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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 [95] had the largest ratio of [.692308000000000034]

# 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 1.00 32 0.062
2 A 2 2 1.00 32 0.062
3 A 2 2 1.00 30 0.067
4 A 2 2 1.00 32 0.062
5 A 2 2 1.00 32 0.062
6 A 2 2 1.00 32 0.062
7 A 4 4 0.92 29 0.138
8 A 4 4 0.93 29 0.138
9 A 4 4 0.95 29 0.138
10 A 4 4 0.98 27 0.148
11 A 7 6 1.03 29 0.207
12 A 4 4 0.96 29 0.138
13 A 4 4 0.88 29 0.138
14 A 4 4 0.88 29 0.138
15 A 4 4 0.88 29 0.138
16 A 7 7 0.97 31 0.226
17 A 7 7 0.96 31 0.226
18 A 7 7 0.94 31 0.226
19 A 7 7 0.94 29 0.241
20 A 8 7 1.00 31 0.226
21 A 7 7 0.88 31 0.226
22 A 7 7 0.86 31 0.226
23 A 7 7 0.90 31 0.226
24 A 7 7 0.92 31 0.226
25 A 3 3 0.89 29 0.103
26 A 3 3 0.91 29 0.103
27 A 3 3 0.93 29 0.103
28 A 3 3 0.96 27 0.111
29 A 3 3 1.00 21 0.143
30 A 5 4 1.04 29 0.138
31 A 3 3 0.94 29 0.103
32 A 3 3 0.83 29 0.103
33 A 3 3 0.85 29 0.103
34 A 3 3 0.84 29 0.103
35 A 11 10 0.80 31 0.323
36 A 11 10 0.78 31 0.323
37 A 11 10 0.78 29 0.345
38 A 11 10 0.84 23 0.435
39 A 18 17 1.85 31 0.548
40 A 11 10 0.77 31 0.323
41 A 14 13 0.80 31 0.419
42 A 18 17 0.85 31 0.548
43 A 3 2 1.00 40 0.050
44 A 6 5 0.68 40 0.125
45 A 6 5 0.68 40 0.125
46 A 5 4 0.95 38 0.105
47 A 3 2 1.00 40 0.050
48 A 3 2 1.00 40 0.050
49 A 3 2 1.00 40 0.050
50 A 5 4 0.93 34 0.118
51 A 7 6 0.94 48 0.125
52 A 6 5 0.99 46 0.109
53 A 6 5 1.00 32 0.156
54 N/A 1 0 1.00 48 0.000
55 N/A 1 0 1.00 48 0.000
56 A 9 8 1.01 39 0.205
57 A 8 7 1.05 39 0.179
58 A 7 6 1.10 37 0.162
59 A 3 3 1.15 25 0.120
60 N/A 1 0 1.00 39 0.000
61 N/A 1 0 1.00 39 0.000
62 N/A 1 0 1.00 28 0.000
63 N/A 1 0 1.00 28 0.000
64 A 7 7 1.16 26 0.269
65 N/A 1 0 1.00 28 0.000
66 N/A 1 0 1.00 28 0.000
67 A 5 4 1.04 45 0.089
68 A 5 4 1.05 45 0.089
69 A 5 4 1.05 43 0.093
70 N/A 2 0 1.00 45 0.000
71 N/A 2 0 1.00 45 0.000
72 N/A 2 0 1.00 48 0.000
73 N/A 2 0 1.00 48 0.000
74 F 0 0 N/A 0.000 N/A
75 F 0 0 N/A 0.000 N/A
76 A 7 6 0.96 32 0.188
77 A 5 5 0.95 32 0.156
78 A 4 4 1.00 30 0.133
79 A 4 3 1.17 29 0.103
80 A 8 7 0.92 32 0.219
81 A 5 5 0.93 32 0.156
82 A 5 5 0.92 34 0.147
83 A 5 5 0.92 34 0.147
84 A 8 7 0.95 32 0.219
85 A 4 3 1.12 31 0.097
86 A 10 9 0.90 34 0.265
87 A 7 7 0.89 34 0.206
88 A 8 7 1.00 19 0.368
89 A 4 3 0.85 24 0.125
90 A 3 3 1.02 34 0.088
91 A 3 3 0.99 55 0.055
92 A 3 3 0.98 58 0.052
93 A 5 5 1.00 11 0.455
94 A 7 6 0.94 13 0.462
95 A 10 9 1.10 13 0.692
96 A 2 2 1.00 13 0.154
97 A 9 8 1.03 15 0.533
98 A 6 5 1.00 15 0.333
99 A 2 2 1.00 13 0.154
100 A 9 8 1.03 15 0.533
101 A 6 5 1.05 15 0.333
102 A 1 1 1.00 38 0.026
103 A 2 2 1.00 50 0.040
104 A 5 4 0.99 42 0.095
105 A 2 2 1.00 62 0.032
106 A 5 4 0.96 49 0.082
107 A 4 3 1.22 42 0.071
108 A 5 4 1.05 65 0.062

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