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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 [.428570999999999980]

# 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 26 0.077
2 A 2 2 1.00 24 0.083
3 A 2 2 1.00 23 0.087
4 A 2 2 1.00 26 0.077
5 A 2 2 1.00 26 0.077
6 A 2 2 1.00 26 0.077
7 A 2 2 1.00 26 0.077
8 A 2 2 1.00 26 0.077
9 A 2 2 1.00 26 0.077
10 A 2 2 1.00 26 0.077
11 A 2 2 1.00 28 0.071
12 A 2 2 1.00 26 0.077
13 A 2 2 1.00 25 0.080
14 A 2 2 1.00 28 0.071
15 A 2 2 1.00 28 0.071
16 A 2 2 1.00 28 0.071
17 A 2 2 1.00 28 0.071
18 A 2 2 1.00 28 0.071
19 A 2 2 1.00 28 0.071
20 A 2 2 1.00 28 0.071
21 A 12 11 1.02 28 0.393
22 A 9 8 1.01 28 0.286
23 A 11 10 1.03 28 0.357
24 A 10 9 1.05 26 0.346
25 A 8 7 1.00 25 0.280
26 A 8 7 1.02 28 0.250
27 A 13 12 1.00 28 0.429
28 A 10 9 1.00 28 0.321
29 A 11 10 0.96 28 0.357
30 A 10 9 0.98 28 0.321
31 A 10 9 0.98 28 0.321
32 A 10 9 0.99 26 0.346
33 A 11 10 0.97 25 0.400
34 A 12 11 1.04 28 0.393
35 A 13 12 1.04 28 0.429
36 A 13 12 1.04 28 0.429
37 A 2 2 1.00 30 0.067
38 A 2 2 1.00 30 0.067
39 A 2 2 1.00 28 0.071
40 A 8 8 1.01 30 0.267
41 A 8 8 1.00 30 0.267
42 A 10 9 0.98 28 0.321
43 A 11 10 0.98 30 0.333
44 A 11 10 0.98 31 0.323
45 A 11 10 0.98 34 0.294
46 A 11 10 0.98 34 0.294
47 A 4 3 1.00 30 0.100
48 A 4 3 0.99 30 0.100
49 A 4 3 0.99 30 0.100
50 A 4 3 0.99 28 0.107
51 A 4 3 1.03 30 0.100
52 A 4 3 1.02 30 0.100
53 A 4 3 1.00 30 0.100
54 A 4 3 1.01 30 0.100
55 A 2 2 1.00 30 0.067
56 A 2 2 1.00 30 0.067
57 A 2 2 1.00 27 0.074
58 A 2 2 1.00 30 0.067
59 A 2 2 1.00 30 0.067
60 A 2 2 1.00 30 0.067
61 A 7 6 1.00 30 0.200
62 A 7 6 1.03 30 0.200
63 A 8 7 1.16 30 0.233
64 A 6 5 1.04 28 0.179
65 A 7 6 1.20 30 0.200
66 A 6 5 1.16 30 0.167
67 A 6 5 1.12 30 0.167
68 A 3 3 1.02 30 0.100
69 A 3 3 1.01 30 0.100
70 A 5 5 0.97 30 0.167
71 A 4 4 0.96 27 0.148
72 A 4 4 1.01 30 0.133
73 A 4 4 1.05 30 0.133
74 A 6 5 0.93 31 0.161
75 A 5 4 1.00 31 0.129
76 A 6 5 0.98 31 0.161
77 A 5 4 0.96 31 0.129
78 A 6 5 0.98 29 0.172
79 A 6 5 1.05 31 0.161
80 A 6 5 1.16 31 0.161
81 A 6 5 1.02 31 0.161
82 A 4 4 1.04 31 0.129
83 A 4 4 1.09 31 0.129
84 A 4 4 1.05 31 0.129
85 A 4 4 1.06 31 0.129
86 A 4 4 1.02 28 0.143
87 A 4 4 1.02 31 0.129
88 A 4 4 0.98 31 0.129
89 A 4 4 0.99 31 0.129
90 A 4 4 0.99 31 0.129
91 A 6 6 1.12 31 0.194
92 A 6 6 1.10 31 0.194
93 A 6 6 1.08 31 0.194
94 A 6 6 1.08 31 0.194
95 A 6 6 1.08 31 0.194
96 A 5 5 1.08 28 0.179
97 A 6 6 1.05 31 0.194
98 A 6 6 1.05 31 0.194
99 A 6 6 1.04 31 0.194
100 A 6 5 1.01 31 0.161
101 A 6 5 1.01 31 0.161
102 A 6 5 1.01 31 0.161
103 A 6 5 1.05 31 0.161
104 A 9 8 1.17 29 0.276
105 A 6 5 1.17 31 0.161
106 A 6 5 1.13 31 0.161
107 A 6 5 1.01 31 0.161
108 A 6 5 1.06 31 0.161
109 A 4 4 1.02 31 0.129
110 A 4 4 1.03 31 0.129
111 A 4 4 1.02 31 0.129
112 A 4 4 1.02 31 0.129
113 A 9 8 1.17 28 0.286
114 A 4 4 1.01 31 0.129
115 A 4 4 1.00 31 0.129
116 A 4 4 1.00 31 0.129
117 A 6 6 1.05 31 0.194
118 A 6 6 1.04 31 0.194
119 A 6 6 1.04 31 0.194
120 A 11 10 1.23 31 0.323
121 A 11 10 1.18 31 0.323
122 A 11 10 1.19 28 0.357
123 A 6 6 1.00 31 0.194
124 A 6 6 1.02 31 0.194
125 A 4 3 0.99 33 0.091
126 A 3 3 1.02 35 0.086
127 A 4 4 1.01 35 0.114
128 A 4 4 0.97 32 0.125
129 A 4 4 1.00 35 0.114
130 A 4 4 1.02 35 0.114
131 A 1 1 1.00 42 0.024
132 A 5 4 1.11 35 0.114
133 A 5 4 1.17 35 0.114
134 A 5 4 1.28 33 0.121
135 A 7 6 1.15 35 0.171
136 A 8 7 1.51 35 0.200
137 A 9 8 1.43 35 0.229
138 A 9 8 1.07 35 0.229
139 A 8 7 0.89 35 0.200
140 A 7 6 1.21 32 0.188
141 A 8 7 1.24 35 0.200
142 A 7 6 0.86 35 0.171
143 A 5 5 0.98 35 0.143
144 A 6 6 0.85 35 0.171
145 A 7 7 0.79 35 0.200

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