[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 [39] had the largest ratio of [.699999999999999956]

# 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 3 3 1.00 20 0.150
2 A 3 3 1.00 18 0.167
3 A 1 1 1.00 16 0.062
4 A 3 3 1.00 20 0.150
5 A 2 2 1.00 20 0.100
6 A 3 3 1.00 22 0.136
7 A 3 3 1.00 20 0.150
8 A 3 3 1.00 18 0.167
9 A 3 3 1.00 22 0.136
10 A 3 3 1.00 22 0.136
11 A 3 3 1.00 22 0.136
12 A 3 3 1.00 22 0.136
13 A 6 5 1.00 22 0.227
14 A 4 3 1.00 22 0.136
15 A 8 7 1.02 20 0.350
16 A 5 5 1.05 18 0.278
17 A 5 5 1.09 22 0.227
18 A 5 5 1.02 22 0.227
19 A 5 5 1.03 22 0.227
20 A 4 4 1.10 22 0.182
21 A 5 4 1.00 22 0.182
22 A 5 4 1.00 22 0.182
23 A 5 4 1.00 22 0.182
24 A 5 5 1.29 22 0.227
25 A 5 5 1.17 22 0.227
26 A 5 5 1.05 20 0.250
27 A 5 5 1.03 18 0.278
28 A 5 5 0.97 22 0.227
29 A 12 11 1.08 24 0.458
30 A 10 9 1.06 22 0.409
31 A 6 5 0.88 20 0.250
32 A 5 4 1.00 24 0.167
33 A 8 7 0.81 24 0.292
34 A 8 7 0.82 24 0.292
35 A 6 5 1.03 24 0.208
36 A 8 7 1.07 24 0.292
37 A 10 9 1.09 24 0.375
38 A 16 15 1.09 22 0.682
39 A 15 14 1.09 20 0.700
40 A 12 11 1.07 24 0.458
41 A 7 6 1.06 24 0.250
42 A 6 5 1.04 24 0.208
43 A 10 9 0.90 24 0.375
44 A 10 9 0.86 24 0.375
45 A 10 9 0.86 24 0.375
46 A 12 11 0.91 24 0.458
47 A 9 8 1.08 24 0.333
48 A 12 11 1.10 24 0.458
49 A 8 7 1.04 24 0.292
50 A 5 4 1.00 24 0.167
51 A 4 3 1.00 22 0.136
52 A 3 2 1.00 20 0.100
53 A 4 3 1.00 24 0.125
54 A 7 6 1.05 24 0.250
55 A 12 11 1.02 24 0.458
56 A 10 9 1.05 24 0.375
57 A 7 6 1.08 24 0.250
58 A 1 1 1.00 24 0.042
59 A 1 1 1.00 24 0.042
60 A 4 3 1.00 24 0.125
61 A 7 6 1.09 22 0.273
62 A 9 8 1.04 20 0.400
63 A 11 10 1.03 24 0.417
64 A 13 12 1.01 24 0.500
65 A 3 3 1.00 18 0.167
66 A 3 3 1.00 18 0.167
67 A 3 3 1.00 16 0.188
68 A 1 1 1.00 14 0.071
69 A 2 2 1.00 18 0.111
70 A 3 3 1.00 18 0.167
71 A 3 3 1.00 18 0.167
72 A 3 3 1.00 20 0.150
73 A 3 3 1.00 20 0.150
74 A 5 4 1.07 18 0.222
75 A 3 3 1.00 16 0.188
76 A 5 4 0.96 20 0.200
77 A 3 3 1.00 20 0.150
78 A 5 4 0.99 20 0.200
79 A 6 6 1.05 20 0.300
80 A 5 4 0.99 20 0.200
81 A 4 4 1.02 20 0.200
82 A 7 6 1.02 20 0.300
83 A 3 3 1.05 20 0.150
84 A 5 4 1.00 20 0.200
85 A 3 3 1.00 18 0.167
86 A 9 8 1.06 16 0.500
87 A 5 5 0.99 20 0.250
88 A 7 6 1.07 20 0.300
89 A 7 6 1.01 20 0.300
90 A 7 7 0.92 20 0.350
91 A 6 5 1.05 20 0.250
92 A 5 5 0.93 20 0.250
93 A 6 5 1.01 20 0.250
94 A 4 4 0.96 20 0.200
95 A 6 5 1.01 20 0.250
96 A 4 4 0.96 20 0.200
97 A 6 5 1.03 20 0.250
98 A 5 5 0.94 20 0.250
99 A 7 6 1.25 18 0.333
100 A 6 6 1.00 16 0.375
101 A 7 6 1.15 20 0.300
102 A 8 8 0.99 20 0.400
103 A 7 6 1.04 20 0.300
104 A 3 3 1.00 20 0.150
105 A 7 7 1.02 24 0.292
106 A 6 5 1.00 24 0.208
107 A 6 6 1.03 24 0.250
108 A 9 8 0.80 24 0.333
109 A 11 10 1.07 24 0.417
110 A 9 9 1.00 24 0.375
111 A 7 6 1.03 24 0.250
112 A 8 8 1.02 24 0.333
113 A 5 4 1.00 24 0.167
114 A 2 2 1.00 24 0.083
115 A 3 2 1.00 24 0.083
116 A 7 7 1.04 24 0.292
117 A 7 7 1.01 24 0.292
118 A 4 3 1.00 24 0.125
119 A 10 10 0.96 24 0.417
120 A 7 6 1.08 24 0.250
121 A 1 1 1.00 34 0.029
122 A 3 3 1.14 27 0.111
123 A 3 2 1.00 18 0.111
124 A 4 3 1.00 18 0.167
125 A 4 3 1.00 17 0.176
126 A 6 5 0.97 18 0.278
127 A 7 6 0.97 18 0.333
128 A 7 6 0.97 17 0.353
129 A 3 2 1.00 18 0.111
130 A 4 3 1.00 18 0.167
131 A 5 4 1.00 22 0.182
132 A 5 4 1.00 24 0.167
133 A 4 3 1.00 20 0.150
134 A 4 3 1.00 20 0.150
135 A 5 4 1.00 24 0.167
136 A 5 4 1.00 26 0.154
137 A 4 3 1.00 18 0.167
138 A 4 3 1.00 18 0.167
139 A 5 4 1.00 20 0.200
140 A 3 2 1.00 36 0.056

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