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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 [140] had the largest ratio of [1.10000000000000009]

# 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 6 4 1.00 8 0.500
2 A 6 4 1.00 8 0.500
3 A 5 4 1.00 8 0.500
4 A 5 4 1.00 8 0.500
5 A 4 4 1.00 8 0.500
6 A 4 4 1.00 8 0.500
7 A 3 3 1.00 6 0.500
8 A 1 1 1.00 4 0.250
9 A 3 3 1.00 8 0.375
10 A 2 2 1.00 8 0.250
11 A 3 3 1.00 8 0.375
12 A 4 4 1.00 8 0.500
13 A 4 4 1.00 8 0.500
14 A 5 4 1.00 8 0.500
15 A 5 4 1.00 8 0.500
16 A 6 4 1.00 8 0.500
17 A 6 4 1.00 8 0.500
18 A 7 4 1.00 8 0.500
19 A 14 10 1.00 14 0.714
20 A 11 9 1.00 14 0.643
21 A 8 7 1.00 12 0.583
22 A 1 1 1.00 6 0.167
23 N/A 0 0 1.00 14 0.000
24 N/A 0 0 1.00 14 0.000
25 A 14 10 1.00 10 1.000
26 A 11 9 1.00 10 0.900
27 A 8 7 1.00 8 0.875
28 A 1 1 1.00 6 0.167
29 N/A 0 0 1.00 10 0.000
30 N/A 0 0 1.00 10 0.000
31 A 23 10 1.00 10 1.000
32 A 19 10 1.00 10 1.000
33 A 16 9 1.00 10 0.900
34 A 12 9 1.00 10 0.900
35 A 10 9 1.00 10 0.900
36 A 8 6 1.00 10 0.600
37 A 5 5 1.00 8 0.625
38 A 4 4 1.00 6 0.667
39 N/A 0 0 1.00 10 0.000
40 N/A 0 0 1.00 10 0.000
41 N/A 0 0 1.00 10 0.000
42 N/A 0 0 1.00 10 0.000
43 A 9 9 1.00 10 0.900
44 N/A 0 0 1.00 10 0.000
45 N/A 0 0 1.00 10 0.000
46 N/A 0 0 1.00 10 0.000
47 A 20 10 1.00 10 1.000
48 N/A 0 0 1.00 10 0.000
49 A 18 13 1.00 16 0.812
50 A 10 9 1.00 14 0.643
51 A 4 3 1.00 8 0.375
52 N/A 0 0 1.00 16 0.000
53 N/A 0 0 1.00 16 0.000
54 A 10 7 1.00 17 0.412
55 A 10 7 1.00 15 0.467
56 A 10 7 1.00 13 0.538
57 A 3 1 1.00 17 0.059
58 A 10 7 1.00 17 0.412
59 A 10 7 1.00 17 0.412
60 A 10 7 1.00 19 0.368
61 A 4 4 1.00 22 0.182
62 A 4 4 1.00 22 0.182
63 A 4 4 1.00 19 0.210
64 A 4 4 1.00 19 0.210
65 A 2 2 1.00 19 0.105
66 A 2 2 1.00 17 0.118
67 A 2 2 1.00 19 0.105
68 A 2 2 1.00 19 0.105
69 A 2 2 1.00 19 0.105
70 A 2 2 1.00 19 0.105
71 A 22 9 1.00 20 0.450
72 A 18 9 1.00 20 0.450
73 A 15 8 1.00 20 0.400
74 A 11 8 1.00 20 0.400
75 A 9 8 1.00 20 0.400
76 A 7 5 1.00 20 0.250
77 A 4 4 1.00 20 0.200
78 A 2 2 1.00 18 0.111
79 A 2 2 1.00 17 0.118
80 N/A 0 0 1.00 20 0.000
81 N/A 0 0 1.00 20 0.000
82 N/A 0 0 1.00 20 0.000
83 A 8 8 1.00 20 0.400
84 N/A 0 0 1.00 20 0.000
85 N/A 0 0 1.00 20 0.000
86 N/A 0 0 1.00 20 0.000
87 A 19 9 1.00 20 0.450
88 N/A 0 0 1.00 20 0.000
89 N/A 0 0 1.00 20 0.000
90 N/A 0 0 1.00 19 0.000
91 A 23 8 1.00 20 0.400
92 A 18 8 1.00 20 0.400
93 A 16 9 1.00 20 0.450
94 A 13 9 1.00 20 0.450
95 A 10 8 1.00 20 0.400
96 A 7 6 1.00 20 0.300
97 A 5 5 1.00 20 0.250
98 A 4 3 1.00 18 0.167
99 A 1 1 1.00 17 0.059
100 N/A 0 0 1.00 20 0.000
101 A 4 4 1.00 20 0.200
102 N/A 0 0 1.00 20 0.000
103 N/A 0 0 1.00 20 0.000
104 N/A 0 0 1.00 20 0.000
105 A 13 9 1.00 20 0.450
106 N/A 0 0 1.00 20 0.000
107 N/A 0 0 1.00 20 0.000
108 N/A 0 0 1.00 20 0.000
