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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 [22] had the largest ratio of [1.60000000000000009]

# 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 6 1.15 8 0.750
2 A 5 5 1.18 8 0.625
3 A 4 4 1.09 8 0.500
4 A 3 3 1.12 6 0.500
5 A 2 2 1.00 4 0.500
6 C 8 7 1.33 8 0.875
7 A 4 3 1.00 8 0.375
8 A 2 2 1.00 8 0.250
9 A 6 5 1.08 8 0.625
10 A 4 4 1.08 8 0.500
11 A 8 7 1.11 8 0.875
12 A 7 7 1.15 10 0.700
13 A 6 6 1.16 10 0.600
14 A 5 5 1.13 10 0.500
15 A 4 4 1.11 8 0.500
16 A 3 3 1.15 6 0.500
17 C 9 8 1.27 10 0.800
18 A 7 6 1.02 10 0.600
19 A 3 3 1.00 10 0.300
20 A 9 8 0.96 10 0.800
21 A 5 5 1.01 10 0.500
22 A 16 16 1.55 10 1.600
23 A 12 12 1.45 10 1.200
24 A 9 9 1.30 10 0.900
25 A 6 6 1.17 8 0.750
26 A 4 4 1.12 6 0.667
27 C 10 9 1.22 10 0.900
28 A 8 7 0.97 10 0.700
29 C 10 9 1.08 10 0.900
30 A 12 11 0.96 10 1.100
31 C 13 12 1.08 10 1.200
32 A 13 13 1.75 10 1.300
33 A 14 14 1.64 10 1.400
34 A 10 10 1.46 10 1.000
35 A 11 11 1.36 10 1.100
36 A 7 7 1.18 8 0.875
37 A 5 5 1.18 6 0.833
38 C 11 10 1.27 10 1.000
39 A 9 8 0.99 10 0.800
40 C 11 10 1.10 10 1.000
41 A 13 12 0.96 10 1.200
42 A 4 3 0.85 10 0.300
43 A 4 3 0.88 10 0.300
44 A 4 3 0.88 10 0.300
45 A 4 3 0.93 10 0.300
46 A 4 3 0.93 10 0.300
47 A 7 6 1.00 8 0.750
48 A 5 4 1.00 6 0.667
49 N/A 1 0 1.00 10 0.000
50 N/A 1 0 1.00 10 0.000
51 A 3 2 0.96 10 0.200
52 A 3 2 1.00 10 0.200
53 A 3 2 1.00 10 0.200
54 A 5 4 1.00 8 0.500
55 A 5 4 1.00 6 0.667
56 N/A 1 0 1.00 10 0.000
57 N/A 1 0 1.00 10 0.000
58 A 6 5 1.35 10 0.500
59 A 10 9 1.31 10 0.900
60 A 10 9 1.27 10 0.900
61 A 10 9 1.09 8 1.125
62 A 7 6 1.07 6 1.000
63 N/A 1 0 1.00 10 0.000
64 N/A 1 0 1.00 10 0.000
65 A 5 4 1.32 10 0.400
66 A 8 7 1.23 10 0.700
67 A 9 8 1.23 10 0.800
68 A 8 7 1.09 8 0.875
69 A 7 6 1.14 6 1.000
70 N/A 1 0 1.00 10 0.000
71 N/A 1 0 1.00 10 0.000
72 A 6 5 0.95 12 0.417
73 A 6 5 0.95 12 0.417
74 A 6 5 0.97 12 0.417
75 A 6 5 0.95 10 0.500
76 A 9 8 1.04 8 1.000
77 N/A 1 0 1.00 12 0.000
78 C 18 17 1.28 12 1.417
79 C 17 16 1.38 12 1.333
80 C 14 13 1.30 12 1.083
81 C 13 12 1.11 10 1.200
82 C 10 9 1.13 8 1.125
83 N/A 1 0 1.00 12 0.000
84 A 17 16 1.28 12 1.333
85 A 11 10 1.36 12 0.833
86 A 15 14 1.28 12 1.167
87 A 9 8 1.06 10 0.800
88 A 11 10 1.10 8 1.250
89 N/A 1 0 1.00 12 0.000
90 A 4 3 0.91 12 0.250
91 A 4 3 0.93 12 0.250
92 A 4 3 0.92 12 0.250
93 C 10 9 1.11 10 0.900
94 C 8 7 1.12 8 0.875
95 N/A 1 0 1.00 12 0.000
96 N/A 1 0 1.00 12 0.000
97 A 3 2 0.94 12 0.167
98 A 3 2 0.96 12 0.167
99 A 3 2 0.96 12 0.167
100 A 9 8 1.07 10 0.800
101 A 9 8 1.09 8 1.000
102 N/A 1 0 1.00 12 0.000
103 A 6 5 1.45 12 0.417
104 C 13 12 1.46 12 1.000
105 C 13 12 1.36 12 1.000
106 C 13 12 1.14 10 1.200
107 C 10 9 1.15 8 1.125
108 N/A 1 0 1.00 12 0.000
109 A 5 4 1.36 12 0.333
110 A 12 11 1.36 12 0.917
111 A 13 12 1.27 12 1.000
112 A 12 11 1.12 10 1.100
113 A 11 10 1.12 8 1.250
114 N/A 1 0 1.00 12 0.000
115 N/A 2 0 1.00 10 0.000
116 N/A 2 0 1.00 10 0.000
117 A 2 2 0.96 10 0.200
118 A 4 4 1.00 8 0.500
119 N/A 1 0 1.00 10 0.000
120 N/A 1 0 1.00 10 0.000
121 N/A 1 0 1.00 10 0.000
122 N/A 1 0 1.00 12 0.000
123 N/A 1 0 1.00 12 0.000
124 N/A 1 0 1.00 12 0.000
125 N/A 1 0 1.00 12 0.000
126 N/A 1 0 1.00 12 0.000
127 A 4 3 0.92 10 0.300
128 A 4 3 0.93 10 0.300
129 A 4 3 0.93 10 0.300
130 C 8 7 1.15 8 0.875
131 C 6 5 1.10 6 0.833
132 N/A 1 0 1.00 10 0.000
133 A 5 5 1.14 12 0.417
134 A 4 4 1.07 12 0.333
135 A 3 3 1.09 10 0.300
136 A 1 1 1.00 8 0.125
137 C 9 8 1.33 12 0.667
138 A 4 3 1.00 12 0.250
139 A 2 2 1.00 12 0.167
140 A 6 5 1.06 12 0.417
141 A 4 4 1.06 12 0.333
142 A 6 5 0.98 16 0.312
143 A 6 5 0.97 14 0.357
144 A 9 8 1.02 12 0.667
145 C 16 15 1.35 16 0.938
146 C 14 13 1.09 14 0.929
147 C 11 10 1.08 12 0.833
148 A 15 14 1.30 16 0.875
149 A 9 8 1.03 14 0.571
150 A 11 10 1.05 12 0.833
151 A 5 4 0.97 16 0.250
152 C 11 10 1.09 14 0.714
153 C 9 8 1.09 12 0.667
154 A 3 2 0.99 16 0.125
155 A 9 8 1.06 14 0.571
156 A 9 8 1.08 12 0.667
157 C 15 14 1.42 16 0.875
158 C 14 13 1.12 14 0.929
159 C 11 10 1.13 12 0.833
160 A 13 12 1.35 16 0.750
161 A 12 11 1.12 14 0.786
162 A 11 10 1.13 12 0.833
163 A 2 2 1.03 18 0.111
164 A 2 2 0.97 16 0.125
165 A 4 4 1.00 14 0.286
166 N/A 1 0 1.00 16 0.000

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