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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 [22] had the largest ratio of [1.19999999999999996]

# 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 5 1.18 8 0.625
2 A 4 4 1.20 8 0.500
3 A 3 3 1.20 6 0.500
4 A 1 1 1.00 8 0.125
5 A 3 3 1.12 8 0.375
6 A 4 4 1.06 8 0.500
7 A 5 5 1.04 8 0.625
8 A 5 5 1.03 8 0.625
9 A 4 4 1.02 8 0.500
10 A 3 3 1.02 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 4 1.00 8 0.500
15 A 3 3 1.01 14 0.214
16 A 3 3 1.06 14 0.214
17 A 3 3 1.13 12 0.250
18 A 1 1 1.00 6 0.167
19 N/A 1 0 1.00 14 0.000
20 N/A 2 0 1.00 14 0.000
21 N/A 4 0 1.00 14 0.000
22 A 13 12 1.52 10 1.200
23 A 9 8 1.30 10 0.800
24 A 6 5 1.20 8 0.625
25 N/A 1 0 1.00 10 0.000
26 A 6 5 1.10 10 0.500
27 A 9 8 1.15 10 0.800
28 A 13 12 1.36 10 1.200
29 A 10 10 1.58 10 1.000
30 A 6 6 1.32 10 0.600
31 A 4 4 1.07 6 0.667
32 N/A 1 0 1.00 10 0.000
33 N/A 1 0 1.00 10 0.000
34 N/A 1 0 1.00 10 0.000
35 A 3 2 0.91 16 0.125
36 A 3 2 0.91 14 0.143
37 A 5 4 1.00 8 0.500
38 N/A 1 0 1.00 16 0.000
39 N/A 1 0 1.00 16 0.000
40 A 6 5 1.00 17 0.294
41 A 6 5 1.18 15 0.333
42 A 6 5 1.00 13 0.385
43 A 4 3 0.98 17 0.176
44 A 6 5 1.00 17 0.294
45 A 6 5 1.16 17 0.294
46 A 6 5 1.13 19 0.263
47 A 3 2 1.00 19 0.105
48 A 3 2 1.00 17 0.118
49 A 3 2 1.00 19 0.105
50 A 3 2 1.00 19 0.105
51 A 3 2 1.00 19 0.105
52 A 3 2 1.00 19 0.105
53 A 9 9 1.12 17 0.529
54 A 5 5 1.06 17 0.294
55 A 2 2 1.00 15 0.133
56 N/A 1 0 1.00 17 0.000
57 N/A 4 0 1.00 17 0.000
58 N/A 8 0 1.00 17 0.000
59 N/A 6 0 1.00 17 0.000
60 N/A 3 0 1.00 17 0.000
61 N/A 1 0 1.00 14 0.000
62 N/A 3 0 1.00 17 0.000
63 N/A 6 0 1.00 17 0.000
64 A 6 6 1.14 19 0.316
65 A 4 4 1.09 19 0.211
66 A 2 2 1.00 17 0.118
67 A 1 1 1.00 19 0.053
68 A 3 3 1.00 19 0.158
69 A 5 5 1.02 19 0.263
70 A 5 5 1.07 19 0.263
71 A 3 3 1.00 19 0.158
72 A 1 1 1.00 16 0.062
73 A 3 3 1.00 19 0.158
74 A 5 5 0.97 19 0.263
75 A 9 9 1.75 18 0.500
76 A 5 5 1.39 18 0.278
77 A 2 2 1.00 16 0.125
78 N/A 1 0 1.00 18 0.000
79 N/A 4 0 1.00 18 0.000
80 N/A 8 0 1.00 18 0.000
81 A 8 7 1.27 18 0.389
82 A 5 4 1.00 18 0.222
83 A 3 2 1.00 15 0.133
84 A 5 4 1.00 18 0.222
85 A 8 7 1.14 18 0.389
86 A 10 10 1.11 19 0.526
87 A 3 3 1.10 17 0.176
88 N/A 1 0 1.00 19 0.000
89 N/A 6 0 1.00 19 0.000
90 N/A 16 0 1.00 19 0.000
91 N/A 5 0 1.00 19 0.000
92 N/A 1 0 1.00 16 0.000
93 N/A 3 0 1.00 19 0.000
94 N/A 9 0 1.00 19 0.000
95 A 1 1 1.00 40 0.025
96 A 5 4 1.00 18 0.222
97 A 5 4 1.00 18 0.222
98 A 5 4 1.00 18 0.222
99 A 5 4 1.00 18 0.222
100 A 5 4 1.00 15 0.267
101 A 5 4 1.00 16 0.250
