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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 [102] had the largest ratio of [40]

# 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 16 12 1.00 31 0.387
2 A 13 8 1.00 31 0.258
3 A 8 6 1.00 29 0.207
4 A 22 19 1.00 31 0.613
5 A 35 22 1.00 31 0.710
6 A 24 17 1.00 31 0.548
7 A 20 12 1.00 31 0.387
8 A 12 9 1.00 29 0.310
9 A 29 23 1.00 31 0.742
10 A 30 18 1.00 31 0.581
11 A 26 15 1.00 31 0.484
12 A 14 10 1.00 29 0.345
13 A 37 28 1.00 31 0.903
14 A 13 7 1.00 31 0.226
15 A 9 7 1.00 31 0.226
16 A 6 5 1.00 29 0.172
17 A 10 7 1.00 31 0.226
18 A 13 10 1.00 31 0.323
19 A 0 0 0.00 0 0.000
20 A 13 9 1.00 35 0.257
21 A 11 8 1.00 33 0.242
22 A 9 7 1.00 25 0.280
23 A 0 0 0.00 0 0.000
24 A 6 6 1.00 10 0.600
25 A 5 5 1.00 10 0.500
26 A 5 5 1.00 8 0.625
27 A 3 3 1.00 6 0.500
28 A 9 6 1.00 10 0.600
29 A 4 4 1.00 10 0.400
30 A 5 5 1.00 10 0.500
31 A 6 6 1.00 10 0.600
32 A 5 4 1.00 8 0.500
33 A 4 4 1.00 8 0.500
34 A 3 3 1.00 8 0.375
35 A 4 4 1.00 8 0.500
36 A 5 5 1.00 8 0.625
37 A 7 6 1.00 10 0.600
38 A 6 6 1.00 10 0.600
39 A 5 5 1.00 10 0.500
40 A 4 4 1.00 10 0.400
41 A 5 5 1.00 10 0.500
42 A 6 6 1.00 10 0.600
43 A 7 7 1.00 14 0.500
44 A 7 7 1.00 15 0.467
45 A 7 7 1.00 19 0.368
46 A 3 3 1.00 14 0.214
47 A 5 5 1.00 10 0.500
48 A 4 4 1.00 10 0.400
49 A 3 3 1.00 8 0.375
50 A 6 6 1.00 6 1.000
51 A 5 5 1.00 10 0.500
52 A 3 3 1.00 10 0.300
53 A 6 6 1.00 10 0.600
54 A 3 3 1.00 8 0.375
55 A 5 5 1.00 6 0.833
56 A 5 5 1.00 10 0.500
57 A 3 3 1.00 10 0.300
58 A 5 5 1.00 10 0.500
59 A 5 4 1.00 10 0.400
60 A 8 6 1.00 10 0.600
61 A 7 6 1.00 8 0.750
62 A 6 6 1.00 6 1.000
63 A 5 5 1.00 10 0.500
64 A 3 3 1.00 10 0.300
65 A 4 4 1.00 10 0.400
66 A 5 4 1.00 10 0.400
67 A 6 4 1.00 10 0.400
68 A 3 3 1.00 12 0.250
69 A 5 5 1.00 10 0.500
70 A 5 5 1.00 10 0.500
71 A 4 4 1.00 12 0.333
72 A 4 4 1.00 14 0.286
73 A 3 2 1.00 14 0.143
74 A 5 4 1.00 14 0.286
75 A 2 2 1.00 14 0.143
76 A 4 3 1.00 12 0.250
77 A 1 1 1.00 14 0.071
78 A 1 1 1.00 14 0.071
79 A 2 2 1.00 14 0.143
80 A 3 2 1.00 14 0.143
81 A 5 4 1.00 14 0.286
82 A 2 2 1.00 14 0.143
83 A 4 3 1.00 12 0.250
84 A 1 1 1.00 14 0.071
85 A 1 1 1.00 14 0.071
86 A 2 2 1.00 14 0.143
87 A 2 2 1.00 16 0.125
88 A 2 2 1.00 16 0.125
89 A 1 1 1.00 16 0.062
90 A 1 1 1.00 16 0.062
91 A 1 1 1.00 16 0.062
92 A 2 2 1.00 16 0.125
93 A 2 2 1.00 16 0.125
94 A 2 2 1.00 16 0.125
95 A 2 2 1.00 16 0.125
96 A 1 1 1.00 16 0.062
97 A 1 1 1.00 16 0.062
98 A 1 1 1.00 16 0.062
99 A 2 2 1.00 16 0.125
100 A 2 2 1.00 16 0.125
101 A 0 0 0.00 0 0.000
102 A 8 8 1.00 40 0.200
103 A 7 7 1.00 40 0.175
104 A 6 7 1.00 38 0.184
105 A 0 0 0.00 0 0.000
106 A 0 0 0.00 0 0.000
107 A 6 6 1.00 10 0.600
108 A 6 4 1.00 10 0.400
109 A 6 4 1.00 10 0.400
110 A 5 4 1.00 8 0.500
111 A 2 2 1.00 6 0.333
112 A 6 5 1.00 10 0.500
113 A 6 4 1.00 10 0.400
114 A 6 6 1.00 10 0.600
115 A 3 3 1.00 19 0.158
116 A 2 2 1.00 17 0.118
117 A 2 2 1.00 26 0.077
118 A 2 2 1.00 26 0.077

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