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2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. 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 given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [269] had the largest ratio of [40]

# 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 1.00 12 0.417
2 A 4 4 1.00 12 0.333
3 A 4 4 1.00 10 0.400
4 A 8 5 1.00 12 0.417
5 A 3 3 1.00 12 0.250
6 A 4 4 1.00 12 0.333
7 A 6 6 1.00 12 0.500
8 A 18 7 1.00 14 0.500
9 A 13 7 1.00 14 0.500
10 A 9 7 1.00 12 0.583
11 A 10 6 1.00 14 0.429
12 A 10 7 1.00 14 0.500
13 A 13 10 1.00 14 0.714
14 A 5 5 1.00 16 0.312
15 A 4 4 1.00 16 0.250
16 A 4 4 1.00 14 0.286
17 A 8 5 1.00 16 0.312
18 A 3 3 1.00 16 0.188
19 A 4 4 1.00 16 0.250
20 A 6 6 1.00 16 0.375
21 A 18 7 1.00 18 0.389
22 A 13 7 1.00 18 0.389
23 A 9 7 1.00 16 0.438
24 A 10 6 1.00 18 0.333
25 A 10 7 1.00 18 0.389
26 A 13 10 1.00 18 0.556
27 A 27 7 1.00 18 0.389
28 A 17 6 1.00 18 0.333
29 A 11 7 1.00 16 0.438
30 A 0 0 0.00 0 0.000
31 A 0 0 0.00 0 0.000
32 A 19 7 1.00 18 0.389
33 A 11 7 1.00 16 0.438
34 A 0 0 0.00 0 0.000
35 A 0 0 0.00 0 0.000
36 A 0 0 0.00 0 0.000
37 A 0 0 0.00 0 0.000
38 A 3 3 1.00 16 0.188
39 A 0 0 0.00 0 0.000
40 A 0 0 0.00 0 0.000
41 A 6 6 1.00 14 0.429
42 A 6 6 1.00 14 0.429
43 A 6 6 1.00 14 0.429
44 A 3 3 1.00 12 0.250
45 A 18 6 1.00 14 0.429
46 A 26 9 1.00 14 0.643
47 A 0 0 0.00 0 0.000
48 A 0 0 0.00 0 0.000
49 A 7 8 1.00 16 0.500
50 A 8 10 1.00 16 0.625
51 A 9 11 1.00 16 0.688
52 A 10 12 1.00 16 0.750
53 A 17 13 1.00 31 0.419
54 A 14 9 1.00 31 0.290
55 A 9 7 1.00 29 0.241
56 A 23 22 1.00 31 0.710
57 A 38 22 1.00 31 0.710
58 A 27 19 1.00 31 0.613
59 A 23 14 1.00 31 0.452
60 A 14 11 1.00 29 0.379
61 F 0 0 N/A 0. N/A
62 A 35 22 1.00 31 0.710
63 A 31 17 1.00 31 0.548
64 A 17 12 1.00 29 0.414
65 A 39 32 1.00 31 1.032
66 A 13 7 1.00 31 0.226
67 A 9 7 1.00 31 0.226
68 A 6 5 1.00 29 0.172
69 A 10 7 1.00 31 0.226
70 A 13 10 1.00 31 0.323
71 A 21 15 1.00 31 0.484
72 A 19 13 1.00 31 0.419
73 A 5 6 1.25 29 0.207
74 A 27 18 1.00 31 0.581
75 A 7 5 1.00 30 0.167
76 A 7 5 1.00 35 0.143
77 A 7 5 1.00 37 0.135
78 A 0 0 0.00 0 0.000
79 A 14 11 1.00 35 0.314
80 A 12 10 1.00 33 0.303
81 A 9 7 1.00 25 0.280
82 A 0 0 0.00 0 0.000
83 A 6 6 1.00 10 0.600
84 A 5 5 1.00 10 0.500
85 A 5 5 1.00 8 0.625
86 A 3 3 1.00 6 0.500
87 A 9 6 1.00 10 0.600
88 A 4 4 1.00 10 0.400
89 A 5 5 1.00 10 0.500
90 A 7 7 1.00 10 0.700
91 A 7 6 1.00 14 0.429
92 A 7 6 1.00 15 0.400
93 A 8 5 1.00 21 0.238
