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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 [172] had the largest ratio of [37]

# 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 5 1.00 20 0.250
2 A 5 5 1.00 20 0.250
3 A 4 4 1.00 18 0.222
4 A 4 4 1.00 17 0.235
5 A 7 7 1.00 20 0.350
6 A 7 7 1.00 20 0.350
7 A 7 7 1.00 20 0.350
8 A 7 5 1.00 20 0.250
9 A 6 5 1.00 20 0.250
10 A 5 4 1.00 18 0.222
11 A 5 4 1.00 17 0.235
12 A 8 7 1.00 20 0.350
13 A 8 8 1.00 20 0.400
14 A 8 7 1.00 20 0.350
15 A 8 5 1.00 20 0.250
16 A 7 5 1.00 20 0.250
17 A 6 4 1.00 18 0.222
18 A 6 4 1.00 17 0.235
19 A 9 7 1.00 20 0.350
20 A 9 8 1.00 20 0.400
21 A 9 8 1.00 20 0.400
22 A 5 4 1.00 20 0.200
23 A 4 4 1.00 20 0.200
24 A 3 3 1.00 18 0.167
25 A 3 3 1.00 17 0.176
26 A 6 6 1.00 20 0.300
27 A 4 4 1.00 20 0.200
28 A 5 5 1.00 20 0.250
29 A 4 4 1.00 20 0.200
30 A 4 4 1.00 20 0.200
31 A 3 3 1.00 18 0.167
32 A 1 1 1.00 17 0.059
33 A 5 5 1.00 20 0.250
34 A 5 5 1.00 20 0.250
35 A 6 6 1.00 20 0.300
36 A 4 4 1.00 20 0.200
37 A 2 2 1.00 20 0.100
38 A 2 2 0.94 18 0.111
39 A 2 2 1.00 17 0.118
40 A 6 5 1.00 20 0.250
41 A 6 5 1.00 20 0.250
42 A 7 6 1.00 20 0.300
43 A 2 2 1.00 18 0.111
44 A 3 3 1.00 19 0.158
45 A 2 2 1.00 13 0.154
46 A 2 2 1.00 13 0.154
47 A 7 5 1.00 25 0.200
48 A 6 5 1.00 25 0.200
49 A 5 4 1.00 25 0.160
50 A 4 4 1.00 25 0.160
51 A 4 4 1.00 25 0.160
52 A 4 4 1.00 25 0.160
53 A 4 4 1.00 23 0.174
54 A 5 4 1.00 22 0.182
55 A 8 6 1.00 25 0.240
56 A 8 5 1.00 25 0.200
57 A 9 6 1.00 25 0.240
58 A 2 2 1.00 16 0.125
59 A 3 2 1.00 20 0.100
60 A 2 2 1.00 22 0.091
61 A 5 3 1.00 25 0.120
62 A 2 1 1.00 26 0.038
63 A 2 1 1.00 26 0.038
64 A 2 1 1.00 24 0.042
65 A 2 1 1.00 23 0.043
66 A 2 1 1.00 26 0.038
67 A 2 1 1.00 26 0.038
68 A 2 1 1.00 26 0.038
69 A 2 1 1.00 26 0.038
70 A 2 1 1.00 28 0.036
71 A 2 1 1.00 28 0.036
72 A 3 2 1.00 26 0.077
73 A 3 2 1.00 25 0.080
74 A 3 2 1.00 28 0.071
75 A 3 2 1.00 28 0.071
76 A 2 1 1.00 28 0.036
77 A 2 1 1.00 28 0.036
78 A 2 1 1.00 28 0.036
79 A 2 1 1.00 28 0.036
80 A 3 2 1.00 26 0.077
81 A 3 2 1.00 25 0.080
82 A 3 2 1.00 28 0.071
83 A 3 2 1.00 28 0.071
84 A 2 1 1.00 28 0.036
85 A 2 1 1.00 28 0.036
86 A 5 4 1.00 28 0.143
