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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 [209] had the largest ratio of [18]

# 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 4 3 1.00 8 0.375
2 A 4 3 1.00 8 0.375
3 A 4 3 1.00 8 0.375
4 A 3 3 1.00 6 0.500
5 A 2 2 1.00 4 0.500
6 A 5 5 1.00 8 0.625
7 A 4 4 1.00 8 0.500
8 A 2 2 1.00 8 0.250
9 A 5 5 1.00 8 0.625
10 A 3 3 1.00 8 0.375
11 A 6 5 1.00 8 0.625
12 A 7 5 1.00 10 0.500
13 A 6 4 1.00 10 0.400
14 A 5 5 1.00 10 0.500
15 A 4 4 1.00 8 0.500
16 A 3 3 1.00 6 0.500
17 A 6 6 1.00 10 0.600
18 A 7 5 1.00 10 0.500
19 A 3 3 1.00 10 0.300
20 A 9 7 1.00 10 0.700
21 A 5 5 1.00 10 0.500
22 A 14 7 1.00 10 0.700
23 A 11 5 1.00 10 0.500
24 A 9 7 1.00 10 0.700
25 A 6 5 1.00 8 0.625
26 A 4 3 1.00 6 0.500
27 A 7 7 1.00 10 0.700
28 A 9 6 1.00 10 0.600
29 A 7 7 1.00 10 0.700
30 A 14 10 1.00 10 1.000
31 A 10 9 1.00 10 0.900
32 A 23 4 1.00 10 0.400
33 A 19 6 1.00 10 0.600
34 A 14 4 1.00 10 0.400
35 A 11 6 1.00 10 0.600
36 A 7 4 1.00 8 0.500
37 A 5 3 1.00 6 0.500
38 A 8 7 1.00 10 0.700
39 A 11 7 1.00 10 0.700
40 A 8 8 1.00 10 0.800
41 A 19 10 1.00 10 1.000
42 A 7 3 1.00 10 0.300
43 A 6 3 1.00 10 0.300
44 A 6 3 1.00 10 0.300
45 A 5 3 1.00 10 0.300
46 A 5 3 1.00 10 0.300
47 A 4 4 1.00 8 0.500
48 A 2 2 1.00 6 0.333
49 A 0 0 0.00 0 0.000
50 A 0 0 0.00 0 0.000
51 A 6 2 1.00 10 0.200
52 A 5 2 1.00 10 0.200
53 A 5 2 1.00 10 0.200
54 A 4 2 1.00 10 0.200
55 A 4 2 1.00 10 0.200
56 A 2 2 1.00 8 0.250
57 A 3 3 1.00 6 0.500
58 A 0 0 0.00 0 0.000
59 A 0 0 0.00 0 0.000
60 A 14 5 1.00 10 0.500
61 A 12 6 1.00 10 0.600
62 A 10 6 1.00 10 0.600
63 A 7 7 1.00 8 0.875
64 A 4 4 1.00 6 0.667
65 A 0 0 0.00 0 0.000
66 A 0 0 0.00 0 0.000
67 A 12 4 1.00 10 0.400
68 A 9 4 1.00 10 0.400
69 A 10 6 1.00 10 0.600
70 A 5 5 1.00 8 0.625
71 A 5 4 1.00 6 0.667
72 A 0 0 0.00 0 0.000
73 A 0 0 0.00 0 0.000
74 A 10 5 1.00 12 0.417
75 A 8 5 1.00 12 0.417
76 A 8 5 1.00 12 0.417
77 A 6 5 1.00 10 0.500
78 A 4 4 1.00 8 0.500
79 A 0 0 0.00 0 0.000
80 A 23 8 1.00 12 0.667
81 A 16 8 1.00 12 0.667
82 A 13 8 1.00 12 0.667
83 A 8 8 1.00 10 0.800
84 A 5 5 1.00 8 0.625
85 A 0 0 0.00 0 0.000
86 A 26 8 1.00 12 0.667
87 A 18 7 1.00 12 0.583
88 A 15 8 1.00 12 0.667
89 A 9 7 1.00 10 0.700
90 A 6 5 1.00 8 0.625
91 A 0 0 0.00 0 0.000
92 A 9 4 1.00 12 0.333
93 A 7 4 1.00 12 0.333
94 A 7 4 1.00 12 0.333
95 A 5 5 1.00 10 0.500
96 A 3 3 1.00 8 0.375
97 A 0 0 0.00 0 0.000
98 A 0 0 0.00 0 0.000
99 A 10 3 1.00 12 0.250
100 A 8 3 1.00 12 0.250
101 A 8 3 1.00 12 0.250
102 A 6 3 1.00 12 0.250
103 A 6 3 1.00 12 0.250
104 A 3 3 1.00 10 0.300
105 A 4 4 1.00 8 0.500
106 A 0 0 0.00 0 0.000
107 A 19 6 1.00 12 0.500
108 A 15 7 1.00 12 0.583
109 A 13 7 1.00 12 0.583
110 A 8 8 1.00 10 0.800
111 A 5 5 1.00 8 0.625
112 A 0 0 0.00 0 0.000
