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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 [22] had the largest ratio of [1.39999999999999991]

# 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 4 1.05 8 0.500
2 A 4 4 1.20 8 0.500
3 A 5 4 1.07 8 0.500
4 A 3 3 1.13 6 0.500
5 A 2 2 1.00 4 0.500
6 A 9 8 1.16 8 1.000
7 A 5 4 1.00 8 0.500
8 A 2 2 1.00 8 0.250
9 A 6 5 1.02 8 0.625
10 A 3 3 1.09 8 0.375
11 A 7 6 1.08 8 0.750
12 A 7 7 1.17 10 0.700
13 A 6 6 1.17 10 0.600
14 A 5 5 1.15 10 0.500
15 A 4 4 1.12 8 0.500
16 A 3 3 1.17 6 0.500
17 A 10 9 1.24 10 0.900
18 A 7 6 1.02 10 0.600
19 A 3 3 1.00 10 0.300
20 A 9 8 0.97 10 0.800
21 A 5 5 1.01 10 0.500
22 A 15 14 1.50 10 1.400
23 A 11 11 1.46 10 1.100
24 A 10 9 1.29 10 0.900
25 A 6 6 1.17 8 0.750
26 A 4 4 1.13 6 0.667
27 A 11 10 1.23 10 1.000
28 A 8 7 1.05 10 0.700
29 A 11 10 1.05 10 1.000
30 A 13 12 1.00 10 1.200
31 A 14 13 1.07 10 1.300
32 A 13 13 1.78 10 1.300
33 A 14 14 1.65 10 1.400
34 A 10 10 1.48 10 1.000
35 A 11 11 1.37 10 1.100
36 A 7 7 1.20 8 0.875
37 A 5 5 1.22 6 0.833
38 A 12 11 1.31 10 1.100
39 A 9 8 1.06 10 0.800
40 A 12 11 1.13 10 1.100
41 A 13 12 1.00 10 1.200
42 A 4 3 0.85 10 0.300
43 A 4 3 0.88 10 0.300
44 A 4 3 0.88 10 0.300
45 A 4 3 0.93 10 0.300
46 A 4 3 0.93 10 0.300
47 A 6 5 1.00 8 0.625
48 A 4 3 1.00 6 0.500
49 N/A 1 0 1.00 10 0.000
50 N/A 1 0 1.00 10 0.000
51 A 3 2 0.92 10 0.200
52 A 3 2 0.94 10 0.200
53 A 3 2 0.94 10 0.200
54 A 3 2 0.98 10 0.200
55 A 3 2 0.98 10 0.200
56 A 4 3 1.00 8 0.375
57 A 5 4 1.00 6 0.667
58 N/A 1 0 1.00 10 0.000
59 N/A 1 0 1.00 10 0.000
60 A 6 5 1.37 10 0.500
61 A 9 8 1.33 10 0.800
62 A 9 8 1.26 10 0.800
63 A 9 8 1.11 8 1.000
64 A 6 5 1.08 6 0.833
65 N/A 1 0 1.00 10 0.000
66 N/A 1 0 1.00 10 0.000
67 A 5 4 1.33 10 0.400
68 A 7 6 1.23 10 0.600
69 A 9 8 1.26 10 0.800
70 A 7 6 1.09 8 0.750
71 A 7 6 1.17 6 1.000
72 N/A 1 0 1.00 10 0.000
73 N/A 1 0 1.00 10 0.000
74 A 6 5 0.99 12 0.417
75 A 6 5 0.99 12 0.417
76 A 6 5 1.02 12 0.417
77 A 6 5 0.97 10 0.500
78 A 6 5 1.00 8 0.625
79 N/A 1 0 1.00 12 0.000
80 A 15 14 1.57 12 1.167
81 A 14 13 1.28 12 1.083
82 A 11 10 1.31 12 0.833
83 A 10 9 1.07 10 0.900
84 A 7 6 1.01 8 0.750
85 N/A 1 0 1.00 12 0.000
86 A 14 13 1.53 12 1.083
87 A 11 10 1.33 12 0.833
88 A 12 11 1.32 12 0.917
89 A 9 8 1.10 10 0.800
90 A 8 7 1.08 8 0.875
91 N/A 1 0 1.00 12 0.000
92 A 4 3 0.95 12 0.250
93 A 4 3 0.97 12 0.250
94 A 4 3 0.97 12 0.250
95 A 7 6 1.00 10 0.600
96 A 5 4 1.00 8 0.500
97 N/A 1 0 1.00 12 0.000
98 N/A 1 0 1.00 12 0.000
99 A 3 2 0.96 12 0.167
100 A 3 2 0.99 12 0.167
101 A 3 2 0.98 12 0.167
102 A 3 2 1.06 12 0.167
103 A 3 2 1.05 12 0.167
104 A 5 4 1.00 10 0.400
105 A 6 5 1.00 8 0.625
106 N/A 1 0 1.00 12 0.000
107 A 6 5 1.47 12 0.417
108 A 10 9 1.33 12 0.750
109 A 10 9 1.41 12 0.750
110 A 10 9 1.06 10 0.900
111 A 7 6 1.07 8 0.750
112 N/A 1 0 1.00 12 0.000
113 A 5 4 1.24 12 0.333
114 A 8 7 1.30 12 0.583
