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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 [31] had the largest ratio of [.666699999999999959]

# 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 3 1.00 8 0.375
2 A 4 3 1.00 8 0.375
3 A 3 3 1.00 6 0.500
4 A 1 1 1.00 8 0.125
5 A 3 3 1.00 8 0.375
6 A 4 3 1.00 8 0.375
7 A 5 3 1.00 8 0.375
8 A 5 3 1.00 8 0.375
9 A 4 3 1.00 8 0.375
10 A 3 3 1.00 8 0.375
11 A 1 1 1.00 4 0.250
12 A 2 2 1.00 8 0.250
13 A 3 3 1.00 8 0.375
14 A 4 3 1.00 8 0.375
15 A 12 5 1.00 14 0.357
16 A 9 5 1.00 14 0.357
17 A 7 5 1.00 12 0.417
18 A 1 1 1.00 6 0.167
19 N/A 0 0 1.00 14 0.000
20 N/A 0 0 1.00 14 0.000
21 N/A 0 0 1.00 14 0.000
22 A 12 6 1.00 10 0.600
23 A 8 6 1.00 10 0.600
24 A 5 5 1.00 8 0.625
25 N/A 0 0 1.00 10 0.000
26 A 5 5 1.00 10 0.500
27 A 8 6 1.00 10 0.600
28 A 12 6 1.00 10 0.600
29 A 10 5 1.00 10 0.500
30 A 6 5 1.00 10 0.500
31 A 4 4 1.00 6 0.667
32 N/A 0 0 1.00 10 0.000
33 N/A 0 0 1.00 10 0.000
34 N/A 0 0 1.00 10 0.000
35 A 16 10 1.00 16 0.625
36 A 10 9 1.00 14 0.643
37 A 4 3 1.00 8 0.375
38 N/A 0 0 1.00 16 0.000
39 N/A 0 0 1.00 16 0.000
40 A 5 5 1.00 17 0.294
41 A 5 5 1.00 15 0.333
42 A 5 5 1.00 13 0.385
43 A 3 1 1.00 17 0.059
44 A 5 5 1.00 17 0.294
45 A 5 5 1.00 17 0.294
46 A 5 5 1.00 19 0.263
47 A 2 2 1.00 19 0.105
48 A 2 2 1.00 17 0.118
49 A 2 2 1.00 19 0.105
50 A 2 2 1.00 19 0.105
51 A 2 2 1.00 19 0.105
52 A 2 2 1.00 19 0.105
53 A 9 4 1.00 17 0.235
54 A 5 4 1.00 17 0.235
55 A 2 2 1.00 15 0.133
56 N/A 0 0 1.00 17 0.000
57 N/A 0 0 1.00 17 0.000
58 N/A 0 0 1.00 17 0.000
59 N/A 0 0 1.00 17 0.000
60 N/A 0 0 1.00 17 0.000
61 N/A 0 0 1.00 14 0.000
62 N/A 0 0 1.00 17 0.000
63 N/A 0 0 1.00 17 0.000
64 A 8 5 1.00 19 0.263
65 A 5 5 1.00 19 0.263
66 A 2 2 1.00 17 0.118
67 A 1 1 1.00 19 0.053
68 A 4 4 1.00 19 0.210
69 A 7 4 1.00 19 0.210
70 A 7 4 1.00 19 0.210
71 A 4 4 1.00 19 0.210
72 A 1 1 1.00 16 0.062
73 A 4 4 1.00 19 0.210
74 A 7 5 1.00 19 0.263
75 A 9 4 1.00 18 0.222
76 A 5 4 1.00 18 0.222
77 A 2 2 1.00 16 0.125
78 N/A 0 0 1.00 18 0.000
79 N/A 0 0 1.00 18 0.000
80 N/A 0 0 1.00 18 0.000
81 A 7 5 1.00 18 0.278
82 A 4 4 1.00 18 0.222
83 A 2 2 1.00 15 0.133
84 A 4 4 1.00 18 0.222
85 A 7 5 1.00 18 0.278
86 A 10 6 1.00 19 0.316
87 A 3 3 1.00 17 0.176
88 N/A 0 0 1.00 19 0.000
89 N/A 0 0 1.00 19 0.000
90 N/A 0 0 1.00 19 0.000
91 N/A 0 0 1.00 19 0.000
92 N/A 0 0 1.00 16 0.000
93 N/A 0 0 1.00 19 0.000
94 N/A 0 0 1.00 19 0.000
95 A 4 3 1.00 40 0.075
96 A 4 4 1.00 18 0.222
97 A 4 4 1.00 18 0.222
98 A 4 4 1.00 18 0.222
99 A 4 4 1.00 18 0.222
100 A 4 4 1.00 15 0.267
101 A 4 4 1.00 16 0.250
102 A 4 4 1.00 15 0.267
