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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 [83] had the largest ratio of [2]

# 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 2 1.00 11 0.182
3 A 2 2 1.00 11 0.182
4 A 2 2 1.00 11 0.182
5 A 1 1 1.00 14 0.071
6 A 4 3 1.00 4 0.750
7 A 2 2 1.00 9 0.222
8 A 5 4 1.00 7 0.571
9 A 4 3 1.00 17 0.176
10 A 4 3 1.00 9 0.333
11 A 8 7 1.00 11 0.636
12 A 5 4 1.00 16 0.250
13 A 4 3 1.00 10 0.300
14 A 1 1 1.00 15 0.067
15 A 2 2 1.00 9 0.222
16 A 1 1 1.00 9 0.111
17 A 1 1 1.00 15 0.067
18 A 2 2 1.00 17 0.118
19 A 4 3 0.75 20 0.150
20 A 1 1 1.00 26 0.038
21 A 1 1 1.00 20 0.050
22 A 4 4 1.00 4 1.000
23 A 7 7 1.00 6 1.167
24 A 10 10 1.13 6 1.667
25 A 9 9 1.12 6 1.500
26 A 4 3 1.00 5 0.600
27 A 4 4 1.22 6 0.667
28 A 3 3 1.00 4 0.750
29 A 4 3 1.00 4 0.750
30 A 5 5 1.21 4 1.250
31 A 4 3 1.00 4 0.750
32 A 7 7 1.29 4 1.750
33 A 3 3 1.00 6 0.500
34 A 6 6 0.97 6 1.000
35 A 6 6 1.12 8 0.750
36 A 3 3 1.00 4 0.750
37 A 4 3 1.00 4 0.750
38 A 5 5 1.21 4 1.250
39 A 6 5 1.12 13 0.385
40 A 4 3 1.11 13 0.231
41 A 2 2 1.00 13 0.154
42 A 3 3 1.00 4 0.750
43 A 5 5 1.00 4 1.250
44 A 3 3 1.00 4 0.750
45 A 5 5 1.00 4 1.250
46 A 4 4 1.00 10 0.400
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 2 1.00 11 0.182
52 A 4 3 1.00 8 0.375
53 A 11 10 1.08 8 1.250
54 A 1 1 1.00 10 0.100
55 A 5 4 1.00 17 0.235
56 A 1 1 1.00 7 0.143
57 A 2 2 1.13 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 3 3 1.00 2 1.500
62 A 1 1 1.00 8 0.125
63 A 2 2 1.18 8 0.250
64 A 3 2 1.00 8 0.250
65 A 3 2 1.00 14 0.143
66 A 4 3 1.00 14 0.214
67 A 3 3 1.26 8 0.375
68 A 1 1 1.00 9 0.111
69 A 1 1 1.00 13 0.077
70 A 3 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 5 4 1.30 7 0.571
74 A 2 2 1.00 5 0.400
75 A 2 2 1.00 7 0.286
76 A 3 3 1.11 7 0.429
77 A 3 3 1.00 9 0.333
78 A 4 3 1.04 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 5 4 1.00 2 2.000
84 A 5 4 1.00 2 2.000
85 A 3 3 1.04 4 0.750
86 A 5 4 1.00 6 0.667
87 A 3 2 1.00 13 0.154
88 A 3 2 1.70 14 0.143
89 A 1 1 1.00 9 0.111
90 A 1 1 1.00 9 0.111
91 A 3 2 1.00 10 0.200
92 A 3 3 0.95 4 0.750
93 A 5 4 1.08 6 0.667
94 A 5 5 1.00 6 0.833
95 A 5 4 1.32 6 0.667
96 A 1 1 1.00 17 0.059
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 3 2 1.00 13 0.154
102 A 7 6 1.22 10 0.600
103 A 4 3 1.38 15 0.200
104 A 5 4 1.00 15 0.267
105 A 4 3 1.00 15 0.200
106 A 2 2 1.00 16 0.125
107 A 2 2 1.00 16 0.125
108 A 3 3 1.00 18 0.167
109 A 3 3 1.00 23 0.130
110 A 2 2 1.00 19 0.105
111 A 7 6 1.04 18 0.333
112 A 4 4 1.00 31 0.129
113 A 4 3 1.00 7 0.429
114 A 4 3 1.00 22 0.136
115 A 2 2 1.00 16 0.125
116 A 2 2 1.00 17 0.118
117 A 2 2 1.00 12 0.167
118 A 3 3 1.00 21 0.143
119 A 2 2 1.00 20 0.100
120 A 4 4 1.00 16 0.250
121 A 3 3 1.00 16 0.188
122 A 2 2 1.00 11 0.182
123 A 4 3 1.00 11 0.273
124 A 2 2 1.00 16 0.125
125 A 2 2 1.00 7 0.286
126 A 7 6 1.12 9 0.667
127 A 2 2 1.00 12 0.167
128 A 3 3 1.00 14 0.214
129 A 5 4 1.43 21 0.190
130 A 3 3 1.00 18 0.167
131 A 2 2 1.00 7 0.286
132 A 4 4 1.00 11 0.364
133 A 4 3 1.80 16 0.188
134 A 3 3 1.00 11 0.273
135 A 2 2 1.00 18 0.111
136 A 3 3 1.00 7 0.429
137 A 9 8 1.06 7 1.143
138 A 4 3 1.00 14 0.214
139 A 1 1 1.00 16 0.062
140 A 5 4 0.58 12 0.333
141 A 4 3 1.00 8 0.375
142 A 4 3 0.36 8 0.375
143 A 2 2 1.00 10 0.200
144 A 6 5 0.50 13 0.385
145 A 4 3 1.00 19 0.158
146 A 2 2 1.00 11 0.182
147 A 6 5 1.00 11 0.455
148 A 2 2 1.00 11 0.182
149 A 1 1 1.00 13 0.077
150 A 5 4 1.16 15 0.267
151 A 4 3 1.00 13 0.231
152 A 2 2 1.00 9 0.222
153 A 4 3 1.00 12 0.250
154 A 3 2 1.00 9 0.222
155 A 8 7 1.06 18 0.389
156 A 2 2 1.00 8 0.250
157 A 6 6 1.00 5 1.200
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 3 2 1.00 14 0.143
164 A 2 2 1.00 9 0.222
165 A 2 2 1.00 8 0.250
166 A 2 2 1.00 7 0.286
167 A 3 3 1.12 9 0.333
168 A 4 4 1.17 9 0.444
169 A 2 2 1.00 21 0.095
170 A 1 1 1.00 4 0.250
171 A 2 2 1.00 4 0.500
172 A 3 2 1.00 8 0.250
173 A 1 1 1.00 11 0.091
174 A 2 2 1.00 16 0.125
175 A 1 1 1.00 9 0.111

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