94 A 7 6 1.00 21 0.286
95 A 6 5 1.00 21 0.238
96 A 5 5 1.00 19 0.263
97 A 4 3 1.00 10 0.300
98 A 7 7 1.00 21 0.333
99 A 5 5 1.00 21 0.238
100 A 4 4 1.00 21 0.190
101 A 6 6 1.00 21 0.286
102 A 6 5 1.00 21 0.238
103 A 8 6 1.00 21 0.286
104 A 9 7 1.00 23 0.304
105 A 8 6 1.00 23 0.261
106 A 7 7 1.00 23 0.304
107 A 6 6 1.00 21 0.286
108 A 4 4 1.00 12 0.333
109 A 8 8 1.00 23 0.348
110 A 9 7 1.00 23 0.304
111 A 5 5 1.00 23 0.217
112 A 11 9 1.00 23 0.391
113 A 19 8 1.00 23 0.348
114 A 14 8 1.00 23 0.348
115 A 12 8 1.00 23 0.348
116 A 8 7 1.00 21 0.333
117 A 6 4 1.00 12 0.333
118 A 9 9 1.00 23 0.391
119 A 11 8 1.00 23 0.348
120 A 9 9 1.00 23 0.391
121 A 15 11 1.00 23 0.478
122 A 16 6 1.00 23 0.261
123 A 13 8 1.00 23 0.348
124 A 9 6 1.00 21 0.286
125 A 6 4 1.00 12 0.333
126 A 10 9 1.00 23 0.391
127 A 13 9 1.00 23 0.391
128 A 10 10 1.00 23 0.435
129 A 21 12 1.00 23 0.522
130 A 14 7 1.00 23 0.304
131 A 11 7 1.00 23 0.304
132 A 11 7 1.00 23 0.304
133 A 8 7 1.00 21 0.333
134 A 5 5 1.00 12 0.417
135 A 0 0 0.00 0 0.000
136 A 13 6 1.00 23 0.261
137 A 10 6 1.00 23 0.261
138 A 10 6 1.00 23 0.261
139 A 6 6 1.00 21 0.286
140 A 6 6 1.00 12 0.500
141 A 0 0 0.00 0 0.000
142 A 26 9 1.00 23 0.391
143 A 20 9 1.00 23 0.391
144 A 18 10 1.00 23 0.435
145 A 11 10 1.00 21 0.476
146 A 7 7 1.00 12 0.583
147 A 0 0 0.00 0 0.000
148 A 24 8 1.00 23 0.348
149 A 17 8 1.00 23 0.348
150 A 18 10 1.00 23 0.435
151 A 9 9 1.00 21 0.429
152 A 8 7 1.00 12 0.583
153 A 0 0 0.00 0 0.000
154 A 21 9 1.00 25 0.360
155 A 16 9 1.00 25 0.360
156 A 16 9 1.00 25 0.360
157 A 11 9 1.00 23 0.391
158 A 8 7 1.00 14 0.500
159 A 0 0 0.00 0 0.000
160 A 27 11 1.00 25 0.440
161 A 24 12 1.00 25 0.480
162 A 13 11 1.00 23 0.478
163 A 9 8 1.00 14 0.571
164 A 0 0 0.00 0 0.000
165 A 29 11 1.00 25 0.440
166 A 26 12 1.00 25 0.480
167 A 14 11 1.00 23 0.478
168 A 10 8 1.00 14 0.571
169 A 0 0 0.00 0 0.000
170 A 35 13 1.00 25 0.520
171 A 16 11 1.00 23 0.478
172 A 11 8 1.00 14 0.571
173 A 0 0 0.00 0 0.000
174 A 20 8 1.00 25 0.320
175 A 15 8 1.00 25 0.320
176 A 15 8 1.00 25 0.320
177 A 10 8 1.00 23 0.348
178 A 7 6 1.00 14 0.429
179 A 0 0 0.00 0 0.000
180 A 19 7 1.00 25 0.280
181 A 14 7 1.00 25 0.280
182 A 14 7 1.00 25 0.280
183 A 8 7 1.00 23 0.304
184 A 8 7 1.00 14 0.500
185 A 0 0 0.00 0 0.000
186 A 36 10 1.00 25 0.400
187 A 26 10 1.00 25 0.400
188 A 24 11 1.00 25 0.440
189 A 13 11 1.00 23 0.478
190 A 9 8 1.00 14 0.571
191 A 0 0 0.00 0 0.000
192 A 34 9 1.00 25 0.360
193 A 23 9 1.00 25 0.360
194 A 24 11 1.00 25 0.440
