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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 [186] had the largest ratio of [26]

# 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 9 6 1.00 10 0.600
2 A 5 5 1.00 10 0.500
3 A 8 6 1.00 10 0.600
4 A 4 4 1.00 8 0.500
5 A 7 5 1.00 6 0.833
6 A 6 6 1.00 10 0.600
7 A 4 3 1.00 10 0.300
8 A 4 4 1.00 10 0.400
9 A 5 5 1.00 10 0.500
10 A 14 9 1.00 10 0.900
11 A 10 10 1.00 10 1.000
12 A 11 8 1.00 10 0.800
13 A 7 7 1.00 8 0.875
14 A 9 6 1.00 6 1.000
15 A 7 7 1.00 10 0.700
16 A 5 3 1.00 10 0.300
17 A 6 6 1.00 10 0.600
18 A 8 6 1.00 10 0.600
19 A 8 6 1.00 12 0.500
20 A 6 4 1.00 12 0.333
21 A 6 6 1.00 12 0.500
22 A 4 4 1.00 12 0.333
23 A 4 4 1.00 12 0.333
24 A 2 2 1.00 10 0.200
25 A 3 2 1.00 8 0.250
26 A 6 6 1.00 12 0.500
27 A 2 2 1.00 12 0.167
28 A 5 5 1.00 12 0.417
29 A 4 4 1.00 12 0.333
30 A 7 5 1.00 12 0.417
31 A 6 4 1.00 12 0.333
32 A 9 5 1.00 12 0.417
33 A 5 5 1.00 14 0.357
34 A 8 6 1.00 14 0.429
35 A 4 4 1.00 12 0.333
36 A 7 5 1.00 10 0.500
37 A 6 6 1.00 14 0.429
38 A 4 3 1.00 14 0.214
39 A 4 3 1.00 14 0.214
40 A 5 5 1.00 14 0.357
41 A 5 3 1.00 14 0.214
42 A 10 10 1.00 14 0.714
43 A 11 8 1.00 14 0.571
44 A 7 7 1.00 12 0.583
45 A 9 6 1.00 10 0.600
46 A 7 7 1.00 14 0.500
47 A 5 3 1.00 14 0.214
48 A 6 6 1.00 14 0.429
49 A 8 6 1.00 14 0.429
50 A 10 6 1.00 14 0.429
51 A 0 0 0.00 0 0.000
52 A 0 0 0.00 0 0.000
53 A 0 0 0.00 0 0.000
54 A 4 4 1.00 14 0.286
55 A 6 6 1.00 14 0.429
56 A 9 5 1.00 14 0.357
57 A 0 0 0.00 0 0.000
58 A 0 0 0.00 0 0.000
59 A 0 0 0.00 0 0.000
60 A 5 5 1.00 14 0.357
61 A 7 7 1.00 14 0.500
62 A 11 6 1.00 14 0.429
63 A 0 0 0.00 0 0.000
64 A 0 0 0.00 0 0.000
65 A 0 0 0.00 0 0.000
66 A 6 5 1.00 14 0.357
67 A 8 7 1.00 14 0.500
68 A 13 6 1.00 14 0.429
69 A 0 0 0.00 0 0.000
70 A 0 0 0.00 0 0.000
71 A 3 3 1.00 14 0.214
72 A 0 0 0.00 0 0.000
73 A 0 0 0.00 0 0.000
74 A 9 7 1.00 16 0.438
75 A 8 7 1.00 16 0.438
76 A 7 7 1.00 14 0.500
77 A 3 2 1.00 8 0.250
78 A 4 2 1.00 16 0.125
79 A 8 7 1.00 16 0.438
80 A 11 8 1.00 16 0.500
81 A 21 12 1.00 18 0.667
82 A 14 10 1.00 18 0.556
83 A 8 8 1.00 18 0.444
84 A 5 5 1.00 18 0.278
85 A 11 10 1.00 18 0.556
86 A 18 13 1.00 18 0.722
87 A 0 0 0.00 0 0.000
88 A 6 6 1.00 19 0.316
89 A 5 6 1.00 19 0.316
90 A 4 4 1.00 16 0.250
91 A 3 4 1.00 19 0.210
92 A 4 5 1.00 19 0.263
93 A 5 6 1.00 19 0.316
94 A 6 6 1.00 19 0.316
95 A 5 5 1.00 19 0.263
