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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 [133] had the largest ratio of [1.11111000000000004]

# 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 5 1.12 9 0.556
2 A 5 5 1.13 9 0.556
3 A 5 5 1.15 9 0.556
4 A 5 5 1.18 7 0.714
5 A 5 4 1.10 5 0.800
6 A 1 1 1.00 9 0.111
7 A 6 6 1.00 9 0.667
8 A 5 5 0.98 9 0.556
9 A 5 5 1.01 9 0.556
10 A 5 5 1.01 9 0.556
11 A 6 6 1.17 9 0.667
12 A 6 6 1.19 9 0.667
13 A 6 6 1.22 7 0.857
14 A 6 5 1.15 5 1.000
15 A 1 1 1.00 9 0.111
16 A 7 7 1.00 9 0.778
17 A 6 6 1.06 9 0.667
18 A 6 6 1.08 9 0.667
19 A 7 6 1.14 11 0.545
20 A 7 6 1.16 11 0.545
21 A 6 5 1.02 9 0.556
22 A 1 1 1.00 11 0.091
23 A 8 7 1.04 11 0.636
24 A 7 6 1.02 11 0.545
25 A 7 6 1.04 11 0.545
26 A 5 5 1.12 11 0.455
27 A 5 5 1.14 11 0.455
28 A 5 5 1.20 7 0.714
29 A 4 4 1.07 11 0.364
30 A 5 5 1.09 11 0.455
31 A 6 6 1.08 11 0.545
32 A 8 7 1.17 11 0.636
33 A 8 7 1.19 11 0.636
34 A 7 6 1.02 9 0.667
35 A 1 1 1.00 11 0.091
36 A 9 8 1.03 11 0.727
37 A 8 7 1.08 11 0.636
38 A 8 7 1.09 11 0.636
39 A 6 6 1.16 11 0.545
40 A 6 6 1.18 11 0.545
41 A 6 6 1.20 7 0.857
42 A 5 5 1.11 11 0.455
43 A 6 6 1.14 11 0.545
44 A 7 7 1.12 11 0.636
45 A 4 4 1.04 11 0.364
46 A 4 4 1.04 9 0.444
47 A 4 4 1.00 7 0.571
48 A 1 1 1.00 11 0.091
49 A 4 4 1.01 11 0.364
50 A 4 4 1.04 11 0.364
51 A 4 4 1.04 11 0.364
52 A 5 5 1.07 11 0.455
53 A 5 5 1.07 9 0.556
54 A 5 5 0.97 7 0.714
55 A 1 1 1.00 11 0.091
56 A 5 5 1.01 11 0.455
57 A 5 5 1.06 11 0.455
58 A 5 5 1.06 11 0.455
59 A 9 8 1.18 13 0.615
60 A 8 7 1.16 13 0.538
61 A 7 6 1.12 13 0.462
62 A 6 5 1.04 13 0.385
63 A 7 6 1.10 13 0.462
64 A 8 7 1.11 13 0.538
65 A 11 10 1.19 13 0.769
66 A 10 9 1.19 13 0.692
67 A 9 8 1.17 13 0.615
68 A 8 7 1.13 13 0.538
69 A 7 6 1.07 13 0.462
70 A 8 7 1.13 13 0.538
71 A 9 8 1.14 13 0.615
72 A 11 10 1.20 15 0.667
73 A 11 10 1.19 15 0.667
74 A 10 9 1.19 15 0.600
75 A 10 9 1.14 15 0.600
76 A 9 8 1.13 15 0.533
77 A 11 10 1.14 15 0.667
78 A 13 12 1.23 15 0.800
79 A 12 11 1.20 15 0.733
80 A 12 11 1.20 15 0.733
81 A 11 10 1.19 15 0.667
82 A 11 10 1.14 15 0.667
83 A 10 9 1.14 15 0.600
84 A 12 11 1.16 15 0.733
85 A 11 10 1.17 15 0.667
86 A 5 5 1.03 15 0.333
87 A 5 5 1.03 15 0.333
88 A 5 5 1.01 15 0.333
89 A 5 5 1.02 15 0.333
90 A 5 5 1.04 15 0.333
91 A 6 6 1.05 15 0.400
92 A 6 6 1.05 15 0.400
93 A 6 6 1.02 15 0.400
94 A 6 6 1.03 15 0.400
95 A 6 6 1.05 15 0.400
96 N/A 3 0 1.00 7 0.000
97 N/A 2 0 1.00 7 0.000
98 N/A 1 0 1.00 7 0.000
