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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 [90] had the largest ratio of [.777777999999999969]

# 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 4 3 1.00 30 0.100
2 A 4 3 0.99 30 0.100
3 A 4 3 0.99 30 0.100
4 A 4 3 0.98 30 0.100
5 A 4 3 1.01 30 0.100
6 A 4 3 0.98 30 0.100
7 A 4 3 1.01 30 0.100
8 A 4 3 1.01 30 0.100
9 A 4 3 1.01 30 0.100
10 A 4 3 1.00 30 0.100
11 A 4 4 1.01 30 0.133
12 A 4 4 1.02 30 0.133
13 A 4 4 1.02 30 0.133
14 A 4 4 1.02 30 0.133
15 A 4 4 1.00 30 0.133
16 A 4 4 1.02 28 0.143
17 A 2 2 1.00 27 0.074
18 A 2 2 1.00 30 0.067
19 A 2 2 1.00 30 0.067
20 A 2 2 1.00 30 0.067
21 A 2 2 1.00 30 0.067
22 A 2 2 1.00 30 0.067
23 A 2 2 1.00 30 0.067
24 A 2 2 1.00 30 0.067
25 A 2 2 1.00 30 0.067
26 A 2 2 1.00 30 0.067
27 A 2 2 1.00 30 0.067
28 A 2 2 1.00 30 0.067
29 A 4 3 0.98 30 0.100
30 A 4 3 0.98 30 0.100
31 A 4 3 0.96 30 0.100
32 A 4 3 0.96 30 0.100
33 A 4 3 0.98 30 0.100
34 A 4 3 0.99 30 0.100
35 A 4 3 0.98 30 0.100
36 A 4 3 0.99 30 0.100
37 A 4 3 0.99 30 0.100
38 A 4 4 1.03 30 0.133
39 A 8 8 1.07 30 0.267
40 A 3 3 1.03 30 0.100
41 A 7 7 1.06 30 0.233
42 A 4 4 1.03 30 0.133
43 A 5 5 1.03 28 0.179
44 A 14 13 0.82 27 0.481
45 A 4 4 1.04 30 0.133
46 A 4 4 1.04 30 0.133
47 A 4 4 1.06 30 0.133
48 A 4 4 1.06 30 0.133
49 A 4 4 1.06 30 0.133
50 A 4 4 1.06 30 0.133
51 A 4 4 1.07 30 0.133
52 A 4 4 1.06 30 0.133
53 A 4 4 1.06 30 0.133
54 A 4 3 0.98 30 0.100
55 A 4 3 0.99 30 0.100
56 A 4 3 0.97 30 0.100
57 A 4 3 0.97 30 0.100
58 A 4 3 0.96 30 0.100
59 A 4 3 0.99 30 0.100
60 A 4 3 0.99 30 0.100
61 A 4 3 0.99 30 0.100
62 A 4 3 1.00 30 0.100
63 A 4 3 0.99 30 0.100
64 A 5 5 1.07 30 0.167
65 A 11 11 1.11 30 0.367
66 A 6 6 1.09 30 0.200
67 A 9 9 1.10 30 0.300
68 A 5 5 1.08 30 0.167
69 A 8 8 1.07 30 0.267
70 A 16 15 0.90 30 0.500
71 A 16 15 0.87 28 0.536
72 A 14 13 0.87 27 0.481
73 A 15 14 0.89 30 0.467
74 A 14 13 0.87 30 0.433
75 A 5 5 1.07 30 0.167
76 A 6 6 1.07 30 0.200
77 A 6 6 1.09 30 0.200
78 A 6 6 1.09 30 0.200
79 A 6 6 1.09 30 0.200
80 A 6 6 1.09 30 0.200
81 A 6 6 1.08 30 0.200
82 A 2 2 1.00 18 0.111
83 A 2 2 1.00 18 0.111
84 A 12 11 1.01 16 0.688
85 A 9 8 0.97 15 0.533
86 A 2 2 1.00 18 0.111
87 A 2 2 1.00 18 0.111
88 A 2 2 0.99 18 0.111
89 A 3 3 1.02 18 0.167
90 A 15 14 1.04 18 0.778
