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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 [197] had the largest ratio of [.719999999999999973]

# 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 5 5 0.90 26 0.192
2 A 5 5 0.90 26 0.192
3 A 7 7 0.92 26 0.269
4 A 7 7 0.74 26 0.269
5 A 5 5 0.95 24 0.208
6 A 3 3 0.91 26 0.115
7 A 3 3 0.93 26 0.115
8 A 3 3 0.92 26 0.115
9 A 3 3 0.92 26 0.115
10 A 3 3 0.91 26 0.115
11 A 5 5 0.90 26 0.192
12 A 10 10 0.93 26 0.385
13 A 9 9 0.76 26 0.346
14 A 7 7 0.92 26 0.269
15 A 5 5 0.99 24 0.208
16 A 5 5 0.91 26 0.192
17 A 3 3 0.91 26 0.115
18 A 3 3 0.92 26 0.115
19 A 3 3 0.92 26 0.115
20 A 3 3 0.91 26 0.115
21 A 5 5 1.00 26 0.192
22 A 5 5 0.89 26 0.192
23 A 3 3 0.91 26 0.115
24 A 3 3 0.93 26 0.115
25 A 3 3 0.92 24 0.125
26 A 8 8 0.96 26 0.308
27 A 7 7 0.74 26 0.269
28 A 11 11 1.02 26 0.423
29 A 5 5 0.88 26 0.192
30 A 5 5 0.89 26 0.192
31 A 5 5 0.88 26 0.192
32 A 3 3 0.91 26 0.115
33 A 3 3 0.92 26 0.115
34 A 3 3 0.92 26 0.115
35 A 3 3 0.91 24 0.125
36 A 5 5 0.91 26 0.192
37 A 11 11 1.01 26 0.423
38 A 9 9 0.79 26 0.346
39 A 14 14 0.98 26 0.538
40 A 5 5 0.89 26 0.192
41 A 5 5 0.87 26 0.192
42 A 7 6 0.90 28 0.214
43 A 7 6 0.91 28 0.214
44 A 7 6 0.94 28 0.214
45 A 7 6 1.03 26 0.231
46 A 7 6 0.91 28 0.214
47 A 8 7 0.92 28 0.250
48 A 9 8 0.91 28 0.286
49 A 10 9 0.90 28 0.321
50 A 8 7 0.87 28 0.250
51 A 8 7 0.88 28 0.250
52 A 8 7 0.93 26 0.269
53 A 7 6 0.93 28 0.214
54 A 8 7 0.91 28 0.250
55 A 9 8 0.92 28 0.286
56 A 10 9 0.91 28 0.321
57 A 7 6 0.85 28 0.214
58 A 7 6 0.86 28 0.214
59 A 7 6 0.90 26 0.231
60 A 7 6 0.87 28 0.214
61 A 7 6 0.95 28 0.214
62 A 7 6 0.88 28 0.214
63 A 7 6 0.90 28 0.214
64 A 7 6 0.89 28 0.214
65 A 13 12 1.02 28 0.429
66 A 11 10 1.02 28 0.357
67 A 8 7 1.01 28 0.250
68 A 7 6 0.98 26 0.231
69 A 10 9 0.98 28 0.321
70 A 11 10 0.94 28 0.357
71 A 13 12 0.93 28 0.429
72 A 13 12 1.05 28 0.429
73 A 11 10 1.05 28 0.357
74 A 9 8 1.19 28 0.286
75 A 8 7 1.29 26 0.269
76 A 11 10 0.99 28 0.357
77 A 14 13 0.98 28 0.464
78 A 16 15 0.97 28 0.536
79 A 16 15 1.08 28 0.536
80 A 14 13 1.08 28 0.464
81 A 11 10 1.11 28 0.357
82 A 11 10 1.07 28 0.357
83 A 10 9 1.38 26 0.346
84 A 15 14 1.00 28 0.500
85 A 16 15 0.99 28 0.536
86 A 11 11 1.01 30 0.367
87 A 9 9 1.01 30 0.300
88 A 7 7 1.00 30 0.233
89 A 5 5 1.00 30 0.167
90 A 4 3 1.00 30 0.100
91 A 6 5 1.00 30 0.167
92 A 8 7 1.01 30 0.233
93 A 10 9 1.02 30 0.300
94 A 11 11 0.99 30 0.367
95 A 7 7 0.67 30 0.233
96 A 7 7 1.00 30 0.233
97 A 6 5 0.62 30 0.167
98 A 6 5 1.00 30 0.167
99 A 8 7 0.99 30 0.233
100 A 10 9 0.99 30 0.300
101 A 9 9 0.56 30 0.300
102 A 11 11 0.99 30 0.367
103 A 9 9 1.01 30 0.300
104 A 6 5 0.47 30 0.167
105 A 7 7 1.00 30 0.233
106 A 6 5 1.00 30 0.167
107 A 8 7 1.01 30 0.233
108 A 10 9 1.01 30 0.300
109 A 12 11 1.00 30 0.367
110 A 6 5 0.40 30 0.167
111 A 6 5 0.45 30 0.167
112 A 6 5 0.61 30 0.167
113 A 4 3 1.00 30 0.100
114 A 6 6 1.04 30 0.200
115 A 6 5 0.57 30 0.167
116 A 6 5 0.41 30 0.167
117 A 6 5 0.40 30 0.167
118 A 7 7 1.00 30 0.233
119 A 6 5 1.00 30 0.167
120 A 6 5 1.00 30 0.167
