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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 [159] had the largest ratio of [3]

# 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 1 1.00 6 0.167
2 A 3 3 1.00 13 0.231
3 A 3 3 1.00 10 0.300
4 A 1 1 1.00 3 0.333
5 A 2 2 1.00 11 0.182
6 A 2 2 1.00 14 0.143
7 A 2 2 1.00 20 0.100
8 A 3 2 1.00 12 0.167
9 A 3 3 1.00 13 0.231
10 A 3 2 1.11 10 0.200
11 A 4 4 1.06 13 0.308
12 A 2 2 1.00 23 0.087
13 A 4 3 0.98 20 0.150
14 A 2 2 1.00 22 0.091
15 A 5 5 1.04 14 0.357
16 A 8 7 1.10 9 0.778
17 A 2 2 1.00 16 0.125
18 A 9 8 1.06 7 1.143
19 A 9 8 1.06 11 0.727
20 A 7 6 1.06 10 0.600
21 A 1 1 1.00 7 0.143
22 A 2 2 1.00 9 0.222
23 A 2 2 1.00 11 0.182
24 A 1 1 1.00 7 0.143
25 A 1 1 1.00 7 0.143
26 A 2 2 1.00 9 0.222
27 A 2 2 1.00 11 0.182
28 A 3 3 1.00 11 0.273
29 A 2 2 1.00 11 0.182
30 A 2 2 1.00 11 0.182
31 A 1 1 1.00 9 0.111
32 A 1 1 1.00 11 0.091
33 A 10 9 1.12 9 1.000
34 A 9 8 0.99 7 1.143
35 A 9 8 0.96 11 0.727
36 A 3 3 1.00 7 0.429
37 A 3 3 1.00 9 0.333
38 A 8 7 0.97 9 0.778
39 A 3 3 1.03 12 0.250
40 A 3 3 1.03 12 0.250
41 A 2 2 1.00 12 0.167
42 A 2 2 1.00 12 0.167
43 A 2 2 1.00 12 0.167
44 A 7 6 1.11 10 0.600
45 A 7 6 1.11 12 0.500
46 A 9 8 1.08 7 1.143
47 A 10 9 0.92 7 1.286
48 A 10 9 1.06 7 1.286
49 A 8 7 1.01 7 1.000
50 A 13 12 1.15 7 1.714
51 A 8 7 1.49 12 0.583
52 A 9 8 1.12 11 0.727
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 1.13 4 0.500
58 A 11 11 1.35 8 1.375
59 A 3 2 1.00 8 0.250
60 A 1 1 1.00 4 0.250
61 A 3 2 1.00 6 0.333
62 A 3 2 1.00 8 0.250
63 A 4 3 1.00 8 0.375
64 A 3 2 1.00 8 0.250
65 A 4 4 1.64 8 0.500
66 A 4 4 1.09 10 0.400
67 A 2 2 1.00 10 0.200
68 A 3 3 1.09 8 0.375
69 A 3 3 1.07 10 0.300
70 A 3 3 1.04 8 0.375
71 A 4 3 1.15 10 0.300
72 A 3 3 1.00 12 0.250
73 A 3 3 1.00 12 0.250
74 A 4 4 1.08 10 0.400
75 N/A 1 0 1.00 5 0.000
76 A 2 2 1.00 2 1.000
77 A 2 2 1.00 2 1.000
78 A 2 2 1.00 2 1.000
79 A 3 3 1.00 2 1.500
80 A 4 4 1.00 6 0.667
81 A 2 2 1.00 2 1.000
82 A 2 2 1.00 2 1.000
83 A 3 3 1.00 4 0.750
84 A 6 5 0.90 8 0.625
85 A 4 3 1.00 4 0.750
86 A 2 2 1.00 4 0.500
87 A 5 4 1.00 11 0.364
88 A 3 3 1.00 4 0.750
89 A 4 3 1.00 4 0.750
90 A 4 3 1.00 4 0.750
91 A 2 2 1.00 7 0.286
