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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 [282] had the largest ratio of [107]

# 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 1 0 1.00 6 0.000
2 A 3 2 1.00 13 0.154
3 A 2 1 1.00 10 0.100
4 A 1 1 1.00 3 0.333
5 A 2 1 1.00 11 0.091
6 A 2 1 1.00 14 0.071
7 A 2 1 1.00 20 0.050
8 A 2 2 1.00 12 0.167
9 A 3 3 1.00 13 0.231
10 A 2 2 1.00 10 0.200
11 A 6 5 1.00 13 0.385
12 A 2 1 1.00 23 0.043
13 A 4 3 1.00 20 0.150
14 A 3 2 1.00 22 0.091
15 A 5 4 1.00 14 0.286
16 A 6 6 1.00 9 0.667
17 A 3 2 1.00 16 0.125
18 A 9 6 1.00 7 0.857
19 A 9 6 1.00 11 0.546
20 A 9 5 1.00 10 0.500
21 A 1 1 1.00 7 0.143
22 A 2 1 1.00 9 0.111
23 A 2 1 1.00 11 0.091
24 A 1 1 1.00 7 0.143
25 A 1 1 1.00 7 0.143
26 A 2 1 1.00 9 0.111
27 A 2 1 1.00 11 0.091
28 A 3 3 1.00 11 0.273
29 A 2 1 1.00 11 0.091
30 A 2 1 1.00 11 0.091
31 A 1 1 1.00 9 0.111
32 A 1 1 1.00 11 0.091
33 A 6 6 1.00 9 0.667
34 A 6 6 1.00 7 0.857
35 A 6 6 1.00 11 0.546
36 A 3 3 1.00 7 0.429
37 A 3 3 1.00 9 0.333
38 A 9 6 1.00 9 0.667
39 A 3 3 1.00 12 0.250
40 A 3 3 1.00 12 0.250
41 A 3 2 1.00 12 0.167
42 A 3 2 1.00 12 0.167
43 A 3 2 1.00 12 0.167
44 A 9 5 1.00 10 0.500
45 A 9 5 1.00 12 0.417
46 A 10 6 1.00 7 0.857
47 A 10 6 1.00 7 0.857
48 A 10 6 1.00 7 0.857
49 A 19 6 1.00 7 0.857
50 A 13 10 1.00 7 1.429
51 A 19 6 1.00 12 0.500
52 A 7 7 1.00 11 0.636
53 A 1 1 1.00 2 0.500
54 A 1 1 1.00 4 0.250
55 A 1 1 1.00 6 0.167
56 A 1 1 1.00 6 0.167
57 A 2 2 1.00 4 0.500
58 A 11 2 1.00 8 0.250
59 A 2 2 1.00 8 0.250
60 A 1 1 1.00 4 0.250
61 A 2 2 1.00 6 0.333
62 A 2 2 1.00 8 0.250
63 A 3 3 1.00 8 0.375
64 A 2 2 1.00 8 0.250
65 A 2 1 1.00 8 0.125
66 A 4 4 1.00 10 0.400
67 A 2 2 1.00 10 0.200
68 A 3 2 1.00 8 0.250
69 A 3 2 1.00 10 0.200
70 A 3 3 1.00 8 0.375
71 A 3 3 1.00 10 0.300
72 A 4 3 1.00 12 0.250
73 A 4 3 1.00 12 0.250
74 A 3 3 1.00 10 0.300
75 A 0 0 0.00 0 0.000
76 A 1 1 1.00 2 0.500
77 A 1 1 1.00 2 0.500
78 A 1 1 1.00 2 0.500
79 A 1 1 1.00 2 0.500
80 A 2 2 1.00 6 0.333
81 A 1 1 1.00 2 0.500
82 A 1 1 1.00 2 0.500
83 A 2 2 1.00 4 0.500
84 A 3 3 1.00 8 0.375
85 A 2 1 1.00 4 0.250
86 A 1 1 1.00 4 0.250
87 A 3 2 1.00 11 0.182
88 A 2 2 1.00 4 0.500
89 A 2 1 1.00 4 0.250
90 A 2 2 1.00 4 0.500
91 A 1 1 1.00 7 0.143
92 A 2 2 1.00 4 0.500
