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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 [16] had the largest ratio of [1.68750000000000000]

# 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 C 14 14 1.25 14 1.000
2 C 12 12 1.19 14 0.857
3 C 8 8 1.20 14 0.571
4 A 6 6 1.00 12 0.500
5 A 7 7 1.00 14 0.500
6 C 11 11 1.18 14 0.786
7 C 13 13 1.07 14 0.929
8 A 9 9 1.03 16 0.562
9 A 6 6 0.96 16 0.375
10 A 6 6 1.02 16 0.375
11 A 3 3 1.00 14 0.214
12 A 3 3 1.00 16 0.188
13 C 11 11 1.16 16 0.688
14 A 6 6 1.32 16 0.375
15 C 14 14 1.06 16 0.875
16 C 28 27 1.47 16 1.688
17 C 21 21 1.28 16 1.312
18 C 13 12 1.22 16 0.750
19 A 8 8 1.00 14 0.571
20 A 3 3 1.00 16 0.188
21 C 3 3 1.09 16 0.188
22 A 11 11 1.32 16 0.688
23 A 12 12 1.38 12 1.000
24 A 12 12 1.35 12 1.000
25 A 5 5 1.06 10 0.500
26 A 7 6 1.03 14 0.429
27 A 6 5 1.02 14 0.357
28 A 5 4 1.00 12 0.333
29 N/A 2 0 1.00 14 0.000
30 N/A 2 0 1.00 14 0.000
31 C 11 10 1.23 16 0.625
32 C 10 9 1.27 16 0.562
33 A 6 6 1.00 14 0.429
34 N/A 2 0 1.00 16 0.000
35 N/A 2 0 1.00 16 0.000
36 A 11 10 1.03 16 0.625
37 A 9 8 1.05 16 0.500
38 A 7 6 1.02 14 0.429
39 N/A 2 0 1.00 16 0.000
40 N/A 2 0 1.00 16 0.000
41 C 16 15 1.18 16 0.938
42 C 13 12 1.14 16 0.750
43 C 10 9 1.12 16 0.562
44 A 7 6 1.00 16 0.375
45 C 10 9 1.15 16 0.562
46 C 13 12 1.13 16 0.750
47 C 16 15 1.18 16 0.938
48 A 6 6 1.03 18 0.333
49 A 6 6 1.03 18 0.333
50 A 3 3 1.00 18 0.167
51 A 3 3 1.00 18 0.167
52 C 10 9 1.13 18 0.500
53 A 6 6 1.27 18 0.333
54 C 13 12 1.10 18 0.667
55 A 9 9 1.21 18 0.500
56 C 20 19 1.43 18 1.056
57 C 17 16 1.43 18 0.889
58 A 3 3 1.00 18 0.167
59 A 3 3 1.00 18 0.167
60 C 3 3 1.09 18 0.167
61 A 11 10 1.45 18 0.556
62 C 14 13 1.45 18 0.722
63 C 13 12 1.19 12 1.000
64 C 10 9 1.16 12 0.750
65 A 7 6 1.00 12 0.500
66 C 10 9 1.20 12 0.750
67 C 13 12 1.17 12 1.000
68 N/A 2 0 1.00 16 0.000
69 N/A 2 0 1.00 16 0.000
70 N/A 4 0 1.00 10 0.000
71 A 1 1 1.00 17 0.059
72 A 1 1 1.00 20 0.050
73 A 1 1 1.00 20 0.050
74 A 1 1 1.00 21 0.048
75 N/A 2 0 1.00 18 0.000
76 A 3 3 1.00 16 0.188
77 A 3 3 1.00 16 0.188
78 A 4 4 1.00 14 0.286
79 N/A 2 0 1.00 14 0.000
80 N/A 2 0 1.00 16 0.000
81 A 4 4 1.00 12 0.333
82 A 4 4 1.00 12 0.333
83 A 4 4 1.00 12 0.333
84 A 4 4 1.00 10 0.400
85 A 4 4 1.00 12 0.333
86 A 4 4 1.00 12 0.333
87 A 4 4 1.00 12 0.333
88 A 3 3 1.00 14 0.214
89 A 3 3 1.00 14 0.214
90 A 3 3 1.00 14 0.214
