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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 [86] had the largest ratio of [.5000]

Table 2.1:Rubi specific breakdown of results for each integral
# 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 2 1 1.00 20 0.050
2 A 2 1 1.00 18 0.056
3 A 1 0 1.00 16 0.000
4 A 2 1 1.00 20 0.050
5 A 2 1 1.00 20 0.050
6 A 3 2 1.00 22 0.091
7 A 3 2 1.00 20 0.100
8 A 3 2 1.00 18 0.111
9 A 3 2 1.00 22 0.091
10 A 3 2 1.00 22 0.091
11 A 7 6 1.00 22 0.273
12 A 6 6 1.00 22 0.273
13 A 5 5 1.00 22 0.227
14 A 3 3 1.00 22 0.136
15 A 7 7 1.00 20 0.350
16 A 8 7 1.00 18 0.389
17 A 8 7 1.00 22 0.318
18 A 8 7 1.00 22 0.318
19 A 8 7 1.00 22 0.318
20 A 7 7 1.00 22 0.318
21 A 4 4 1.00 22 0.182
22 A 4 4 1.00 22 0.182
23 A 4 4 1.00 22 0.182
24 A 8 7 1.00 22 0.318
25 A 8 7 1.00 22 0.318
26 A 8 7 1.00 20 0.350
27 A 8 7 1.00 18 0.389
28 A 8 7 1.00 22 0.318
29 A 8 6 1.00 24 0.250
30 A 7 6 1.00 22 0.273
31 A 5 5 1.00 20 0.250
32 A 4 4 1.00 24 0.167
33 A 7 6 1.00 24 0.250
34 A 7 6 1.00 24 0.250
35 A 5 5 1.00 24 0.208
36 A 6 5 1.00 24 0.208
37 A 7 5 1.00 24 0.208
38 A 10 7 1.00 22 0.318
39 A 10 7 1.00 20 0.350
40 A 8 7 1.00 24 0.292
41 A 6 5 1.00 24 0.208
42 A 5 4 1.00 24 0.167
43 A 8 7 1.00 24 0.292
44 A 8 7 1.00 24 0.292
45 A 8 7 1.00 24 0.292
46 A 9 8 1.00 24 0.333
47 A 7 6 1.00 24 0.250
48 A 8 6 1.00 24 0.250
49 A 6 6 1.00 24 0.250
50 A 4 4 1.00 24 0.167
51 A 3 3 1.00 22 0.136
52 A 2 2 1.00 20 0.100
53 A 3 3 1.00 24 0.125
54 A 5 5 1.00 24 0.208
55 A 8 6 1.00 24 0.250
56 A 7 6 1.00 24 0.250
57 A 6 6 1.00 24 0.250
58 A 1 1 1.00 24 0.042
59 A 1 1 1.00 24 0.042
60 A 3 3 1.00 24 0.125
61 A 5 5 1.00 22 0.227
62 A 6 5 1.00 20 0.250
63 A 7 5 1.00 24 0.208
64 A 8 5 1.00 24 0.208
65 A 2 1 1.00 18 0.056
66 A 2 1 1.00 18 0.056
67 A 2 1 1.00 16 0.062
68 A 1 0 1.00 14 0.000
69 A 2 1 1.00 18 0.056
70 A 2 1 1.00 18 0.056
71 A 2 1 1.00 18 0.056
72 A 3 2 1.00 20 0.100
73 A 3 2 1.00 20 0.100
74 A 4 3 1.00 18 0.167
75 A 3 2 1.00 16 0.125
76 A 4 3 1.00 20 0.150
77 A 3 2 1.00 20 0.100
78 A 8 7 1.00 20 0.350
79 A 6 5 1.00 20 0.250
80 A 7 7 1.00 20 0.350
81 A 5 4 1.00 20 0.200
82 A 6 6 1.00 20 0.300
83 A 4 3 1.00 20 0.150
84 A 4 4 1.00 20 0.200
85 A 4 3 1.00 18 0.167
86 A 8 8 1.00 16 0.500
87 A 5 4 1.00 20 0.200
88 A 9 8 1.00 20 0.400
89 A 9 8 1.00 20 0.400
90 A 7 5 1.00 20 0.250
91 A 8 8 1.00 20 0.400
92 A 6 5 1.00 20 0.250
93 A 5 5 1.00 20 0.250
94 A 5 4 1.00 20 0.200
95 A 5 5 1.00 20 0.250
96 A 5 4 1.00 20 0.200
97 A 5 5 1.00 20 0.250
98 A 5 4 1.00 20 0.200
99 A 9 8 1.00 18 0.444
100 A 6 5 1.00 16 0.312
101 A 9 8 1.00 20 0.400
102 A 7 5 1.00 20 0.250
103 A 9 8 1.00 20 0.400
104 A 5 5 1.00 24 0.208
105 A 8 7 1.00 24 0.292
106 A 8 8 1.00 24 0.333
107 A 6 5 1.00 24 0.208
108 A 4 4 1.00 24 0.167
109 A 2 2 1.00 24 0.083
110 A 3 3 1.00 24 0.125
111 A 5 5 1.00 24 0.208
112 A 1 1 1.00 34 0.029
113 A 2 2 1.00 18 0.111
114 A 3 3 1.00 18 0.167
115 A 3 3 1.00 17 0.176
116 A 5 5 1.00 18 0.278
117 A 6 6 1.00 18 0.333
118 A 6 6 1.00 17 0.353
119 A 2 2 1.00 18 0.111
120 A 3 3 1.00 18 0.167
121 A 3 3 1.00 22 0.136
122 A 3 3 1.00 24 0.125
123 A 3 3 1.00 20 0.150
124 A 3 3 1.00 20 0.150
125 A 3 3 1.00 24 0.125
126 A 3 3 1.00 26 0.115
127 A 3 3 1.00 18 0.167
128 A 3 3 1.00 18 0.167
129 A 3 3 1.00 20 0.150
130 A 2 2 1.00 36 0.056

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