102 A 5 4 1.00 15 0.267
103 A 5 4 1.00 16 0.250
104 A 5 5 1.18 8 0.625
105 A 4 4 1.20 8 0.500
106 A 3 3 1.17 6 0.500
107 A 2 2 1.00 8 0.250
108 A 3 3 1.20 8 0.375
109 A 4 4 1.06 8 0.500
110 A 5 5 1.04 8 0.625
111 A 5 5 1.03 8 0.625
112 A 4 4 1.02 8 0.500
113 A 3 3 1.02 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 4 1.00 8 0.500
118 A 3 3 1.00 14 0.214
119 A 3 3 1.05 14 0.214
120 A 3 3 1.11 12 0.250
121 A 1 1 1.00 6 0.167
122 N/A 1 0 1.00 14 0.000
123 N/A 2 0 1.00 14 0.000
124 N/A 4 0 1.00 14 0.000
125 A 13 12 1.53 10 1.200
126 A 9 8 1.30 10 0.800
127 A 6 5 1.18 8 0.625
128 N/A 1 0 1.00 10 0.000
129 A 6 5 1.12 10 0.500
130 A 9 8 1.17 10 0.800
131 A 13 12 1.37 10 1.200
132 A 10 10 1.59 10 1.000
133 A 6 6 1.33 10 0.600
134 A 4 4 1.07 6 0.667
135 N/A 1 0 1.00 10 0.000
136 N/A 1 0 1.00 10 0.000
137 N/A 1 0 1.00 10 0.000
138 A 3 2 0.91 16 0.125
139 A 3 2 0.91 14 0.143
140 A 5 4 1.00 8 0.500
141 N/A 1 0 1.00 16 0.000
142 N/A 1 0 1.00 16 0.000
143 A 6 5 1.00 17 0.294
144 A 6 5 1.18 15 0.333
145 A 6 5 1.00 13 0.385
146 A 4 3 0.98 17 0.176
147 A 6 5 1.00 17 0.294
148 A 6 5 1.16 17 0.294
149 A 6 5 1.13 19 0.263
150 A 3 2 1.00 19 0.105
151 A 3 2 1.00 17 0.118
152 A 3 2 1.00 19 0.105
153 A 3 2 1.00 19 0.105
154 A 3 2 1.00 19 0.105
155 A 3 2 1.00 19 0.105
156 A 9 9 1.12 17 0.529
157 A 5 5 1.06 17 0.294
158 A 2 2 1.00 15 0.133
159 N/A 1 0 1.00 17 0.000
160 N/A 4 0 1.00 17 0.000
161 N/A 8 0 1.00 17 0.000
162 N/A 6 0 1.00 17 0.000
163 N/A 3 0 1.00 17 0.000
164 N/A 1 0 1.00 14 0.000
165 N/A 3 0 1.00 17 0.000
166 N/A 6 0 1.00 17 0.000
167 A 6 6 1.14 19 0.316
168 A 4 4 1.06 19 0.211
169 A 2 2 1.00 17 0.118
170 A 3 3 1.00 19 0.158
171 A 5 5 1.00 19 0.263
172 A 7 7 1.00 19 0.368
173 A 7 7 1.09 19 0.368
174 A 5 5 1.04 19 0.263
175 A 3 3 1.00 16 0.188
176 A 5 5 1.11 19 0.263
177 A 7 7 1.01 19 0.368
178 A 9 9 1.76 18 0.500
179 A 5 5 1.40 18 0.278
180 A 2 2 1.00 16 0.125
181 N/A 1 0 1.00 18 0.000
182 N/A 4 0 1.00 18 0.000
183 N/A 8 0 1.00 18 0.000
184 A 8 7 1.28 18 0.389
185 A 5 4 1.00 18 0.222
186 A 3 2 1.00 15 0.133
187 A 5 4 1.00 18 0.222
188 A 8 7 1.15 18 0.389
189 A 10 10 1.11 19 0.526
190 A 3 3 1.10 17 0.176
191 N/A 1 0 1.00 19 0.000
192 N/A 6 0 1.00 19 0.000
193 N/A 16 0 1.00 19 0.000
194 N/A 5 0 1.00 19 0.000
195 N/A 1 0 1.00 16 0.000
196 N/A 3 0 1.00 19 0.000
197 N/A 9 0 1.00 19 0.000
198 A 1 1 1.00 40 0.025
199 A 7 6 1.01 18 0.333
200 A 7 6 1.01 18 0.333
201 A 7 6 1.04 18 0.333
202 A 7 6 1.04 18 0.333
203 A 7 6 1.04 15 0.400
204 A 7 6 1.03 16 0.375
205 A 7 6 1.04 15 0.400
206 A 7 6 1.04 16 0.375