87 A 5 4 1.00 28 0.143
88 A 5 4 1.00 28 0.143
89 A 5 4 1.00 26 0.154
90 A 5 4 1.00 25 0.160
91 A 5 4 1.00 28 0.143
92 A 5 4 1.00 28 0.143
93 A 5 4 1.00 28 0.143
94 A 6 5 1.00 28 0.179
95 A 6 5 1.00 28 0.179
96 A 6 5 1.00 28 0.179
97 A 6 5 1.00 26 0.192
98 A 4 4 1.00 25 0.160
99 A 6 5 1.00 28 0.179
100 A 6 5 1.00 28 0.179
101 A 6 5 1.00 28 0.179
102 A 7 5 1.00 28 0.179
103 A 6 5 1.00 28 0.179
104 A 5 4 1.00 28 0.143
105 A 4 4 1.00 26 0.154
106 A 3 3 1.00 25 0.120
107 A 7 6 1.00 28 0.214
108 A 7 5 1.00 28 0.179
109 A 7 5 1.00 28 0.179
110 A 4 3 1.00 17 0.176
111 A 4 3 1.00 17 0.176
112 A 4 4 1.00 21 0.190
113 A 6 5 1.00 15 0.333
114 A 3 2 1.00 30 0.067
115 A 3 2 1.00 30 0.067
116 A 3 2 1.00 30 0.067
117 A 3 2 1.00 27 0.074
118 A 3 2 1.00 30 0.067
119 A 3 2 1.00 30 0.067
120 A 3 2 1.00 30 0.067
121 A 3 2 1.00 30 0.067
122 A 3 2 1.00 30 0.067
123 A 3 2 1.00 30 0.067
124 A 5 4 1.00 30 0.133
125 A 5 4 1.00 30 0.133
126 A 5 4 1.00 30 0.133
127 A 4 3 1.00 27 0.111
128 A 4 3 1.00 30 0.100
129 A 4 3 1.00 30 0.100
130 A 4 3 1.00 30 0.100
131 A 4 3 1.00 30 0.100
132 A 4 3 1.00 30 0.100
133 A 6 5 1.00 30 0.167
134 A 6 5 1.00 30 0.167
135 A 6 5 1.00 30 0.167
136 A 6 5 1.00 30 0.167
137 A 4 4 1.00 27 0.148
138 A 4 4 1.00 30 0.133
139 A 5 4 1.00 30 0.133
140 A 5 3 1.00 30 0.100
141 A 5 3 1.00 30 0.100
142 A 5 3 1.00 30 0.100
143 A 3 2 1.00 32 0.062
144 A 3 2 1.00 32 0.062
145 A 3 2 1.00 30 0.067
146 A 5 4 1.00 32 0.125
147 A 6 5 1.00 32 0.156
148 A 6 6 1.00 32 0.188
149 A 6 6 1.00 32 0.188
150 A 7 7 1.00 32 0.219
151 A 7 6 1.00 32 0.188
152 A 6 6 1.00 32 0.188
153 A 5 5 1.00 29 0.172
154 A 6 6 1.00 32 0.188
155 A 6 6 1.00 32 0.188
156 A 6 6 1.00 32 0.188
157 A 5 3 1.00 32 0.094
158 A 6 4 1.00 32 0.125
159 A 11 9 1.00 32 0.281
160 A 10 9 1.00 32 0.281
161 A 9 9 1.00 32 0.281
162 A 8 8 1.07 32 0.250
163 A 5 4 1.00 29 0.138
164 A 6 5 0.97 32 0.156
165 A 7 5 1.00 32 0.156
166 A 8 4 0.98 32 0.125
167 A 9 5 1.00 32 0.156
168 A 10 5 0.97 32 0.156
169 A 4 3 1.00 33 0.091
170 A 4 3 1.00 33 0.091
171 A 4 3 1.00 31 0.097
172 A 10 9 0.98 37 0.243
173 A 6 5 1.17 34 0.147
174 A 6 4 1.00 37 0.108

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