 15 0.067
139 A 2 2 1.00 8 0.250
140 A 3 2 1.00 9 0.222
141 A 3 2 1.00 16 0.125
142 A 3 2 1.00 16 0.125
143 A 4 3 1.00 18 0.167
144 A 3 2 1.00 16 0.125
145 A 3 2 1.00 14 0.143
146 A 3 2 1.00 16 0.125
147 A 4 4 1.00 16 0.250
148 A 3 1 1.00 20 0.050
149 A 3 2 1.00 14 0.143
150 A 3 2 1.00 14 0.143
151 A 3 2 1.00 16 0.125
152 A 3 2 1.00 16 0.125
153 A 4 3 1.00 10 0.300
154 A 5 6 1.00 9 0.667
155 A 5 6 1.00 11 0.546
156 A 15 8 1.00 11 0.727
157 A 5 6 1.00 9 0.667
158 A 7 8 1.00 11 0.727
159 A 15 8 1.00 11 0.727
160 A 4 3 1.00 12 0.250
161 A 5 5 1.00 5 1.000
162 A 6 6 1.00 7 0.857
163 A 6 6 1.00 7 0.857
164 A 5 5 1.00 5 1.000
165 A 6 6 1.00 7 0.857
166 A 6 6 1.00 7 0.857
167 A 7 5 1.00 5 1.000
168 A 8 6 1.00 7 0.857
169 A 8 6 1.00 7 0.857
170 A 7 5 1.00 5 1.000
171 A 8 6 1.00 7 0.857
172 A 8 6 1.00 7 0.857
173 A 5 5 1.00 5 1.000
174 A 6 6 1.00 7 0.857
175 A 6 6 1.00 7 0.857
176 A 5 5 1.00 5 1.000
177 A 6 6 1.00 7 0.857
178 A 6 6 1.00 7 0.857
179 A 3 3 1.00 16 0.188
180 A 3 2 1.00 10 0.200
181 A 5 4 1.00 10 0.400
182 A 3 4 1.00 8 0.500
183 A 2 3 1.00 6 0.500
184 A 4 4 1.00 10 0.400
185 A 2 2 1.00 35 0.057
186 A 3 3 1.00 8 0.375
187 A 2 3 1.00 6 0.500
188 A 2 2 1.00 6 0.333
189 A 4 5 1.00 6 0.833
190 A 2 2 1.00 6 0.333
191 A 10 9 1.00 8 1.125
192 A 7 7 1.00 8 0.875
193 A 8 8 1.00 7 1.143
194 A 3 4 1.00 8 0.500
195 A 5 6 1.00 9 0.667
196 A 7 8 1.00 11 0.727
197 A 15 8 1.00 11 0.727
198 A 5 6 1.00 9 0.667
199 A 7 8 1.00 11 0.727
200 A 15 8 1.00 11 0.727
201 A 5 5 1.00 5 1.000
202 A 6 6 1.00 7 0.857
203 A 6 6 1.00 7 0.857
204 A 5 5 1.00 5 1.000
205 A 6 6 1.00 7 0.857
206 A 6 6 1.00 7 0.857
207 A 7 5 1.00 3 1.667
208 A 7 5 1.00 5 1.000
209 A 8 6 1.00 7 0.857
210 A 8 6 1.00 7 0.857
211 A 7 5 1.00 3 1.667
212 A 7 5 1.00 5 1.000
213 A 8 6 1.00 7 0.857
214 A 8 6 1.00 7 0.857
215 A 5 5 1.00 5 1.000
216 A 6 6 1.00 7 0.857
217 A 6 6 1.00 7 0.857
218 A 5 5 1.00 5 1.000
219 A 6 6 1.00 7 0.857
220 A 6 6 1.00 7 0.857
221 A 2 2 1.00 35 0.057
222 A 3 3 1.00 8 0.375
223 A 1 1 1.00 8 0.125
224 A 3 3 1.00 10 0.300
225 A 2 1 1.00 16 0.062
226 A 3 3 1.00 9 0.333
227 A 2 2 1.00 10 0.200
228 A 3 2 1.00 10 0.200