96 A 5 5 1.00 19 0.263
97 A 7 6 1.00 17 0.353
98 A 12 12 1.00 19 0.632
99 A 14 14 1.00 19 0.737
100 A 6 7 1.00 21 0.333
101 A 5 6 1.00 18 0.333
102 A 5 6 1.00 21 0.286
103 A 5 6 1.00 21 0.286
104 A 5 6 1.00 21 0.286
105 A 6 7 1.00 21 0.333
106 A 5 6 1.00 21 0.286
107 A 7 6 1.00 19 0.316
108 A 13 14 1.00 21 0.667
109 A 15 16 1.00 21 0.762
110 A 24 11 1.00 21 0.524
111 A 26 9 1.00 19 0.474
112 A 19 7 1.00 18 0.389
113 A 19 7 1.00 21 0.333
114 A 24 10 1.00 21 0.476
115 A 32 15 1.00 21 0.714
116 A 30 13 1.00 21 0.619
117 A 8 6 1.00 19 0.316
118 A 25 11 1.00 21 0.524
119 A 50 13 1.00 21 0.619
120 A 27 10 1.00 21 0.476
121 A 47 11 1.00 18 0.611
122 A 50 13 1.00 21 0.619
123 A 35 14 1.00 21 0.667
124 A 6 7 1.00 21 0.333
125 A 9 7 1.00 19 0.368
126 A 30 12 1.00 21 0.571
127 A 35 11 1.00 21 0.524
128 A 63 12 1.00 21 0.571
129 A 81 12 1.00 18 0.667
130 A 12 12 1.00 23 0.522
131 A 11 12 1.00 23 0.522
132 A 10 10 1.00 21 0.476
133 A 0 0 0.00 0 0.000
134 A 0 0 0.00 0 0.000
135 A 0 0 0.00 0 0.000
136 A 0 0 0.00 0 0.000
137 A 0 0 0.00 0 0.000
138 A 9 10 1.00 23 0.435
139 A 10 11 1.00 23 0.478
140 A 12 12 1.00 23 0.522
141 A 11 11 1.00 21 0.524
142 A 0 0 0.00 0 0.000
143 A 0 0 0.00 0 0.000
144 A 0 0 0.00 0 0.000
145 A 0 0 0.00 0 0.000
146 A 0 0 0.00 0 0.000
147 A 0 0 0.00 0 0.000
148 A 10 11 1.00 23 0.478
149 A 11 11 1.00 23 0.478
150 A 11 12 1.00 23 0.522
151 A 10 12 1.00 23 0.522
152 A 10 10 1.00 21 0.476
153 A 0 0 0.00 0 0.000
154 A 0 0 0.00 0 0.000
155 A 0 0 0.00 0 0.000
156 A 0 0 0.00 0 0.000
157 A 9 10 1.00 23 0.435
158 A 9 11 1.00 23 0.478
159 A 10 11 1.00 23 0.478
160 A 9 11 1.00 23 0.478
161 A 5 5 1.00 21 0.238
162 A 0 0 0.00 0 0.000
163 A 0 0 0.00 0 0.000
164 A 0 0 0.00 0 0.000
165 A 0 0 0.00 0 0.000
166 A 4 5 1.00 20 0.250
167 A 8 10 1.00 23 0.435
168 A 10 11 1.00 23 0.478
169 A 7 8 1.00 23 0.348
170 A 6 6 1.00 21 0.286
171 A 0 0 0.00 0 0.000
172 A 0 0 0.00 0 0.000
173 A 0 0 0.00 0 0.000
174 A 0 0 0.00 0 0.000
175 A 8 9 1.00 23 0.391
176 A 8 10 1.00 20 0.500
177 A 5 6 0.97 23 0.261
178 A 5 6 0.95 23 0.261
179 A 4 5 0.93 21 0.238
180 A 0 0 0.00 0 0.000
181 A 0 0 0.00 0 0.000
182 A 0 0 0.00 0 0.000
183 A 0 0 0.00 0 0.000
184 A 0 0 0.00 0 0.000
185 A 0 0 0.00 0 0.000
186 A 15 10 1.00 26 0.385
187 A 12 10 1.00 26 0.385
188 A 7 8 1.00 26 0.308
189 A 0 0 0.00 0 0.000
190 A 0 0 0.00 0 0.000

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