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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 [136] had the largest ratio of [16]

# 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 4 3 1.00 8 0.375
2 A 4 3 1.00 8 0.375
3 A 4 3 1.00 8 0.375
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 4 4 1.00 8 0.500
8 A 2 2 1.00 8 0.250
9 A 5 5 1.00 8 0.625
10 A 3 3 1.00 8 0.375
11 A 6 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 14 7 1.00 10 0.700
23 A 11 5 1.00 10 0.500
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 14 10 1.00 10 1.000
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 6 2 1.00 10 0.200
52 A 5 2 1.00 10 0.200
53 A 5 2 1.00 10 0.200
54 A 4 2 1.00 10 0.200
55 A 4 2 1.00 10 0.200
56 A 2 2 1.00 8 0.250
57 A 3 3 1.00 6 0.500
58 A 0 0 0.00 0 0.000
59 A 0 0 0.00 0 0.000
60 A 14 5 1.00 10 0.500
61 A 12 6 1.00 10 0.600
62 A 10 6 1.00 10 0.600
63 A 7 7 1.00 8 0.875
64 A 4 4 1.00 6 0.667
65 A 0 0 0.00 0 0.000
66 A 0 0 0.00 0 0.000
67 A 12 4 1.00 10 0.400
68 A 9 4 1.00 10 0.400
69 A 10 6 1.00 10 0.600
70 A 5 5 1.00 8 0.625
71 A 5 4 1.00 6 0.667
72 A 0 0 0.00 0 0.000
73 A 0 0 0.00 0 0.000
74 A 19 7 1.00 12 0.583
75 A 14 7 1.00 12 0.583
76 A 14 7 1.00 12 0.583
77 A 9 7 1.00 10 0.700
78 A 7 6 1.00 8 0.750
79 A 0 0 0.00 0 0.000
80 A 41 10 1.00 12 0.833
81 A 25 10 1.00 12 0.833
82 A 22 10 1.00 12 0.833
83 A 11 10 1.00 10 1.000
84 A 8 7 1.00 8 0.875
85 A 0 0 0.00 0 0.000
86 A 44 10 1.00 12 0.833
87 A 27 9 1.00 12 0.750
88 A 24 10 1.00 12 0.833
89 A 12 9 1.00 10 0.900
90 A 9 7 1.00 8 0.875
91 A 0 0 0.00 0 0.000
92 A 18 6 1.00 12 0.500
93 A 13 6 1.00 12 0.500
94 A 13 6 1.00 12 0.500
95 A 8 7 1.00 10 0.700
96 A 6 5 1.00 8 0.625
97 A 0 0 0.00 0 0.000
98 A 0 0 0.00 0 0.000
99 A 17 5 1.00 12 0.417
100 A 12 5 1.00 12 0.417
101 A 12 5 1.00 12 0.417
102 A 6 5 1.00 10 0.500
103 A 7 6 1.00 8 0.750
104 A 0 0 0.00 0 0.000
105 A 34 8 1.00 12 0.667
106 A 24 9 1.00 12 0.750
107 A 22 9 1.00 12 0.750
108 A 11 10 1.00 10 1.000
109 A 8 7 1.00 8 0.875
110 A 0 0 0.00 0 0.000
111 A 32 7 1.00 12 0.583
112 A 21 7 1.00 12 0.583
113 A 22 9 1.00 12 0.750
114 A 9 8 1.00 10 0.800
115 A 9 7 1.00 8 0.875
116 A 0 0 0.00 0 0.000
117 A 0 0 0.00 0 0.000
118 A 0 0 0.00 0 0.000
119 A 2 2 1.00 10 0.200
120 A 2 2 1.00 8 0.250
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 0 0 0.00 0 0.000
128 A 0 0 0.00 0 0.000
129 A 12 4 1.00 10 0.400
130 A 9 4 1.00 10 0.400
131 A 9 4 1.00 10 0.400
132 A 6 5 1.00 8 0.625
133 A 4 3 1.00 6 0.500
134 A 0 0 0.00 0 0.000
135 A 0 0 0.00 0 0.000
136 A 14 7 1.00 16 0.438
137 A 9 7 1.00 14 0.500
138 A 7 6 1.00 12 0.500
139 A 22 10 1.00 16 0.625
140 A 11 10 1.00 14 0.714
141 A 8 7 1.00 12 0.583
142 A 24 10 1.00 16 0.625
143 A 12 9 1.00 14 0.643
144 A 9 7 1.00 12 0.583
145 A 13 6 1.00 16 0.375
146 A 8 7 1.00 14 0.500
147 A 6 5 1.00 12 0.417
148 A 12 5 1.00 16 0.312
149 A 6 5 1.00 14 0.357
150 A 7 6 1.00 12 0.500
151 A 22 9 1.00 16 0.562
152 A 11 10 1.00 14 0.714
153 A 8 7 1.00 12 0.583
154 A 22 9 1.00 16 0.562
155 A 9 8 1.00 14 0.571
156 A 9 7 1.00 12 0.583

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