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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 [112] had the largest ratio of [1.04167000000000010]

# 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 5 0.95 22 0.227
2 A 6 5 0.97 22 0.227
3 A 6 5 1.03 20 0.250
4 A 6 5 0.87 22 0.227
5 A 9 8 0.92 22 0.364
6 A 11 10 0.93 22 0.455
7 A 9 9 1.17 24 0.375
8 A 8 8 1.11 24 0.333
9 A 5 5 1.09 22 0.227
10 A 7 6 0.87 24 0.250
11 A 11 10 0.93 24 0.417
12 A 18 17 1.49 24 0.708
13 A 14 13 1.32 24 0.542
14 A 10 9 1.20 22 0.409
15 A 8 7 0.88 24 0.292
16 A 16 15 0.89 24 0.625
17 A 5 4 0.75 20 0.200
18 A 5 4 0.78 20 0.200
19 A 5 4 0.90 18 0.222
20 N/A 1 0 1.00 20 0.000
21 N/A 1 0 1.00 20 0.000
22 A 5 4 0.84 20 0.200
23 A 5 4 0.88 20 0.200
24 A 5 4 0.98 18 0.222
25 N/A 2 0 1.00 20 0.000
26 N/A 2 0 1.00 20 0.000
27 A 5 4 0.77 24 0.167
28 A 5 4 0.78 24 0.167
29 A 5 4 0.84 22 0.182
30 N/A 1 0 1.00 24 0.000
31 N/A 1 0 1.00 24 0.000
32 A 6 5 0.80 24 0.208
33 A 6 5 0.82 24 0.208
34 A 6 5 0.89 22 0.227
35 N/A 2 0 1.00 24 0.000
36 N/A 2 0 1.00 24 0.000
37 A 8 8 1.07 24 0.333
38 A 6 6 1.07 24 0.250
39 A 3 3 1.00 24 0.125
40 A 1 1 1.00 24 0.042
41 A 2 2 1.00 24 0.083
42 A 4 4 1.04 24 0.167
43 A 6 6 1.08 24 0.250
44 A 10 10 1.20 26 0.385
45 A 5 5 0.98 26 0.192
46 A 1 1 1.00 26 0.038
47 A 8 7 0.99 26 0.269
48 A 11 10 1.00 26 0.385
49 A 3 3 1.00 14 0.214
50 A 1 1 1.00 21 0.048
51 A 8 8 1.06 24 0.333
52 A 6 6 1.10 24 0.250
53 A 3 3 1.00 24 0.125
54 A 1 1 1.00 24 0.042
55 A 2 2 1.00 24 0.083
56 A 4 4 1.03 24 0.167
57 A 6 6 1.06 24 0.250
58 A 10 10 1.12 26 0.385
59 A 5 5 0.88 26 0.192
60 A 1 1 1.00 26 0.038
61 A 8 7 0.72 26 0.269
62 A 11 10 0.87 26 0.385
63 A 14 14 1.04 22 0.636
64 A 6 6 0.79 22 0.273
65 A 1 1 1.00 22 0.045
66 A 9 8 0.65 22 0.364
67 A 13 12 0.76 22 0.545
68 A 5 4 0.47 26 0.154
69 A 5 4 0.51 26 0.154
70 A 5 4 0.59 26 0.154
71 A 1 1 1.00 26 0.038
72 N/A 1 0 1.00 26 0.000
73 N/A 1 0 1.00 26 0.000
74 A 6 5 0.56 26 0.192
75 A 6 5 0.65 26 0.192
76 A 12 11 0.80 26 0.423
77 A 1 1 1.00 26 0.038
78 N/A 2 0 1.00 26 0.000
79 N/A 2 0 1.00 26 0.000
80 A 17 16 1.11 26 0.615
81 A 15 14 0.97 24 0.583
82 A 12 11 0.98 12 0.917
83 N/A 1 0 1.00 26 0.000
84 N/A 4 0 1.00 26 0.000
85 A 19 18 1.25 26 0.692
86 A 17 16 1.29 24 0.667
87 A 12 11 0.97 12 0.917
88 N/A 1 0 1.00 26 0.000
89 N/A 5 0 1.00 26 0.000
90 A 5 4 0.92 26 0.154
91 A 5 4 0.93 26 0.154
92 A 5 4 0.96 24 0.167
93 A 10 9 1.01 12 0.750
94 N/A 1 0 1.00 26 0.000
95 N/A 1 0 1.00 26 0.000
96 A 6 5 0.93 26 0.192
97 A 6 5 0.94 26 0.192
98 A 6 5 1.01 24 0.208
99 A 12 11 1.01 12 0.917