91 A 12 11 1.00 18 0.611
92 A 11 10 1.00 18 0.556
93 A 12 11 0.99 16 0.688
94 A 11 10 1.01 15 0.667
95 A 5 5 1.03 18 0.278
96 A 4 4 1.05 18 0.222
97 A 4 4 1.03 18 0.222
98 A 2 2 1.00 16 0.125
99 A 2 2 1.00 16 0.125
100 A 2 2 1.00 16 0.125
101 A 8 7 1.10 14 0.500
102 A 2 2 1.00 16 0.125
103 A 2 2 1.00 16 0.125
104 A 2 2 1.00 16 0.125
105 A 9 8 1.10 14 0.571
106 A 8 7 1.00 16 0.438
107 A 2 2 1.00 21 0.095
108 A 2 2 1.00 19 0.105
109 A 2 2 0.98 18 0.111
110 A 2 2 1.00 21 0.095
111 A 2 2 1.00 21 0.095
112 A 2 2 1.00 21 0.095
113 A 3 3 1.00 23 0.130
114 A 3 3 1.00 21 0.143
115 A 3 3 1.00 20 0.150
116 A 2 2 1.00 23 0.087
117 A 2 2 1.00 23 0.087
118 A 2 2 1.00 23 0.087
119 A 3 3 1.00 23 0.130
120 A 3 3 1.00 21 0.143
121 A 3 3 1.00 20 0.150
122 A 2 2 1.00 23 0.087
123 A 2 2 1.00 23 0.087
124 A 2 2 1.00 23 0.087
125 A 3 3 1.00 23 0.130
126 A 3 3 1.00 21 0.143
127 A 3 3 1.00 20 0.150
128 A 2 2 1.00 23 0.087
129 A 2 2 1.00 23 0.087
130 A 2 2 1.00 23 0.087
131 A 2 2 1.00 23 0.087
132 A 2 2 1.00 23 0.087
133 A 2 2 1.00 21 0.095
134 A 11 10 0.97 20 0.500
135 A 2 2 1.00 23 0.087
136 A 2 2 1.00 23 0.087
137 A 2 2 1.00 23 0.087
138 A 3 3 1.02 23 0.130
139 A 14 13 1.00 23 0.565
140 A 10 9 1.01 23 0.391
141 A 12 11 1.02 21 0.524
142 A 11 10 0.98 20 0.500
143 A 4 4 1.05 23 0.174
144 A 4 4 1.05 23 0.174
145 A 4 4 1.05 23 0.174
146 A 12 11 1.07 23 0.478
147 A 13 12 1.02 23 0.522
148 A 13 12 0.97 23 0.522
149 A 12 11 1.03 23 0.478
150 A 14 13 0.99 21 0.619
151 A 13 12 1.01 20 0.600
152 A 6 6 1.11 23 0.261
153 A 6 6 1.12 23 0.261
154 A 6 6 1.13 23 0.261
155 A 15 14 1.08 23 0.609
156 A 13 12 1.15 23 0.522
157 A 14 13 1.00 23 0.565
158 A 16 15 1.00 23 0.652
159 A 14 13 1.05 23 0.565
160 A 16 15 1.01 21 0.714
161 A 15 14 1.04 20 0.700
162 A 8 8 1.16 23 0.348
163 A 8 8 1.17 23 0.348
164 A 8 8 1.17 23 0.348
165 A 2 2 1.00 20 0.100
166 A 6 5 1.00 20 0.250
167 A 5 4 1.00 18 0.222
168 A 6 5 1.00 20 0.250
169 A 5 4 1.00 18 0.222
170 A 2 2 1.00 36 0.056
171 A 2 2 1.00 36 0.056
172 A 2 2 1.00 36 0.056
173 A 2 2 1.00 34 0.059
174 A 2 2 1.00 33 0.061
175 A 2 2 1.00 36 0.056
176 A 2 2 1.00 36 0.056
177 A 2 2 1.00 36 0.056
178 A 2 2 1.00 36 0.056
179 A 2 2 1.00 36 0.056
180 A 2 2 1.00 38 0.053
181 A 2 2 1.00 38 0.053
182 A 3 3 1.00 38 0.079
183 A 3 3 1.00 36 0.083
