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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 [123] had the largest ratio of [2.07691999999999988]

# 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 2 2 1.00 6 0.333
2 A 4 3 1.00 8 0.375
3 A 4 4 1.00 8 0.500
4 C 4 3 1.23 8 0.375
5 A 6 6 1.09 8 0.750
6 C 4 3 1.12 8 0.375
7 C 4 3 1.42 6 0.500
8 C 4 3 1.14 6 0.500
9 A 6 6 1.00 10 0.600
10 A 6 6 1.00 10 0.600
11 A 4 4 1.00 10 0.400
12 A 4 4 1.00 10 0.400
13 A 6 6 1.00 10 0.600
14 A 6 6 1.00 10 0.600
15 A 8 8 1.02 12 0.667
16 A 6 6 1.00 12 0.500
17 A 6 6 1.00 12 0.500
18 A 4 4 1.00 12 0.333
19 A 4 4 1.00 12 0.333
20 A 6 6 1.00 12 0.500
21 A 6 6 1.00 12 0.500
22 A 8 8 1.08 12 0.667
23 A 4 4 1.00 10 0.400
24 A 7 6 1.16 12 0.500
25 A 6 5 1.12 12 0.417
26 A 5 4 1.05 12 0.333
27 A 4 3 1.00 12 0.250
28 A 4 3 1.18 12 0.250
29 A 5 4 1.12 12 0.333
30 A 6 5 1.16 12 0.417
31 A 7 6 1.18 12 0.500
32 A 7 6 1.20 10 0.600
33 A 6 5 1.15 10 0.500
34 A 5 4 1.12 10 0.400
35 A 4 3 1.23 10 0.300
36 A 5 4 1.31 10 0.400
37 A 6 5 1.40 10 0.500
38 A 7 6 1.45 10 0.600
39 A 14 14 0.88 10 1.400
40 A 10 10 1.09 10 1.000
41 A 8 8 1.15 10 0.800
42 A 8 8 1.19 10 0.800
43 A 10 10 1.00 10 1.000
44 A 14 14 0.92 10 1.400
45 C 6 5 0.52 10 0.500
46 C 6 5 0.58 10 0.500
47 C 6 5 0.75 10 0.500
48 A 6 5 1.00 10 0.500
49 A 5 5 0.81 10 0.500
50 A 9 9 0.72 10 0.900
51 A 13 13 0.70 10 1.300
52 A 16 15 1.05 13 1.154
53 C 16 15 1.35 13 1.154
54 A 11 11 0.96 13 0.846
55 A 12 11 1.12 11 1.000
56 C 19 18 1.27 11 1.636
57 A 13 12 1.00 13 0.923
58 C 23 22 1.28 13 1.692
59 C 16 15 1.18 13 1.154
60 A 15 14 1.19 13 1.077
61 A 12 11 1.00 13 0.846
62 A 14 13 1.18 13 1.000
63 A 12 11 0.95 11 1.000
64 A 14 13 1.11 11 1.182
65 A 11 10 1.17 13 0.769
66 A 15 14 1.51 13 1.077
67 A 16 15 1.22 13 1.154
68 C 13 12 1.13 13 0.923
69 C 11 10 1.13 13 0.769
70 A 9 9 1.02 13 0.692
71 A 8 8 1.04 11 0.727
72 A 2 2 1.00 11 0.182
73 A 5 5 1.00 13 0.385
74 A 7 7 1.00 13 0.538
75 A 11 10 1.04 13 0.769
76 A 3 3 1.00 12 0.250
77 A 3 3 1.00 13 0.231
78 A 10 9 1.04 14 0.643
79 A 7 6 1.00 14 0.429
80 A 4 3 1.00 14 0.214
81 A 8 7 1.00 14 0.500
82 A 11 10 1.05 14 0.714
83 A 4 3 1.00 15 0.200
84 A 8 7 1.00 15 0.467
85 A 4 3 1.00 10 0.300
86 A 4 3 1.00 10 0.300
87 A 5 5 1.07 12 0.417
88 A 3 3 1.01 12 0.250
89 A 7 6 1.00 12 0.500
90 A 1 1 1.00 10 0.100
91 A 6 5 1.00 12 0.417
92 A 11 10 1.23 12 0.833
93 A 14 13 1.25 12 1.083
94 A 2 2 1.00 14 0.143
95 A 18 17 1.17 13 1.308
96 A 16 15 1.15 13 1.154
97 A 13 12 1.13 13 0.923
98 A 10 9 1.05 11 0.818
99 A 6 5 1.00 11 0.455
