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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 [24] had the largest ratio of [1]

# 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 3 3 0.56 31 0.097
2 A 3 3 0.58 31 0.097
3 A 3 3 0.59 29 0.103
4 A 7 7 0.70 31 0.226
5 A 7 7 0.73 31 0.226
6 A 3 3 0.52 31 0.097
7 A 3 3 0.54 31 0.097
8 A 3 3 0.52 29 0.103
9 A 3 3 0.66 31 0.097
10 A 3 3 0.49 31 0.097
11 A 3 3 0.51 31 0.097
12 A 3 3 0.50 29 0.103
13 A 3 3 0.62 31 0.097
14 A 3 3 0.58 31 0.097
15 A 3 3 0.60 31 0.097
16 A 3 3 0.69 29 0.103
17 A 10 9 0.75 31 0.290
18 A 15 14 0.75 31 0.452
19 N/A 1 0 1.00 35 0.000
20 A 9 8 1.02 35 0.229
21 A 8 7 1.05 33 0.212
22 A 8 7 1.00 25 0.280
23 N/A 1 0 1.00 35 0.000
24 A 11 10 1.21 10 1.000
25 A 8 7 1.31 10 0.700
26 A 9 8 1.08 8 1.000
27 A 4 3 0.94 6 0.500
28 A 9 8 1.00 10 0.800
29 A 6 5 1.06 10 0.500
30 A 8 7 1.06 10 0.700
31 A 9 8 1.13 10 0.800
32 A 6 5 0.96 8 0.625
33 A 5 4 1.11 8 0.500
34 A 5 4 1.00 8 0.500
35 A 6 5 0.95 8 0.625
36 A 7 6 0.89 8 0.750
37 A 9 8 0.95 10 0.800
38 A 8 7 0.94 10 0.700
39 A 7 6 0.96 10 0.600
40 A 6 5 1.00 10 0.500
41 A 7 6 0.97 10 0.600
42 A 8 7 0.96 10 0.700
43 A 12 11 1.02 14 0.786
44 A 11 10 1.01 15 0.667
45 A 9 8 0.97 19 0.421
46 A 3 3 1.00 14 0.214
47 A 6 5 1.12 10 0.500
48 A 4 4 1.11 10 0.400
49 A 4 3 0.97 8 0.375
50 A 6 6 1.07 6 1.000
51 A 7 6 1.15 10 0.600
52 A 3 3 1.00 10 0.300
53 A 7 6 1.02 10 0.600
54 A 3 3 1.00 8 0.375
55 A 6 5 1.00 6 0.833
56 A 7 6 1.12 10 0.600
57 A 3 3 1.00 10 0.300
58 A 6 5 1.12 10 0.500
59 A 6 5 1.07 10 0.500
60 A 9 8 1.17 10 0.800
61 A 8 7 1.13 8 0.875
62 A 7 6 1.08 6 1.000
63 A 7 6 1.23 10 0.600
64 A 3 3 1.00 10 0.300
65 A 4 4 1.10 10 0.400
66 A 5 5 1.15 10 0.500
67 A 6 6 1.17 10 0.600
68 A 4 3 1.04 12 0.250
69 A 7 6 1.06 10 0.600
70 A 7 6 1.15 10 0.600
71 A 5 4 0.79 12 0.333
72 A 5 4 0.81 14 0.286
73 A 3 3 1.00 14 0.214
74 A 2 2 0.97 14 0.143
75 A 2 2 1.00 14 0.143
76 A 1 1 1.00 12 0.083
77 A 1 1 1.00 14 0.071
78 A 1 1 1.00 14 0.071
79 A 2 2 1.01 14 0.143
80 A 3 3 1.00 14 0.214
81 A 2 2 0.97 14 0.143
82 A 2 2 1.00 14 0.143
83 A 1 1 1.00 12 0.083
84 A 1 1 1.00 14 0.071
85 A 1 1 1.00 14 0.071
86 A 2 2 1.02 14 0.143
87 A 2 2 1.01 16 0.125
88 A 2 2 1.03 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 1.02 16 0.125
93 A 2 2 1.00 16 0.125
94 A 2 2 1.01 16 0.125
95 A 2 2 1.03 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 1.02 16 0.125
100 A 2 2 1.00 16 0.125
101 N/A 1 0 1.00 40 0.000
102 A 10 9 1.02 40 0.225
103 A 9 8 1.03 40 0.200
104 A 8 7 1.01 38 0.184
105 N/A 1 0 1.00 40 0.000
106 N/A 1 0 1.00 40 0.000
107 A 8 7 1.02 10 0.700
108 A 5 4 0.91 10 0.400
109 A 5 4 0.93 10 0.400
110 A 6 5 1.02 8 0.625
111 A 3 2 1.08 6 0.333
112 A 5 4 1.00 10 0.400
113 A 5 4 1.01 10 0.400
114 A 7 6 1.02 10 0.600
115 A 5 4 1.00 19 0.211
116 A 4 3 1.00 17 0.176
117 A 3 2 1.00 26 0.077
118 A 3 2 1.00 26 0.077

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