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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 [142] had the largest ratio of [2.60000000000000009]

# 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 6 6 1.17 8 0.750
2 A 12 11 1.15 8 1.375
3 A 5 5 1.14 8 0.625
4 A 10 9 1.11 8 1.125
5 A 4 4 1.11 8 0.500
6 A 7 6 1.03 8 0.750
7 A 3 3 1.02 6 0.500
8 A 1 1 1.00 4 0.250
9 A 4 4 1.00 8 0.500
10 A 2 2 1.00 8 0.250
11 A 3 3 0.95 8 0.375
12 A 7 6 1.06 8 0.750
13 A 4 4 1.03 8 0.500
14 A 10 9 1.08 8 1.125
15 A 5 5 1.04 8 0.625
16 A 12 11 1.09 8 1.375
17 A 6 6 1.07 8 0.750
18 A 15 14 1.09 8 1.750
19 A 4 3 0.92 14 0.214
20 A 4 3 0.95 14 0.214
21 A 4 3 0.95 12 0.250
22 A 1 1 1.00 6 0.167
23 N/A 1 0 1.00 14 0.000
24 N/A 1 0 1.00 14 0.000
25 A 4 3 0.86 10 0.300
26 A 4 3 0.90 10 0.300
27 A 4 3 0.88 8 0.375
28 A 1 1 1.00 6 0.167
29 N/A 1 0 1.00 10 0.000
30 N/A 1 0 1.00 10 0.000
31 F 0 0 N/A 0.000 N/A
32 A 18 18 1.92 10 1.800
33 A 26 25 1.35 10 2.500
34 A 12 12 1.65 10 1.200
35 A 14 13 1.29 10 1.300
36 A 7 7 1.36 10 0.700
37 A 7 6 1.04 8 0.750
38 A 4 4 1.11 6 0.667
39 N/A 1 0 1.00 10 0.000
40 N/A 2 0 1.00 10 0.000
41 N/A 2 0 1.00 10 0.000
42 N/A 5 0 1.00 10 0.000
43 A 13 12 1.12 10 1.200
44 N/A 9 0 1.00 10 0.000
45 N/A 18 0 1.00 10 0.000
46 N/A 14 0 1.00 10 0.000
47 F 0 0 N/A 0.000 N/A
48 N/A 20 0 1.00 10 0.000
49 A 3 2 0.93 16 0.125
50 A 3 2 0.92 14 0.143
51 A 5 4 1.03 8 0.500
52 N/A 1 0 1.00 16 0.000
53 N/A 1 0 1.00 16 0.000
54 A 8 7 1.11 17 0.412
55 A 8 7 1.11 15 0.467
56 A 8 7 1.11 13 0.538
57 A 4 3 0.98 17 0.176
58 A 8 7 1.11 17 0.412
59 A 8 7 1.11 17 0.412
60 A 8 7 1.22 19 0.368
61 A 6 5 1.00 22 0.227
62 A 6 5 1.00 22 0.227
63 A 5 4 0.98 19 0.211
64 A 5 4 0.98 19 0.211
65 A 3 2 1.00 19 0.105
66 A 3 2 1.00 17 0.118
67 A 3 2 1.00 19 0.105
68 A 3 2 1.00 19 0.105
69 A 3 2 1.00 19 0.105
70 A 3 2 1.00 19 0.105
71 F 0 0 N/A 0.000 N/A
72 B 17 17 2.04 20 0.850
73 A 25 24 1.36 20 1.200
74 A 11 11 1.73 20 0.550
75 A 13 12 1.34 20 0.600
76 A 6 6 1.43 20 0.300
77 A 6 5 0.96 20 0.250
78 A 2 2 1.00 18 0.111
79 A 3 2 1.00 17 0.118
80 N/A 1 0 1.00 20 0.000
81 N/A 1 0 1.00 20 0.000
82 N/A 4 0 1.00 20 0.000
83 A 12 11 1.13 20 0.550
84 N/A 8 0 1.00 20 0.000
85 N/A 17 0 1.00 20 0.000
86 N/A 13 0 1.00 20 0.000
87 F 0 0 N/A 0.000 N/A
88 N/A 19 0 1.00 20 0.000
89 N/A 31 0 1.00 20 0.000
90 N/A 1 0 1.00 19 0.000
91 F 0 0 N/A 0.000 N/A
92 B 18 18 2.02 20 0.900
93 A 25 24 1.54 20 1.200
94 A 12 12 1.70 20 0.600
95 A 16 15 1.16 20 0.750
96 A 7 7 1.38 20 0.350
97 A 7 6 1.07 20 0.300
98 A 3 3 1.00 18 0.167
99 A 1 1 1.00 17 0.059
100 N/A 1 0 1.00 20 0.000
101 A 5 4 1.00 20 0.200
102 N/A 4 0 1.00 20 0.000
103 N/A 8 0 1.00 20 0.000
104 N/A 8 0 1.00 20 0.000
105 A 21 20 1.32 20 1.000
106 N/A 13 0 1.00 20 0.000
107 N/A 28 0 1.00 20 0.000
108 N/A 19 0 1.00 20 0.000
