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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 [60] had the largest ratio of [.406250000000000000]

# 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 C 2 2 228.00 32 0.062
2 A 4 4 1.01 47 0.085
3 A 7 7 1.22 69 0.101
4 A 2 2 1.00 30 0.067
5 A 2 2 1.00 30 0.067
6 A 2 2 1.00 28 0.071
7 A 2 2 1.00 23 0.087
8 A 2 2 1.00 30 0.067
9 A 2 2 1.00 30 0.067
10 A 2 2 1.00 30 0.067
11 A 3 3 0.70 30 0.100
12 A 6 5 0.86 28 0.179
13 A 5 4 1.03 23 0.174
14 A 4 4 1.13 30 0.133
15 A 3 3 1.07 30 0.100
16 A 4 4 1.05 20 0.200
17 A 3 3 1.09 20 0.150
18 A 7 6 1.06 18 0.333
19 A 5 4 1.00 17 0.235
20 A 3 3 1.09 20 0.150
21 A 3 3 1.05 20 0.150
22 A 3 3 1.04 20 0.150
23 A 11 10 0.83 32 0.312
24 A 9 8 0.83 32 0.250
25 A 7 6 0.87 30 0.200
26 A 7 6 0.95 25 0.240
27 A 10 9 1.07 32 0.281
28 A 10 9 1.06 32 0.281
29 A 11 10 1.05 32 0.312
30 A 10 9 1.33 32 0.281
31 A 7 6 0.91 32 0.188
32 A 9 8 0.88 32 0.250
33 A 12 11 0.69 32 0.344
34 A 10 9 0.71 32 0.281
35 A 8 7 0.79 30 0.233
36 A 8 7 0.89 25 0.280
37 A 12 11 1.05 32 0.344
38 A 12 11 1.03 32 0.344
39 A 13 12 1.03 32 0.375
40 A 12 11 1.02 32 0.344
41 A 12 11 1.42 32 0.344
42 A 12 11 1.48 32 0.344
43 A 8 7 0.83 32 0.219
44 A 10 9 0.77 32 0.281
45 A 11 10 1.14 32 0.312
46 A 9 8 1.13 32 0.250
47 A 7 6 1.11 30 0.200
48 A 10 9 1.06 32 0.281
49 A 10 9 1.06 32 0.281
50 A 10 9 1.05 32 0.281
51 A 12 11 1.16 32 0.344
52 A 10 9 1.14 32 0.281
53 A 8 7 1.13 30 0.233
54 A 12 11 1.09 32 0.344
55 A 12 11 1.08 32 0.344
56 A 12 11 1.11 32 0.344
57 A 12 11 1.16 32 0.344
58 A 11 10 1.15 32 0.312
59 A 9 8 1.14 30 0.267
60 A 14 13 1.11 32 0.406
61 A 14 13 1.10 32 0.406
62 A 14 13 1.10 32 0.406
63 A 10 9 1.05 32 0.281
64 A 8 7 1.05 32 0.219
65 A 6 5 1.07 30 0.167
66 A 6 5 1.04 25 0.200
67 A 8 7 1.05 32 0.219
68 A 8 7 1.16 32 0.219
69 A 6 5 1.06 32 0.156
70 A 8 7 0.78 32 0.219
71 A 6 5 0.75 32 0.156
72 A 6 5 0.96 30 0.167
73 A 5 4 1.03 25 0.160
74 A 5 4 1.02 32 0.125
75 A 6 5 1.02 32 0.156
76 A 8 7 1.06 32 0.219
77 A 9 8 1.12 32 0.250
78 A 8 7 1.11 32 0.219
79 A 6 5 1.07 30 0.167
80 A 8 7 1.06 32 0.219
81 A 8 7 1.04 32 0.219
82 A 6 5 1.06 32 0.156
83 A 10 9 1.04 32 0.281
84 A 8 7 1.02 32 0.219
85 A 6 5 1.02 30 0.167
86 A 5 4 1.00 32 0.125
87 A 6 5 1.03 32 0.156
88 A 8 7 1.04 32 0.219
89 A 8 7 1.05 32 0.219
90 A 7 6 1.04 32 0.188
91 A 3 3 1.00 30 0.100
92 A 7 6 1.06 32 0.188
93 A 8 7 1.07 32 0.219
94 A 10 9 1.08 32 0.281
95 A 11 10 1.05 34 0.294
96 A 9 8 1.05 34 0.235
97 A 9 8 1.07 34 0.235
98 A 9 8 1.04 34 0.235
99 A 9 8 1.04 34 0.235
100 A 11 10 1.05 34 0.294
101 A 11 10 1.07 34 0.294
102 A 9 8 1.07 34 0.235
103 A 7 6 1.06 34 0.176
