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2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. 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 given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [163] had the largest ratio of [18]

# 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 6 4 1.00 8 0.500
2 A 5 5 1.00 8 0.625
3 A 4 4 1.00 8 0.500
4 A 3 3 1.00 6 0.500
5 A 2 2 1.00 4 0.500
6 A 5 5 1.00 8 0.625
7 A 3 3 1.00 8 0.375
8 A 2 2 1.00 8 0.250
9 A 5 5 1.00 8 0.625
10 A 4 4 1.00 8 0.500
11 A 7 5 1.00 8 0.625
12 A 7 5 1.00 10 0.500
13 A 6 4 1.00 10 0.400
14 A 5 5 1.00 10 0.500
15 A 4 4 1.00 8 0.500
16 A 3 3 1.00 6 0.500
17 A 6 6 1.00 10 0.600
18 A 7 5 1.00 10 0.500
19 A 3 3 1.00 10 0.300
20 A 9 7 1.00 10 0.700
21 A 5 5 1.00 10 0.500
22 A 16 7 1.00 10 0.700
23 A 12 7 1.00 10 0.700
24 A 9 7 1.00 10 0.700
25 A 6 5 1.00 8 0.625
26 A 4 3 1.00 6 0.500
27 A 7 7 1.00 10 0.700
28 A 9 6 1.00 10 0.600
29 A 7 7 1.00 10 0.700
30 A 13 9 1.00 10 0.900
31 A 10 9 1.00 10 0.900
32 A 23 4 1.00 10 0.400
33 A 19 6 1.00 10 0.600
34 A 14 4 1.00 10 0.400
35 A 11 6 1.00 10 0.600
36 A 7 4 1.00 8 0.500
37 A 5 3 1.00 6 0.500
38 A 8 7 1.00 10 0.700
39 A 11 7 1.00 10 0.700
40 A 8 8 1.00 10 0.800
41 A 19 10 1.00 10 1.000
42 A 7 3 1.00 10 0.300
43 A 6 3 1.00 10 0.300
44 A 6 3 1.00 10 0.300
45 A 5 3 1.00 10 0.300
46 A 5 3 1.00 10 0.300
47 A 4 4 1.00 8 0.500
48 A 2 2 1.00 6 0.333
49 A 0 0 0.00 0 0.000
50 A 0 0 0.00 0 0.000
51 A 5 2 1.00 10 0.200
52 A 4 2 1.00 10 0.200
53 A 4 2 1.00 10 0.200
54 A 2 2 1.00 8 0.250
55 A 3 3 1.00 6 0.500
56 A 0 0 0.00 0 0.000
57 A 0 0 0.00 0 0.000
58 A 14 5 1.00 10 0.500
59 A 12 6 1.00 10 0.600
60 A 10 6 1.00 10 0.600
61 A 7 7 1.00 8 0.875
62 A 4 4 1.00 6 0.667
63 A 0 0 0.00 0 0.000
64 A 0 0 0.00 0 0.000
65 A 12 4 1.00 10 0.400
66 A 9 4 1.00 10 0.400
67 A 10 6 1.00 10 0.600
68 A 5 5 1.00 8 0.625
69 A 5 4 1.00 6 0.667
70 A 0 0 0.00 0 0.000
71 A 0 0 0.00 0 0.000
72 A 19 7 1.00 12 0.583
73 A 14 7 1.00 12 0.583
74 A 14 7 1.00 12 0.583
75 A 9 7 1.00 10 0.700
76 A 7 6 1.00 8 0.750
77 A 0 0 0.00 0 0.000
78 A 41 10 1.00 12 0.833
79 A 25 10 1.00 12 0.833
80 A 22 10 1.00 12 0.833
81 A 11 10 1.00 10 1.000
82 A 8 7 1.00 8 0.875
83 A 0 0 0.00 0 0.000
84 A 44 10 1.00 12 0.833
85 A 27 9 1.00 12 0.750
86 A 24 10 1.00 12 0.833
87 A 12 9 1.00 10 0.900
88 A 9 7 1.00 8 0.875
89 A 0 0 0.00 0 0.000
90 A 18 6 1.00 12 0.500
91 A 13 6 1.00 12 0.500
92 A 13 6 1.00 12 0.500
93 A 8 7 1.00 10 0.700
94 A 6 5 1.00 8 0.625
95 A 0 0 0.00 0 0.000
96 A 0 0 0.00 0 0.000
97 A 17 5 1.00 12 0.417
98 A 12 5 1.00 12 0.417
99 A 12 5 1.00 12 0.417
100 A 6 5 1.00 10 0.500
101 A 7 6 1.00 8 0.750
102 A 0 0 0.00 0 0.000
103 A 34 8 1.00 12 0.667
104 A 24 9 1.00 12 0.750
105 A 22 9 1.00 12 0.750
106 A 11 10 1.00 10 1.000
107 A 8 7 1.00 8 0.875
108 A 0 0 0.00 0 0.000
109 A 32 7 1.00 12 0.583
110 A 21 7 1.00 12 0.583
111 A 22 9 1.00 12 0.750
112 A 9 8 1.00 10 0.800
113 A 9 7 1.00 8 0.875
114 A 0 0 0.00 0 0.000
115 A 0 0 0.00 0 0.000
116 A 0 0 0.00 0 0.000
117 A 2 2 1.00 10 0.200
118 A 4 4 1.00 8 0.500
119 A 0 0 0.00 0 0.000
120 A 0 0 0.00 0 0.000
121 A 0 0 0.00 0 0.000
122 A 0 0 0.00 0 0.000
123 A 0 0 0.00 0 0.000
124 A 0 0 0.00 0 0.000
125 A 0 0 0.00 0 0.000
126 A 0 0 0.00 0 0.000
127 A 12 4 1.00 10 0.400
128 A 9 4 1.00 10 0.400
129 A 9 4 1.00 10 0.400
130 A 6 5 1.00 8 0.625
131 A 4 3 1.00 6 0.500
132 A 0 0 0.00 0 0.000
133 A 5 5 1.00 12 0.417
134 A 4 4 1.00 12 0.333
135 A 3 3 1.00 10 0.300
136 A 3 2 1.00 8 0.250
137 A 5 5 1.00 12 0.417
138 A 3 3 1.00 12 0.250
139 A 2 2 1.00 12 0.167
140 A 5 5 1.00 12 0.417
141 A 4 4 1.00 12 0.333
142 A 14 7 1.00 16 0.438
143 A 9 7 1.00 14 0.500
144 A 7 6 1.00 12 0.500
145 A 22 10 1.00 16 0.625
146 A 11 10 1.00 14 0.714
147 A 8 7 1.00 12 0.583
148 A 24 10 1.00 16 0.625
149 A 12 9 1.00 14 0.643
150 A 9 7 1.00 12 0.583
151 A 13 6 1.00 16 0.375
152 A 8 7 1.00 14 0.500
153 A 6 5 1.00 12 0.417
154 A 12 5 1.00 16 0.312
155 A 6 5 1.00 14 0.357
156 A 7 6 1.00 12 0.500
157 A 22 9 1.00 16 0.562
158 A 11 10 1.00 14 0.714
159 A 8 7 1.00 12 0.583
160 A 22 9 1.00 16 0.562
161 A 9 8 1.00 14 0.571
162 A 9 7 1.00 12 0.583
163 A 2 2 1.00 18 0.111
164 A 2 2 1.00 16 0.125
165 A 4 4 1.00 14 0.286
166 A 0 0 0.00 0 0.000

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