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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 [45] had the largest ratio of [.200000000000000011]

# 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 1.08 25 0.080
2 A 2 2 0.97 25 0.080
3 A 3 3 1.16 23 0.130
4 A 2 2 0.93 17 0.118
5 A 2 2 1.08 17 0.118
6 A 2 2 1.00 23 0.087
7 A 2 2 1.00 25 0.080
8 A 2 2 1.04 27 0.074
9 A 2 2 0.90 27 0.074
10 A 2 2 1.01 25 0.080
11 A 2 2 0.93 19 0.105
12 A 2 2 1.00 23 0.087
13 A 2 2 0.86 19 0.105
14 A 2 2 1.00 25 0.080
15 A 2 2 1.08 27 0.074
16 A 2 2 0.98 27 0.074
17 A 2 2 1.08 25 0.080
18 A 3 3 1.06 19 0.158
19 A 2 2 1.12 25 0.080
20 A 2 2 1.00 25 0.080
21 A 2 2 0.93 19 0.105
22 A 2 2 1.12 25 0.080
23 A 2 2 1.00 23 0.087
24 A 2 2 1.06 17 0.118
25 A 1 1 1.00 17 0.059
26 A 2 2 1.75 23 0.087
27 A 2 2 1.58 25 0.080
28 A 2 2 1.47 25 0.080
29 A 2 2 1.00 25 0.080
30 A 2 2 0.86 19 0.105
31 A 2 2 1.00 23 0.087
32 A 1 1 1.14 19 0.053
33 A 2 2 1.55 25 0.080
34 B 2 2 2.81 27 0.074
35 A 2 2 1.49 27 0.074
36 A 2 2 0.94 19 0.105
37 A 2 2 1.00 25 0.080
38 A 2 2 1.00 25 0.080
39 A 1 1 1.38 19 0.053
40 A 2 2 1.48 25 0.080
41 A 2 2 1.50 27 0.074
42 B 2 2 3.28 27 0.074
43 A 2 2 0.99 27 0.074
44 A 2 2 0.92 27 0.074
45 A 5 5 1.02 25 0.200
46 A 1 1 0.87 19 0.053
47 A 2 2 1.00 19 0.105
48 A 2 2 1.00 25 0.080
49 A 2 2 1.10 27 0.074
50 A 2 2 1.00 29 0.069
51 A 2 2 0.88 29 0.069
52 A 2 2 0.98 27 0.074
53 A 3 3 0.84 21 0.143
54 A 2 2 1.05 25 0.080
55 A 2 2 0.91 21 0.095
56 A 2 2 1.00 27 0.074
57 A 2 2 0.99 29 0.069
58 A 2 2 0.93 29 0.069
59 A 2 2 0.99 27 0.074
60 A 2 2 0.99 21 0.095
61 A 2 2 1.00 27 0.074
62 A 2 2 1.00 27 0.074
63 A 2 2 1.02 21 0.095
64 A 2 2 1.00 27 0.074
65 A 2 2 1.04 25 0.080
66 A 2 2 1.00 19 0.105
67 A 1 1 1.12 19 0.053
68 B 2 2 3.19 25 0.080
69 A 2 2 1.26 27 0.074
70 A 2 2 1.00 27 0.074
71 A 2 2 1.00 27 0.074
72 A 2 2 0.91 21 0.095
73 A 2 2 1.00 25 0.080
74 A 1 1 1.73 21 0.048
75 A 2 2 1.27 27 0.074
76 B 2 2 2.87 29 0.069
77 A 2 2 1.62 29 0.069
78 A 2 2 1.02 21 0.095
79 A 2 2 1.00 27 0.074
80 A 2 2 1.11 27 0.074
81 A 2 2 1.05 21 0.095
82 A 2 2 1.00 27 0.074
83 A 2 2 1.41 29 0.069