103 A 4 4 1.00 16 0.250
104 A 5 3 1.00 8 0.375
105 A 4 3 1.00 8 0.375
106 A 3 3 1.00 6 0.500
107 A 2 2 1.00 8 0.250
108 A 3 3 1.00 8 0.375
109 A 4 3 1.00 8 0.375
110 A 5 3 1.00 8 0.375
111 A 5 3 1.00 8 0.375
112 A 4 3 1.00 8 0.375
113 A 3 3 1.00 8 0.375
114 A 1 1 1.00 4 0.250
115 A 2 2 1.00 8 0.250
116 A 3 3 1.00 8 0.375
117 A 4 3 1.00 8 0.375
118 A 12 5 1.00 14 0.357
119 A 9 5 1.00 14 0.357
120 A 7 5 1.00 12 0.417
121 A 1 1 1.00 6 0.167
122 N/A 0 0 1.00 14 0.000
123 N/A 0 0 1.00 14 0.000
124 N/A 0 0 1.00 14 0.000
125 A 12 6 1.00 10 0.600
126 A 8 6 1.00 10 0.600
127 A 5 5 1.00 8 0.625
128 N/A 0 0 1.00 10 0.000
129 A 5 5 1.00 10 0.500
130 A 8 6 1.00 10 0.600
131 A 12 6 1.00 10 0.600
132 A 10 5 1.00 10 0.500
133 A 6 5 1.00 10 0.500
134 A 4 4 1.00 6 0.667
135 N/A 0 0 1.00 10 0.000
136 N/A 0 0 1.00 10 0.000
137 N/A 0 0 1.00 10 0.000
138 A 16 10 1.00 16 0.625
139 A 10 9 1.00 14 0.643
140 A 4 3 1.00 8 0.375
141 N/A 0 0 1.00 16 0.000
142 N/A 0 0 1.00 16 0.000
143 A 5 5 1.00 17 0.294
144 A 5 5 1.00 15 0.333
145 A 5 5 1.00 13 0.385
146 A 3 1 1.00 17 0.059
147 A 5 5 1.00 17 0.294
148 A 5 5 1.00 17 0.294
149 A 5 5 1.00 19 0.263
150 A 2 2 1.00 19 0.105
151 A 2 2 1.00 17 0.118
152 A 2 2 1.00 19 0.105
153 A 2 2 1.00 19 0.105
154 A 2 2 1.00 19 0.105
155 A 2 2 1.00 19 0.105
156 A 9 4 1.00 17 0.235
157 A 5 4 1.00 17 0.235
158 A 2 2 1.00 15 0.133
159 N/A 0 0 1.00 17 0.000
160 N/A 0 0 1.00 17 0.000
161 N/A 0 0 1.00 17 0.000
162 N/A 0 0 1.00 17 0.000
163 N/A 0 0 1.00 17 0.000
164 N/A 0 0 1.00 14 0.000
165 N/A 0 0 1.00 17 0.000
166 N/A 0 0 1.00 17 0.000
167 A 8 5 1.00 19 0.263
168 A 5 5 1.00 19 0.263
169 A 2 2 1.00 17 0.118
170 A 3 3 1.00 19 0.158
171 A 6 6 1.00 19 0.316
172 A 9 6 1.00 19 0.316
173 A 9 6 1.00 19 0.316
174 A 6 6 1.00 19 0.316
175 A 3 3 1.00 16 0.188
176 A 6 6 1.00 19 0.316
177 A 9 7 1.00 19 0.368
178 A 9 4 1.00 18 0.222
179 A 5 4 1.00 18 0.222
180 A 2 2 1.00 16 0.125
181 N/A 0 0 1.00 18 0.000
182 N/A 0 0 1.00 18 0.000
183 N/A 0 0 1.00 18 0.000
184 A 7 5 1.00 18 0.278
185 A 4 4 1.00 18 0.222
186 A 2 2 1.00 15 0.133
187 A 4 4 1.00 18 0.222
188 A 7 5 1.00 18 0.278
189 A 10 6 1.00 19 0.316
190 A 3 3 1.00 17 0.176
191 N/A 0 0 1.00 19 0.000
192 N/A 0 0 1.00 19 0.000
193 N/A 0 0 1.00 19 0.000
194 N/A 0 0 1.00 19 0.000
195 N/A 0 0 1.00 16 0.000
196 N/A 0 0 1.00 19 0.000
197 N/A 0 0 1.00 19 0.000
198 A 4 3 1.00 40 0.075
199 A 6 6 1.00 18 0.333
200 A 6 6 1.00 18 0.333
201 A 6 6 1.00 18 0.333
202 A 6 6 1.00 18 0.333
203 A 6 6 1.00 15 0.400
204 A 6 6 1.00 16 0.375
205 A 6 6 1.00 15 0.400
206 A 6 6 1.00 16 0.375
207 A 5 3 1.00 8 0.375
