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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 [188] had the largest ratio of [1.11111000000000004]

# 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 2 1.00 22 0.091
2 A 3 2 1.00 22 0.091
3 F 0 0 N/A 0.000 N/A
4 A 2 2 1.00 14 0.143
5 A 2 2 1.00 12 0.167
6 A 2 2 1.00 10 0.200
7 A 3 3 1.00 17 0.176
8 A 2 2 0.97 46 0.043
9 A 2 2 0.97 46 0.043
10 A 2 2 0.96 46 0.043
11 A 2 2 0.97 44 0.045
12 A 2 2 0.97 42 0.048
13 A 2 2 0.97 46 0.043
14 A 2 2 0.97 46 0.043
15 A 2 2 1.02 26 0.077
16 A 2 2 0.99 26 0.077
17 A 2 2 0.98 26 0.077
18 A 2 2 0.97 26 0.077
19 A 2 2 0.98 24 0.083
20 A 2 2 0.97 22 0.091
21 A 2 2 0.97 26 0.077
22 A 2 2 1.01 26 0.077
23 A 2 2 0.95 26 0.077
24 A 2 2 0.95 26 0.077
25 A 2 2 0.94 26 0.077
26 A 2 2 0.98 26 0.077
27 A 2 2 0.97 26 0.077
28 A 2 2 0.97 26 0.077
29 A 2 2 0.90 26 0.077
30 A 3 3 1.00 15 0.200
31 A 3 3 1.00 11 0.273
32 A 2 2 1.00 11 0.182
33 A 2 2 1.00 52 0.038
34 A 5 5 1.00 52 0.096
35 A 2 2 1.00 14 0.143
36 A 2 2 1.03 54 0.037
37 A 3 3 1.00 54 0.056
38 A 5 5 1.00 54 0.093
39 A 3 3 1.47 13 0.231
40 A 3 3 1.00 18 0.167
41 A 3 3 1.00 22 0.136
42 A 3 3 1.00 16 0.188
43 A 3 3 1.00 16 0.188
44 A 3 3 1.00 15 0.200
45 A 3 3 1.00 17 0.176
46 A 3 3 1.00 15 0.200
47 A 5 4 1.33 15 0.267
48 A 5 4 1.32 15 0.267
49 A 1 1 1.00 15 0.067
50 A 1 1 1.00 20 0.050
51 A 3 3 1.00 15 0.200
52 A 3 3 1.00 13 0.231
53 A 4 4 1.00 17 0.235
54 A 4 4 1.00 25 0.160
55 A 2 2 1.00 20 0.100
56 A 4 4 1.00 18 0.222
57 A 3 3 1.00 20 0.150
58 A 1 1 1.00 22 0.045
59 A 1 1 1.00 17 0.059
60 A 8 7 1.20 27 0.259
61 A 8 7 1.12 20 0.350
62 A 3 3 1.09 38 0.079
63 A 10 10 1.07 50 0.200
64 F 0 0 N/A 0.000 N/A
65 F 0 0 N/A 0.000 N/A
66 A 1 1 1.00 16 0.062
67 A 3 3 1.23 16 0.188
68 A 2 2 1.98 17 0.118
69 B 2 2 2.21 25 0.080
70 B 5 5 4.68 81 0.062
71 A 3 2 1.07 22 0.091
72 A 3 2 1.03 23 0.087
73 A 3 2 1.00 22 0.091
74 A 3 2 1.03 23 0.087
75 A 3 2 1.07 24 0.083
76 A 3 2 1.03 25 0.080
77 A 3 2 1.18 31 0.065
78 A 3 2 1.08 32 0.062
79 A 3 2 1.07 35 0.057
80 A 3 2 1.04 36 0.056
81 A 3 2 1.00 24 0.083
82 A 3 2 1.00 31 0.065
83 A 3 2 1.00 35 0.057
84 A 1 1 1.00 22 0.045
85 A 1 1 1.00 18 0.056
86 B 3 3 2.91 26 0.115
87 B 2 2 2.91 28 0.071
88 A 1 1 1.00 18 0.056
89 A 1 1 1.00 20 0.050
90 A 1 1 1.00 21 0.048
91 A 6 5 1.03 14 0.357
92 A 8 7 1.03 13 0.538
93 A 6 5 1.12 16 0.312
94 A 8 7 1.12 18 0.389
95 A 2 2 1.00 14 0.143
96 A 3 3 1.00 16 0.188
97 B 3 3 4.68 40 0.075
98 F 0 0 N/A 0.000 N/A
99 B 4 4 4.68 69 0.058
100 F 0 0 N/A 0.000 N/A
101 B 5 5 4.68 80 0.062
102 A 4 3 1.04 17 0.176
103 A 4 3 1.08 17 0.176
104 A 4 3 1.08 15 0.200
105 A 2 2 1.14 20 0.100
