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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 [30] had the largest ratio of [1.39999999999999991]

# 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 1.02 12 0.333
2 A 4 4 1.16 12 0.333
3 A 5 4 1.05 12 0.333
4 A 3 3 1.10 10 0.300
5 A 1 1 1.00 8 0.125
6 A 9 8 1.13 12 0.667
7 A 5 4 1.00 12 0.333
8 A 2 2 1.00 12 0.167
9 A 6 5 1.00 12 0.417
10 A 3 3 1.06 12 0.250
11 A 7 6 1.05 12 0.500
12 A 6 6 1.12 14 0.429
13 A 5 5 1.07 14 0.357
14 A 4 4 1.11 12 0.333
15 A 3 3 1.09 10 0.300
16 A 10 9 1.17 14 0.643
17 A 7 6 0.96 14 0.429
18 A 3 3 0.96 14 0.214
19 A 9 8 0.92 14 0.571
20 A 5 5 0.96 14 0.357
21 A 11 11 1.33 14 0.786
22 A 9 8 1.18 14 0.571
23 A 6 6 1.10 12 0.500
24 A 3 3 1.05 10 0.300
25 A 11 10 1.15 14 0.714
26 A 8 7 0.98 14 0.500
27 A 11 10 1.02 14 0.714
28 A 13 12 0.94 14 0.857
29 A 14 13 1.02 14 0.929
30 A 14 14 1.65 10 1.400
31 A 10 10 1.48 10 1.000
32 A 11 11 1.37 10 1.100
33 A 7 7 1.20 8 0.875
34 A 5 5 1.22 6 0.833
35 A 12 11 1.31 10 1.100
36 A 9 8 1.06 10 0.800
37 A 12 11 1.13 10 1.100
38 A 13 12 1.00 10 1.200
39 A 4 3 0.84 14 0.214
40 A 5 4 0.86 14 0.286
41 A 4 3 0.86 14 0.214
42 A 11 10 0.89 12 0.833
43 A 8 7 0.91 10 0.700
44 N/A 1 0 1.00 14 0.000
45 N/A 1 0 1.00 14 0.000
46 A 3 2 0.87 14 0.143
47 A 3 2 0.90 14 0.143
48 A 3 2 0.90 14 0.143
49 A 8 7 0.96 12 0.583
50 A 10 9 0.97 10 0.900
51 N/A 1 0 1.00 14 0.000
52 N/A 1 0 1.00 14 0.000
53 A 6 5 1.37 14 0.357
54 A 14 13 1.31 14 0.929
55 A 13 12 1.26 14 0.857
56 A 14 13 1.05 12 1.083
57 A 10 9 1.00 10 0.900
58 N/A 1 0 1.00 14 0.000
59 N/A 1 0 1.00 14 0.000
60 A 5 4 1.33 10 0.400
61 A 7 6 1.23 10 0.600
62 A 9 8 1.26 10 0.800
63 A 7 6 1.09 8 0.750
64 A 7 6 1.17 6 1.000
65 N/A 1 0 1.00 10 0.000
66 N/A 1 0 1.00 10 0.000
67 A 6 5 1.14 16 0.312
68 A 9 8 1.10 16 0.500
69 A 5 4 1.10 16 0.250
70 A 8 7 1.06 16 0.438
71 A 4 3 1.00 16 0.188
72 A 9 8 1.06 16 0.500
73 A 2 2 1.04 18 0.111
74 A 2 2 1.04 18 0.111
75 A 2 2 1.02 18 0.111
76 A 2 2 1.02 18 0.111
77 A 2 2 1.00 18 0.111
78 N/A 2 0 1.00 18 0.000
79 N/A 2 0 1.00 18 0.000
80 N/A 2 0 1.00 18 0.000
81 N/A 2 0 1.00 18 0.000
82 N/A 1 0 1.00 18 0.000
83 N/A 1 0 1.00 18 0.000
84 N/A 1 0 1.00 18 0.000
85 N/A 1 0 1.00 18 0.000
86 N/A 1 0 1.00 18 0.000
87 N/A 1 0 1.00 18 0.000
88 N/A 1 0 1.00 18 0.000
89 N/A 1 0 1.00 18 0.000
90 N/A 2 0 1.00 12 0.000
91 N/A 2 0 1.00 12 0.000
92 A 2 2 0.99 12 0.167
93 A 2 2 1.00 10 0.200
94 N/A 1 0 1.00 12 0.000
95 N/A 1 0 1.00 12 0.000