100 N/A 2 0 1.00 26 0.000
101 N/A 2 0 1.00 26 0.000
102 A 13 12 1.15 24 0.500
103 A 9 8 1.00 24 0.333
104 A 1 1 1.00 24 0.042
105 N/A 2 0 1.00 24 0.000
106 N/A 3 0 1.00 24 0.000
107 A 14 13 0.93 24 0.542
108 A 8 7 0.75 24 0.292
109 A 1 1 1.00 24 0.042
110 N/A 2 0 1.00 24 0.000
111 N/A 5 0 1.00 24 0.000
112 A 26 25 1.10 24 1.042
113 A 12 11 0.82 24 0.458
114 A 1 1 1.00 24 0.042
115 N/A 2 0 1.00 24 0.000
116 N/A 5 0 1.00 24 0.000
117 A 14 13 1.15 24 0.542
118 A 9 8 1.00 24 0.333
119 A 1 1 1.00 24 0.042
120 N/A 3 0 1.00 24 0.000
121 N/A 5 0 1.00 24 0.000
122 A 15 14 0.97 24 0.583
123 A 8 7 0.78 24 0.292
124 A 1 1 1.00 24 0.042
125 N/A 3 0 1.00 24 0.000
126 N/A 7 0 1.00 24 0.000
127 A 5 4 0.57 24 0.167
128 A 5 4 0.62 24 0.167
129 A 5 4 0.68 24 0.167
130 A 1 1 1.00 24 0.042
131 N/A 1 0 1.00 24 0.000
132 N/A 1 0 1.00 24 0.000
133 A 5 4 0.72 24 0.167
134 A 5 4 0.84 24 0.167
135 A 8 7 1.00 24 0.292
136 A 1 1 1.00 24 0.042
137 N/A 2 0 1.00 24 0.000
138 N/A 2 0 1.00 24 0.000
139 A 10 9 1.02 24 0.375
140 A 6 5 1.03 24 0.208
141 A 1 1 1.00 24 0.042
142 N/A 2 0 1.00 24 0.000
143 N/A 2 0 1.00 24 0.000
144 A 6 5 1.00 18 0.278
145 A 6 5 1.00 18 0.278
146 A 6 5 1.01 18 0.278
147 A 6 5 1.04 16 0.312
148 A 1 1 1.00 8 0.125
149 A 2 2 1.00 18 0.111
150 A 2 2 1.00 20 0.100
151 A 2 2 1.00 20 0.100
152 A 2 2 1.00 18 0.111
153 A 3 3 1.09 10 0.300
154 A 2 2 1.00 20 0.100
155 A 2 2 1.00 20 0.100
156 A 2 2 1.00 18 0.111
157 A 8 7 0.91 10 0.700
158 N/A 1 0 1.00 20 0.000
159 N/A 1 0 1.00 20 0.000
160 A 2 2 1.00 20 0.100
161 A 2 2 1.00 18 0.111
162 A 10 9 0.97 10 0.900
163 N/A 1 0 1.00 20 0.000
164 N/A 1 0 1.00 20 0.000
165 N/A 1 0 1.00 20 0.000
166 N/A 1 0 1.00 20 0.000
167 A 6 5 1.00 20 0.250
168 A 7 6 1.01 20 0.300
169 A 9 8 1.07 20 0.400
170 N/A 1 0 1.00 22 0.000
171 N/A 1 0 1.00 22 0.000
172 N/A 1 0 1.00 22 0.000
173 N/A 1 0 1.00 22 0.000
174 N/A 1 0 1.00 22 0.000
175 N/A 1 0 1.00 22 0.000
176 N/A 1 0 1.00 22 0.000
177 N/A 1 0 1.00 22 0.000
178 N/A 1 0 1.00 22 0.000
179 N/A 1 0 1.00 22 0.000
180 N/A 1 0 1.00 22 0.000
181 N/A 1 0 1.00 22 0.000
182 A 2 2 1.00 22 0.091
183 A 2 2 1.00 20 0.100
184 A 12 11 0.98 12 0.917
185 N/A 1 0 1.00 22 0.000
186 N/A 1 0 1.00 22 0.000
187 A 2 2 1.00 20 0.100
188 A 12 11 0.97 12 0.917
189 N/A 1 0 1.00 22 0.000
190 N/A 1 0 1.00 22 0.000
191 A 2 2 1.00 22 0.091
192 A 2 2 1.00 20 0.100
193 A 10 9 1.01 12 0.750
194 N/A 1 0 1.00 22 0.000
195 N/A 1 0 1.00 22 0.000
196 A 2 2 1.00 20 0.100
197 A 12 11 1.01 12 0.917
198 N/A 1 0 1.00 22 0.000
199 N/A 1 0 1.00 22 0.000

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