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

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 [119] had the largest ratio of [40]

# 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 4 3 1.00 8 0.375
5 A 3 3 1.00 6 0.500
6 A 2 2 1.00 4 0.500
7 A 3 2 1.00 8 0.250
8 A 5 5 1.00 8 0.625
9 A 3 3 1.00 8 0.375
10 A 4 3 1.00 8 0.375
11 A 4 3 1.00 8 0.375
12 A 15 7 1.00 10 0.700
13 A 14 9 1.00 10 0.900
14 A 10 7 1.00 10 0.700
15 A 9 8 1.00 10 0.800
16 A 5 5 1.00 8 0.625
17 A 5 5 1.00 6 0.833
18 A 6 5 1.00 10 0.500
19 A 4 4 1.00 10 0.400
20 A 8 7 1.00 10 0.700
21 A 8 7 1.00 10 0.700
22 A 13 8 1.00 10 0.800
23 A 33 11 1.00 10 1.100
24 A 22 11 1.00 10 1.100
25 A 18 10 1.00 10 1.000
26 A 11 9 1.00 10 0.900
27 A 8 8 1.00 8 1.000
28 A 5 6 1.00 6 1.000
29 A 8 6 1.00 10 0.600
30 A 5 6 1.00 10 0.600
31 A 7 6 1.00 10 0.600
32 A 14 11 1.00 10 1.100
33 A 16 8 1.00 10 0.800
34 A 0 0 0.00 0 0.000
35 A 0 0 0.00 0 0.000
36 A 2 2 1.00 8 0.250
37 A 9 7 1.00 13 0.538
38 A 8 8 1.00 13 0.615
39 A 4 4 1.00 13 0.308
40 A 4 4 1.00 11 0.364
41 A 1 1 1.00 10 0.100
42 A 3 3 1.00 13 0.231
43 A 7 7 1.00 13 0.538
44 A 7 7 1.00 13 0.538
45 A 12 8 1.00 13 0.615
46 A 28 15 1.00 15 1.000
47 A 10 5 1.00 13 0.385
48 A 25 13 1.00 12 1.083
49 A 15 7 1.00 15 0.467
50 A 31 19 1.00 15 1.267
51 A 1 1 1.00 12 0.083
52 A 1 1 1.00 12 0.083
53 A 4 4 1.00 14 0.286
54 A 4 4 1.00 14 0.286
55 A 5 5 1.00 14 0.357
56 A 5 4 1.00 12 0.333
57 A 27 13 1.00 14 0.929
58 A 24 12 1.00 14 0.857
59 A 0 0 0.00 0 0.000
60 A 0 0 0.00 0 0.000
61 A 5 6 1.00 16 0.375
62 A 7 9 1.00 16 0.562
63 A 8 9 1.00 16 0.562
64 A 8 9 1.00 16 0.562
65 A 3 3 1.00 14 0.214
66 A 2 2 1.00 14 0.143
67 A 1 1 1.00 14 0.071
68 A 2 2 1.00 14 0.143
69 A 3 2 1.00 14 0.143
70 A 3 3 1.00 11 0.273
71 A 4 3 1.00 11 0.273
72 A 2 2 1.00 10 0.200
73 A 4 4 1.00 12 0.333
74 A 4 3 1.00 10 0.300
75 A 4 4 1.00 10 0.400
76 A 2 2 1.00 8 0.250
77 A 4 3 1.00 10 0.300
78 A 5 5 1.00 10 0.500
79 A 4 4 1.00 10 0.400
80 A 11 8 1.00 10 0.800
81 A 11 8 1.00 10 0.800
82 A 10 7 1.00 6 1.167
83 A 10 7 1.00 10 0.700
84 A 11 8 1.00 10 0.800
85 A 6 4 1.00 10 0.400
86 A 5 4 1.00 8 0.500
87 A 4 4 1.00 6 0.667
88 A 4 3 1.00 10 0.300
89 A 4 4 1.00 10 0.400
90 A 5 4 1.00 10 0.400
91 A 3 2 1.00 12 0.167
92 A 3 2 1.00 12 0.167
93 A 2 2 1.00 12 0.167
94 A 4 4 1.00 12 0.333
95 A 3 2 1.00 12 0.167
96 A 3 3 1.00 4 0.750
97 A 4 3 1.00 10 0.300
98 A 4 3 1.00 10 0.300
99 A 7 6 1.00 10 0.600
100 A 7 6 1.00 10 0.600
101 A 7 6 1.00 8 0.750
102 A 3 3 1.00 6 0.500
103 A 5 5 1.00 10 0.500
104 A 7 7 1.00 10 0.700
105 A 8 7 1.00 10 0.700
106 A 8 7 1.00 10 0.700
107 A 15 5 1.00 16 0.312
108 A 5 5 1.00 14 0.357
109 A 37 10 1.25 16 0.625
110 A 57 11 1.11 16 0.688
111 A 55 16 1.00 18 0.889
112 A 65 19 1.00 18 1.056
113 A 12 8 1.00 19 0.421
114 A 2 2 1.00 28 0.071
115 A 3 3 1.00 33 0.091
116 A 0 0 0.00 0 0.000
117 A 0 0 0.00 0 0.000
