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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 [67] had the largest ratio of [.599999999999999978]

# 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 2 2 1.00 18 0.111
2 A 2 2 0.92 18 0.111
3 A 2 2 1.00 18 0.111
4 A 1 1 1.00 16 0.062
5 A 1 1 1.00 16 0.062
6 A 1 1 1.00 18 0.056
7 A 2 2 1.11 18 0.111
8 A 2 2 1.10 18 0.111
9 A 3 3 1.09 8 0.375
10 A 2 2 1.00 18 0.111
11 A 2 2 0.92 18 0.111
12 A 2 2 1.00 18 0.111
13 A 1 1 1.00 16 0.062
14 A 1 1 1.00 16 0.062
15 A 1 1 1.00 18 0.056
16 A 2 2 1.09 18 0.111
17 A 2 2 1.10 18 0.111
18 A 3 3 1.09 8 0.375
19 A 2 2 0.98 18 0.111
20 A 2 2 1.00 18 0.111
21 A 2 2 1.00 16 0.125
22 A 2 2 1.00 16 0.125
23 A 2 2 1.00 18 0.111
24 A 2 2 0.98 18 0.111
25 A 5 5 1.03 27 0.185
26 A 2 2 1.26 18 0.111
27 A 2 2 1.25 18 0.111
28 F 0 0 N/A 0.000 N/A
29 N/A 2 0 1.00 21 0.000
30 N/A 2 0 1.00 23 0.000
31 A 4 4 1.00 44 0.091
32 F 0 0 N/A 0.000 N/A
33 A 4 4 1.00 43 0.093
34 B 3 3 19.24 35 0.086
35 A 1 1 1.00 30 0.033
36 A 3 3 1.00 38 0.079
37 A 3 3 1.00 38 0.079
38 A 3 3 1.02 20 0.150
39 A 2 2 1.00 22 0.091
40 A 2 2 1.00 22 0.091
41 A 2 2 1.00 22 0.091
42 A 2 2 1.00 24 0.083
43 A 2 2 1.00 24 0.083
44 A 2 2 1.00 22 0.091
45 A 2 2 1.00 24 0.083
46 A 2 2 1.00 24 0.083
47 A 2 2 1.00 7 0.286
48 A 4 4 1.00 9 0.444
49 A 2 2 1.00 7 0.286
50 A 4 4 1.00 9 0.444
51 A 2 2 1.00 19 0.105
52 A 1 1 1.00 15 0.067
53 A 3 3 0.99 26 0.115
54 A 4 4 0.96 27 0.148
55 A 3 3 0.96 26 0.115
56 A 3 3 0.96 27 0.111
57 A 2 2 1.00 10 0.200
58 A 2 2 1.00 10 0.200
59 A 2 2 1.00 12 0.167
60 A 2 2 1.00 12 0.167
61 A 3 2 1.11 15 0.133
62 A 4 3 1.00 8 0.375
63 A 5 4 1.00 12 0.333
64 A 4 3 1.00 8 0.375
65 A 4 3 1.00 12 0.250
66 A 4 3 1.00 12 0.250
67 A 7 6 1.00 10 0.600
68 A 4 3 1.13 26 0.115
69 A 4 3 1.00 8 0.375
70 A 4 3 1.00 8 0.375
71 A 5 4 1.00 12 0.333
72 A 5 4 1.00 10 0.400
73 A 1 1 1.00 10 0.100
74 A 2 2 1.00 12 0.167
75 A 2 2 1.00 15 0.133
76 A 2 2 1.00 12 0.167
77 A 2 2 1.00 14 0.143
78 A 2 2 1.00 17 0.118
79 A 2 2 1.00 16 0.125
80 A 2 2 1.00 18 0.111
81 A 2 2 1.00 18 0.111
82 A 2 2 1.00 19 0.105
83 A 2 2 1.00 21 0.095
84 A 2 2 1.00 21 0.095
85 A 2 2 1.00 16 0.125
86 A 2 2 1.00 18 0.111
87 A 2 2 1.00 18 0.111
88 A 2 2 1.00 18 0.111
89 A 2 2 1.00 20 0.100
90 A 2 2 1.00 20 0.100
91 A 2 2 1.00 21 0.095
92 A 2 2 1.00 23 0.087
93 A 2 2 1.00 23 0.087
94 A 2 2 1.00 19 0.105
95 A 2 2 1.00 21 0.095
96 A 2 2 1.00 21 0.095
97 A 2 2 1.00 21 0.095
98 A 2 2 1.00 23 0.087
99 A 2 2 1.00 23 0.087
100 A 2 2 1.00 24 0.083
101 A 2 2 1.00 26 0.077
102 A 2 2 1.00 26 0.077
103 A 2 2 1.00 24 0.083
104 A 1 1 1.00 10 0.100
105 A 2 2 1.00 12 0.167
106 A 2 2 1.00 15 0.133
107 A 2 2 1.00 12 0.167
108 A 2 2 1.00 14 0.143
109 A 2 2 1.00 17 0.118
110 A 2 2 1.00 16 0.125
111 A 2 2 1.00 18 0.111
112 A 2 2 1.00 18 0.111
113 A 2 2 1.00 19 0.105
114 A 2 2 1.00 21 0.095
115 A 2 2 1.00 21 0.095
116 A 2 2 1.00 16 0.125
117 A 2 2 1.00 18 0.111
118 A 2 2 1.00 18 0.111
119 A 2 2 1.00 18 0.111
120 A 2 2 1.00 20 0.100
121 A 2 2 1.00 20 0.100
122 A 2 2 1.00 21 0.095
123 A 2 2 1.00 23 0.087
124 A 2 2 1.00 23 0.087
125 A 2 2 1.00 19 0.105
126 A 2 2 1.00 21 0.095
127 A 2 2 1.00 21 0.095
128 A 2 2 1.00 21 0.095
129 A 2 2 1.00 23 0.087
130 A 2 2 1.00 23 0.087
131 A 2 2 1.00 24 0.083
132 A 2 2 1.00 26 0.077
133 A 2 2 1.00 26 0.077
134 A 2 2 1.00 24 0.083
135 A 4 4 0.94 22 0.182
136 A 4 4 0.99 20 0.200
137 A 2 2 1.00 22 0.091
138 A 3 3 1.07 22 0.136
139 A 4 4 0.94 22 0.182
140 A 4 4 0.99 20 0.200
141 A 2 2 1.00 22 0.091
142 A 3 3 1.07 22 0.136

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