109 A 26 9 1.00 20 0.450
110 A 6 4 1.00 8 0.500
111 A 6 4 1.00 8 0.500
112 A 5 4 1.00 8 0.500
113 A 5 4 1.00 8 0.500
114 A 4 4 1.00 8 0.500
115 A 4 4 1.00 8 0.500
116 A 3 3 1.00 6 0.500
117 A 1 1 1.00 4 0.250
118 A 3 3 1.00 8 0.375
119 A 2 2 1.00 8 0.250
120 A 3 3 1.00 8 0.375
121 A 4 4 1.00 8 0.500
122 A 4 4 1.00 8 0.500
123 A 5 4 1.00 8 0.500
124 A 5 4 1.00 8 0.500
125 A 6 4 1.00 8 0.500
126 A 6 4 1.00 8 0.500
127 A 7 4 1.00 8 0.500
128 A 14 10 1.00 14 0.714
129 A 11 9 1.00 14 0.643
130 A 8 7 1.00 12 0.583
131 A 1 1 1.00 6 0.167
132 N/A 0 0 1.00 14 0.000
133 N/A 0 0 1.00 14 0.000
134 A 14 10 1.00 10 1.000
135 A 11 9 1.00 10 0.900
136 A 8 7 1.00 8 0.875
137 A 1 1 1.00 6 0.167
138 N/A 0 0 1.00 10 0.000
139 N/A 0 0 1.00 10 0.000
140 A 23 11 1.00 10 1.100
141 A 19 10 1.00 10 1.000
142 A 16 10 1.00 10 1.000
143 A 12 9 1.00 10 0.900
144 A 10 10 1.00 10 1.000
145 A 8 6 1.00 10 0.600
146 A 5 5 1.00 8 0.625
147 A 4 4 1.00 6 0.667
148 N/A 0 0 1.00 10 0.000
149 N/A 0 0 1.00 10 0.000
150 N/A 0 0 1.00 10 0.000
151 N/A 0 0 1.00 10 0.000
152 A 9 9 1.00 10 0.900
153 N/A 0 0 1.00 10 0.000
154 N/A 0 0 1.00 10 0.000
155 N/A 0 0 1.00 10 0.000
156 A 20 10 1.00 10 1.000
157 N/A 0 0 1.00 10 0.000
158 A 18 13 1.00 16 0.812
159 A 10 9 1.00 14 0.643
160 A 4 3 1.00 8 0.375
161 N/A 0 0 1.00 16 0.000
162 N/A 0 0 1.00 16 0.000
163 A 10 7 1.00 17 0.412
164 A 10 7 1.00 15 0.467
165 A 10 7 1.00 13 0.538
166 A 3 1 1.00 17 0.059
167 A 10 7 1.00 17 0.412
168 A 10 7 1.00 17 0.412
169 A 10 7 1.00 19 0.368
170 A 4 4 1.00 22 0.182
171 A 4 4 1.00 22 0.182
172 A 4 4 1.00 19 0.210
173 A 4 4 1.00 19 0.210
174 A 2 2 1.00 19 0.105
175 A 2 2 1.00 17 0.118
176 A 2 2 1.00 19 0.105
177 A 2 2 1.00 19 0.105
178 A 2 2 1.00 19 0.105
179 A 2 2 1.00 19 0.105
180 A 22 10 1.00 20 0.500
181 A 18 9 1.00 20 0.450
182 A 15 9 1.00 20 0.450
183 A 11 8 1.00 20 0.400
184 A 9 9 1.00 20 0.450
185 A 7 5 1.00 20 0.250
186 A 4 4 1.00 20 0.200
187 A 2 2 1.00 18 0.111
188 A 2 2 1.00 17 0.118
189 N/A 0 0 1.00 20 0.000
190 N/A 0 0 1.00 20 0.000
191 N/A 0 0 1.00 20 0.000
192 A 8 8 1.00 20 0.400
193 N/A 0 0 1.00 20 0.000
194 N/A 0 0 1.00 20 0.000
195 N/A 0 0 1.00 20 0.000
196 A 19 9 1.00 20 0.450
197 N/A 0 0 1.00 20 0.000
198 N/A 0 0 1.00 20 0.000
199 N/A 0 0 1.00 19 0.000
200 A 23 9 1.00 20 0.450
201 A 18 8 1.00 20 0.400
202 A 16 10 1.00 20 0.500
203 A 13 9 1.00 20 0.450
204 A 10 9 1.00 20 0.450
205 A 7 6 1.00 20 0.300
206 A 5 5 1.00 20 0.250
207 A 4 3 1.00 18 0.167
208 A 1 1 1.00 17 0.059
209 N/A 0 0 1.00 20 0.000
210 A 4 4 1.00 20 0.200
211 N/A 0 0 1.00 20 0.000
212 N/A 0 0 1.00 20 0.000
213 N/A 0 0 1.00 20 0.000
214 A 13 9 1.00 20 0.450
215 N/A 0 0 1.00 20 0.000
216 N/A 0 0 1.00 20 0.000
217 N/A 0 0 1.00 20 0.000
218 A 26 9 1.00 20 0.450

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