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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 [.928571000000000035]

# 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 5 4 0.67 22 0.182
2 A 6 5 0.58 22 0.227
3 A 5 4 0.78 20 0.200
4 A 5 4 0.93 14 0.286
5 A 6 5 0.75 14 0.357
6 A 6 5 0.60 20 0.250
7 A 7 6 0.86 22 0.273
8 A 6 5 0.55 24 0.208
9 A 5 4 0.75 24 0.167
10 A 6 5 0.55 22 0.227
11 A 5 4 0.71 16 0.250
12 A 6 5 0.71 20 0.250
13 A 5 4 0.67 16 0.250
14 A 6 5 0.60 22 0.227
15 A 5 4 0.62 24 0.167
16 A 6 5 0.57 24 0.208
17 A 5 4 0.67 22 0.182
18 A 6 5 0.58 16 0.312
19 A 5 4 0.65 22 0.182
20 A 6 5 0.61 22 0.227
21 A 6 5 0.70 16 0.312
22 A 5 4 0.64 22 0.182
23 A 6 5 0.65 20 0.250
24 A 6 5 0.75 14 0.357
25 A 4 3 0.67 14 0.214
26 A 6 5 0.71 20 0.250
27 A 6 5 0.69 22 0.227
28 A 9 8 0.80 22 0.364
29 A 6 5 0.61 22 0.227
30 A 5 4 0.66 16 0.250
31 A 6 5 0.63 20 0.250
32 A 5 4 0.81 16 0.250
33 A 6 5 0.68 22 0.227
34 A 7 6 0.80 24 0.250
35 A 6 5 0.62 24 0.208
36 A 6 5 0.69 16 0.312
37 A 6 5 0.53 22 0.227
38 A 7 6 0.86 22 0.273
39 A 4 3 0.77 16 0.188
40 A 9 8 0.79 22 0.364
41 A 6 5 0.62 24 0.208
42 A 8 7 0.79 24 0.292
43 A 6 5 0.61 24 0.208
44 A 5 4 0.62 24 0.167
45 A 6 5 0.85 22 0.227
46 A 4 3 0.74 16 0.188
47 A 7 6 0.74 16 0.375
48 A 7 6 0.58 22 0.273
49 A 6 5 0.53 24 0.208
50 A 5 4 0.56 26 0.154
51 A 5 4 0.68 26 0.154
52 A 5 4 0.59 24 0.167
53 A 6 5 0.59 18 0.278
54 A 5 4 0.63 22 0.182
55 A 6 5 0.60 18 0.278
56 A 8 7 0.67 24 0.292
57 A 6 5 0.63 26 0.192
58 A 5 4 0.58 26 0.154
59 A 6 5 0.63 24 0.208
60 A 5 4 0.56 18 0.222
61 A 6 5 0.54 24 0.208
62 A 5 4 0.61 24 0.167
63 A 7 6 0.58 18 0.333
64 A 6 5 0.53 24 0.208
65 A 5 4 0.63 22 0.182
66 A 7 6 0.71 16 0.375
67 A 5 4 0.60 16 0.250
68 A 4 3 0.71 22 0.136
69 A 7 6 0.65 24 0.250
70 A 6 5 0.63 24 0.208
71 A 5 4 0.60 24 0.167
72 A 6 5 0.58 18 0.278
73 A 7 6 0.61 22 0.273
74 A 6 5 0.54 18 0.278
75 A 7 6 0.64 24 0.250
76 A 6 5 0.77 26 0.192
77 A 11 10 0.84 26 0.385
78 A 7 6 0.55 18 0.333
79 A 9 8 0.66 24 0.333
80 A 6 5 0.52 24 0.208
81 A 6 5 0.77 18 0.278
82 A 6 5 0.61 24 0.208
83 A 11 10 0.73 26 0.385
84 A 4 3 0.77 26 0.115
85 A 15 14 0.91 26 0.538
86 A 6 5 0.56 26 0.192
87 A 12 11 1.44 12 0.917
88 A 13 12 1.47 14 0.857
89 A 14 13 1.43 14 0.929
90 A 15 14 1.42 16 0.875
91 A 7 6 1.29 12 0.500
92 A 8 7 1.31 14 0.500
93 A 9 8 1.25 14 0.571
94 A 10 9 1.30 16 0.562
95 A 2 2 1.29 24 0.083
96 A 2 2 1.28 24 0.083
97 A 3 3 1.29 22 0.136
98 A 1 1 1.19 16 0.062
99 A 2 2 0.99 16 0.125
100 A 2 2 1.21 22 0.091
101 A 2 2 1.21 24 0.083
102 A 2 2 1.28 26 0.077
103 A 2 2 1.22 26 0.077
104 A 2 2 1.28 24 0.083
105 A 2 2 1.42 18 0.111
106 A 2 2 1.04 22 0.091
107 A 2 2 1.32 18 0.111
108 A 2 2 1.22 24 0.083
109 A 2 2 1.29 26 0.077
110 A 2 2 1.28 26 0.077
111 A 2 2 1.29 24 0.083
112 A 2 2 1.44 18 0.111
113 A 2 2 1.06 24 0.083
114 A 2 2 1.16 24 0.083
115 A 2 2 1.20 18 0.111
116 A 2 2 1.06 24 0.083
117 A 2 2 1.04 22 0.091
118 A 2 2 0.99 16 0.125
119 A 1 1 0.99 16 0.062
120 B 2 2 2.58 22 0.091
121 A 2 2 0.75 24 0.083
122 A 2 2 0.74 24 0.083
123 A 2 2 1.18 24 0.083
124 A 2 2 1.36 18 0.111
125 A 2 2 1.29 22 0.091
126 A 1 1 0.95 18 0.056
127 A 2 2 0.77 24 0.083
128 B 2 2 5.33 26 0.077
129 A 2 2 0.97 26 0.077
130 A 2 2 1.26 18 0.111
131 A 2 2 1.27 24 0.083
132 A 2 2 1.24 24 0.083
133 A 2 2 1.88 18 0.111
134 A 2 2 0.77 24 0.083
135 A 2 2 0.94 26 0.077
136 B 2 2 8.25 26 0.077
137 A 2 2 0.89 34 0.059
138 F 0 0 N/A 0.000 N/A
139 A 2 2 0.99 34 0.059
140 A 2 2 0.89 34 0.059
141 F 0 0 N/A 0.000 N/A
142 A 2 2 0.99 34 0.059
143 A 3 3 0.81 34 0.088
144 F 0 0 N/A 0.000 N/A
145 A 3 3 0.80 34 0.088
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 F 0 0 N/A 0.000 N/A
151 F 0 0 N/A 0.000 N/A
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 A 4 4 0.98 30 0.133
159 F 0 0 N/A 0.000 N/A
160 A 4 4 1.32 30 0.133
161 A 4 4 0.98 30 0.133
162 F 0 0 N/A 0.000 N/A
163 A 4 4 1.27 30 0.133
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
171 F 0 0 N/A 0.000 N/A
172 F 0 0 N/A 0.000 N/A
173 F 0 0 N/A 0.000 N/A
174 F 0 0 N/A 0.000 N/A
175 F 0 0 N/A 0.000 N/A
176 F 0 0 N/A 0.000 N/A
177 F 0 0 N/A 0.000 N/A
178 F 0 0 N/A 0.000 N/A

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