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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 [201] had the largest ratio of [1.22222000000000008]

# 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 3 0.97 12 0.250
2 A 5 4 1.00 12 0.333
3 A 3 3 0.98 12 0.250
4 A 5 4 1.02 12 0.333
5 A 3 3 1.00 10 0.300
6 A 1 1 1.00 8 0.125
7 A 1 1 1.00 12 0.083
8 A 6 5 1.06 12 0.417
9 A 3 3 0.92 12 0.250
10 A 5 4 0.96 12 0.333
11 A 4 4 0.96 12 0.333
12 A 5 4 0.95 12 0.333
13 A 15 14 1.41 14 1.000
14 A 14 13 1.23 14 0.929
15 A 10 9 1.21 14 0.643
16 A 10 9 1.09 14 0.643
17 A 4 4 1.04 12 0.333
18 A 6 5 1.19 10 0.500
19 A 4 4 1.22 14 0.286
20 A 4 4 1.08 14 0.286
21 A 9 8 0.96 14 0.571
22 A 8 8 0.92 14 0.571
23 A 14 13 1.16 14 0.929
24 B 18 17 2.02 14 1.214
25 A 16 15 1.39 14 1.071
26 A 14 13 1.57 14 0.929
27 A 10 10 1.10 14 0.714
28 A 9 8 1.12 12 0.667
29 A 5 5 1.14 10 0.500
30 A 5 5 1.15 14 0.357
31 A 5 5 1.13 14 0.357
32 A 7 7 0.97 14 0.500
33 A 15 14 0.98 14 1.000
34 A 11 11 1.29 14 0.786
35 A 8 7 1.15 16 0.438
36 A 8 7 1.16 16 0.438
37 A 7 6 1.12 16 0.375
38 A 7 6 1.08 16 0.375
39 A 6 5 1.12 16 0.312
40 A 8 7 1.12 16 0.438
41 A 7 6 1.14 16 0.375
42 A 9 8 1.14 16 0.500
43 N/A 1 0 1.00 16 0.000
44 N/A 1 0 1.00 16 0.000
45 A 2 2 1.00 14 0.143
46 N/A 1 0 1.00 16 0.000
47 N/A 1 0 1.00 16 0.000
48 N/A 1 0 1.00 10 0.000
49 N/A 1 0 1.00 16 0.000
50 A 5 4 0.98 14 0.286
51 A 5 4 1.02 14 0.286
52 A 5 4 1.00 14 0.286
53 A 2 2 0.88 12 0.167
54 A 3 2 1.20 14 0.143
55 A 6 5 1.05 14 0.357
56 A 5 4 0.93 14 0.286
57 A 5 4 0.96 14 0.286
58 A 5 5 1.14 14 0.357
59 A 5 5 1.11 14 0.357
60 A 1 1 1.00 10 0.100
61 A 4 4 1.20 14 0.286
62 A 5 5 1.10 14 0.357
63 A 5 5 1.13 14 0.357
64 A 11 10 1.22 16 0.625
65 A 11 10 1.11 16 0.625
66 A 6 5 1.01 16 0.312
67 A 7 6 1.11 14 0.429
68 A 6 5 1.19 16 0.312
69 A 6 5 1.05 16 0.312
70 A 10 9 0.99 16 0.562
71 A 2 2 1.00 16 0.125
72 A 2 2 1.00 16 0.125
73 A 2 2 1.00 12 0.167
74 A 2 2 1.00 16 0.125
75 A 2 2 1.00 16 0.125
76 A 2 2 1.00 16 0.125
77 A 10 9 1.12 16 0.562
78 A 7 6 1.07 14 0.429
79 A 7 6 1.16 16 0.375
80 A 7 6 1.06 16 0.375
81 A 9 8 0.99 16 0.500
82 A 17 16 1.39 18 0.889
83 A 16 15 1.36 18 0.833
84 A 16 15 1.36 18 0.833
85 A 16 15 1.41 18 0.833
86 A 16 15 1.42 18 0.833
87 A 15 14 1.35 18 0.778
88 A 17 16 1.37 18 0.889
89 A 17 16 1.36 18 0.889
90 A 5 4 0.85 20 0.200
91 A 5 4 0.85 20 0.200
92 A 5 4 0.82 20 0.200
93 A 5 4 0.82 20 0.200
94 N/A 1 0 1.00 18 0.000
95 N/A 1 0 1.00 18 0.000
96 A 2 2 1.00 16 0.125
97 N/A 1 0 1.00 18 0.000
98 N/A 1 0 1.00 18 0.000
99 A 5 4 0.98 14 0.286
100 A 5 4 1.02 14 0.286
101 A 5 4 1.00 14 0.286
102 A 2 2 0.88 14 0.143
103 A 3 2 1.20 14 0.143
104 A 6 5 1.05 14 0.357
105 A 5 4 0.93 14 0.286
106 A 5 4 0.96 14 0.286
107 A 12 11 1.26 14 0.786
108 A 1 1 1.00 10 0.100
109 A 11 10 1.27 14 0.714
110 A 11 10 1.10 14 0.714
111 A 12 11 1.35 14 0.786
112 A 11 10 1.07 14 0.714
113 A 11 10 1.34 12 0.833
114 A 10 9 1.06 14 0.643
115 A 12 11 1.33 14 0.786
116 A 11 10 1.22 16 0.625
117 A 11 10 1.11 16 0.625
118 A 6 5 1.01 16 0.312
119 A 7 6 1.08 16 0.375
120 A 6 5 1.16 16 0.312
