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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 [17] had the largest ratio of [.800000000000000044]

# 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 4 3 0.99 21 0.143
2 A 4 3 0.98 21 0.143
3 A 5 4 1.02 21 0.190
4 A 4 3 1.05 21 0.143
5 A 4 3 1.02 21 0.143
6 A 13 12 0.85 21 0.571
7 A 12 11 0.91 21 0.524
8 A 11 10 0.86 19 0.526
9 A 11 10 0.86 18 0.556
10 A 13 12 0.85 21 0.571
11 A 13 12 0.91 21 0.571
12 A 4 3 0.99 20 0.150
13 A 4 3 0.98 20 0.150
14 A 5 4 1.02 20 0.200
15 A 4 3 1.06 20 0.150
16 A 4 3 1.03 20 0.150
17 A 17 16 1.17 20 0.800
18 A 13 12 1.12 20 0.600
19 A 12 11 1.15 17 0.647
20 A 14 13 1.11 20 0.650
21 A 16 15 1.16 20 0.750
22 A 15 14 1.12 20 0.700
23 A 13 12 1.09 20 0.600
24 A 11 10 1.11 18 0.556
25 A 13 12 1.09 20 0.600
26 A 15 14 1.12 20 0.700
27 A 10 9 1.20 18 0.500
28 A 2 2 1.12 22 0.091
29 A 2 2 1.12 22 0.091
30 A 2 2 1.36 22 0.091
31 A 2 2 1.37 22 0.091
32 F 0 0 N/A 0.000 N/A
33 F 0 0 N/A 0.000 N/A
34 F 0 0 N/A 0.000 N/A
35 F 0 0 N/A 0.000 N/A
36 A 4 3 0.99 25 0.120
37 A 4 3 0.98 25 0.120
38 A 6 5 1.03 25 0.200
39 A 4 3 1.04 25 0.120
40 A 4 3 1.02 25 0.120
41 A 13 12 0.80 25 0.480
42 A 12 11 0.77 25 0.440
43 A 11 10 0.84 23 0.435
44 A 11 10 0.81 22 0.455
45 A 12 11 0.84 25 0.440
46 A 13 12 0.81 25 0.480
47 A 4 3 1.04 23 0.130
48 A 4 3 1.00 23 0.130
49 A 7 6 1.03 23 0.261
50 A 4 3 1.07 23 0.130
51 A 4 3 1.00 23 0.130
52 A 11 10 0.85 23 0.435
53 A 11 10 0.95 23 0.435
54 A 11 10 0.90 23 0.435
55 A 9 8 0.89 21 0.381
56 A 9 8 0.85 20 0.400
57 A 10 9 0.89 23 0.391
58 A 11 10 0.85 23 0.435
59 A 8 7 1.14 21 0.333
60 A 4 3 1.15 21 0.143
61 A 5 4 1.15 18 0.222
62 A 2 2 1.00 27 0.074
63 A 2 2 1.00 27 0.074
64 A 2 2 1.12 27 0.074
65 A 2 2 1.11 27 0.074
66 A 6 6 0.96 27 0.222
67 A 5 5 1.00 27 0.185
68 A 4 4 1.03 24 0.167
69 A 4 4 1.03 27 0.148
70 A 5 5 1.09 27 0.185
71 A 6 6 1.07 27 0.222
72 A 6 5 1.04 25 0.200
73 A 4 3 1.00 25 0.120
74 A 4 3 1.01 25 0.120
75 A 6 5 1.00 25 0.200
76 A 8 7 0.99 25 0.280
77 A 2 2 1.00 25 0.080
78 A 2 2 1.00 23 0.087
79 A 2 2 1.00 25 0.080
80 A 2 2 1.00 25 0.080
81 A 2 2 1.00 25 0.080
82 A 2 2 1.00 25 0.080
83 A 2 2 1.00 22 0.091
84 A 2 2 1.00 25 0.080
85 A 2 2 1.00 25 0.080
86 A 9 8 1.02 27 0.296
87 A 6 5 1.00 27 0.185
88 A 4 3 1.00 27 0.111
89 A 4 3 1.00 27 0.111
90 A 4 3 0.99 27 0.111
91 N/A 1 0 1.00 27 0.000
92 N/A 1 0 1.00 25 0.000
93 N/A 1 0 1.00 27 0.000
94 N/A 1 0 1.00 27 0.000
95 N/A 1 0 1.00 27 0.000
96 N/A 1 0 1.00 27 0.000
97 N/A 1 0 1.00 24 0.000
98 N/A 1 0 1.00 27 0.000
99 N/A 1 0 1.00 27 0.000
100 A 10 9 0.97 27 0.333
101 A 8 7 0.95 27 0.259
102 A 4 3 0.99 27 0.111
103 A 4 3 0.99 27 0.111
104 A 4 3 0.99 27 0.111
105 N/A 1 0 1.00 27 0.000
106 N/A 1 0 1.00 25 0.000
107 N/A 1 0 1.00 27 0.000
108 N/A 1 0 1.00 27 0.000
109 N/A 1 0 1.00 27 0.000
110 N/A 1 0 1.00 27 0.000
111 N/A 1 0 1.00 24 0.000
112 N/A 1 0 1.00 27 0.000
113 N/A 1 0 1.00 27 0.000

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