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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 [1.58299999999999996]

# 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 5 4 1.00 8 0.500
2 A 6 4 1.00 8 0.500
3 A 5 4 1.00 8 0.500
4 A 4 4 1.00 6 0.667
5 A 1 1 1.00 4 0.250
6 A 1 1 1.00 8 0.125
7 A 4 4 1.00 8 0.500
8 A 5 4 1.00 8 0.500
9 N/A 0 0 1.00 10 0.000
10 A 19 11 1.00 10 1.100
11 A 15 10 1.00 10 1.000
12 A 10 8 1.00 8 1.000
13 A 6 5 1.00 6 0.833
14 N/A 0 0 1.00 10 0.000
15 N/A 0 0 1.00 10 0.000
16 N/A 0 0 1.00 10 0.000
17 N/A 0 0 1.00 10 0.000
18 A 14 6 1.00 10 0.600
19 A 10 6 1.00 10 0.600
20 A 7 6 1.00 8 0.750
21 A 1 1 1.00 6 0.167
22 N/A 0 0 1.00 10 0.000
23 A 7 5 1.00 10 0.500
24 A 11 6 1.00 10 0.600
25 N/A 0 0 1.00 12 0.000
26 A 39 19 1.00 12 1.583
27 A 17 14 1.00 10 1.400
28 A 5 5 1.00 8 0.625
29 N/A 0 0 1.00 12 0.000
30 N/A 0 0 1.00 12 0.000
31 N/A 0 0 1.00 12 0.000
32 A 7 5 1.00 17 0.294
33 A 7 5 1.00 15 0.333
34 A 7 5 1.00 13 0.385
35 A 3 1 1.00 17 0.059
36 A 7 5 1.00 17 0.294
37 A 7 5 1.00 17 0.294
38 A 7 5 1.00 19 0.263
39 A 14 10 1.00 12 0.833
40 N/A 0 0 1.00 12 0.000
41 A 1 1 1.00 12 0.083
42 A 5 4 1.00 9 0.444
43 A 9 7 1.00 10 0.700
44 A 14 9 1.00 12 0.750
45 A 18 10 1.00 12 0.833
46 N/A 0 0 1.00 12 0.000
47 A 7 6 1.00 12 0.500
48 N/A 0 0 1.00 12 0.000
49 A 5 4 1.00 9 0.444
50 A 9 7 1.00 10 0.700
51 A 13 9 1.00 12 0.750
52 A 20 11 1.00 12 0.917
53 A 6 4 1.00 9 0.444
54 A 6 4 1.00 9 0.444
55 A 21 16 1.00 16 1.000
56 A 11 9 1.00 14 0.643
57 A 4 4 1.00 13 0.308
58 N/A 0 0 1.00 16 0.000
59 A 21 14 1.00 16 0.875
60 A 12 10 1.00 14 0.714
61 A 4 3 1.00 13 0.231
62 N/A 0 0 1.00 16 0.000
63 A 24 10 1.00 14 0.714
64 A 9 5 1.00 13 0.385
65 N/A 0 0 1.00 16 0.000
66 A 24 9 1.00 14 0.643
67 A 9 5 1.00 13 0.385
68 N/A 0 0 1.00 16 0.000
69 A 5 4 1.00 8 0.500
70 A 6 4 1.00 8 0.500
71 A 5 4 1.00 8 0.500
72 A 4 4 1.00 6 0.667
73 A 1 1 1.00 4 0.250
74 A 1 1 1.00 8 0.125
75 A 4 4 1.00 8 0.500
76 A 5 4 1.00 8 0.500
77 N/A 0 0 1.00 10 0.000
78 A 19 11 1.00 10 1.100
79 A 15 10 1.00 10 1.000
80 A 10 8 1.00 8 1.000
81 A 6 5 1.00 6 0.833
82 N/A 0 0 1.00 10 0.000
83 N/A 0 0 1.00 10 0.000
84 N/A 0 0 1.00 10 0.000
85 N/A 0 0 1.00 10 0.000
86 A 14 6 1.00 10 0.600
87 A 10 6 1.00 10 0.600
88 A 7 6 1.00 8 0.750
89 A 1 1 1.00 6 0.167
90 N/A 0 0 1.00 10 0.000
91 A 7 5 1.00 10 0.500
92 A 11 6 1.00 10 0.600
93 N/A 0 0 1.00 12 0.000
94 A 39 19 1.00 12 1.583
95 A 17 14 1.00 10 1.400
96 A 5 5 1.00 8 0.625
97 N/A 0 0 1.00 12 0.000
98 N/A 0 0 1.00 12 0.000
99 N/A 0 0 1.00 12 0.000
100 A 7 5 1.00 17 0.294
101 A 7 5 1.00 15 0.333
102 A 7 5 1.00 13 0.385
103 A 3 1 1.00 17 0.059
104 A 7 5 1.00 17 0.294
105 A 7 5 1.00 17 0.294
106 A 7 5 1.00 19 0.263
107 N/A 0 0 1.00 12 0.000
108 A 7 6 1.00 12 0.500
109 N/A 0 0 1.00 12 0.000
110 A 5 4 1.00 9 0.444
111 A 9 7 1.00 10 0.700
112 A 13 9 1.00 12 0.750
113 A 20 11 1.00 12 0.917
114 A 14 10 1.00 12 0.833
115 N/A 0 0 1.00 12 0.000
116 A 1 1 1.00 12 0.083
117 A 5 4 1.00 9 0.444
118 A 9 7 1.00 10 0.700
119 A 14 9 1.00 12 0.750
120 A 18 10 1.00 12 0.833
121 A 6 4 1.00 9 0.444
122 A 6 4 1.00 9 0.444
123 A 21 14 1.00 16 0.875
124 A 12 10 1.00 14 0.714
125 A 4 3 1.00 13 0.231
126 N/A 0 0 1.00 16 0.000
127 A 21 16 1.00 16 1.000
128 A 11 9 1.00 14 0.643
129 A 4 4 1.00 13 0.308
130 N/A 0 0 1.00 16 0.000
131 A 24 9 1.00 14 0.643
132 A 9 5 1.00 13 0.385
133 N/A 0 0 1.00 16 0.000
134 A 24 10 1.00 14 0.714
135 A 9 5 1.00 13 0.385
136 N/A 0 0 1.00 16 0.000

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