104 A 7 6 1.07 34 0.176
105 A 9 8 1.06 34 0.235
106 A 11 10 1.07 34 0.294
107 A 7 6 0.99 30 0.200
108 A 6 5 1.00 32 0.156
109 A 7 6 1.00 34 0.176
110 F 0 0 N/A 0.000 N/A
111 A 1 1 1.00 47 0.021
112 A 2 2 1.00 75 0.027
113 B 2 2 47.15 97 0.021
114 A 3 3 1.00 16 0.188
115 A 10 9 1.07 33 0.273
116 A 8 7 1.07 31 0.226
117 A 8 7 1.07 30 0.233
118 A 10 9 1.08 33 0.273
119 A 9 8 1.09 33 0.242
120 A 10 9 1.10 33 0.273
121 A 8 7 1.08 33 0.212
122 A 10 9 1.08 33 0.273
123 A 12 11 1.08 33 0.333
124 A 2 2 0.97 36 0.056
125 A 2 2 1.04 36 0.056
126 A 2 2 1.00 34 0.059
127 A 2 2 1.00 29 0.069
128 A 2 2 1.00 36 0.056
129 A 2 2 1.00 36 0.056
130 A 2 2 1.00 36 0.056
131 A 2 2 1.48 38 0.053
132 A 2 2 1.03 38 0.053
133 A 2 2 1.00 36 0.056
134 A 2 2 1.00 31 0.065
135 A 2 2 1.00 38 0.053
136 A 2 2 1.00 38 0.053
137 A 2 2 1.00 38 0.053
138 A 2 2 1.00 38 0.053
139 A 2 2 1.00 38 0.053
140 A 2 2 1.00 38 0.053
141 A 2 2 1.00 36 0.056
142 A 2 2 1.00 31 0.065
143 A 2 2 1.00 38 0.053
144 A 2 2 1.00 38 0.053
145 A 2 2 1.00 38 0.053
146 A 4 4 0.84 38 0.105
147 A 4 4 0.89 38 0.105
148 A 4 4 0.95 36 0.111
149 A 4 4 1.05 31 0.129
150 A 4 4 1.03 38 0.105
151 A 4 4 1.00 38 0.105
152 A 4 4 1.00 38 0.105
153 A 6 6 0.79 38 0.158
154 A 6 6 0.86 38 0.158
155 A 10 9 1.05 36 0.250
156 A 7 6 1.12 31 0.194
157 A 6 6 1.07 38 0.158
158 A 6 6 1.01 38 0.158
159 A 11 10 1.14 38 0.263
160 A 11 10 1.16 33 0.303
161 A 14 13 1.11 40 0.325
162 A 14 13 1.09 40 0.325
163 A 14 13 1.05 40 0.325
164 A 12 11 1.09 40 0.275
165 A 14 13 1.11 40 0.325
166 A 13 12 1.11 40 0.300
167 A 10 9 1.12 40 0.225
168 A 13 12 1.13 40 0.300
169 A 12 11 1.15 38 0.289
170 A 12 11 1.17 33 0.333
171 A 15 14 1.11 40 0.350
172 A 16 15 1.07 40 0.375
173 A 15 14 1.07 40 0.350
174 A 14 13 1.08 40 0.325
175 A 15 14 1.10 40 0.350
176 A 15 14 1.16 40 0.350
177 A 15 14 1.12 40 0.350
178 A 16 15 1.12 40 0.375
179 A 11 10 1.14 40 0.250
180 A 10 9 1.11 38 0.237
181 A 10 9 1.15 33 0.273
182 A 12 11 1.16 40 0.275
183 A 12 11 1.07 40 0.275
184 A 12 11 1.05 40 0.275
185 A 11 10 1.10 40 0.250
186 A 9 8 1.11 40 0.200
187 A 11 10 1.12 40 0.250
188 A 9 8 1.15 38 0.211
189 A 8 7 1.10 33 0.212
190 A 10 9 1.01 40 0.225
191 A 10 9 1.06 40 0.225
192 A 8 7 1.05 40 0.175
193 A 10 9 1.04 40 0.225
194 A 10 9 1.12 40 0.225
195 A 8 7 1.09 38 0.184
196 A 7 6 1.04 33 0.182
197 A 7 6 1.06 40 0.150
198 A 8 7 1.09 40 0.175
199 A 10 9 1.08 40 0.225
200 A 12 11 1.08 40 0.275
201 A 7 6 1.06 35 0.171
202 A 7 6 1.06 36 0.167
203 A 2 2 1.00 38 0.053
204 A 2 2 1.00 38 0.053
205 A 2 2 1.00 36 0.056
206 A 2 2 1.00 38 0.053
207 A 4 4 1.01 38 0.105

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