99 N/A 2 0 1.00 7 0.000
100 N/A 3 0 1.00 7 0.000
101 A 1 1 1.00 15 0.067
102 A 4 4 1.09 11 0.364
103 A 5 5 1.12 11 0.455
104 A 6 6 1.18 11 0.545
105 A 5 5 1.07 13 0.385
106 A 6 6 1.12 13 0.462
107 A 7 7 1.15 13 0.538
108 A 5 5 1.07 13 0.385
109 A 6 6 1.12 13 0.462
110 A 7 7 1.15 13 0.538
111 A 5 5 1.05 13 0.385
112 A 6 6 1.06 13 0.462
113 A 7 7 1.10 13 0.538
114 N/A 1 0 1.00 7 0.000
115 N/A 1 0 1.00 5 0.000
116 A 1 1 1.00 9 0.111
117 N/A 1 0 1.00 9 0.000
118 N/A 1 0 1.00 9 0.000
119 N/A 1 0 1.00 9 0.000
120 N/A 1 0 1.00 7 0.000
121 A 1 1 1.00 11 0.091
122 N/A 1 0 1.00 11 0.000
123 N/A 1 0 1.00 11 0.000
124 A 3 3 1.02 13 0.231
125 A 3 3 1.03 11 0.273
126 A 9 8 1.12 9 0.889
127 A 4 3 1.14 13 0.231
128 A 3 3 0.98 13 0.231
129 A 3 3 0.90 13 0.231
130 A 3 3 0.94 13 0.231
131 A 2 2 0.98 13 0.154
132 A 2 2 0.99 11 0.182
133 A 11 10 1.11 9 1.111
134 N/A 2 0 1.00 13 0.000
135 A 2 2 1.07 13 0.154
136 A 2 2 0.96 13 0.154
137 A 3 3 0.96 17 0.176
138 A 3 3 0.97 17 0.176
139 A 3 3 1.00 15 0.200
140 A 9 8 1.12 9 0.889
141 A 4 3 1.26 17 0.176
142 A 3 3 0.99 17 0.176
143 A 3 3 0.88 17 0.176
144 A 3 3 0.91 17 0.176
145 A 6 5 1.02 9 0.556
146 A 7 6 1.02 12 0.500
147 A 2 2 1.00 12 0.167
148 A 3 3 1.00 15 0.200
149 A 1 1 1.00 34 0.029
150 A 1 1 1.00 34 0.029
151 A 1 1 1.00 34 0.029
152 A 2 2 1.00 37 0.054
153 A 2 2 1.00 53 0.038
154 A 2 2 1.00 53 0.038
155 A 5 4 1.00 76 0.053
156 A 6 5 1.22 19 0.263
157 A 5 4 1.15 19 0.211
158 A 4 3 1.00 17 0.176
159 A 3 2 1.00 15 0.133
160 N/A 2 0 1.00 19 0.000
161 A 5 5 1.44 16 0.312
162 A 5 5 1.41 16 0.312
163 A 4 4 1.13 14 0.286
164 A 9 8 1.23 13 0.615
165 A 1 1 1.00 16 0.062
166 A 4 4 0.99 16 0.250
167 A 5 5 1.05 16 0.312
168 A 5 5 1.20 16 0.312
169 A 5 5 1.26 16 0.312
170 A 8 7 0.96 20 0.350
171 A 8 7 1.00 18 0.389
172 A 9 8 1.17 17 0.471
173 A 3 3 1.00 20 0.150
174 A 8 7 0.99 20 0.350
175 A 11 10 0.91 20 0.500
176 A 15 14 1.01 20 0.700
177 A 2 2 1.13 27 0.074
178 A 2 2 1.05 25 0.080
179 A 5 5 1.03 24 0.208
180 N/A 1 0 1.00 27 0.000
181 A 2 2 0.97 27 0.074
182 A 2 2 0.93 27 0.074
183 A 2 2 1.00 27 0.074
184 A 2 2 1.12 21 0.095
185 A 2 2 1.13 19 0.105
186 A 2 2 1.24 18 0.111
187 A 12 11 1.16 21 0.524
188 A 7 7 0.95 21 0.333
189 A 2 2 1.17 21 0.095
190 A 2 2 1.08 21 0.095
191 A 2 2 1.09 21 0.095
192 A 2 2 1.09 24 0.083
193 A 2 2 1.11 23 0.087
194 A 5 5 1.24 26 0.192
195 A 4 4 1.18 26 0.154
196 A 4 4 1.16 26 0.154
197 A 2 2 1.08 26 0.077
198 A 2 2 1.05 26 0.077

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