109 F 0 0 N/A 0.000 N/A
110 A 6 6 1.16 8 0.750
111 A 13 12 1.15 8 1.500
112 A 5 5 1.14 8 0.625
113 A 10 9 1.11 8 1.125
114 A 4 4 1.09 8 0.500
115 A 8 7 1.03 8 0.875
116 A 3 3 1.02 6 0.500
117 A 1 1 1.00 4 0.250
118 A 4 4 1.00 8 0.500
119 A 2 2 1.00 8 0.250
120 A 3 3 0.98 8 0.375
121 A 8 7 1.06 8 0.875
122 A 4 4 1.01 8 0.500
123 A 10 9 1.08 8 1.125
124 A 5 5 1.05 8 0.625
125 A 13 12 1.09 8 1.500
126 A 6 6 1.06 8 0.750
127 A 15 14 1.09 8 1.750
128 A 4 3 0.91 14 0.214
129 A 4 3 0.94 14 0.214
130 A 4 3 0.94 12 0.250
131 A 1 1 1.00 6 0.167
132 N/A 1 0 1.00 14 0.000
133 N/A 1 0 1.00 14 0.000
134 A 4 3 0.86 10 0.300
135 A 4 3 0.89 10 0.300
136 A 4 3 0.88 8 0.375
137 A 1 1 1.00 6 0.167
138 N/A 1 0 1.00 10 0.000
139 N/A 1 0 1.00 10 0.000
140 F 0 0 N/A 0.000 N/A
141 A 18 18 1.91 10 1.800
142 A 27 26 1.34 10 2.600
143 A 12 12 1.64 10 1.200
144 A 14 13 1.29 10 1.300
145 A 7 7 1.35 10 0.700
146 A 7 6 1.03 8 0.750
147 A 4 4 1.11 6 0.667
148 N/A 1 0 1.00 10 0.000
149 N/A 2 0 1.00 10 0.000
150 N/A 2 0 1.00 10 0.000
151 N/A 5 0 1.00 10 0.000
152 A 13 12 1.12 10 1.200
153 N/A 9 0 1.00 10 0.000
154 N/A 18 0 1.00 10 0.000
155 N/A 14 0 1.00 10 0.000
156 F 0 0 N/A 0.000 N/A
157 N/A 20 0 1.00 10 0.000
158 A 3 2 0.93 16 0.125
159 A 3 2 0.92 14 0.143
160 A 5 4 1.03 8 0.500
161 N/A 1 0 1.00 16 0.000
162 N/A 1 0 1.00 16 0.000
163 A 8 7 1.11 17 0.412
164 A 8 7 1.11 15 0.467
165 A 8 7 1.11 13 0.538
166 A 4 3 0.98 17 0.176
167 A 8 7 1.11 17 0.412
168 A 8 7 1.11 17 0.412
169 A 8 7 1.22 19 0.368
170 A 6 5 1.00 22 0.227
171 A 6 5 1.00 22 0.227
172 A 5 4 0.98 19 0.211
173 A 5 4 0.99 19 0.211
174 A 3 2 1.00 19 0.105
175 A 3 2 1.00 17 0.118
176 A 3 2 1.00 19 0.105
177 A 3 2 1.00 19 0.105
178 A 3 2 1.00 19 0.105
179 A 3 2 1.00 19 0.105
180 F 0 0 N/A 0.000 N/A
181 B 17 17 2.04 20 0.850
182 A 26 25 1.36 20 1.250
183 A 11 11 1.73 20 0.550
184 A 13 12 1.34 20 0.600
185 A 6 6 1.43 20 0.300
186 A 6 5 0.97 20 0.250
187 A 2 2 1.00 18 0.111
188 A 3 2 1.00 17 0.118
189 N/A 1 0 1.00 20 0.000
190 N/A 1 0 1.00 20 0.000
191 N/A 4 0 1.00 20 0.000
192 A 12 11 1.13 20 0.550
193 N/A 8 0 1.00 20 0.000
194 N/A 17 0 1.00 20 0.000
195 N/A 13 0 1.00 20 0.000
196 F 0 0 N/A 0.000 N/A
197 N/A 19 0 1.00 20 0.000
198 N/A 31 0 1.00 20 0.000
199 N/A 1 0 1.00 19 0.000
200 F 0 0 N/A 0.000 N/A
201 B 18 18 2.00 20 0.900
202 A 26 25 1.54 20 1.250
203 A 12 12 1.69 20 0.600
204 A 17 16 1.15 20 0.800
205 A 7 7 1.36 20 0.350
206 A 7 6 1.07 20 0.300
207 A 3 3 0.98 18 0.167
208 A 1 1 1.00 17 0.059
209 N/A 1 0 1.00 20 0.000
210 A 5 4 1.00 20 0.200
211 N/A 4 0 1.00 20 0.000
212 N/A 8 0 1.00 20 0.000
213 N/A 8 0 1.00 20 0.000
214 A 21 20 1.32 20 1.000
215 N/A 13 0 1.00 20 0.000
216 N/A 28 0 1.00 20 0.000
217 N/A 19 0 1.00 20 0.000
218 F 0 0 N/A 0.000 N/A

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