118 A 4 4 1.00 35 0.114
119 A 5 5 1.00 40 0.125
120 A 0 0 0.00 0 0.000
121 A 0 0 0.00 0 0.000
122 A 5 4 1.00 14 0.286
123 A 4 4 1.00 12 0.333
124 A 4 3 1.00 14 0.214
125 A 6 6 1.00 14 0.429
126 A 5 4 1.00 12 0.333
127 A 5 4 1.00 19 0.210
128 A 0 0 0.00 0 0.000
129 A 7 6 1.00 18 0.333
130 A 7 6 1.00 18 0.333
131 A 7 6 1.00 16 0.375
132 A 4 3 1.00 10 0.300
133 A 5 5 1.00 18 0.278
134 A 8 8 1.00 18 0.444
135 A 9 8 1.00 18 0.444
136 A 16 13 1.00 20 0.650
137 A 13 10 1.00 18 0.556
138 A 6 6 1.00 12 0.500
139 A 2 2 1.00 20 0.100
140 A 25 25 1.00 20 1.250
141 A 21 14 1.00 20 0.700
142 A 15 11 1.00 18 0.611
143 A 6 7 1.00 12 0.583
144 A 2 2 1.00 20 0.100
145 A 35 22 1.00 20 1.100
146 A 6 4 1.00 18 0.222
147 A 0 0 0.00 0 0.000
148 A 0 0 0.00 0 0.000
149 A 4 4 1.00 12 0.333
150 A 4 4 1.00 14 0.286
151 A 0 0 0.00 0 0.000
152 A 9 7 1.00 40 0.175
153 A 7 6 1.00 40 0.150
154 A 4 4 1.00 38 0.105
155 A 0 0 0.00 0 0.000
156 A 0 0 0.00 0 0.000
157 A 2 2 1.00 7 0.286
158 A 11 6 1.00 15 0.400
159 A 9 5 1.00 13 0.385
160 A 7 4 1.00 11 0.364
161 A 0 0 0.00 0 0.000
162 A 7 7 1.00 21 0.333
163 A 6 6 1.00 19 0.316
164 A 5 5 1.00 17 0.294
165 A 0 0 0.00 0 0.000
166 A 7 7 1.00 22 0.318
167 A 6 6 1.00 20 0.300
168 A 5 5 1.00 18 0.278
169 A 0 0 0.00 0 0.000
170 A 2 2 1.00 7 0.286
171 A 11 6 1.00 15 0.400
172 A 9 5 1.00 13 0.385
173 A 7 4 1.00 11 0.364
174 A 0 0 0.00 0 0.000
175 A 7 7 1.00 21 0.333
176 A 6 6 1.00 19 0.316
177 A 5 5 1.00 17 0.294
178 A 0 0 0.00 0 0.000
179 A 7 7 1.00 22 0.318
180 A 6 6 1.00 20 0.300
181 A 5 5 1.00 18 0.278
182 A 0 0 0.00 0 0.000
183 A 12 6 1.00 15 0.400
184 A 10 6 1.00 15 0.400
185 A 8 5 1.00 13 0.385
186 A 6 4 1.00 7 0.571
187 A 0 0 0.00 0 0.000
188 A 11 6 1.00 15 0.400
189 A 9 5 1.00 13 0.385
190 A 7 4 1.00 11 0.364
191 A 0 0 0.00 0 0.000
192 A 7 7 1.00 19 0.368
193 A 6 6 1.00 17 0.353
194 A 5 5 1.00 15 0.333
195 A 0 0 0.00 0 0.000
196 A 7 7 1.00 22 0.318
197 A 6 6 1.00 20 0.300
198 A 5 5 1.00 18 0.278
199 A 0 0 0.00 0 0.000
200 A 12 6 1.00 15 0.400
201 A 10 6 1.00 15 0.400
202 A 8 5 1.00 13 0.385
203 A 6 4 1.00 7 0.571
204 A 0 0 0.00 0 0.000
205 A 11 6 1.00 15 0.400
206 A 9 5 1.00 13 0.385
207 A 7 4 1.00 11 0.364
208 A 0 0 0.00 0 0.000
209 A 7 7 1.00 19 0.368
210 A 6 6 1.00 17 0.353
211 A 5 5 1.00 15 0.333
212 A 0 0 0.00 0 0.000
213 A 7 7 1.00 22 0.318
214 A 6 6 1.00 20 0.300
215 A 5 5 1.00 18 0.278
216 A 0 0 0.00 0 0.000
217 A 13 9 1.00 24 0.375
218 A 4 3 1.00 4 0.750
219 A 7 4 1.00 6 0.667
220 A 9 5 1.00 8 0.625
221 A 4 3 1.00 8 0.375
222 A 7 4 1.00 10 0.400
223 A 9 5 1.00 12 0.417
224 A 6 6 1.00 12 0.500
225 A 25 8 1.00 14 0.571
226 A 29 9 1.00 16 0.562
227 A 5 6 1.00 10 0.600
228 A 1 1 1.00 19 0.053
229 A 5 5 1.00 20 0.250
230 A 8 7 1.00 20 0.350
231 A 13 10 1.00 20 0.500
232 A 13 10 1.00 20 0.500
233 A 8 7 1.00 20 0.350
234 A 5 5 1.00 20 0.250

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