229 A 3 2 1.00 12 0.167
230 A 4 3 1.00 8 0.375
231 A 2 2 1.00 12 0.167
232 A 2 2 1.00 12 0.167
233 A 2 2 1.00 14 0.143
234 A 6 6 1.00 14 0.429
235 A 1 1 1.00 8 0.125
236 A 2 2 1.00 4 0.500
237 A 1 1 1.00 10 0.100
238 A 3 1 1.00 11 0.091
239 A 3 3 1.00 6 0.500
240 A 2 2 1.00 8 0.250
241 A 2 2 1.00 14 0.143
242 A 2 2 1.00 6 0.333
243 A 4 3 1.00 10 0.300
244 A 4 3 1.00 14 0.214
245 A 2 2 1.00 12 0.167
246 A 2 2 1.00 14 0.143
247 A 2 2 1.00 14 0.143
248 A 2 2 1.00 14 0.143
249 A 2 2 1.00 14 0.143
250 A 2 1 1.00 15 0.067
251 A 2 1 1.00 17 0.059
252 A 7 6 1.00 17 0.353
253 A 10 6 1.00 17 0.353
254 A 3 1 1.00 17 0.059
255 A 3 2 1.00 17 0.118
256 A 8 7 1.00 17 0.412
257 A 11 7 1.00 17 0.412
258 A 3 2 1.00 18 0.111
259 A 5 4 1.00 26 0.154
260 A 5 4 1.00 21 0.190
261 A 7 5 1.00 27 0.185
262 A 2 2 1.00 10 0.200
263 A 3 3 1.00 12 0.250
264 A 3 3 1.00 12 0.250
265 A 3 3 1.00 12 0.250
266 A 8 7 1.00 15 0.467
267 A 7 7 1.00 15 0.467
268 A 1 1 1.00 8 0.125
269 A 6 6 1.00 19 0.316
270 A 5 4 1.00 19 0.210
271 A 2 1 1.00 14 0.071
272 A 8 7 1.00 24 0.292
273 A 4 3 1.00 8 0.375
274 A 2 2 1.00 9 0.222
275 A 2 2 1.00 10 0.200
276 A 8 6 1.00 22 0.273
277 A 5 6 1.00 18 0.333
278 A 5 6 1.00 20 0.300
279 A 5 6 1.00 25 0.240
280 A 1 1 1.00 39 0.026
281 A 1 1 1.00 39 0.026
282 A 2 2 1.00 8 0.250
283 A 3 3 1.00 10 0.300
284 A 5 5 1.24 12 0.417
285 A 3 4 1.00 10 0.400
286 N/A 0 0 1.00 10 0.000
287 N/A 0 0 1.00 8 0.000
288 N/A 0 0 1.00 6 0.000
289 N/A 0 0 1.00 10 0.000
290 N/A 0 0 1.00 10 0.000
291 A 2 2 1.00 14 0.143
292 A 2 2 1.00 16 0.125
293 A 8 6 1.00 14 0.429
294 A 5 3 1.00 14 0.214
295 A 6 4 1.00 14 0.286
296 A 4 4 1.00 12 0.333
297 A 5 3 1.00 14 0.214
298 A 7 4 1.00 14 0.286
299 A 2 1 1.00 14 0.071
300 A 3 3 1.00 6 0.500
301 A 4 4 1.00 13 0.308
302 A 4 4 1.00 14 0.286
303 A 4 4 1.00 17 0.235
304 A 4 4 1.00 18 0.222
305 A 13 13 1.00 10 1.300
306 A 12 12 1.00 8 1.500
307 A 7 6 1.00 6 1.000
308 N/A 0 0 1.00 10 0.000
309 N/A 0 0 1.00 10 0.000
310 A 14 12 1.00 13 0.923
311 A 13 11 1.00 11 1.000
312 A 7 6 1.00 9 0.667
313 N/A 0 0 1.00 13 0.000
314 N/A 0 0 1.00 13 0.000

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