113 A 17 5 1.00 12 0.417
114 A 12 5 1.00 12 0.417
115 A 13 7 1.00 12 0.583
116 A 6 6 1.00 10 0.600
117 A 6 5 1.00 8 0.625
118 A 0 0 0.00 0 0.000
119 A 0 0 0.00 0 0.000
120 A 0 0 0.00 0 0.000
121 A 2 2 1.00 12 0.167
122 A 2 2 1.00 10 0.200
123 A 0 0 0.00 0 0.000
124 A 0 0 0.00 0 0.000
125 A 0 0 0.00 0 0.000
126 A 0 0 0.00 0 0.000
127 A 0 0 0.00 0 0.000
128 A 0 0 0.00 0 0.000
129 A 0 0 0.00 0 0.000
130 A 9 4 1.00 10 0.400
131 A 9 4 1.00 10 0.400
132 A 6 5 1.00 8 0.625
133 A 4 3 1.00 6 0.500
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 0 0 0.00 0 0.000
139 A 0 0 0.00 0 0.000
140 A 4 3 1.00 12 0.250
141 A 4 3 1.00 12 0.250
142 A 3 3 1.00 10 0.300
143 A 3 2 1.00 8 0.250
144 A 5 5 1.00 12 0.417
145 A 4 4 1.00 12 0.333
146 A 2 2 1.00 12 0.167
147 A 5 5 1.00 12 0.417
148 A 5 5 1.00 14 0.357
149 A 4 4 1.00 12 0.333
150 A 3 3 1.00 10 0.300
151 A 6 6 1.00 14 0.429
152 A 7 5 1.00 14 0.357
153 A 10 7 1.00 14 0.500
154 A 6 5 1.00 12 0.417
155 A 5 3 1.00 10 0.300
156 A 7 7 1.00 14 0.500
157 A 9 6 1.00 14 0.429
158 A 9 5 1.00 14 0.357
159 A 6 6 1.00 12 0.500
160 A 4 4 1.00 10 0.400
161 A 0 0 0.00 0 0.000
162 A 0 0 0.00 0 0.000
163 A 8 4 1.00 14 0.286
164 A 4 4 1.00 12 0.333
165 A 5 5 1.00 10 0.500
166 A 0 0 0.00 0 0.000
167 A 0 0 0.00 0 0.000
168 A 16 8 1.00 14 0.571
169 A 9 9 1.00 12 0.750
170 A 6 6 1.00 10 0.600
171 A 0 0 0.00 0 0.000
172 A 0 0 0.00 0 0.000
173 A 14 8 1.00 16 0.500
174 A 9 8 1.00 14 0.571
175 A 7 7 1.00 12 0.583
176 A 0 0 0.00 0 0.000
177 A 0 0 0.00 0 0.000
178 A 22 11 1.00 16 0.688
179 A 11 11 1.00 14 0.786
180 A 8 8 1.00 12 0.667
181 A 0 0 0.00 0 0.000
182 A 0 0 0.00 0 0.000
183 A 24 11 1.00 16 0.688
184 A 12 10 1.00 14 0.714
185 A 9 8 1.00 12 0.667
186 A 0 0 0.00 0 0.000
187 A 0 0 0.00 0 0.000
188 A 13 7 1.00 16 0.438
189 A 8 8 1.00 14 0.571
190 A 6 6 1.00 12 0.500
191 A 0 0 0.00 0 0.000
192 A 0 0 0.00 0 0.000
193 A 12 6 1.00 16 0.375
194 A 6 6 1.00 14 0.429
195 A 7 7 1.00 12 0.583
196 A 0 0 0.00 0 0.000
197 A 0 0 0.00 0 0.000
198 A 22 10 1.00 16 0.625
199 A 11 11 1.00 14 0.786
200 A 8 8 1.00 12 0.667
201 A 0 0 0.00 0 0.000
202 A 0 0 0.00 0 0.000
203 A 5 4 1.00 16 0.250
204 A 7 7 1.00 16 0.438
205 A 4 4 1.00 16 0.250
206 A 6 6 1.00 16 0.375
207 A 3 3 1.00 16 0.188
208 A 7 7 1.00 16 0.438
209 A 2 2 1.00 18 0.111
210 A 2 2 1.00 18 0.111
211 A 2 2 1.00 18 0.111
212 A 2 2 1.00 18 0.111
213 A 2 2 1.00 18 0.111
214 A 2 2 1.00 18 0.111
215 A 0 0 0.00 0 0.000
216 A 0 0 0.00 0 0.000
217 A 0 0 0.00 0 0.000
218 A 0 0 0.00 0 0.000
219 A 0 0 0.00 0 0.000
220 A 0 0 0.00 0 0.000
221 A 0 0 0.00 0 0.000
222 A 0 0 0.00 0 0.000
223 A 0 0 0.00 0 0.000
224 A 0 0 0.00 0 0.000
225 A 0 0 0.00 0 0.000
226 A 0 0 0.00 0 0.000
227 A 0 0 0.00 0 0.000

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