207 A 5 5 1.18 8 0.625
208 A 4 4 1.20 8 0.500
209 A 3 3 1.20 6 0.500
210 A 1 1 1.00 8 0.125
211 A 3 3 1.12 8 0.375
212 A 4 4 1.04 8 0.500
213 A 5 5 1.03 8 0.625
214 A 5 5 1.03 8 0.625
215 A 4 4 1.02 8 0.500
216 A 3 3 1.02 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 4 1.00 8 0.500
221 A 3 3 1.00 14 0.214
222 A 3 3 1.05 14 0.214
223 A 3 3 1.11 12 0.250
224 A 1 1 1.00 6 0.167
225 N/A 1 0 1.00 14 0.000
226 N/A 2 0 1.00 14 0.000
227 N/A 4 0 1.00 14 0.000
228 A 13 12 1.54 10 1.200
229 A 9 8 1.31 10 0.800
230 A 6 5 1.18 8 0.625
231 N/A 1 0 1.00 10 0.000
232 A 6 5 1.12 10 0.500
233 A 9 8 1.15 10 0.800
234 A 13 12 1.35 10 1.200
235 A 10 10 1.60 10 1.000
236 A 6 6 1.34 10 0.600
237 A 4 4 1.09 6 0.667
238 N/A 1 0 1.00 10 0.000
239 N/A 1 0 1.00 10 0.000
240 N/A 1 0 1.00 10 0.000
241 A 3 2 0.91 16 0.125
242 A 3 2 0.91 14 0.143
243 A 5 4 1.01 8 0.500
244 N/A 1 0 1.00 16 0.000
245 N/A 1 0 1.00 16 0.000
246 A 6 5 1.00 17 0.294
247 A 6 5 1.18 15 0.333
248 A 6 5 1.00 13 0.385
249 A 4 3 0.98 17 0.176
250 A 6 5 1.00 17 0.294
251 A 6 5 1.18 17 0.294
252 A 6 5 1.13 19 0.263
253 A 3 2 1.00 18 0.111
254 A 3 2 1.00 16 0.125
255 A 3 2 1.00 18 0.111
256 A 3 2 1.00 18 0.111
257 A 3 2 1.00 18 0.111
258 A 3 2 1.00 18 0.111
259 A 9 9 1.13 17 0.529
260 A 5 5 1.07 17 0.294
261 A 2 2 1.00 15 0.133
262 N/A 1 0 1.00 17 0.000
263 N/A 4 0 1.00 17 0.000
264 N/A 8 0 1.00 17 0.000
265 N/A 6 0 1.00 17 0.000
266 N/A 3 0 1.00 17 0.000
267 N/A 1 0 1.00 14 0.000
268 N/A 3 0 1.00 17 0.000
269 N/A 6 0 1.00 17 0.000
270 A 6 6 1.13 18 0.333
271 A 4 4 1.07 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 5 1.02 18 0.278
276 A 7 7 1.11 18 0.389
277 A 5 5 1.07 18 0.278
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 5 0.97 18 0.278
282 A 7 7 1.00 18 0.389
283 A 9 9 1.78 19 0.474
284 A 5 5 1.41 19 0.263
285 A 2 2 1.00 17 0.118
286 N/A 1 0 1.00 19 0.000
287 N/A 4 0 1.00 19 0.000
288 N/A 8 0 1.00 19 0.000
289 A 8 7 1.27 19 0.368
290 A 5 4 1.00 19 0.211
291 A 3 2 1.00 16 0.125
292 A 5 4 1.00 19 0.211
293 A 8 7 1.14 19 0.368
294 A 10 10 1.03 19 0.526
295 A 3 3 1.00 17 0.176
296 N/A 1 0 1.00 19 0.000
297 N/A 6 0 1.00 19 0.000
298 N/A 16 0 1.00 19 0.000
299 N/A 5 0 1.00 19 0.000
300 N/A 1 0 1.00 16 0.000
301 N/A 3 0 1.00 19 0.000
302 N/A 9 0 1.00 19 0.000
303 A 1 1 1.00 40 0.025
304 A 5 4 1.00 18 0.222
305 A 5 4 1.00 18 0.222
306 A 5 4 1.00 18 0.222
307 A 5 4 1.00 18 0.222
308 A 5 4 1.00 15 0.267
309 A 5 4 1.00 16 0.250
310 A 5 4 1.00 15 0.267
311 A 5 4 1.00 16 0.250

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