106 A 2 2 1.14 20 0.100
107 A 2 2 1.12 18 0.111
108 A 4 3 1.02 24 0.125
109 A 4 3 1.06 24 0.125
110 A 4 3 1.11 22 0.136
111 F 0 0 N/A 0.000 N/A
112 F 0 0 N/A 0.000 N/A
113 F 0 0 N/A 0.000 N/A
114 A 2 2 1.00 15 0.133
115 A 3 3 1.00 35 0.086
116 A 3 3 1.00 46 0.065
117 A 4 4 1.00 66 0.061
118 A 5 4 1.00 19 0.211
119 A 6 5 1.00 23 0.217
120 A 6 5 1.00 21 0.238
121 A 5 4 1.00 21 0.190
122 A 5 4 1.00 33 0.121
123 A 6 5 1.00 35 0.143
124 A 6 5 1.00 36 0.139
125 A 5 4 1.00 36 0.111
126 A 5 4 1.00 24 0.167
127 A 6 5 1.00 20 0.250
128 A 6 5 1.00 24 0.208
129 A 6 5 1.00 22 0.227
130 A 6 5 1.00 22 0.227
131 A 10 9 0.98 15 0.600
132 A 9 8 0.98 17 0.471
133 A 9 8 1.00 15 0.533
134 A 10 9 0.94 17 0.529
135 A 1 1 1.00 24 0.042
136 A 1 1 1.00 25 0.040
137 A 1 1 1.00 27 0.037
138 A 1 1 1.00 17 0.059
139 A 3 3 0.97 25 0.120
140 A 1 1 1.00 25 0.040
141 A 1 1 1.00 21 0.048
142 A 1 1 1.00 24 0.042
143 A 4 4 1.23 19 0.211
144 A 8 8 0.97 19 0.421
145 A 6 6 1.02 19 0.316
146 A 4 4 0.98 17 0.235
147 A 2 2 1.00 19 0.105
148 A 2 2 1.00 19 0.105
149 A 2 2 1.30 19 0.105
150 A 2 2 1.29 19 0.105
151 A 4 4 1.00 19 0.211
152 A 2 2 1.00 17 0.118
153 A 2 2 1.00 19 0.105
154 A 2 2 1.00 19 0.105
155 A 2 2 1.32 19 0.105
156 A 5 5 0.98 19 0.263
157 A 4 4 1.00 19 0.211
158 A 2 2 1.00 17 0.118
159 A 2 2 1.00 19 0.105
160 A 2 2 1.00 19 0.105
161 A 2 2 1.45 15 0.133
162 A 2 2 1.19 15 0.133
163 A 2 2 0.94 13 0.154
164 A 1 1 1.00 7 0.143
165 A 2 2 1.00 15 0.133
166 A 2 2 1.00 15 0.133
167 A 3 3 1.08 17 0.176
168 A 2 2 1.14 17 0.118
169 A 2 2 1.00 15 0.133
170 A 2 2 1.00 9 0.222
171 A 2 2 1.00 17 0.118
172 A 2 2 1.00 17 0.118
173 A 2 2 1.29 17 0.118
174 A 2 2 1.32 17 0.118
175 A 2 2 1.31 15 0.133
176 A 9 8 1.49 9 0.889
177 A 2 2 1.26 17 0.118
178 A 2 2 1.25 17 0.118
179 A 5 5 1.25 17 0.294
180 A 4 4 1.31 17 0.235
181 A 4 4 1.30 15 0.267
182 A 10 9 1.49 9 1.000
183 A 2 2 1.22 17 0.118
184 A 2 2 1.22 17 0.118
185 A 6 6 1.24 17 0.353
186 A 6 6 1.30 17 0.353
187 A 6 6 1.31 15 0.400
188 A 11 10 1.49 9 1.111
189 A 2 2 1.19 17 0.118
190 A 2 2 1.19 17 0.118
191 A 2 2 1.00 19 0.105
192 A 2 2 1.00 19 0.105
193 A 2 2 1.00 17 0.118
194 A 2 2 1.00 11 0.182
195 A 17 16 1.09 19 0.842
196 A 13 12 1.50 19 0.632
197 F 0 0 N/A 0.000 N/A
198 A 2 2 1.00 19 0.105
199 A 2 2 1.00 19 0.105
200 A 2 2 1.00 17 0.118
201 A 3 3 1.04 11 0.273
202 A 22 21 1.10 19 1.105
203 B 14 13 2.19 19 0.684
204 A 2 2 1.00 19 0.105
205 A 2 2 1.00 19 0.105
206 A 2 2 1.00 17 0.118
207 A 1 1 1.00 11 0.091
208 A 9 8 1.07 19 0.421
209 A 16 15 1.05 19 0.789
210 A 18 17 1.03 19 0.895
211 A 7 7 0.96 19 0.368
212 A 6 6 0.99 19 0.316
213 A 4 4 1.00 17 0.235
214 A 2 2 1.00 11 0.182