195 A 11 10 1.00 23 0.435
196 A 10 8 1.00 14 0.571
197 A 0 0 0.00 0 0.000
198 A 8 6 1.00 23 0.261
199 A 8 6 1.00 23 0.261
200 A 6 6 1.00 23 0.261
201 A 6 6 1.00 23 0.261
202 A 4 4 1.00 23 0.174
203 A 4 4 1.00 23 0.174
204 A 7 7 1.00 23 0.304
205 A 7 7 1.00 23 0.304
206 A 3 3 1.00 25 0.120
207 A 3 3 1.00 25 0.120
208 A 3 3 1.00 25 0.120
209 A 3 3 1.00 25 0.120
210 A 3 3 1.00 25 0.120
211 A 3 3 1.00 25 0.120
212 A 3 3 1.00 25 0.120
213 A 3 3 1.00 25 0.120
214 A 0 0 0.00 0 0.000
215 A 0 0 0.00 0 0.000
216 A 0 0 0.00 0 0.000
217 A 0 0 0.00 0 0.000
218 A 0 0 0.00 0 0.000
219 A 0 0 0.00 0 0.000
220 A 0 0 0.00 0 0.000
221 A 0 0 0.00 0 0.000
222 A 0 0 0.00 0 0.000
223 A 0 0 0.00 0 0.000
224 A 0 0 0.00 0 0.000
225 A 0 0 0.00 0 0.000
226 A 0 0 0.00 0 0.000
227 A 0 0 0.00 0 0.000
228 A 3 3 1.00 23 0.130
229 A 5 5 1.05 21 0.238
230 A 0 0 0.00 0 0.000
231 A 5 5 1.00 10 0.500
232 A 7 5 1.00 10 0.500
233 A 6 5 1.00 8 0.625
234 A 5 5 1.00 6 0.833
235 A 5 5 1.00 10 0.500
236 A 3 3 1.00 10 0.300
237 A 4 4 1.00 10 0.400
238 A 3 3 1.00 4 0.750
239 A 5 5 1.00 10 0.500
240 A 3 2 1.00 14 0.143
241 A 7 6 1.00 14 0.429
242 A 2 2 1.00 14 0.143
243 A 6 5 1.00 12 0.417
244 A 1 1 1.00 14 0.071
245 A 1 1 1.00 14 0.071
246 A 2 2 1.00 14 0.143
247 A 3 2 1.00 14 0.143
248 A 5 4 1.00 14 0.286
249 A 2 2 1.00 14 0.143
250 A 4 3 1.00 12 0.250
251 A 1 1 1.00 14 0.071
252 A 1 1 1.00 14 0.071
253 A 2 2 1.00 14 0.143
254 A 2 2 1.00 16 0.125
255 A 2 2 1.00 16 0.125
256 A 1 1 1.00 16 0.062
257 A 1 1 1.00 16 0.062
258 A 1 1 1.00 16 0.062
259 A 2 2 1.00 16 0.125
260 A 2 2 1.00 16 0.125
261 A 2 2 1.00 16 0.125
262 A 2 2 1.00 16 0.125
263 A 1 1 1.00 16 0.062
264 A 1 1 1.00 16 0.062
265 A 1 1 1.00 16 0.062
266 A 2 2 1.00 16 0.125
267 A 2 2 1.00 16 0.125
268 A 0 0 0.00 0 0.000
269 A 8 8 1.00 40 0.200
270 A 7 7 1.00 40 0.175
271 A 6 7 1.00 38 0.184
272 A 0 0 0.00 0 0.000
273 A 0 0 0.00 0 0.000
274 A 6 6 1.00 10 0.600
275 A 5 4 1.00 12 0.333
276 A 5 4 1.00 12 0.333
277 A 5 4 1.00 10 0.400
278 A 5 4 1.00 8 0.500
279 A 9 8 1.00 12 0.667
280 A 9 8 1.00 12 0.667
281 A 7 5 1.00 12 0.417
282 A 8 6 1.00 12 0.500
283 A 10 7 1.00 12 0.583
284 A 37 8 1.00 14 0.571
285 A 27 8 1.00 14 0.571
286 A 17 8 1.00 12 0.667
287 A 7 4 1.00 10 0.400
288 A 0 0 0.00 0 0.000
289 A 0 0 0.00 0 0.000
290 A 7 7 1.00 19 0.368
291 A 2 2 1.00 20 0.100
292 A 4 4 1.00 12 0.333
293 A 4 4 1.00 14 0.286
294 A 5 5 1.00 10 0.500
295 A 2 2 1.00 26 0.077
296 A 2 2 1.00 26 0.077

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