[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 [72] had the largest ratio of [.342899999999999983]

# 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 1 1.00 21 0.048
2 A 2 1 1.00 23 0.043
3 A 2 1 1.00 25 0.040
4 A 2 1 1.00 27 0.037
5 A 2 1 1.00 29 0.034
6 A 2 1 1.00 17 0.059
7 A 3 2 1.00 22 0.091
8 A 6 5 1.00 25 0.200
9 A 5 5 1.00 25 0.200
10 A 4 4 1.00 23 0.174
11 A 4 4 1.00 18 0.222
12 A 6 4 1.00 25 0.160
13 A 6 4 1.00 25 0.160
14 A 7 5 1.00 25 0.200
15 A 6 5 1.00 25 0.200
16 A 5 5 1.00 25 0.200
17 A 4 4 1.00 23 0.174
18 A 4 4 1.00 18 0.222
19 A 6 5 1.00 25 0.200
20 A 6 5 1.00 25 0.200
21 A 7 6 1.00 25 0.240
22 A 8 6 1.00 26 0.231
23 A 7 6 1.00 26 0.231
24 A 6 6 1.00 24 0.250
25 A 4 4 1.00 23 0.174
26 A 5 5 1.00 26 0.192
27 A 3 3 1.00 26 0.115
28 A 4 4 1.00 26 0.154
29 A 5 4 1.00 26 0.154
30 A 6 4 1.00 26 0.154
31 A 4 4 1.00 24 0.167
32 A 5 5 1.00 36 0.139
33 A 3 3 1.00 45 0.067
34 A 5 5 1.00 39 0.128
35 A 10 8 1.00 35 0.229
36 A 9 8 1.00 35 0.229
37 A 8 6 1.00 33 0.182
38 A 7 7 1.00 28 0.250
39 A 10 10 1.00 35 0.286
40 A 10 10 1.00 35 0.286
41 A 11 11 1.00 35 0.314
42 A 12 11 1.00 35 0.314
43 A 12 10 1.00 35 0.286
44 A 9 8 1.00 35 0.229
45 A 8 8 1.00 35 0.229
46 A 7 6 1.00 33 0.182
47 A 6 6 1.00 28 0.214
48 A 9 9 1.00 35 0.257
49 A 10 10 1.00 35 0.286
50 A 11 11 1.00 35 0.314
51 A 8 8 1.00 35 0.229
52 A 7 7 1.00 35 0.200
53 A 6 6 1.00 33 0.182
54 A 2 2 1.00 28 0.071
55 A 6 6 1.00 35 0.171
56 A 10 10 1.00 35 0.286
57 A 11 11 1.00 35 0.314
58 A 8 6 1.00 35 0.171
59 A 11 8 1.00 35 0.229
60 A 8 8 1.00 35 0.229
61 A 7 7 1.00 35 0.200
62 A 7 7 1.00 35 0.200
63 A 5 5 1.00 33 0.152
64 A 2 2 1.00 28 0.071
65 A 3 3 1.00 35 0.086
66 A 10 10 1.00 35 0.286
67 A 11 11 1.00 35 0.314
68 A 3 3 1.00 36 0.083
69 A 6 5 1.00 33 0.152
70 A 4 3 1.00 35 0.086
71 A 10 8 1.00 35 0.229
72 A 18 12 1.00 35 0.343
73 A 3 3 1.00 36 0.083
74 A 4 4 1.00 31 0.129
75 A 3 3 1.00 40 0.075
76 A 4 4 1.00 31 0.129
77 A 12 10 1.00 37 0.270
78 A 11 10 1.00 37 0.270
79 A 10 10 1.00 37 0.270
80 A 9 9 1.00 37 0.243
81 A 9 9 1.00 37 0.243
82 A 10 10 1.00 37 0.270
83 A 9 9 1.00 37 0.243
84 A 10 9 1.00 37 0.243
85 A 11 10 1.00 37 0.270
86 A 10 10 1.00 37 0.270
87 A 9 9 1.00 37 0.243
88 A 9 8 1.00 37 0.216
89 A 7 7 1.00 37 0.189
90 A 8 8 1.00 37 0.216
91 A 9 9 1.00 37 0.243
92 A 10 9 1.00 37 0.243
93 A 10 10 1.00 37 0.270
94 A 9 9 1.00 37 0.243
95 A 9 8 1.00 37 0.216
96 A 2 2 1.00 37 0.054
97 B 5 5 3.25 37 0.135
98 A 8 8 1.00 37 0.216
99 A 7 7 1.00 37 0.189
100 A 2 2 1.29 37 0.054
101 A 9 9 1.00 37 0.243
102 A 12 10 1.00 37 0.270
103 A 2 2 1.00 37 0.054
104 A 2 2 1.00 37 0.054
105 A 8 7 1.38 37 0.189
106 A 8 8 1.00 37 0.216
107 A 10 8 1.00 37 0.216
108 A 2 2 1.00 37 0.054
109 A 2 2 1.23 37 0.054
110 A 5 5 1.00 37 0.135
111 F 0 0 N/A 0.000 N/A
112 A 8 3 1.00 25 0.120
113 A 6 3 1.00 25 0.120
114 A 4 2 1.00 25 0.080
115 A 3 2 1.00 23 0.087
116 A 3 2 1.00 22 0.091
117 A 5 3 1.00 25 0.120
118 A 6 3 1.00 25 0.120
119 A 2 1 1.00 23 0.043
120 A 2 2 1.01 25 0.080
121 A 3 2 1.00 27 0.074
122 A 5 2 1.00 29 0.069
123 A 6 3 1.00 25 0.120
124 A 3 3 1.00 25 0.120
125 A 3 3 1.00 29 0.103
126 A 3 3 1.00 27 0.111
127 A 3 3 1.00 29 0.103
128 A 3 3 1.01 29 0.103
129 A 3 3 1.00 29 0.103
130 A 3 3 1.00 29 0.103
131 A 4 3 1.00 29 0.103
132 A 10 9 0.99 31 0.290
133 A 9 8 0.99 31 0.258
134 A 3 3 0.99 29 0.103
135 A 3 3 0.99 24 0.125
136 A 5 5 1.07 27 0.185
137 A 5 5 1.00 29 0.172
138 A 7 4 1.00 29 0.138
139 A 31 5 1.00 29 0.172
140 A 15 5 1.00 29 0.172
141 A 7 4 1.00 27 0.148
142 A 3 3 1.00 22 0.136
143 N/A 0 0 1.00 29 0.000
144 A 7 4 1.00 33 0.121
145 A 7 4 1.00 34 0.118
146 A 5 5 1.00 34 0.147
147 A 3 3 0.99 34 0.088
148 A 4 3 1.00 34 0.088
149 A 4 4 1.00 31 0.129
150 A 4 4 1.00 30 0.133
151 A 7 7 1.00 33 0.212
152 A 7 7 1.00 33 0.212
153 A 6 6 1.00 33 0.182
154 A 5 5 1.74 30 0.167
155 B 5 5 2.60 29 0.172
156 B 8 8 2.45 32 0.250
157 B 8 8 2.45 32 0.250
158 A 6 6 1.55 32 0.188
159 A 7 7 1.47 32 0.219

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