215 A 18 17 1.08 19 0.895
216 A 13 12 1.51 19 0.632
217 A 2 2 1.00 17 0.118
218 A 2 2 1.00 17 0.118
219 A 2 2 1.00 15 0.133
220 A 2 2 1.00 9 0.222
221 A 11 10 1.02 17 0.588
222 F 0 0 N/A 0.000 N/A
223 A 2 2 1.16 20 0.100
224 A 2 2 1.07 20 0.100
225 A 2 2 0.96 18 0.111
226 A 1 1 1.00 12 0.083
227 A 2 2 1.00 20 0.100
228 A 2 2 1.00 20 0.100
229 A 2 2 1.40 22 0.091
230 A 2 2 1.00 22 0.091
231 A 2 2 1.00 20 0.100
232 A 2 2 1.00 14 0.143
233 A 2 2 1.00 22 0.091
234 A 2 2 1.00 22 0.091
235 A 10 9 1.01 22 0.409
236 A 8 7 1.00 22 0.318
237 A 8 7 1.01 20 0.350
238 A 2 2 1.00 14 0.143
239 A 2 2 1.00 22 0.091
240 A 2 2 1.00 22 0.091
241 A 12 11 0.94 22 0.500
242 A 11 10 0.93 22 0.455
243 A 11 10 0.96 20 0.500
244 A 4 4 0.94 14 0.286
245 A 2 2 1.00 22 0.091
246 F 0 0 N/A 0.000 N/A
247 A 14 13 0.96 24 0.542
248 A 12 11 0.97 24 0.458
249 A 12 11 1.02 22 0.500
250 A 5 5 1.01 16 0.312
251 A 16 15 1.07 24 0.625
252 F 0 0 N/A 0.000 N/A
253 F 0 0 N/A 0.000 N/A
254 A 17 16 0.94 24 0.667
255 A 15 14 0.96 24 0.583
256 A 15 14 1.02 22 0.636
257 A 7 7 1.01 16 0.438
258 A 23 22 0.98 24 0.917
259 F 0 0 N/A 0.000 N/A
260 A 11 10 1.00 24 0.417
261 A 10 9 1.00 24 0.375
262 A 7 6 1.00 22 0.273
263 A 1 1 1.00 16 0.062
264 A 9 8 1.05 24 0.333
265 A 16 15 1.00 24 0.625
266 A 11 10 0.96 24 0.417
267 A 10 9 0.96 24 0.375
268 A 11 10 0.98 22 0.455
269 A 6 6 0.99 16 0.375
270 A 16 15 1.03 24 0.625
271 F 0 0 N/A 0.000 N/A
272 A 6 5 1.15 29 0.172
273 A 7 6 1.15 28 0.214
274 A 7 6 1.15 29 0.207
275 A 6 5 1.14 27 0.185
276 A 7 6 1.14 26 0.231
277 A 7 6 1.14 28 0.214
278 A 7 6 1.14 26 0.231
279 A 7 6 1.14 27 0.222
280 A 7 6 1.14 27 0.222
281 A 4 4 0.99 24 0.167
282 A 4 3 1.32 30 0.100
283 A 1 1 1.00 30 0.033
284 A 4 3 1.00 21 0.143
285 A 4 3 1.00 67 0.045
286 A 2 2 1.03 30 0.067
287 A 2 2 1.01 30 0.067
288 A 2 2 1.02 28 0.071
289 A 2 2 0.97 22 0.091
290 A 2 2 0.97 30 0.067
291 A 2 2 0.78 37 0.054
292 A 2 2 0.99 30 0.067
293 C 2 2 0.75 42 0.048
294 F 0 0 N/A 0.000 N/A
295 A 7 7 1.00 19 0.368
296 A 5 5 1.02 19 0.263
297 A 3 3 0.91 17 0.176
298 A 2 2 1.00 9 0.222
299 A 2 2 1.00 19 0.105
300 A 2 2 1.00 19 0.105
301 A 2 2 1.00 19 0.105
302 F 0 0 N/A 0.000 N/A
303 F 0 0 N/A 0.000 N/A
304 A 2 2 1.00 17 0.118
305 A 2 2 1.00 9 0.222
306 A 2 2 1.00 19 0.105
307 A 2 2 1.00 19 0.105
308 A 2 2 1.00 19 0.105
309 A 2 2 1.00 19 0.105
310 A 2 2 1.00 19 0.105
311 A 2 2 1.00 17 0.118
312 A 2 2 1.00 9 0.222
313 F 0 0 N/A 0.000 N/A
314 F 0 0 N/A 0.000 N/A
315 A 2 2 1.00 17 0.118
316 A 2 2 1.00 17 0.118
317 A 2 2 1.00 15 0.133
318 A 2 2 1.00 9 0.222
319 F 0 0 N/A 0.000 N/A
320 F 0 0 N/A 0.000 N/A

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