91 A 3 3 1.00 12 0.250
92 A 3 3 1.00 14 0.214
93 A 3 3 1.00 14 0.214
94 A 3 3 1.00 14 0.214
95 A 1 1 1.00 20 0.050
96 A 1 1 1.00 20 0.050
97 A 1 1 1.00 20 0.050
98 A 1 1 1.00 24 0.042
99 A 3 3 1.00 18 0.167
100 A 3 3 1.00 18 0.167
101 A 3 3 1.00 16 0.188
102 A 3 3 1.00 18 0.167
103 A 3 3 1.00 18 0.167
104 A 3 3 1.00 18 0.167
105 A 3 3 0.95 20 0.150
106 A 3 3 1.00 20 0.150
107 A 3 3 0.83 18 0.167
108 A 5 5 0.96 20 0.250
109 C 5 5 1.08 20 0.250
110 A 7 7 1.44 20 0.350
111 C 13 12 1.09 20 0.600
112 C 12 11 1.11 20 0.550
113 A 8 8 1.04 18 0.444
114 N/A 2 0 1.00 20 0.000
115 N/A 2 0 1.00 20 0.000
116 C 16 15 1.00 20 0.750
117 C 16 15 0.98 20 0.750
118 A 10 10 0.97 18 0.556
119 N/A 2 0 1.00 20 0.000
120 N/A 2 0 1.00 20 0.000
121 C 14 14 1.15 18 0.778
122 C 10 10 1.12 18 0.556
123 A 8 8 1.25 16 0.500
124 A 9 9 0.69 18 0.500
125 C 13 13 0.81 18 0.722
126 C 15 15 0.75 18 0.833
127 C 14 14 1.01 14 1.000
128 C 10 10 1.04 14 0.714
129 A 8 8 1.09 12 0.667
130 A 4 4 1.00 14 0.286
131 A 8 8 0.93 14 0.571
132 C 10 10 0.94 14 0.714
133 C 23 23 0.92 14 1.643
134 C 15 14 0.88 14 1.000
135 A 10 10 0.82 12 0.833
136 A 5 5 0.73 14 0.357
137 C 5 5 0.81 14 0.357
138 A 8 8 0.83 14 0.571
139 A 9 8 0.62 18 0.444
140 A 8 7 0.63 18 0.389
141 A 7 6 0.66 16 0.375
142 N/A 2 0 1.00 18 0.000
143 N/A 2 0 1.00 18 0.000
144 A 13 12 0.57 14 0.857
145 A 11 10 0.60 14 0.714
146 A 9 8 0.69 12 0.667
147 N/A 2 0 1.00 14 0.000
148 N/A 2 0 1.00 14 0.000
149 N/A 2 0 1.00 18 0.000
150 N/A 2 0 1.00 20 0.000
151 A 5 5 0.96 20 0.250
152 A 5 5 0.98 20 0.250
153 A 3 3 1.00 18 0.167
154 N/A 2 0 1.00 20 0.000
155 N/A 2 0 1.00 20 0.000
156 A 3 3 1.00 18 0.167
157 A 3 3 1.00 18 0.167
158 A 3 3 1.00 16 0.188
159 A 3 3 1.00 18 0.167
160 A 3 3 1.00 18 0.167
161 A 3 3 1.00 18 0.167
162 A 3 3 0.95 20 0.150
163 A 3 3 1.00 20 0.150
164 A 3 3 0.97 18 0.167
165 A 3 3 1.00 20 0.150
166 A 3 3 1.00 20 0.150
167 A 3 3 1.00 20 0.150
168 A 10 9 0.91 20 0.450
169 A 9 8 0.93 20 0.400
170 A 8 7 0.99 18 0.389
171 N/A 2 0 1.00 20 0.000
172 N/A 2 0 1.00 20 0.000
173 A 18 17 0.91 20 0.850
174 A 16 15 0.93 20 0.750
175 A 14 13 1.03 18 0.722
176 N/A 2 0 1.00 20 0.000
177 N/A 2 0 1.00 20 0.000
178 N/A 2 0 1.00 20 0.000
179 A 3 3 1.00 20 0.150
180 A 3 3 1.00 20 0.150
181 A 3 3 1.00 18 0.167
182 N/A 2 0 1.00 20 0.000
183 N/A 2 0 1.00 20 0.000

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