[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 [16] had the largest ratio of [1.50000000000000000]

# 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 12 12 1.11 14 0.857
2 A 10 10 1.09 14 0.714
3 A 7 7 1.06 14 0.500
4 A 5 5 1.00 12 0.417
5 A 5 5 1.00 14 0.357
6 A 8 8 1.04 14 0.571
7 A 10 10 1.01 14 0.714
8 A 13 13 1.06 14 0.929
9 A 9 9 1.03 16 0.562
10 A 6 6 1.04 16 0.375
11 A 6 6 1.02 16 0.375
12 A 3 3 1.00 14 0.214
13 A 3 3 1.00 16 0.188
14 A 8 8 1.04 16 0.500
15 A 6 6 1.30 16 0.375
16 A 25 24 1.35 16 1.500
17 A 18 18 1.23 16 1.125
18 A 12 11 1.11 16 0.688
19 A 7 7 0.99 14 0.500
20 A 3 3 1.00 16 0.188
21 A 3 3 1.02 16 0.188
22 A 9 9 1.32 16 0.562
23 A 12 12 1.38 12 1.000
24 A 12 12 1.35 12 1.000
25 A 5 5 1.06 10 0.500
26 A 3 3 1.00 12 0.250
27 A 3 3 1.06 12 0.250
28 A 5 5 1.53 12 0.417
29 A 7 6 1.09 14 0.429
30 A 6 5 1.06 14 0.357
31 A 5 4 1.00 12 0.333
32 N/A 2 0 1.00 14 0.000
33 A 10 9 1.20 16 0.562
34 A 9 8 1.18 16 0.500
35 A 5 5 1.00 14 0.357
36 N/A 2 0 1.00 16 0.000
37 A 11 10 1.06 16 0.625
38 A 9 8 1.07 16 0.500
39 A 7 6 1.01 14 0.429
40 N/A 2 0 1.00 16 0.000
41 A 16 15 1.04 16 0.938
42 A 13 12 1.04 16 0.750
43 A 11 10 1.02 16 0.625
44 A 8 7 1.00 16 0.438
45 A 11 10 1.04 16 0.625
46 A 13 12 1.05 16 0.750
47 A 16 15 1.07 16 0.938
48 A 6 6 1.03 18 0.333
49 A 6 6 1.03 18 0.333
50 A 3 3 1.00 18 0.167
51 A 3 3 1.00 18 0.167
52 A 11 10 1.04 18 0.556
53 A 6 6 1.25 18 0.333
54 A 14 13 1.03 18 0.722
55 A 9 9 1.20 18 0.500
56 A 20 19 1.40 18 1.056
57 A 17 16 1.42 18 0.889
58 A 3 3 1.00 18 0.167
59 A 3 3 1.00 18 0.167
60 A 3 3 1.06 18 0.167
61 A 12 11 1.52 18 0.611
62 A 15 14 1.42 18 0.778
63 A 9 8 1.00 8 1.000
64 A 7 6 1.00 8 0.750
65 A 4 3 1.00 8 0.375
66 A 7 6 1.00 8 0.750
67 A 9 9 1.05 16 0.562
68 A 6 6 1.05 16 0.375
69 A 6 6 1.05 16 0.375
70 A 4 4 1.00 16 0.250
71 A 4 4 1.00 16 0.250
72 A 6 6 1.05 16 0.375
73 A 6 6 1.06 16 0.375
74 A 9 9 1.06 16 0.562
75 N/A 2 0 1.00 12 0.000
76 A 2 2 1.00 10 0.200
77 N/A 2 0 1.00 14 0.000
78 N/A 4 0 1.00 12 0.000
79 A 4 4 1.00 10 0.400
80 N/A 2 0 1.00 14 0.000
81 A 1 1 1.00 28 0.036
82 N/A 4 0 1.00 10 0.000
83 N/A 2 0 1.00 12 0.000
84 A 2 2 1.00 10 0.200
85 N/A 2 0 1.00 14 0.000
86 N/A 4 0 1.00 12 0.000
87 A 4 4 1.00 10 0.400
88 N/A 2 0 1.00 14 0.000
89 A 1 1 1.00 25 0.040
90 A 1 1 1.00 17 0.059
91 A 1 1 1.00 20 0.050
92 A 1 1 1.00 20 0.050
93 A 1 1 1.00 21 0.048
94 A 1 1 1.00 20 0.050