92 A 4 4 1.00 4 1.000
93 A 7 7 1.00 6 1.167
94 A 3 3 1.00 6 0.500
95 A 6 6 1.12 8 0.750
96 A 6 6 0.97 6 1.000
97 A 5 5 1.00 4 1.250
98 A 7 7 1.06 6 1.167
99 A 3 3 1.00 6 0.500
100 A 6 6 1.12 8 0.750
101 A 7 7 0.94 6 1.167
102 A 2 2 1.00 6 0.333
103 A 2 2 1.00 6 0.333
104 A 4 4 1.00 6 0.667
105 A 3 3 1.00 8 0.375
106 A 4 4 1.00 4 1.000
107 A 2 2 1.00 6 0.333
108 A 2 2 1.00 6 0.333
109 A 2 2 1.00 6 0.333
110 A 3 3 1.18 6 0.500
111 A 2 2 1.00 6 0.333
112 A 2 2 1.00 6 0.333
113 A 3 3 1.00 8 0.375
114 A 4 3 0.89 8 0.375
115 A 3 3 1.00 8 0.375
116 A 4 3 1.00 8 0.375
117 A 4 3 1.00 8 0.375
118 A 2 2 1.00 6 0.333
119 A 2 2 1.00 8 0.250
120 A 2 2 1.00 6 0.333
121 A 2 2 1.00 8 0.250
122 A 5 4 1.15 8 0.500
123 A 5 4 1.11 10 0.400
124 A 6 6 1.07 12 0.500
125 A 2 2 1.00 7 0.286
126 A 6 6 1.07 12 0.500
127 A 7 7 1.00 4 1.750
128 A 16 15 1.20 8 1.875
129 A 21 20 1.92 8 2.500
130 A 5 5 1.00 6 0.833
131 A 2 2 1.00 9 0.222
132 A 5 5 1.21 9 0.556
133 A 5 4 1.00 9 0.444
134 A 1 1 1.00 6 0.167
135 A 1 1 1.00 6 0.167
136 A 2 2 1.00 7 0.286
137 A 2 2 1.00 7 0.286
138 A 4 4 1.00 9 0.444
139 A 3 3 1.01 9 0.333
140 A 4 4 1.01 9 0.444
141 A 3 3 1.01 9 0.333
142 A 3 3 1.00 11 0.273
143 A 3 3 1.00 11 0.273
144 A 12 11 1.14 10 1.100
145 N/A 1 0 1.00 11 0.000
146 A 6 5 1.50 9 0.556
147 A 8 7 1.08 15 0.467
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 5 4 1.25 11 0.364
155 A 4 3 1.00 13 0.231
156 A 1 1 1.00 9 0.111
157 A 3 2 1.00 18 0.111
158 A 2 2 1.00 7 0.286
159 A 21 21 1.23 7 3.000
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 2 2 1.00 12 0.167
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 2 2 1.00 12 0.167
169 F 0 0 N/A 0.000 N/A
170 N/A 3 0 1.00 9 0.000
171 A 2 2 1.00 6 0.333
172 A 3 3 1.00 7 0.429
173 A 3 3 1.00 10 0.300
174 A 1 1 1.00 13 0.077
175 A 5 4 1.00 12 0.333
176 A 5 4 0.98 19 0.211
177 A 1 1 1.00 9 0.111
178 A 2 2 1.00 11 0.182
179 A 2 2 1.00 13 0.154
180 A 4 3 1.00 13 0.231
181 A 4 3 1.00 13 0.231
182 A 1 1 1.00 9 0.111
183 A 2 2 1.00 11 0.182
184 A 2 2 1.00 13 0.154
185 A 3 2 1.00 13 0.154
186 A 4 3 1.00 13 0.231
187 A 1 1 1.00 11 0.091
188 A 2 2 1.00 13 0.154
189 A 9 8 0.98 18 0.444
190 A 3 2 1.00 9 0.222
191 A 5 4 1.00 13 0.308
192 A 6 5 1.00 6 0.833