121 A 6 5 0.43 30 0.167
122 A 10 10 0.70 30 0.333
123 A 6 5 0.37 30 0.167
124 A 6 5 0.40 30 0.167
125 A 6 5 1.00 30 0.167
126 A 8 7 0.99 30 0.233
127 A 8 7 1.01 30 0.233
128 A 6 5 0.40 30 0.167
129 A 6 5 0.37 30 0.167
130 A 14 14 0.58 30 0.467
131 A 4 3 1.00 24 0.125
132 A 5 4 1.00 26 0.154
133 A 5 4 1.00 26 0.154
134 A 5 4 1.00 26 0.154
135 A 5 4 1.00 24 0.167
136 A 5 4 1.00 26 0.154
137 A 5 4 1.00 26 0.154
138 A 6 5 0.90 28 0.179
139 A 6 5 1.00 28 0.179
140 A 4 3 1.00 28 0.107
141 A 7 6 1.06 28 0.214
142 A 9 8 0.95 28 0.286
143 A 9 8 0.99 27 0.296
144 A 5 5 1.00 27 0.185
145 A 5 5 1.00 27 0.185
146 A 9 9 1.02 27 0.333
147 A 5 4 0.78 27 0.148
148 A 5 4 0.81 27 0.148
149 A 5 4 0.88 27 0.148
150 A 7 6 1.00 25 0.240
151 A 8 7 1.00 27 0.259
152 A 9 8 0.89 27 0.296
153 A 11 10 0.93 27 0.370
154 A 11 10 0.96 27 0.370
155 A 9 8 0.97 27 0.296
156 A 10 9 1.03 25 0.360
157 A 8 7 1.00 27 0.259
158 A 10 9 0.90 27 0.333
159 A 12 11 0.93 27 0.407
160 A 6 5 0.76 27 0.185
161 A 6 5 0.77 27 0.185
162 A 13 12 1.06 25 0.480
163 A 6 5 0.80 27 0.185
164 A 6 5 0.75 27 0.185
165 A 6 5 0.76 27 0.185
166 A 6 5 0.76 27 0.185
167 A 6 5 0.78 27 0.185
168 A 8 7 1.00 25 0.280
169 A 12 11 1.07 27 0.407
170 A 6 5 0.72 27 0.185
171 A 6 5 0.75 27 0.185
172 A 6 5 0.72 27 0.185
173 A 6 5 0.71 27 0.185
174 A 11 10 1.05 25 0.400
175 A 6 5 0.69 27 0.185
176 A 6 5 0.70 27 0.185
177 A 6 5 0.72 27 0.185
178 A 6 5 0.72 27 0.185
179 A 6 5 0.71 27 0.185
180 A 14 13 1.07 25 0.520
181 A 6 5 0.71 27 0.185
182 A 6 5 0.71 27 0.185
183 A 6 5 0.73 27 0.185
184 A 8 7 1.00 29 0.241
185 A 4 3 1.00 29 0.103
186 A 8 7 1.00 29 0.241
187 A 8 7 1.00 29 0.241
188 A 8 7 1.00 29 0.241
189 A 8 7 1.00 23 0.304
190 A 11 10 1.23 23 0.435
191 A 14 13 1.23 23 0.565
192 A 11 10 1.19 25 0.400
193 A 13 12 1.14 25 0.480
194 A 16 15 1.15 25 0.600
195 A 13 12 1.19 25 0.480
196 A 15 14 1.12 25 0.560
197 A 19 18 1.10 25 0.720
198 A 8 8 1.00 25 0.320
199 A 5 5 1.00 27 0.185
200 A 11 11 1.00 25 0.440
201 A 8 8 1.01 27 0.296
202 A 14 14 1.01 25 0.560
203 A 5 5 1.00 25 0.200
204 A 5 5 1.00 27 0.185
205 A 11 11 1.08 25 0.440
206 A 14 14 1.05 25 0.560
207 A 5 5 1.00 29 0.172
208 A 2 2 1.00 29 0.069
209 A 8 8 1.00 29 0.276
210 A 13 13 0.92 29 0.448
211 A 10 10 0.93 29 0.345
212 A 13 13 0.92 29 0.448
213 A 17 17 0.94 29 0.586
214 A 13 13 0.96 29 0.448
215 A 16 16 0.94 29 0.552
216 A 19 19 0.95 29 0.655
217 F 0 0 N/A 0.000 N/A
218 A 2 2 1.00 29 0.069
219 A 5 5 1.00 29 0.172
220 A 11 11 1.10 29 0.379
221 N/A 4 0 1.00 29 0.000
222 N/A 2 0 1.00 29 0.000
223 N/A 2 0 1.00 29 0.000
224 N/A 4 0 1.00 29 0.000
225 N/A 2 0 1.00 29 0.000
226 N/A 2 0 1.00 29 0.000
227 N/A 4 0 1.00 29 0.000
228 N/A 2 0 1.00 29 0.000
229 N/A 2 0 1.00 29 0.000
230 A 8 7 1.00 27 0.259
231 A 12 12 1.10 27 0.444
232 A 13 13 1.11 27 0.481
233 A 8 8 1.13 25 0.320
234 A 10 10 1.13 27 0.370
235 A 13 13 1.08 27 0.481
236 N/A 4 0 1.00 27 0.000
237 A 15 15 1.09 27 0.556
238 A 13 13 1.08 27 0.481
239 A 8 8 1.13 25 0.320
240 A 11 10 1.07 27 0.370
241 A 7 7 1.02 27 0.259

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