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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 [27] had the largest ratio of [1.14285999999999999]

# 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 3 3 1.88 7 0.429
2 A 3 3 1.00 7 0.429
3 A 3 3 1.00 7 0.429
4 A 2 2 1.00 7 0.286
5 A 2 2 1.00 13 0.154
6 A 2 2 1.00 14 0.143
7 A 2 2 1.00 13 0.154
8 A 2 2 1.00 15 0.133
9 A 2 2 1.00 15 0.133
10 A 2 2 1.00 17 0.118
11 A 2 2 1.00 17 0.118
12 A 2 2 1.00 17 0.118
13 C 3 3 1.53 7 0.429
14 C 3 3 1.47 7 0.429
15 C 3 3 1.47 7 0.429
16 A 2 2 1.00 7 0.286
17 A 2 2 1.00 13 0.154
18 A 2 2 1.00 15 0.133
19 A 2 2 1.00 15 0.133
20 A 2 2 1.00 15 0.133
21 A 2 2 1.00 17 0.118
22 A 2 2 1.00 17 0.118
23 A 2 2 1.00 15 0.133
24 A 2 2 1.00 17 0.118
25 A 2 2 1.00 17 0.118
26 A 7 6 1.42 7 0.857
27 A 9 8 1.00 7 1.143
28 A 9 8 1.07 7 1.143
29 A 7 6 1.04 7 0.857
30 A 7 6 1.07 7 0.857
31 A 2 2 1.21 7 0.286
32 A 4 4 1.00 13 0.308
33 A 11 10 1.00 15 0.667
34 A 16 15 1.19 15 1.000
35 A 2 2 1.21 13 0.154
36 A 6 5 1.40 7 0.714
37 A 5 4 1.00 7 0.571
38 A 6 5 1.07 7 0.714
39 A 5 4 1.01 7 0.571
40 A 6 5 1.11 7 0.714
41 A 5 5 1.00 13 0.385
42 A 10 9 1.00 15 0.600
43 C 18 17 1.29 15 1.133
44 A 2 2 1.22 13 0.154
45 A 5 4 1.00 7 0.571
46 A 9 8 1.29 7 1.143
47 A 6 5 1.00 7 0.714
48 A 7 6 1.13 7 0.857
49 A 6 5 1.00 7 0.714
50 A 5 5 1.00 13 0.385
51 A 7 6 1.00 15 0.400
52 A 8 7 1.00 15 0.467
53 A 9 8 0.94 15 0.533
54 F 0 0 N/A 0.000 N/A
55 F 0 0 N/A 0.000 N/A
56 F 0 0 N/A 0.000 N/A
57 F 0 0 N/A 0.000 N/A
58 F 0 0 N/A 0.000 N/A
59 F 0 0 N/A 0.000 N/A
60 F 0 0 N/A 0.000 N/A
61 F 0 0 N/A 0.000 N/A
62 F 0 0 N/A 0.000 N/A
63 F 0 0 N/A 0.000 N/A
64 F 0 0 N/A 0.000 N/A
65 F 0 0 N/A 0.000 N/A
66 A 4 4 1.00 7 0.571
67 A 4 3 1.00 7 0.429
68 A 5 4 1.00 7 0.571
69 A 5 4 1.09 7 0.571
70 A 6 5 1.06 7 0.714
71 C 5 5 1.15 13 0.385
72 A 7 6 1.00 15 0.400
73 A 9 8 1.00 15 0.533
74 C 12 11 1.04 15 0.733
75 F 0 0 N/A 0.000 N/A
76 F 0 0 N/A 0.000 N/A
77 F 0 0 N/A 0.000 N/A
78 F 0 0 N/A 0.000 N/A
79 F 0 0 N/A 0.000 N/A
80 F 0 0 N/A 0.000 N/A
81 F 0 0 N/A 0.000 N/A
82 F 0 0 N/A 0.000 N/A
83 F 0 0 N/A 0.000 N/A
84 F 0 0 N/A 0.000 N/A
85 F 0 0 N/A 0.000 N/A
86 F 0 0 N/A 0.000 N/A
87 C 3 3 2.88 7 0.429
88 C 3 3 1.47 7 0.429
89 C 3 3 1.47 7 0.429
90 A 2 2 1.00 7 0.286
91 A 2 2 1.00 7 0.286
92 A 2 2 1.00 7 0.286
93 A 2 2 1.00 7 0.286
94 A 2 2 1.00 7 0.286
95 A 2 2 1.00 13 0.154
96 A 2 2 1.00 14 0.143
97 A 2 2 1.00 13 0.154
98 A 2 2 1.00 15 0.133
99 A 2 2 1.00 15 0.133
100 A 2 2 1.00 17 0.118
101 A 2 2 1.00 17 0.118
102 A 2 2 1.00 17 0.118
103 A 7 6 1.42 7 0.857
104 A 6 5 1.00 7 0.714
105 A 9 8 1.07 7 1.143
106 A 6 5 1.01 7 0.714
107 A 7 6 1.07 7 0.857
108 A 5 5 1.00 13 0.385
109 A 10 9 1.00 15 0.600
110 A 17 16 1.19 15 1.067
111 A 2 2 1.21 13 0.154
112 A 7 6 1.40 7 0.857
113 B 9 8 2.75 7 1.143
114 A 7 6 1.07 7 0.857
115 A 6 5 1.31 7 0.714
116 A 7 6 1.11 7 0.857
117 A 2 2 1.23 7 0.286
118 A 5 5 1.00 13 0.385
119 A 10 9 1.00 15 0.600
120 C 18 17 1.29 15 1.133
121 A 2 2 1.22 13 0.154
122 A 4 3 1.00 7 0.429
123 A 4 3 1.00 7 0.429
124 A 5 4 1.00 7 0.571
125 A 5 4 1.22 7 0.571
126 A 5 4 1.00 7 0.571
127 A 5 5 1.00 13 0.385
128 A 7 6 1.00 15 0.400
129 A 8 7 1.00 15 0.467
130 A 9 8 0.94 15 0.533
131 F 0 0 N/A 0.000 N/A
132 F 0 0 N/A 0.000 N/A
133 F 0 0 N/A 0.000 N/A
134 F 0 0 N/A 0.000 N/A
135 F 0 0 N/A 0.000 N/A
136 F 0 0 N/A 0.000 N/A
137 F 0 0 N/A 0.000 N/A
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 A 7 7 1.00 7 1.000
144 A 9 8 1.29 7 1.143
145 A 6 5 1.00 7 0.714
146 A 8 7 1.13 7 1.000
147 A 7 6 1.03 7 0.857
148 C 5 5 1.15 13 0.385
149 A 7 6 1.00 15 0.400
150 A 9 8 1.00 15 0.533
151 C 12 11 1.15 15 0.733
152 F 0 0 N/A 0.000 N/A
153 F 0 0 N/A 0.000 N/A
154 F 0 0 N/A 0.000 N/A
155 F 0 0 N/A 0.000 N/A
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 A 5 5 1.24 13 0.385
165 A 5 5 1.17 14 0.357
166 C 5 5 1.43 13 0.385
167 C 5 5 1.39 14 0.357
168 A 4 4 1.00 13 0.308
169 A 4 4 1.00 14 0.286
170 C 4 4 1.22 13 0.308
171 C 4 4 1.24 14 0.286

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