208 A 4 3 1.00 8 0.375
209 A 3 3 1.00 6 0.500
210 A 1 1 1.00 8 0.125
211 A 3 3 1.00 8 0.375
212 A 4 3 1.00 8 0.375
213 A 5 3 1.00 8 0.375
214 A 5 3 1.00 8 0.375
215 A 4 3 1.00 8 0.375
216 A 3 3 1.00 8 0.375
217 A 1 1 1.00 4 0.250
218 A 2 2 1.00 8 0.250
219 A 3 3 1.00 8 0.375
220 A 4 3 1.00 8 0.375
221 A 12 5 1.00 14 0.357
222 A 9 5 1.00 14 0.357
223 A 7 5 1.00 12 0.417
224 A 1 1 1.00 6 0.167
225 N/A 0 0 1.00 14 0.000
226 N/A 0 0 1.00 14 0.000
227 N/A 0 0 1.00 14 0.000
228 A 12 6 1.00 10 0.600
229 A 8 6 1.00 10 0.600
230 A 5 5 1.00 8 0.625
231 N/A 0 0 1.00 10 0.000
232 A 5 5 1.00 10 0.500
233 A 8 6 1.00 10 0.600
234 A 12 6 1.00 10 0.600
235 A 10 5 1.00 10 0.500
236 A 6 5 1.00 10 0.500
237 A 4 4 1.00 6 0.667
238 N/A 0 0 1.00 10 0.000
239 N/A 0 0 1.00 10 0.000
240 N/A 0 0 1.00 10 0.000
241 A 16 10 1.00 16 0.625
242 A 10 9 1.00 14 0.643
243 A 4 3 1.00 8 0.375
244 N/A 0 0 1.00 16 0.000
245 N/A 0 0 1.00 16 0.000
246 A 5 5 1.00 17 0.294
247 A 5 5 1.00 15 0.333
248 A 5 5 1.00 13 0.385
249 A 3 1 1.00 17 0.059
250 A 5 5 1.00 17 0.294
251 A 5 5 1.00 17 0.294
252 A 5 5 1.00 19 0.263
253 A 2 2 1.00 18 0.111
254 A 2 2 1.00 16 0.125
255 A 2 2 1.00 18 0.111
256 A 2 2 1.00 18 0.111
257 A 2 2 1.00 18 0.111
258 A 2 2 1.00 18 0.111
259 A 9 4 1.00 17 0.235
260 A 5 4 1.00 17 0.235
261 A 2 2 1.00 15 0.133
262 N/A 0 0 1.00 17 0.000
263 N/A 0 0 1.00 17 0.000
264 N/A 0 0 1.00 17 0.000
265 N/A 0 0 1.00 17 0.000
266 N/A 0 0 1.00 17 0.000
267 N/A 0 0 1.00 14 0.000
268 N/A 0 0 1.00 17 0.000
269 N/A 0 0 1.00 17 0.000
270 A 6 4 1.00 18 0.222
271 A 4 4 1.00 18 0.222
272 A 2 2 1.00 16 0.125
273 A 1 1 1.00 18 0.056
274 A 3 3 1.00 18 0.167
275 A 5 3 1.00 18 0.167
276 A 7 3 1.00 18 0.167
277 A 5 3 1.00 18 0.167
278 A 3 3 1.00 18 0.167
279 A 1 1 1.00 15 0.067
280 A 3 3 1.00 18 0.167
281 A 5 4 1.00 18 0.222
282 A 7 4 1.00 18 0.222
283 A 9 4 1.00 19 0.210
284 A 5 4 1.00 19 0.210
285 A 2 2 1.00 17 0.118
286 N/A 0 0 1.00 19 0.000
287 N/A 0 0 1.00 19 0.000
288 N/A 0 0 1.00 19 0.000
289 A 7 5 1.00 19 0.263
290 A 4 4 1.00 19 0.210
291 A 2 2 1.00 16 0.125
292 A 4 4 1.00 19 0.210
293 A 7 5 1.00 19 0.263
294 A 10 6 1.00 19 0.316
295 A 3 3 1.00 17 0.176
296 N/A 0 0 1.00 19 0.000
297 N/A 0 0 1.00 19 0.000
298 N/A 0 0 1.00 19 0.000
299 N/A 0 0 1.00 19 0.000
300 N/A 0 0 1.00 16 0.000
301 N/A 0 0 1.00 19 0.000
302 N/A 0 0 1.00 19 0.000
303 A 5 3 1.00 40 0.075
304 A 4 4 1.00 18 0.222
305 A 4 4 1.00 18 0.222
306 A 4 4 1.00 18 0.222
307 A 4 4 1.00 18 0.222
308 A 4 4 1.00 15 0.267
309 A 4 4 1.00 16 0.250
310 A 4 4 1.00 15 0.267
311 A 4 4 1.00 16 0.250

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