121 A 6 5 1.01 16 0.312
122 A 10 9 0.99 16 0.562
123 A 10 9 0.95 16 0.562
124 A 12 11 1.06 16 0.688
125 A 10 9 1.14 16 0.562
126 A 7 6 1.10 16 0.375
127 A 7 6 1.14 16 0.375
128 A 7 6 1.11 16 0.375
129 A 9 8 1.01 16 0.500
130 N/A 1 0 1.00 18 0.000
131 N/A 1 0 1.00 18 0.000
132 A 2 2 1.00 16 0.125
133 N/A 1 0 1.00 18 0.000
134 N/A 1 0 1.00 18 0.000
135 A 4 4 0.96 14 0.286
136 A 7 6 0.93 14 0.429
137 A 4 4 0.90 12 0.333
138 A 1 1 1.00 10 0.100
139 A 3 2 1.10 14 0.143
140 A 2 2 1.00 14 0.143
141 A 4 4 1.00 14 0.286
142 A 7 6 1.15 14 0.429
143 A 15 14 1.14 16 0.875
144 A 10 9 0.92 16 0.562
145 A 10 9 0.99 14 0.643
146 A 10 9 1.08 12 0.750
147 A 6 5 1.20 16 0.312
148 A 7 6 1.16 16 0.375
149 A 6 5 1.00 16 0.312
150 A 13 12 1.31 16 0.750
151 A 16 15 1.00 16 0.938
152 A 9 8 0.97 14 0.571
153 A 9 9 1.12 12 0.750
154 A 7 6 1.13 16 0.375
155 A 7 6 1.11 16 0.375
156 A 10 9 1.11 16 0.562
157 A 7 6 0.96 14 0.429
158 A 7 6 0.93 14 0.429
159 A 7 6 0.91 14 0.429
160 A 3 3 0.87 12 0.250
161 A 3 2 1.23 14 0.143
162 A 2 2 1.00 14 0.143
163 A 7 6 1.00 14 0.429
164 A 7 6 1.15 14 0.429
165 A 7 7 1.14 14 0.500
166 A 6 6 1.07 14 0.429
167 A 1 1 1.00 10 0.100
168 A 5 5 1.20 14 0.357
169 A 7 7 1.11 14 0.500
170 A 6 6 1.14 14 0.429
171 A 10 9 0.94 16 0.562
172 A 6 5 0.96 14 0.357
173 A 6 5 1.13 16 0.312
174 A 7 6 1.06 16 0.375
175 A 6 5 0.94 16 0.312
176 A 3 3 1.00 16 0.188
177 A 3 3 1.00 16 0.188
178 A 3 3 1.00 12 0.250
179 A 3 3 1.03 16 0.188
180 A 3 3 1.00 16 0.188
181 N/A 1 0 1.00 18 0.000
182 N/A 1 0 1.00 18 0.000
183 A 4 3 1.04 16 0.188
184 N/A 1 0 1.00 18 0.000
185 N/A 1 0 1.00 18 0.000
186 A 8 7 1.15 16 0.438
187 A 7 6 1.12 16 0.375
188 A 6 5 1.08 14 0.357
189 A 1 1 1.00 12 0.083
190 A 3 2 1.38 16 0.125
191 A 5 4 1.08 16 0.250
192 A 6 5 0.98 16 0.312
193 A 7 6 1.00 16 0.375
194 A 21 20 1.45 18 1.111
195 A 16 15 1.31 18 0.833
196 A 11 10 1.23 16 0.625
197 A 6 5 1.13 14 0.357
198 A 6 5 1.22 18 0.278
199 A 10 9 1.05 18 0.500
200 A 15 14 1.14 18 0.778
201 B 23 22 2.54 18 1.222
202 B 19 18 2.01 18 1.000
203 A 15 14 1.52 16 0.875
204 A 10 9 1.20 14 0.643
205 A 7 6 1.17 18 0.333
206 A 9 8 1.06 18 0.444
207 A 13 12 1.31 18 0.667
208 A 3 3 0.92 12 0.250
209 A 3 3 0.90 12 0.250
210 A 2 2 1.00 12 0.167
211 A 4 4 1.00 12 0.333
212 A 13 12 1.32 16 0.750
213 A 6 5 1.10 16 0.312
214 A 13 12 1.25 14 0.857
215 A 1 1 1.21 12 0.083
216 A 3 2 1.24 16 0.125
217 A 12 11 1.27 16 0.688
218 A 13 12 1.31 16 0.750
219 A 6 5 1.04 16 0.312
220 A 6 5 1.01 18 0.278
221 A 6 5 1.15 18 0.278
222 A 10 9 0.99 18 0.500
223 A 2 2 1.00 14 0.143
224 A 2 2 1.00 12 0.167
225 A 1 1 1.00 10 0.100
226 A 3 2 1.00 14 0.143
227 A 2 2 1.00 14 0.143
228 A 2 2 1.01 14 0.143
229 A 2 2 1.00 14 0.143
230 N/A 1 0 1.00 14 0.000
231 N/A 1 0 1.00 12 0.000
232 A 6 5 1.10 16 0.312
233 N/A 1 0 1.00 16 0.000
234 N/A 1 0 1.00 16 0.000
235 A 3 2 0.93 10 0.200
236 A 3 2 1.17 10 0.200
237 A 3 3 1.00 4 0.750
238 N/A 1 0 1.00 18 0.000
239 N/A 1 0 1.00 18 0.000
240 A 3 3 1.07 16 0.188
241 N/A 1 0 1.00 18 0.000
242 N/A 1 0 1.00 18 0.000

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