184 A 3 3 1.00 35 0.086
185 A 3 3 1.00 38 0.079
186 A 3 3 1.00 38 0.079
187 A 3 3 1.00 38 0.079
188 A 2 2 1.00 38 0.053
189 A 2 2 1.00 38 0.053
190 A 2 2 1.00 38 0.053
191 A 2 2 1.00 38 0.053
192 A 3 3 1.00 38 0.079
193 A 3 3 1.00 36 0.083
194 A 3 3 1.00 35 0.086
195 A 3 3 1.00 38 0.079
196 A 3 3 1.00 38 0.079
197 A 3 3 1.00 38 0.079
198 A 2 2 1.00 38 0.053
199 A 2 2 1.00 38 0.053
200 A 8 8 1.01 38 0.211
201 A 8 8 1.02 38 0.211
202 A 8 8 1.02 36 0.222
203 A 2 2 1.00 35 0.057
204 A 2 2 1.00 38 0.053
205 A 2 2 1.00 38 0.053
206 A 2 2 1.00 38 0.053
207 A 2 2 1.00 38 0.053
208 A 2 2 1.00 38 0.053
209 A 3 3 0.99 38 0.079
210 A 4 4 1.00 38 0.105
211 A 3 3 0.96 38 0.079
212 A 4 4 1.01 36 0.111
213 A 14 13 0.96 35 0.371
214 A 4 4 1.03 38 0.105
215 A 4 4 1.07 38 0.105
216 A 4 4 1.06 38 0.105
217 A 4 4 1.05 38 0.105
218 A 5 5 1.06 38 0.132
219 A 16 15 1.04 38 0.395
220 A 12 11 1.03 38 0.289
221 A 14 13 1.03 36 0.361
222 A 13 12 0.99 35 0.343
223 A 6 6 1.06 38 0.158
224 A 6 6 1.10 38 0.158
225 A 6 6 1.11 38 0.158
226 A 6 6 1.09 38 0.158
227 A 12 12 1.03 25 0.480
228 A 10 10 1.02 25 0.400
229 A 7 7 1.02 23 0.304
230 A 5 5 1.01 22 0.227
231 A 8 7 1.01 25 0.280
232 A 10 9 1.02 25 0.360
233 A 12 11 1.02 25 0.440
234 A 10 10 1.05 25 0.400
235 A 8 8 1.03 25 0.320
236 A 7 7 1.02 25 0.280
237 A 4 4 1.02 25 0.160
238 A 7 7 1.01 23 0.304
239 A 5 5 0.99 22 0.227
240 A 12 11 1.01 25 0.440
241 A 14 13 1.02 25 0.520
242 A 19 19 1.01 35 0.543
243 A 16 16 1.01 35 0.457
244 A 13 13 1.00 33 0.394
245 A 11 11 0.99 32 0.344
246 A 14 13 1.00 35 0.371
247 A 14 13 1.02 35 0.371
248 A 13 12 1.03 35 0.343
249 A 16 15 1.06 35 0.429
250 A 18 17 1.04 35 0.486
251 A 14 13 1.00 35 0.371
252 A 15 14 1.02 35 0.400
253 A 18 17 1.01 35 0.486
254 A 20 19 1.01 35 0.543
255 A 21 21 1.00 35 0.600
256 A 18 18 1.00 35 0.514
257 A 15 15 0.99 33 0.455
258 A 13 13 0.99 32 0.406
259 A 16 15 1.00 35 0.429
260 A 16 15 1.03 35 0.429
261 A 15 14 1.02 35 0.400
262 A 18 17 1.05 35 0.486
263 A 20 19 1.04 35 0.543
264 A 16 15 1.03 35 0.429
265 A 18 17 1.04 35 0.486
266 A 20 19 1.03 35 0.543
267 A 16 15 1.00 35 0.429
268 A 18 17 1.02 35 0.486
269 A 20 19 1.00 35 0.543
270 A 22 21 1.01 35 0.600
271 A 4 4 1.18 20 0.200
272 A 2 2 1.17 21 0.095
273 A 2 2 1.17 23 0.087

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