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

2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. 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 given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [108] had the largest ratio of [65]

# 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 16 10 1.00 32 0.312
2 A 13 8 1.00 32 0.250
3 A 10 6 1.00 30 0.200
4 A 12 7 1.00 32 0.219
5 A 15 9 1.00 32 0.281
6 A 18 11 1.00 32 0.344
7 A 4 3 1.00 29 0.103
8 A 4 3 1.00 29 0.103
9 A 4 3 1.00 29 0.103
10 A 4 2 1.00 27 0.074
11 A 6 6 1.00 29 0.207
12 A 5 4 1.00 29 0.138
13 A 4 3 1.00 29 0.103
14 A 4 3 1.00 29 0.103
15 A 4 3 1.00 29 0.103
16 A 32 14 1.00 31 0.452
17 A 28 14 1.00 31 0.452
18 A 24 14 1.00 31 0.452
19 A 20 13 1.00 29 0.448
20 A 19 15 1.00 31 0.484
21 A 20 12 1.00 31 0.387
22 A 24 13 1.00 31 0.419
23 A 28 13 1.00 31 0.419
24 A 32 13 1.00 31 0.419
25 A 5 2 1.00 29 0.069
26 A 5 2 1.00 29 0.069
27 A 5 2 1.00 29 0.069
28 A 5 2 1.00 27 0.074
29 A 3 3 1.00 21 0.143
30 A 7 4 1.00 29 0.138
31 A 7 3 1.00 29 0.103
32 A 5 2 1.00 29 0.069
33 A 5 2 1.00 29 0.069
34 A 5 2 1.00 29 0.069
35 A 49 14 1.00 31 0.452
36 A 47 15 1.00 31 0.484
37 A 39 15 1.00 29 0.517
38 A 10 9 1.00 23 0.391
39 A 29 14 1.42 31 0.452
40 A 31 10 1.00 31 0.323
41 A 43 14 1.00 31 0.452
42 A 57 15 1.00 31 0.484
43 A 2 2 1.00 40 0.050
44 A 5 5 1.00 40 0.125
45 A 5 5 1.00 40 0.125
46 A 4 4 1.00 38 0.105
47 A 2 2 1.00 40 0.050
48 A 2 2 1.00 40 0.050
49 A 2 2 1.00 40 0.050
50 A 4 4 1.00 34 0.118
51 A 11 6 1.00 48 0.125
52 A 9 5 1.00 46 0.109
53 A 7 4 1.00 32 0.125
54 A 0 0 0.00 0 0.000
55 A 0 0 0.00 0 0.000
56 A 13 6 1.00 39 0.154
57 A 11 6 1.00 39 0.154
58 A 9 5 1.00 37 0.135
59 A 5 3 1.00 25 0.120
60 A 0 0 0.00 0 0.000
61 A 0 0 0.00 0 0.000
62 A 0 0 0.00 0 0.000
63 A 0 0 0.00 0 0.000
64 A 5 5 1.00 26 0.192
65 A 0 0 0.00 0 0.000
66 A 0 0 0.00 0 0.000
67 A 14 7 1.00 45 0.156
68 A 12 7 1.00 45 0.156
69 A 10 6 1.00 43 0.140
70 A 0 0 0.00 0 0.000
71 A 0 0 0.00 0 0.000
72 A 0 0 0.00 0 0.000
73 A 0 0 0.00 0 0.000
74 F 0 0 N/A 0. N/A
75 F 0 0 N/A 0. N/A
76 A 30 9 1.00 32 0.281
77 A 27 10 1.00 32 0.312
78 A 18 6 1.00 30 0.200
79 A 7 4 1.00 29 0.138
80 A 29 11 1.00 32 0.344
81 A 31 12 1.00 32 0.375
82 A 37 14 1.00 34 0.412
83 A 30 12 1.00 34 0.353
84 A 21 9 1.00 32 0.281
85 A 7 4 1.00 31 0.129
86 A 31 12 1.00 34 0.353
87 A 40 16 1.00 34 0.471
88 A 5 5 1.00 19 0.263
89 A 3 3 1.00 24 0.125
90 A 3 3 1.00 34 0.088
91 A 3 3 1.00 55 0.055
92 A 3 3 1.00 58 0.052
93 A 4 4 1.00 11 0.364
94 A 5 5 1.00 13 0.385
95 A 7 7 1.00 13 0.538
96 A 2 2 1.00 13 0.154
97 A 6 6 1.00 15 0.400
98 A 5 5 1.00 15 0.333
99 A 2 2 1.00 13 0.154
100 A 6 6 1.00 15 0.400
101 A 5 5 1.00 15 0.333
102 A 1 1 1.00 38 0.026
103 A 2 2 1.00 50 0.040
104 A 4 4 1.00 42 0.095
105 A 2 2 1.00 62 0.032
106 A 4 4 1.00 49 0.082
107 A 9 5 1.00 42 0.119
108 A 10 6 1.00 65 0.092

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