100 A 9 8 1.00 13 0.615
101 A 11 10 1.05 13 0.769
102 A 13 12 1.11 13 0.923
103 A 11 11 1.19 13 0.846
104 A 7 6 0.72 13 0.462
105 A 6 6 1.13 13 0.462
106 A 7 6 1.07 13 0.462
107 A 4 4 1.07 13 0.308
108 A 5 4 1.00 11 0.364
109 A 7 6 0.90 11 0.545
110 A 10 10 1.11 13 0.769
111 A 7 6 0.84 13 0.462
112 A 12 12 1.16 13 0.923
113 A 6 5 1.04 13 0.385
114 A 8 8 1.00 13 0.615
115 A 6 5 1.07 13 0.385
116 A 12 11 1.21 13 0.846
117 A 6 5 1.23 13 0.385
118 A 15 14 1.19 13 1.077
119 A 7 6 1.16 11 0.545
120 A 6 5 1.23 11 0.455
121 A 18 17 0.91 13 1.308
122 A 6 5 1.23 13 0.385
123 C 28 27 0.87 13 2.077
124 A 6 5 1.19 13 0.385
125 A 8 7 0.78 23 0.304
126 A 7 6 0.81 23 0.261
127 A 7 6 0.98 21 0.286
128 A 7 6 1.11 21 0.286
129 A 14 13 1.75 23 0.565
130 A 14 14 1.00 23 0.609
131 A 2 2 1.00 14 0.143
132 A 4 4 1.00 23 0.174
133 A 8 7 0.83 23 0.304
134 A 7 6 0.90 23 0.261
135 A 6 5 1.00 21 0.238
136 A 7 6 1.11 21 0.286
137 A 8 7 1.55 23 0.304
138 A 3 3 1.00 23 0.130
139 A 11 11 1.00 23 0.478
140 A 2 2 1.00 14 0.143
141 A 4 4 1.00 23 0.174
142 A 8 7 0.80 23 0.304
143 A 7 6 0.90 23 0.261
144 A 7 6 0.98 21 0.286
145 F 0 0 N/A 0.000 N/A
146 A 8 7 1.43 23 0.304
147 A 3 3 1.00 23 0.130
148 A 14 14 1.11 23 0.609
149 A 11 11 1.08 14 0.786
150 A 4 4 1.00 23 0.174
151 A 7 6 0.55 25 0.240
152 A 7 6 0.62 25 0.240
153 A 5 4 1.00 25 0.160
154 A 5 4 1.00 25 0.160
155 A 6 5 0.80 25 0.200
156 A 7 6 0.46 25 0.240
157 A 7 6 0.41 25 0.240
158 A 7 6 1.38 15 0.400
159 A 4 3 0.96 15 0.200
160 A 9 8 1.19 15 0.533
161 A 7 6 1.07 15 0.400
162 A 6 5 1.39 13 0.385
163 A 7 6 1.08 11 0.545
164 A 6 5 1.00 15 0.333
165 A 6 5 1.00 15 0.333
166 A 7 6 1.39 15 0.400
167 A 4 3 1.22 15 0.200
168 A 6 5 1.49 15 0.333
169 A 9 8 1.03 15 0.533
170 A 8 7 1.26 15 0.467
171 A 4 3 0.96 15 0.200
172 A 10 9 1.07 15 0.600
173 A 8 7 1.09 15 0.467
174 A 7 6 1.34 15 0.400
175 A 8 7 0.99 15 0.467
176 A 9 8 1.14 13 0.615
177 A 8 7 1.00 11 0.636
178 A 8 7 1.00 15 0.467
179 A 4 3 1.20 15 0.200
180 A 6 5 1.32 15 0.333
181 A 7 6 0.97 15 0.400
182 A 5 4 0.89 11 0.364
183 A 5 4 0.97 13 0.308
184 A 5 4 0.99 13 0.308
185 A 5 4 0.97 13 0.308
186 C 1 1 3.48 44 0.023
187 A 4 3 1.04 15 0.200
188 A 5 4 1.00 15 0.267
189 A 4 3 1.08 20 0.150
190 A 4 3 1.63 21 0.143
191 A 4 3 1.00 15 0.200
192 A 5 4 1.00 17 0.235
193 A 6 5 0.96 17 0.294
194 C 5 4 1.07 17 0.235
195 A 8 7 1.00 17 0.412
196 A 8 7 0.98 19 0.368
197 A 8 7 0.98 19 0.368
198 A 6 5 1.00 19 0.263
199 A 6 5 1.00 19 0.263
200 A 8 7 0.98 19 0.368
201 A 8 7 0.98 19 0.368

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