84 B 2 2 5.05 29 0.069
85 B 2 2 2.23 29 0.069
86 A 2 2 1.28 29 0.069
87 A 2 2 1.45 24 0.083
88 A 2 2 1.50 24 0.083
89 A 3 3 1.45 22 0.136
90 A 1 1 1.53 16 0.062
91 A 2 2 1.00 16 0.125
92 A 2 2 1.30 22 0.091
93 A 2 2 1.33 24 0.083
94 A 2 2 1.47 26 0.077
95 A 2 2 1.34 26 0.077
96 A 2 2 1.47 24 0.083
97 A 2 2 1.28 18 0.111
98 A 2 2 1.10 22 0.091
99 A 2 2 1.30 18 0.111
100 A 2 2 1.33 24 0.083
101 A 2 2 1.45 26 0.077
102 A 2 2 1.49 26 0.077
103 A 2 2 1.45 24 0.083
104 A 2 2 1.44 18 0.111
105 A 2 2 1.11 24 0.083
106 A 2 2 1.26 24 0.083
107 A 2 2 1.22 18 0.111
108 A 2 2 1.10 24 0.083
109 A 2 2 1.10 22 0.091
110 A 2 2 1.00 16 0.125
111 A 1 1 1.00 16 0.062
112 B 2 2 2.75 22 0.091
113 A 2 2 0.79 24 0.083
114 A 2 2 0.78 24 0.083
115 A 2 2 1.26 24 0.083
116 A 2 2 1.34 18 0.111
117 A 2 2 1.33 22 0.091
118 A 1 1 0.95 18 0.056
119 A 2 2 0.82 24 0.083
120 B 2 2 5.73 26 0.077
121 A 2 2 1.07 26 0.077
122 A 2 2 1.27 18 0.111
123 A 2 2 1.35 24 0.083
124 A 2 2 1.36 24 0.083
125 A 2 2 1.83 18 0.111
126 A 2 2 0.80 24 0.083
127 A 2 2 1.01 26 0.077
128 B 2 2 8.82 26 0.077
129 A 2 2 1.34 34 0.059
130 F 0 0 N/A 0.000 N/A
131 A 2 2 1.00 34 0.059
132 A 2 2 1.36 34 0.059
133 F 0 0 N/A 0.000 N/A
134 A 2 2 1.00 34 0.059
135 A 3 3 0.82 34 0.088
136 F 0 0 N/A 0.000 N/A
137 A 3 3 0.82 34 0.088
138 F 0 0 N/A 0.000 N/A
139 F 0 0 N/A 0.000 N/A
140 F 0 0 N/A 0.000 N/A
141 F 0 0 N/A 0.000 N/A
142 F 0 0 N/A 0.000 N/A
143 F 0 0 N/A 0.000 N/A
144 F 0 0 N/A 0.000 N/A
145 F 0 0 N/A 0.000 N/A
146 F 0 0 N/A 0.000 N/A
147 F 0 0 N/A 0.000 N/A
148 F 0 0 N/A 0.000 N/A
149 F 0 0 N/A 0.000 N/A
150 A 4 4 0.99 30 0.133
151 F 0 0 N/A 0.000 N/A
152 A 4 4 1.35 30 0.133
153 A 4 4 0.99 30 0.133
154 F 0 0 N/A 0.000 N/A
155 A 4 4 1.33 30 0.133
156 F 0 0 N/A 0.000 N/A
157 F 0 0 N/A 0.000 N/A
158 F 0 0 N/A 0.000 N/A
159 F 0 0 N/A 0.000 N/A
160 F 0 0 N/A 0.000 N/A
161 F 0 0 N/A 0.000 N/A
162 F 0 0 N/A 0.000 N/A
163 F 0 0 N/A 0.000 N/A
164 F 0 0 N/A 0.000 N/A
165 F 0 0 N/A 0.000 N/A
166 F 0 0 N/A 0.000 N/A
167 F 0 0 N/A 0.000 N/A
168 F 0 0 N/A 0.000 N/A
169 F 0 0 N/A 0.000 N/A
170 F 0 0 N/A 0.000 N/A

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