115 A 10 9 1.32 12 0.750
116 A 8 7 1.11 10 0.700
117 A 8 7 1.12 8 0.875
118 N/A 1 0 1.00 12 0.000
119 N/A 2 0 1.00 12 0.000
120 N/A 2 0 1.00 12 0.000
121 A 2 2 0.99 12 0.167
122 A 2 2 1.00 10 0.200
123 N/A 1 0 1.00 12 0.000
124 N/A 1 0 1.00 12 0.000
125 N/A 1 0 1.00 14 0.000
126 N/A 1 0 1.00 14 0.000
127 N/A 1 0 1.00 14 0.000
128 N/A 1 0 1.00 14 0.000
129 N/A 1 0 1.00 12 0.000
130 A 4 3 0.95 10 0.300
131 A 4 3 0.95 10 0.300
132 A 7 6 1.01 8 0.750
133 A 6 5 0.97 6 0.833
134 N/A 1 0 1.00 10 0.000
135 N/A 1 0 1.00 10 0.000
136 N/A 1 0 1.00 14 0.000
137 N/A 1 0 1.00 14 0.000
138 N/A 1 0 1.00 14 0.000
139 N/A 1 0 1.00 14 0.000
140 A 4 4 1.16 12 0.333
141 A 5 4 1.05 12 0.333
142 A 3 3 1.10 10 0.300
143 A 1 1 1.00 8 0.125
144 A 9 8 1.13 12 0.667
145 A 5 4 1.00 12 0.333
146 A 2 2 1.00 12 0.167
147 A 6 5 1.00 12 0.417
148 A 5 5 1.07 14 0.357
149 A 4 4 1.11 12 0.333
150 A 3 3 1.09 10 0.300
151 A 10 9 1.17 14 0.643
152 A 7 6 0.96 14 0.429
153 A 9 8 1.13 14 0.571
154 A 6 6 1.10 12 0.500
155 A 3 3 1.01 10 0.300
156 A 11 10 1.15 14 0.714
157 A 8 7 0.98 14 0.500
158 A 4 3 0.86 14 0.214
159 A 11 10 0.89 12 0.833
160 A 8 7 0.91 10 0.700
161 N/A 1 0 1.00 14 0.000
162 N/A 1 0 1.00 14 0.000
163 A 3 2 0.90 14 0.143
164 A 8 7 0.96 12 0.583
165 A 10 9 0.97 10 0.900
166 N/A 1 0 1.00 14 0.000
167 N/A 1 0 1.00 14 0.000
168 A 13 12 1.26 14 0.857
169 A 14 13 1.05 12 1.083
170 A 10 9 1.00 10 0.900
171 N/A 1 0 1.00 14 0.000
172 N/A 1 0 1.00 14 0.000
173 A 7 6 0.98 16 0.375
174 A 6 5 0.96 14 0.357
175 A 12 11 0.98 12 0.917
176 N/A 1 0 1.00 16 0.000
177 N/A 1 0 1.00 16 0.000
178 A 16 15 1.35 16 0.938
179 A 16 15 1.03 14 1.071
180 A 12 11 0.97 12 0.917
181 N/A 1 0 1.00 16 0.000
182 N/A 1 0 1.00 16 0.000
183 A 18 17 1.32 16 1.062
184 A 9 8 1.03 14 0.571
185 A 14 13 1.00 12 1.083
186 N/A 1 0 1.00 16 0.000
187 N/A 1 0 1.00 16 0.000
188 A 4 3 0.98 16 0.188
189 A 13 12 0.99 14 0.857
190 A 10 9 1.01 12 0.750
191 N/A 1 0 1.00 16 0.000
192 N/A 1 0 1.00 16 0.000
193 A 3 2 1.03 16 0.125
194 A 10 9 1.01 14 0.643
195 A 12 11 1.01 12 0.917
196 N/A 1 0 1.00 16 0.000
197 N/A 1 0 1.00 16 0.000
198 A 15 14 1.46 16 0.875
199 A 16 15 1.04 14 1.071
200 A 12 11 1.04 12 0.917
201 N/A 1 0 1.00 16 0.000
202 N/A 1 0 1.00 16 0.000
203 A 6 5 1.14 16 0.312
204 A 9 8 1.10 16 0.500
205 A 5 4 1.10 16 0.250
206 A 8 7 1.06 16 0.438
207 A 4 3 1.00 16 0.188
208 A 9 8 1.06 16 0.500
209 A 2 2 1.04 18 0.111
210 A 2 2 1.04 18 0.111
211 A 2 2 1.04 18 0.111
212 A 2 2 1.02 18 0.111
213 A 2 2 1.02 18 0.111
214 A 2 2 1.00 18 0.111
215 N/A 2 0 1.00 18 0.000
216 N/A 2 0 1.00 18 0.000
217 N/A 2 0 1.00 18 0.000
218 N/A 2 0 1.00 18 0.000
219 N/A 2 0 1.00 18 0.000
220 N/A 1 0 1.00 18 0.000
221 N/A 1 0 1.00 18 0.000
222 N/A 1 0 1.00 18 0.000
223 N/A 1 0 1.00 18 0.000
224 N/A 1 0 1.00 18 0.000
225 N/A 1 0 1.00 18 0.000
226 N/A 1 0 1.00 18 0.000
227 N/A 1 0 1.00 18 0.000

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