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2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. 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 given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [112] had the largest ratio of [31]

# 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 1 1 1.00 9 0.111
2 A 2 1 1.00 11 0.091
3 A 2 1 1.00 11 0.091
4 A 2 1 1.00 11 0.091
5 A 1 1 1.00 14 0.071
6 A 2 1 1.00 4 0.250
7 A 2 1 1.00 9 0.111
8 A 2 2 1.00 7 0.286
9 A 2 2 1.00 17 0.118
10 A 2 2 1.00 9 0.222
11 A 3 3 1.00 11 0.273
12 A 3 3 1.00 16 0.188
13 A 2 2 1.00 10 0.200
14 A 1 1 1.00 15 0.067
15 A 2 1 1.00 9 0.111
16 A 1 1 1.00 9 0.111
17 A 1 1 1.00 15 0.067
18 A 1 1 1.00 17 0.059
19 A 3 2 1.00 20 0.100
20 A 1 1 1.00 26 0.038
21 A 2 2 1.00 20 0.100
22 A 2 2 1.00 4 0.500
23 A 3 2 1.00 6 0.333
24 A 4 2 1.00 6 0.333
25 A 4 2 1.00 6 0.333
26 A 2 2 1.00 5 0.400
27 A 3 3 1.00 6 0.500
28 A 2 2 1.00 4 0.500
29 A 2 1 1.00 4 0.250
30 A 3 2 1.00 4 0.500
31 A 2 1 1.00 4 0.250
32 A 4 2 1.00 4 0.500
33 A 2 2 1.00 6 0.333
34 A 3 3 1.00 6 0.500
35 A 4 4 1.00 8 0.500
36 A 2 2 1.00 4 0.500
37 A 2 1 1.00 4 0.250
38 A 3 2 1.00 4 0.500
39 A 5 3 1.00 13 0.231
40 A 3 2 1.00 13 0.154
41 A 2 2 1.00 13 0.154
42 A 2 2 1.00 4 0.500
43 A 3 2 1.00 4 0.500
44 A 2 2 1.00 4 0.500
45 A 3 2 1.00 4 0.500
46 A 2 2 1.00 10 0.200
47 A 1 1 1.00 11 0.091
48 A 1 1 1.00 9 0.111
49 A 1 1 1.00 13 0.077
50 A 1 1 1.00 11 0.091
51 A 2 1 1.00 11 0.091
52 A 2 2 1.00 8 0.250
53 A 5 3 1.00 8 0.375
54 A 1 1 1.00 10 0.100
55 A 3 2 1.00 17 0.118
56 A 1 1 1.00 7 0.143
57 A 2 2 1.00 4 0.500
58 A 1 1 1.00 4 0.250
59 A 2 2 1.00 6 0.333
60 A 1 1 1.00 5 0.200
61 A 1 1 1.00 2 0.500
62 A 1 1 1.00 8 0.125
63 A 2 2 1.00 8 0.250
64 A 2 2 1.00 8 0.250
65 A 2 2 1.00 14 0.143
66 A 3 2 1.00 14 0.143
67 A 3 2 1.00 8 0.250
68 A 1 1 1.00 9 0.111
69 A 1 1 1.00 13 0.077
70 A 2 2 1.00 9 0.222
71 A 1 1 1.00 6 0.167
72 A 1 1 1.00 6 0.167
73 A 4 4 1.00 7 0.571
74 A 2 2 1.00 5 0.400
75 A 2 2 1.00 7 0.286
76 A 3 2 1.00 7 0.286
77 A 3 2 1.00 9 0.222
78 A 3 3 1.00 7 0.429
79 A 2 2 1.00 11 0.182
80 A 1 1 1.00 10 0.100
81 A 1 1 1.00 10 0.100
82 A 2 2 1.00 2 1.000
83 A 4 4 1.00 2 2.000
84 A 4 4 1.00 2 2.000