93 A 3 2 1.00 6 0.333
94 A 2 2 1.00 6 0.333
95 A 4 4 1.00 8 0.500
96 A 3 3 1.00 6 0.500
97 A 2 2 1.00 4 0.500
98 A 3 2 1.00 6 0.333
99 A 2 2 1.00 6 0.333
100 A 4 4 1.00 8 0.500
101 A 3 3 1.00 6 0.500
102 A 1 1 1.00 6 0.167
103 A 1 1 1.00 6 0.167
104 A 2 2 1.00 6 0.333
105 A 3 2 1.00 8 0.250
106 A 2 2 1.00 4 0.500
107 A 1 1 1.00 6 0.167
108 A 1 1 1.00 6 0.167
109 A 1 1 1.00 6 0.167
110 A 1 1 1.00 6 0.167
111 A 1 1 1.00 6 0.167
112 A 1 1 1.00 6 0.167
113 A 2 2 1.00 8 0.250
114 A 2 1 1.00 8 0.125
115 A 2 2 1.00 8 0.250
116 A 2 1 1.00 8 0.125
117 A 2 2 1.00 8 0.250
118 A 1 1 1.00 6 0.167
119 A 1 1 1.00 8 0.125
120 A 1 1 1.00 6 0.167
121 A 1 1 1.00 8 0.125
122 A 3 3 1.00 8 0.375
123 A 3 3 1.00 10 0.300
124 A 4 4 1.00 12 0.333
125 A 1 1 1.00 7 0.143
126 A 4 4 1.00 12 0.333
127 A 2 2 1.00 4 0.500
128 A 17 8 1.00 8 1.000
129 A 34 9 1.00 8 1.125
130 A 3 3 1.00 6 0.500
131 A 1 1 1.00 9 0.111
132 A 3 3 1.00 9 0.333
133 A 3 2 1.00 9 0.222
134 A 1 1 1.00 6 0.167
135 A 1 1 1.00 6 0.167
136 A 4 3 1.00 7 0.429
137 A 4 3 1.00 7 0.429
138 A 11 5 1.00 9 0.556
139 A 11 5 1.00 9 0.556
140 A 25 5 1.00 9 0.556
141 A 25 5 1.00 9 0.556
142 A 5 2 1.00 11 0.182
143 A 5 2 1.00 11 0.182
144 A 6 4 1.00 10 0.400
145 A 0 0 0.00 0 0.000
146 A 4 3 1.00 9 0.333
147 A 5 5 1.00 15 0.333
148 A 1 1 1.00 3 0.333
149 A 1 1 1.00 3 0.333
150 A 1 1 1.00 3 0.333
151 A 1 1 1.00 3 0.333
152 A 1 1 1.00 5 0.200
153 A 1 1 1.00 9 0.111
154 A 4 4 1.00 11 0.364
155 A 3 2 1.00 13 0.154
156 A 2 2 1.00 9 0.222
157 A 2 2 1.00 18 0.111
158 A 2 2 1.00 7 0.286
159 A 21 2 1.00 7 0.286
160 A 2 2 1.00 9 0.222
161 A 2 2 1.00 7 0.286
162 A 2 2 1.00 7 0.286
163 A 5 3 1.00 12 0.250
164 A 1 1 1.00 14 0.071
165 A 1 1 1.00 7 0.143
166 A 1 1 1.00 5 0.200
167 A 1 1 1.00 7 0.143
168 A 7 3 1.00 12 0.250
169 F 0 0 N/A 0 N/A
170 A 0 0 0.00 0 0.000
171 A 2 3 1.00 6 0.500
172 A 5 5 1.00 7 0.714
173 A 3 3 1.00 10 0.300
174 A 1 0 1.00 13 0.000
175 A 4 4 1.00 12 0.333
176 A 5 4 1.00 19 0.210
177 A 1 1 1.00 9 0.111
178 A 2 1 1.00 11 0.091
179 A 2 1 1.00 13 0.077
180 A 3 3 1.00 13 0.231
181 A 3 3 1.00 13 0.231
182 A 1 1 1.00 9 0.111
183 A 2 1 1.00 11 0.091
184 A 2 1 1.00 13 0.077
185 A 2 2 1.00 13 0.154
186 A 3 3 1.00 13 0.231
187 A 1 1 1.00 11 0.091
188 A 2 1 1.00 13 0.077
189 A 6 6 1.00 18 0.333
190 A 2 2 1.00 9 0.222
