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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 [26] had the largest ratio of [.607142999999999988]

# 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 2 1.01 23 0.087
2 A 2 2 1.00 26 0.077
3 A 3 3 1.00 25 0.120
4 A 3 3 1.00 28 0.107
5 A 3 3 1.00 25 0.120
6 A 3 3 1.00 28 0.107
7 A 3 3 1.00 25 0.120
8 A 3 3 1.00 28 0.107
9 A 2 2 1.01 26 0.077
10 A 2 2 1.01 29 0.069
11 A 2 2 1.30 25 0.080
12 A 2 2 1.26 28 0.071
13 A 4 4 1.26 25 0.160
14 A 3 3 1.22 28 0.107
15 A 6 6 1.26 25 0.240
16 A 5 5 1.14 28 0.179
17 A 8 8 1.26 25 0.320
18 A 7 7 1.08 28 0.250
19 A 14 14 1.05 28 0.500
20 A 12 12 1.02 28 0.429
21 A 11 11 1.03 25 0.440
22 A 12 12 1.03 28 0.429
23 A 12 12 1.03 28 0.429
24 A 12 12 1.02 28 0.429
25 A 15 15 0.99 28 0.536
26 A 17 17 1.00 28 0.607
27 A 13 13 1.07 28 0.464
28 A 11 11 1.04 28 0.393
29 A 9 9 1.04 25 0.360
30 A 10 10 1.03 28 0.357
31 A 13 13 1.01 28 0.464
32 A 16 16 1.04 28 0.571
33 A 14 14 1.12 28 0.500
34 A 11 11 1.05 28 0.393
35 A 9 9 1.03 28 0.321
36 A 8 8 1.05 25 0.320
37 A 11 11 1.07 28 0.393
38 A 14 14 1.06 28 0.500
39 A 7 7 0.99 27 0.259
40 A 9 9 1.01 27 0.333
41 A 2 2 1.01 30 0.067
42 A 2 2 1.00 30 0.067
43 A 2 2 0.99 28 0.071
44 A 2 2 1.00 27 0.074
45 A 2 2 1.00 30 0.067
46 A 2 2 1.00 30 0.067
47 A 2 2 1.00 30 0.067
48 A 2 2 1.04 30 0.067
49 A 9 8 0.96 30 0.267
50 A 4 4 0.96 30 0.133
51 A 4 4 0.98 30 0.133
52 A 4 4 0.97 30 0.133
53 A 4 4 0.97 30 0.133
54 A 2 2 1.02 30 0.067
55 A 2 2 1.01 30 0.067
56 A 2 2 0.99 28 0.071
57 A 2 2 1.00 27 0.074
58 A 2 2 1.00 30 0.067
59 A 2 2 1.00 30 0.067
60 A 2 2 1.00 30 0.067
61 A 2 2 1.00 30 0.067
62 A 4 4 0.97 30 0.133
63 A 4 4 0.95 30 0.133
64 A 4 4 0.94 30 0.133
65 A 4 4 0.93 30 0.133
66 A 11 10 0.87 30 0.333
67 A 6 6 0.88 30 0.200
68 A 6 6 0.91 30 0.200
69 A 6 6 0.90 30 0.200
70 A 6 6 0.90 30 0.200
71 A 6 6 0.90 30 0.200
72 A 2 2 1.01 30 0.067
73 A 2 2 1.00 30 0.067
74 A 2 2 1.00 30 0.067
75 A 2 2 1.00 28 0.071
76 A 2 2 1.00 27 0.074
77 A 7 6 1.00 30 0.200
78 A 2 2 1.07 30 0.067
79 A 2 2 1.07 30 0.067
80 A 2 2 1.07 30 0.067
81 A 2 2 1.06 30 0.067
82 A 2 2 1.06 30 0.067
83 A 3 3 0.97 30 0.100
84 A 3 3 0.96 30 0.100
85 A 4 4 0.94 30 0.133
86 A 3 3 0.90 30 0.100
87 A 4 4 0.96 30 0.133
88 A 4 4 0.96 28 0.143
89 A 6 6 0.97 27 0.222
90 A 9 8 1.03 30 0.267
91 A 4 4 1.10 30 0.133
92 A 4 4 1.08 30 0.133
93 A 2 2 1.14 27 0.074
94 A 2 2 1.14 27 0.074
95 A 2 2 1.13 24 0.083
96 A 5 5 1.05 27 0.185
97 A 5 5 1.02 27 0.185
98 A 7 7 1.27 27 0.259
99 A 2 2 1.14 27 0.074
100 A 2 2 1.13 24 0.083
101 A 5 5 1.05 27 0.185
102 A 5 5 1.03 27 0.185
103 A 5 5 1.01 27 0.185
104 A 4 4 1.44 27 0.148
105 A 4 4 1.11 27 0.148
106 A 4 4 1.16 24 0.167
107 A 7 7 1.40 27 0.259
108 A 10 10 1.49 27 0.370
109 A 2 2 1.00 30 0.067
110 A 2 2 1.09 27 0.074
111 A 2 2 1.14 32 0.062
112 A 2 2 1.19 25 0.080
113 A 2 2 1.00 28 0.071

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