85 A 3 3 1.00 4 0.750
86 A 4 4 1.00 6 0.667
87 A 2 2 1.00 13 0.154
88 A 2 2 1.00 14 0.143
89 A 1 1 1.00 9 0.111
90 A 1 1 1.00 9 0.111
91 A 2 2 1.00 10 0.200
92 A 3 3 1.00 4 0.750
93 A 4 3 1.00 6 0.500
94 A 5 5 1.00 6 0.833
95 A 4 4 1.00 6 0.667
96 A 1 3 1.00 17 0.176
97 A 2 2 1.00 11 0.182
98 A 1 1 1.00 15 0.067
99 A 1 1 1.00 14 0.071
100 A 2 2 1.00 11 0.182
101 A 2 2 1.00 13 0.154
102 A 5 6 1.00 10 0.600
103 A 3 3 1.00 15 0.200
104 A 4 4 1.00 15 0.267
105 A 3 3 1.00 15 0.200
106 A 3 2 1.00 16 0.125
107 A 3 2 1.00 16 0.125
108 A 6 4 1.00 18 0.222
109 A 3 2 1.00 23 0.087
110 A 2 1 1.00 19 0.053
111 A 5 5 1.00 18 0.278
112 A 6 5 1.00 31 0.161
113 A 2 2 1.00 7 0.286
114 A 3 2 1.00 22 0.091
115 A 2 1 1.00 16 0.062
116 A 2 1 1.00 17 0.059
117 A 2 1 1.00 12 0.083
118 A 3 2 1.00 21 0.095
119 A 2 1 1.00 20 0.050
120 A 3 3 1.00 16 0.188
121 A 4 3 1.00 16 0.188
122 A 2 1 1.00 11 0.091
123 A 3 2 1.00 11 0.182
124 A 2 1 1.00 16 0.062
125 A 2 1 1.00 7 0.143
126 A 5 5 1.00 9 0.556
127 A 4 3 1.00 12 0.250
128 A 3 2 1.00 14 0.143
129 A 4 4 1.00 21 0.190
130 A 3 2 1.00 18 0.111
131 A 2 2 1.00 7 0.286
132 A 3 3 1.00 11 0.273
133 A 3 2 1.00 16 0.125
134 A 3 2 1.00 11 0.182
135 A 5 4 1.00 18 0.222
136 A 3 3 1.00 7 0.429
137 A 9 6 1.00 7 0.857
138 A 3 3 1.00 14 0.214
139 A 1 1 1.00 16 0.062
140 A 3 3 1.00 12 0.250
141 A 2 2 1.00 8 0.250
142 A 2 2 1.00 8 0.250
143 A 1 1 1.00 10 0.100
144 A 3 3 1.00 13 0.231
145 A 2 1 1.00 19 0.053
146 A 1 1 1.00 11 0.091
147 A 3 3 1.00 11 0.273
148 A 2 2 1.00 11 0.182
149 A 1 1 1.00 13 0.077
150 A 4 4 1.00 15 0.267
151 A 3 3 1.00 13 0.231
152 A 2 2 1.00 9 0.222
153 A 3 3 1.00 12 0.250
154 A 2 2 1.00 9 0.222
155 A 6 6 1.00 18 0.333
156 A 2 2 1.00 8 0.250
157 A 3 3 1.00 5 0.600
158 A 1 1 1.00 7 0.143
159 A 1 1 1.00 9 0.111
160 A 2 2 1.00 7 0.286
161 A 2 2 1.00 5 0.400
162 A 1 1 1.00 14 0.071
163 A 2 2 1.00 14 0.143
164 A 2 2 1.00 9 0.222
165 A 2 3 1.00 8 0.375
166 A 2 2 1.00 7 0.286
167 A 3 2 1.00 9 0.222
168 A 4 2 1.00 9 0.222
169 A 1 1 1.00 21 0.048
170 A 1 1 1.00 4 0.250
171 A 2 2 1.00 4 0.500
172 A 2 2 1.00 8 0.250
173 A 1 1 1.00 11 0.091
174 A 4 2 1.00 16 0.125
175 A 1 1 1.00 9 0.111

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