191 A 4 3 1.00 13 0.231
192 A 3 3 1.00 6 0.500
193 A 1 1 1.00 13 0.077
194 A 2 2 1.00 13 0.154
195 A 3 3 1.00 13 0.231
196 A 3 3 1.00 14 0.214
197 A 3 3 1.00 18 0.167
198 A 1 1 1.00 20 0.050
199 A 1 1 1.00 9 0.111
200 A 3 2 1.00 65 0.031
201 A 5 4 1.00 68 0.059
202 A 5 2 1.00 21 0.095
203 A 6 6 1.00 21 0.286
204 A 4 3 1.00 23 0.130
205 A 2 2 1.00 16 0.125
206 A 3 3 1.00 25 0.120
207 A 2 2 1.00 24 0.083
208 A 2 2 1.00 29 0.069
209 A 1 1 1.00 18 0.056
210 A 1 1 1.00 23 0.043
211 A 3 3 1.00 24 0.125
212 A 3 3 1.00 22 0.136
213 A 3 3 1.00 26 0.115
214 A 3 3 1.00 31 0.097
215 A 3 3 1.00 16 0.188
216 A 1 1 1.00 8 0.125
217 A 2 2 1.00 6 0.333
218 A 1 1 1.00 20 0.050
219 A 3 2 1.00 13 0.154
220 A 2 2 1.00 13 0.154
221 A 3 3 1.00 9 0.333
222 A 2 2 1.00 13 0.154
223 A 2 1 1.00 11 0.091
224 A 5 5 1.00 13 0.385
225 A 2 2 1.00 4 0.500
226 A 2 2 1.00 4 0.500
227 A 1 1 1.00 4 0.250
228 A 1 1 1.00 28 0.036
229 A 4 2 1.00 11 0.182
230 A 3 3 1.00 4 0.750
231 A 3 3 1.00 4 0.750
232 A 3 3 1.00 8 0.375
233 A 3 2 1.00 7 0.286
234 A 3 2 1.00 7 0.286
235 A 1 1 1.00 8 0.125
236 A 1 1 1.00 10 0.100
237 A 1 1 1.00 8 0.125
238 A 1 1 1.00 10 0.100
239 A 3 3 1.00 17 0.176
240 A 4 3 1.00 13 0.231
241 A 2 2 1.00 11 0.182
242 A 4 3 1.00 13 0.231
243 A 3 3 1.00 8 0.375
244 A 1 1 1.00 2 0.500
245 A 3 2 1.00 4 0.500
246 A 1 1 1.00 2 0.500
247 A 1 1 1.00 2 0.500
248 A 1 1 1.00 3 0.333
249 A 4 3 1.00 12 0.250
250 A 2 1 1.00 13 0.077
251 A 3 3 1.00 14 0.214
252 A 14 8 1.00 12 0.667
253 A 4 3 1.00 7 0.429
254 A 1 1 1.00 5 0.200
255 A 6 6 1.00 9 0.667
256 A 2 2 1.00 9 0.222
257 A 10 3 1.00 15 0.200
258 A 6 2 1.00 11 0.182
259 A 6 6 1.00 7 0.857
260 A 1 1 1.00 9 0.111
261 A 2 2 1.00 9 0.222
262 A 2 1 1.00 7 0.143
263 A 2 2 1.00 2 1.000
264 A 4 3 1.00 6 0.500
265 A 4 2 1.00 17 0.118
266 A 2 2 1.00 4 0.500
267 A 2 1 1.00 19 0.053
268 A 1 1 1.00 11 0.091
269 A 1 1 1.00 9 0.111
270 A 2 2 1.00 12 0.167
271 A 3 2 1.00 24 0.083
272 A 2 1 1.00 29 0.034
273 A 0 0 0.00 0 0.000
274 A 9 7 1.00 54 0.130
275 A 4 3 1.00 21 0.143
276 A 1 1 1.00 2 0.500
277 A 1 1 1.00 4 0.250
278 F 0 0 N/A 0 N/A
279 F 0 0 N/A 0 N/A
280 A 1 1 1.00 85 0.012
281 F 0 0 N/A 0 N/A
282 A 20 8 1.00 107 0.075
283 A 2 2 1.00 7 0.286
284 F 0 0 N/A 0 N/A

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