96 A 6 5 0.99 12 0.417
97 A 6 5 0.99 12 0.417
98 A 6 5 1.02 12 0.417
99 A 6 5 0.97 10 0.500
100 A 6 5 1.00 8 0.625
101 N/A 1 0 1.00 12 0.000
102 A 15 14 1.57 12 1.167
103 A 14 13 1.28 12 1.083
104 A 11 10 1.31 12 0.833
105 A 10 9 1.07 10 0.900
106 A 7 6 1.01 8 0.750
107 N/A 1 0 1.00 12 0.000
108 A 14 13 1.53 12 1.083
109 A 11 10 1.33 12 0.833
110 A 12 11 1.32 12 0.917
111 A 9 8 1.10 10 0.800
112 A 8 7 1.08 8 0.875
113 N/A 1 0 1.00 12 0.000
114 A 4 3 0.95 12 0.250
115 A 4 3 0.97 12 0.250
116 A 4 3 0.97 12 0.250
117 A 7 6 1.00 10 0.600
118 A 5 4 1.00 8 0.500
119 N/A 1 0 1.00 12 0.000
120 N/A 1 0 1.00 12 0.000
121 A 3 2 0.96 12 0.167
122 A 3 2 0.99 12 0.167
123 A 3 2 0.98 12 0.167
124 A 3 2 1.06 12 0.167
125 A 3 2 1.05 12 0.167
126 A 5 4 1.00 10 0.400
127 A 6 5 1.00 8 0.625
128 N/A 1 0 1.00 12 0.000
129 A 6 5 1.47 12 0.417
130 A 10 9 1.33 12 0.750
131 A 10 9 1.41 12 0.750
132 A 10 9 1.06 10 0.900
133 A 7 6 1.07 8 0.750
134 N/A 1 0 1.00 12 0.000
135 A 5 4 1.24 12 0.333
136 A 8 7 1.30 12 0.583
137 A 10 9 1.32 12 0.750
138 A 8 7 1.11 10 0.700
139 A 8 7 1.12 8 0.875
140 N/A 1 0 1.00 12 0.000
141 A 7 6 0.98 16 0.375
142 A 6 5 0.96 14 0.357
143 A 12 11 0.98 12 0.917
144 N/A 1 0 1.00 16 0.000
145 N/A 1 0 1.00 16 0.000
146 A 16 15 1.35 16 0.938
147 A 16 15 1.03 14 1.071
148 A 12 11 0.97 12 0.917
149 N/A 1 0 1.00 16 0.000
150 N/A 1 0 1.00 16 0.000
151 A 18 17 1.32 16 1.062
152 A 9 8 1.03 14 0.571
153 A 14 13 1.00 12 1.083
154 N/A 1 0 1.00 16 0.000
155 N/A 1 0 1.00 16 0.000
156 A 4 3 0.98 16 0.188
157 A 13 12 0.99 14 0.857
158 A 10 9 1.01 12 0.750
159 N/A 1 0 1.00 16 0.000
160 N/A 1 0 1.00 16 0.000
161 A 3 2 1.03 16 0.125
162 A 10 9 1.01 14 0.643
163 A 12 11 1.01 12 0.917
164 N/A 1 0 1.00 16 0.000
165 N/A 1 0 1.00 16 0.000
166 A 15 14 1.46 16 0.875
167 A 16 15 1.04 14 1.071
168 A 12 11 1.04 12 0.917
169 N/A 1 0 1.00 16 0.000
170 N/A 1 0 1.00 16 0.000
171 N/A 1 0 1.00 14 0.000
172 N/A 1 0 1.00 14 0.000
173 N/A 1 0 1.00 14 0.000
174 N/A 1 0 1.00 14 0.000
175 A 4 3 0.95 10 0.300
176 A 4 3 0.95 10 0.300
177 A 7 6 1.01 8 0.750
178 A 6 5 0.97 6 0.833
179 N/A 1 0 1.00 10 0.000
180 N/A 1 0 1.00 10 0.000
181 N/A 1 0 1.00 14 0.000
182 N/A 1 0 1.00 14 0.000
183 N/A 1 0 1.00 14 0.000
184 N/A 1 0 1.00 14 0.000
185 N/A 1 0 1.00 12 0.000
186 F 0 0 N/A 0.000 N/A
187 F 0 0 N/A 0.000 N/A
188 F 0 0 N/A 0.000 N/A
189 F 0 0 N/A 0.000 N/A
190 N/A 1 0 1.00 20 0.000
191 N/A 1 0 1.00 20 0.000

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