193 A 1 1 1.00 13 0.077
194 A 3 2 1.00 13 0.154
195 A 4 3 1.00 13 0.231
196 A 4 3 1.00 14 0.214
197 A 4 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 5 4 1.00 65 0.062
201 A 4 4 1.25 68 0.059
202 A 1 1 1.00 21 0.048
203 A 8 7 1.12 21 0.333
204 A 5 4 1.00 23 0.174
205 A 3 2 1.00 16 0.125
206 A 4 3 1.00 25 0.120
207 A 3 2 1.00 24 0.083
208 A 3 2 1.00 29 0.069
209 A 1 1 0.20 18 0.056
210 A 1 1 0.23 23 0.043
211 A 4 3 0.38 24 0.125
212 A 4 3 0.23 22 0.136
213 A 4 3 1.00 26 0.115
214 A 4 3 1.00 31 0.097
215 A 5 4 1.00 16 0.250
216 A 1 1 1.00 8 0.125
217 A 4 4 1.00 6 0.667
218 A 1 1 1.00 20 0.050
219 A 4 3 0.96 13 0.231
220 A 2 2 1.00 13 0.154
221 A 3 3 1.00 9 0.333
222 A 3 2 1.00 13 0.154
223 A 2 2 1.00 11 0.182
224 A 6 5 1.01 13 0.385
225 C 5 5 2.00 4 1.250
226 A 6 6 1.00 4 1.500
227 A 3 3 1.00 4 0.750
228 A 1 1 1.00 28 0.036
229 A 2 2 1.00 11 0.182
230 A 3 3 0.95 4 0.750
231 A 3 3 0.95 4 0.750
232 A 4 3 1.09 8 0.375
233 A 2 2 1.00 7 0.286
234 A 2 2 1.00 7 0.286
235 A 2 2 1.00 8 0.250
236 A 2 2 1.00 10 0.200
237 A 2 2 1.00 8 0.250
238 A 2 2 1.00 10 0.200
239 A 3 3 1.00 17 0.176
240 A 5 4 0.54 13 0.308
241 A 3 2 1.00 11 0.182
242 A 5 4 1.12 13 0.308
243 A 3 3 1.21 8 0.375
244 A 3 3 1.00 2 1.500
245 A 5 5 1.00 4 1.250
246 A 3 3 1.00 2 1.500
247 A 3 3 1.00 2 1.500
248 A 1 1 1.00 3 0.333
249 A 4 4 0.73 12 0.333
250 A 2 2 1.00 13 0.154
251 A 3 3 1.12 14 0.214
252 A 2 2 1.00 12 0.167
253 A 2 2 1.00 7 0.286
254 A 1 1 1.00 5 0.200
255 A 8 7 1.12 9 0.778
256 A 3 2 1.00 9 0.222
257 A 2 2 1.00 15 0.133
258 A 1 1 1.00 11 0.091
259 A 8 7 0.95 7 1.000
260 A 1 1 1.00 9 0.111
261 A 2 2 1.00 9 0.222
262 A 2 2 1.00 7 0.286
263 A 2 2 1.00 2 1.000
264 A 5 4 1.08 6 0.667
265 A 5 4 0.81 17 0.235
266 A 3 3 1.00 4 0.750
267 A 2 2 1.00 19 0.105
268 A 1 1 1.00 11 0.091
269 A 1 1 1.00 9 0.111
270 A 3 2 1.14 12 0.167
271 A 3 3 1.00 24 0.125
272 A 2 2 1.00 29 0.069
273 N/A 1 0 1.00 12 0.000
274 A 1 1 1.00 54 0.019
275 A 4 4 0.90 21 0.190
276 A 1 1 1.00 2 0.500
277 A 1 1 1.00 4 0.250
278 F 0 0 N/A 0.000 N/A
279 F 0 0 N/A 0.000 N/A
280 A 1 1 1.00 85 0.012
281 F 0 0 N/A 0.000 N/A
282 A 4 4 0.93 107 0.037
283 A 4 4 1.00 7 0.571
284 F 0 0 N/A 0.000 N/A

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