[prev] [prev-tail] [tail] [up]

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 [64] had the largest ratio of [.531250000000000000]

# 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 24 0.083
2 A 2 2 1.00 24 0.083
3 A 2 2 1.00 24 0.083
4 A 2 2 1.00 22 0.091
5 A 4 4 1.07 24 0.167
6 A 4 4 1.03 24 0.167
7 A 4 4 1.08 24 0.167
8 A 5 5 0.98 24 0.208
9 A 2 2 1.00 26 0.077
10 A 2 2 1.00 26 0.077
11 A 2 2 1.00 24 0.083
12 A 6 6 1.10 26 0.231
13 A 6 6 1.05 26 0.231
14 A 5 5 1.07 26 0.192
15 A 6 6 1.09 26 0.231
16 A 2 2 1.00 26 0.077
17 A 2 2 1.00 26 0.077
18 A 2 2 1.00 24 0.083
19 A 7 7 1.10 26 0.269
20 A 7 7 1.05 26 0.269
21 A 6 6 1.07 26 0.231
22 A 7 7 1.07 26 0.269
23 A 8 8 0.88 30 0.267
24 A 7 7 0.91 30 0.233
25 A 6 6 0.95 30 0.200
26 A 6 6 0.96 30 0.200
27 A 5 5 1.01 30 0.167
28 A 7 7 1.05 30 0.233
29 A 9 9 0.89 30 0.300
30 F 0 0 N/A 0.000 N/A
31 A 7 7 0.92 30 0.233
32 A 9 9 0.94 30 0.300
33 A 7 7 1.04 30 0.233
34 A 9 9 1.05 30 0.300
35 A 9 9 0.90 30 0.300
36 A 7 7 0.92 30 0.233
37 A 6 6 0.94 30 0.200
38 A 4 4 1.00 30 0.133
39 A 3 3 1.00 30 0.100
40 A 5 5 1.05 30 0.167
41 A 7 7 1.08 30 0.233
42 A 9 9 0.92 30 0.300
43 A 8 8 0.95 30 0.267
44 A 6 6 1.01 30 0.200
45 A 3 3 1.00 30 0.100
46 A 5 5 1.03 30 0.167
47 A 7 7 1.06 30 0.233
48 A 3 3 1.00 30 0.100
49 A 9 9 1.04 31 0.290
50 A 8 8 1.05 31 0.258
51 A 9 9 1.05 32 0.281
52 A 4 4 1.01 30 0.133
53 A 6 6 0.95 30 0.200
54 A 7 7 0.92 30 0.233
55 A 2 2 1.00 87 0.023
56 A 5 5 1.06 81 0.062
57 A 8 7 1.05 28 0.250
58 A 16 15 0.99 30 0.500
59 A 10 9 1.01 30 0.300
60 A 6 5 1.00 28 0.179
61 A 3 2 1.00 21 0.095
62 A 4 3 1.00 30 0.100
63 A 10 9 0.99 30 0.300
64 A 17 17 1.17 32 0.531
65 A 8 8 0.96 32 0.250
66 A 6 6 1.01 32 0.188
67 A 1 1 1.00 32 0.031
68 A 3 3 1.00 32 0.094
69 A 8 8 1.00 32 0.250
70 A 12 12 1.02 32 0.375
71 A 16 16 1.08 32 0.500
72 A 8 8 0.94 32 0.250
73 A 6 6 0.99 32 0.188
74 A 3 3 1.00 32 0.094
75 A 8 8 1.00 32 0.250
76 A 12 12 0.97 32 0.375
77 A 13 13 0.96 32 0.406
78 A 6 6 1.01 32 0.188
79 A 1 1 1.00 32 0.031
80 A 3 3 1.00 32 0.094
81 A 5 5 1.00 32 0.156
82 A 9 9 1.01 32 0.281
83 A 17 17 0.84 32 0.531
84 A 3 3 1.00 32 0.094
85 A 3 3 1.00 32 0.094
86 A 5 5 1.01 32 0.156
87 A 9 9 0.97 32 0.281
88 A 13 13 0.97 32 0.406
89 A 8 8 0.97 28 0.286
90 A 6 6 0.98 28 0.214
91 A 1 1 1.00 28 0.036
92 A 3 3 1.00 28 0.107
93 A 8 8 1.01 28 0.286
94 A 6 6 1.01 32 0.188
95 A 1 1 1.00 32 0.031
96 A 1 1 1.00 32 0.031
97 A 3 3 1.00 30 0.100
98 A 6 5 1.00 28 0.179
99 A 11 11 1.00 33 0.333
100 A 8 8 0.99 32 0.250
101 A 11 11 1.01 33 0.333
102 A 8 8 0.92 32 0.250
103 N/A 1 0 1.00 34 0.000
104 A 8 7 1.00 34 0.206
105 A 3 2 1.00 34 0.059
106 A 3 2 1.00 34 0.059
107 N/A 1 0 1.00 34 0.000
108 A 9 8 1.55 34 0.235
109 A 6 5 1.78 34 0.147
110 N/A 1 0 1.00 34 0.000
111 A 8 7 1.00 34 0.206
112 N/A 1 0 1.00 34 0.000
113 A 3 2 1.00 34 0.059
114 A 3 2 1.00 34 0.059
115 N/A 1 0 1.00 34 0.000

[prev] [prev-tail] [front] [up]