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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 [89] had the largest ratio of [.857099999999999973]

# 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 3 0.333
2 A 1 1 1.00 3 0.333
3 A 1 1 1.00 3 0.333
4 A 1 1 1.00 3 0.333
5 A 1 1 1.00 2 0.500
6 A 1 1 1.00 2 0.500
7 A 2 2 1.00 4 0.500
8 A 2 2 1.00 4 0.500
9 A 2 2 1.00 5 0.400
10 A 2 2 1.00 5 0.400
11 A 1 1 1.00 2 0.500
12 A 1 1 1.00 2 0.500
13 A 1 1 0.71 2 0.500
14 A 1 1 0.50 2 0.500
15 A 1 1 1.00 7 0.143
16 A 1 1 1.00 9 0.111
17 A 1 1 1.00 11 0.091
18 A 1 1 1.00 9 0.111
19 A 2 2 1.00 9 0.222
20 A 1 1 1.00 2 0.500
21 A 1 1 1.00 2 0.500
22 A 2 2 1.00 4 0.500
23 A 2 2 1.00 4 0.500
24 A 1 1 1.00 2 0.500
25 A 1 1 1.00 2 0.500
26 A 1 1 0.71 2 0.500
27 A 1 1 1.00 7 0.143
28 A 1 1 1.00 7 0.143
29 A 2 1 1.00 9 0.111
30 A 2 1 1.00 11 0.091
31 A 1 1 1.00 7 0.143
32 A 2 1 0.96 9 0.111
33 A 2 1 1.00 11 0.091
34 A 1 1 1.00 7 0.143
35 A 1 1 0.74 9 0.111
36 A 2 1 1.11 11 0.091
37 A 2 1 0.88 11 0.091
38 A 1 1 1.00 7 0.143
39 A 2 1 1.20 9 0.111
40 A 1 1 0.50 11 0.091
41 A 2 1 1.16 11 0.091
42 A 1 1 1.00 7 0.143
43 A 2 1 1.20 9 0.111
44 A 2 1 1.24 11 0.091
45 A 1 1 0.36 11 0.091
46 A 3 3 1.20 11 0.273
47 A 2 1 1.17 11 0.091
48 A 2 1 1.14 11 0.091
49 A 2 1 1.05 11 0.091
50 A 2 1 1.02 11 0.091
51 A 2 1 1.13 11 0.091
52 A 2 1 1.12 11 0.091
53 A 2 1 1.19 11 0.091
54 A 2 1 1.12 11 0.091
55 A 2 1 1.13 11 0.091
56 A 2 1 1.18 11 0.091
57 A 2 1 1.11 11 0.091
58 A 2 1 1.13 11 0.091
59 A 2 1 1.18 11 0.091
60 A 1 1 1.20 9 0.111
61 A 1 1 1.08 13 0.077
62 A 6 6 1.22 9 0.667
63 A 6 6 1.14 11 0.546
64 A 1 1 1.00 13 0.077
65 A 7 7 1.19 13 0.538
66 A 7 7 1.10 13 0.538
67 A 7 7 1.20 9 0.778
68 A 7 7 1.10 11 0.636
69 A 1 1 1.00 13 0.077
70 A 7 7 1.17 13 0.538
71 A 4 4 1.05 13 0.308
72 A 7 7 1.11 13 0.538
73 A 7 7 1.17 13 0.538
74 A 3 2 1.00 13 0.154
75 A 8 8 1.11 13 0.615
76 A 8 8 1.16 13 0.615
77 B 9 6 2.94 9 0.667
78 A 2 2 1.16 11 0.182
79 B 9 6 2.94 13 0.462
80 A 1 1 1.00 13 0.077
81 B 10 7 2.49 9 0.778
82 A 3 3 1.02 11 0.273
83 B 10 7 2.37 13 0.538
84 A 1 1 1.00 13 0.077
85 A 4 4 1.05 13 0.308
86 B 10 7 2.68 13 0.538
87 A 1 1 1.00 5 0.200
88 A 1 1 1.00 7 0.143
89 A 6 6 0.95 7 0.857
90 A 9 6 1.31 7 0.857
91 A 1 1 1.00 7 0.143
92 A 1 1 1.00 9 0.111
93 A 1 1 1.00 7 0.143
94 A 6 6 0.93 9 0.667
95 A 3 3 1.44 9 0.333
96 A 2 1 1.00 7 0.143
97 A 1 1 1.00 9 0.111
98 A 6 6 1.02 9 0.667
99 A 2 2 1.00 9 0.222
100 A 2 1 1.00 9 0.111
101 A 1 1 1.00 11 0.091
102 A 6 6 1.00 11 0.546
103 A 2 2 0.40 11 0.182
104 A 4 4 1.08 11 0.364
105 A 4 4 1.07 13 0.308
106 A 2 1 1.04 13 0.077
107 A 3 2 1.44 15 0.133
108 A 2 1 1.26 16 0.062
109 A 2 2 1.81 13 0.154
110 A 3 3 1.29 13 0.231
111 A 4 3 1.18 13 0.231
112 A 5 3 1.19 13 0.231
113 A 3 3 1.50 13 0.231
114 A 3 3 1.48 13 0.231
115 A 4 4 1.14 13 0.308
116 A 5 4 1.01 13 0.308
117 A 4 3 1.23 13 0.231
118 A 4 4 1.16 13 0.308
119 A 4 3 0.80 13 0.231
120 A 5 4 0.81 13 0.308
121 A 10 7 1.94 15 0.467
122 A 10 7 1.90 15 0.467
123 A 11 8 1.80 15 0.533
124 A 11 8 1.81 15 0.533
125 A 11 8 1.72 15 0.533
126 A 11 8 1.69 15 0.533
127 A 11 8 1.76 15 0.533
128 A 11 8 1.73 15 0.533
129 A 12 8 1.65 15 0.533
130 A 12 8 1.63 15 0.533
131 A 12 9 1.74 15 0.600
132 A 12 9 1.37 15 0.600
133 A 1 1 1.00 9 0.111
134 A 2 1 1.19 11 0.091
135 A 2 1 1.31 13 0.077
136 A 3 3 1.50 11 0.273
137 B 3 2 2.19 13 0.154
138 A 3 2 1.72 15 0.133
139 A 2 2 0.55 13 0.154
140 A 3 3 0.65 13 0.231
141 A 3 3 0.64 13 0.231
142 A 4 4 0.72 13 0.308
143 A 5 4 1.15 15 0.267
144 A 5 5 0.86 15 0.333
145 A 5 4 0.67 15 0.267
146 A 3 3 0.61 13 0.231
147 A 4 3 0.84 13 0.231
148 A 4 4 1.05 15 0.267
149 A 5 5 1.24 15 0.333
150 A 6 5 1.38 15 0.333
151 A 5 5 1.61 15 0.333
152 A 5 5 0.99 13 0.385
153 A 5 5 0.80 13 0.385
154 A 6 6 0.91 13 0.462
155 A 6 6 1.55 15 0.400
156 A 7 6 1.69 15 0.400
157 A 4 4 1.01 13 0.308
158 A 6 6 1.48 15 0.400
159 A 6 6 1.32 15 0.400
160 A 3 2 0.34 15 0.133
161 A 5 5 0.95 13 0.385
162 A 6 5 1.11 13 0.385
163 A 2 1 0.91 15 0.067

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