95 A 1 1 1.00 20 0.050
96 A 1 1 1.00 20 0.050
97 A 1 1 1.00 24 0.042
98 N/A 2 0 1.00 18 0.000
99 A 3 3 1.00 16 0.188
100 A 3 3 1.00 16 0.188
101 A 4 4 1.00 14 0.286
102 N/A 2 0 1.00 14 0.000
103 N/A 2 0 1.00 16 0.000
104 A 4 4 1.00 12 0.333
105 A 4 4 1.00 12 0.333
106 A 4 4 1.00 12 0.333
107 A 4 4 1.00 10 0.400
108 A 4 4 1.00 12 0.333
109 A 4 4 1.00 12 0.333
110 A 4 4 1.00 12 0.333
111 A 3 3 1.00 14 0.214
112 A 3 3 1.00 14 0.214
113 A 3 3 1.00 14 0.214
114 A 3 3 1.00 12 0.250
115 A 3 3 1.00 14 0.214
116 A 3 3 1.00 14 0.214
117 A 3 3 1.00 14 0.214
118 A 3 3 1.00 18 0.167
119 A 3 3 1.00 18 0.167
120 A 3 3 1.00 16 0.188
121 A 3 3 1.00 18 0.167
122 A 3 3 1.00 18 0.167
123 A 3 3 1.00 20 0.150
124 A 3 3 1.00 20 0.150
125 A 3 3 1.00 18 0.167
126 A 5 5 0.96 20 0.250
127 A 5 5 1.01 20 0.250
128 A 12 11 1.09 20 0.550
129 A 11 10 1.07 20 0.500
130 A 7 7 1.04 18 0.389
131 N/A 2 0 1.00 20 0.000
132 N/A 2 0 1.00 20 0.000
133 A 15 14 1.01 20 0.700
134 A 15 14 0.97 20 0.700
135 A 9 9 0.97 18 0.500
136 N/A 2 0 1.00 20 0.000
137 N/A 2 0 1.00 20 0.000
138 A 12 11 1.12 21 0.524
139 A 11 10 1.08 21 0.476
140 A 7 7 1.06 19 0.368
141 N/A 2 0 1.00 21 0.000
142 N/A 2 0 1.00 21 0.000
143 A 12 12 1.09 18 0.667
144 A 9 9 1.06 18 0.500
145 A 7 7 1.25 16 0.438
146 A 2 2 1.00 14 0.143
147 A 7 7 0.69 18 0.389
148 A 10 10 0.74 18 0.556
149 A 12 12 0.72 18 0.667
150 A 12 12 0.93 14 0.857
151 A 9 9 0.92 14 0.643
152 A 7 7 1.09 12 0.583
153 A 2 2 1.00 10 0.200
154 A 4 4 1.00 14 0.286
155 A 7 7 0.93 14 0.500
156 A 9 9 0.84 14 0.643
157 A 11 11 0.89 15 0.733
158 A 9 9 0.89 15 0.600
159 A 6 6 1.06 13 0.462
160 A 2 2 1.00 11 0.182
161 A 4 4 1.00 15 0.267
162 A 6 6 0.91 15 0.400
163 A 9 9 0.83 15 0.600
164 A 20 20 0.89 14 1.429
165 A 14 13 0.79 14 0.929
166 A 9 9 0.82 12 0.750
167 A 5 5 0.73 14 0.357
168 A 5 5 0.73 14 0.357
169 A 8 8 0.83 14 0.571
170 A 9 8 0.64 18 0.444
171 A 8 7 0.64 18 0.389
172 A 7 6 0.66 16 0.375
173 A 4 3 1.00 14 0.214
174 N/A 2 0 1.00 18 0.000
175 A 9 8 0.64 15 0.533
176 A 8 7 0.63 15 0.467
177 A 7 6 0.66 13 0.462
178 A 4 3 1.00 11 0.273
179 N/A 2 0 1.00 15 0.000
180 A 13 12 0.62 14 0.857
181 A 11 10 0.62 14 0.714
182 A 9 8 0.69 12 0.667
183 N/A 2 0 1.00 14 0.000
184 N/A 2 0 1.00 18 0.000
185 A 10 9 0.92 12 0.750
186 A 9 8 0.97 16 0.500
187 A 8 7 1.00 14 0.500
188 N/A 2 0 1.00 12 0.000
189 A 13 12 1.03 18 0.667

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