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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 [10] had the largest ratio of [1.50000000000000000]

# 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 11 10 1.02 10 1.000
2 A 11 10 1.12 10 1.000
3 A 9 8 0.99 10 0.800
4 A 9 8 1.13 8 1.000
5 A 7 6 1.02 6 1.000
6 C 9 8 1.23 10 0.800
7 C 11 10 1.41 10 1.000
8 A 7 6 1.12 10 0.600
9 A 11 10 1.19 10 1.000
10 A 16 15 1.07 10 1.500
11 C 16 15 1.08 10 1.500
12 A 11 10 0.94 10 1.000
13 C 12 11 1.12 8 1.375
14 A 8 7 0.94 6 1.167
15 C 10 9 1.20 10 0.900
16 C 13 12 1.39 10 1.200
17 A 12 11 1.15 10 1.100
18 C 15 14 1.37 10 1.400
19 A 9 9 1.08 12 0.750
20 A 6 6 1.23 12 0.500
21 A 7 7 1.06 12 0.583
22 A 4 4 1.26 12 0.333
23 A 5 5 1.03 12 0.417
24 A 2 2 1.00 10 0.200
25 A 1 1 1.00 8 0.125
26 C 10 9 1.39 12 0.750
27 A 2 2 1.00 12 0.167
28 A 7 6 1.02 12 0.500
29 A 4 4 1.26 12 0.333
30 A 9 8 1.03 12 0.667
31 A 6 6 1.20 12 0.500
32 A 11 10 1.04 12 0.833
33 A 11 10 1.06 14 0.714
34 A 9 8 0.94 14 0.571
35 A 9 8 1.11 12 0.667
36 A 7 6 0.96 10 0.600
37 C 9 8 1.19 14 0.571
38 C 11 10 1.30 14 0.714
39 A 7 6 1.02 14 0.429
40 A 11 10 1.11 14 0.714
41 A 8 7 1.05 14 0.500
42 C 16 15 1.04 14 1.071
43 A 11 10 0.93 14 0.714
44 C 12 11 1.08 12 0.917
45 A 8 7 0.91 10 0.700
46 C 10 9 1.14 14 0.643
47 C 13 12 1.27 14 0.857
48 A 12 11 1.12 14 0.786
49 C 15 14 1.29 14 1.000
50 A 15 14 1.30 14 1.000
51 N/A 1 0 1.00 12 0.000
52 N/A 1 0 1.00 10 0.000
53 N/A 1 0 1.00 14 0.000
54 C 10 9 1.17 14 0.643
55 C 12 11 1.05 14 0.786
56 A 4 3 0.94 14 0.214
57 N/A 1 0 1.00 12 0.000
58 N/A 1 0 1.00 10 0.000
59 N/A 1 0 1.00 14 0.000
60 C 12 11 1.20 14 0.786
61 C 14 13 1.09 14 0.929
62 A 4 3 0.95 14 0.214
63 N/A 1 0 1.00 12 0.000
64 N/A 1 0 1.00 10 0.000
65 N/A 1 0 1.00 14 0.000
66 C 16 15 1.24 14 1.071
67 C 18 17 1.16 14 1.214
68 A 4 3 0.95 14 0.214
69 N/A 1 0 1.00 16 0.000
70 N/A 1 0 1.00 16 0.000
71 A 3 3 1.00 14 0.214
72 N/A 1 0 1.00 16 0.000
73 N/A 1 0 1.00 16 0.000
74 A 13 12 0.74 16 0.750
75 A 12 11 0.74 16 0.688
76 A 10 9 0.74 14 0.643
77 A 1 1 1.00 8 0.125
78 A 2 2 1.00 16 0.125
79 A 3 3 0.90 16 0.188
80 A 3 3 0.80 16 0.188
81 A 14 13 0.89 18 0.722
82 A 12 11 0.92 18 0.611
83 A 3 3 0.91 18 0.167
84 A 6 5 1.17 18 0.278
85 A 13 12 0.91 18 0.667
86 A 16 15 0.71 18 0.833
87 N/A 2 0 1.00 16 0.000
88 A 6 6 0.72 19 0.316
89 A 5 5 0.76 19 0.263
90 A 4 4 0.86 16 0.250
91 A 4 4 0.83 19 0.211
92 A 4 4 0.87 19 0.211
93 A 5 5 0.77 19 0.263
94 A 6 6 0.71 19 0.316
95 A 6 5 0.74 19 0.263
96 A 6 5 0.78 19 0.263
97 A 6 5 0.77 17 0.294
98 A 6 5 1.09 19 0.263
99 A 6 5 1.12 19 0.263
100 A 7 7 0.77 21 0.333
101 A 6 6 0.86 18 0.333
102 A 6 6 0.80 21 0.286
103 A 6 6 0.81 21 0.286
104 A 6 6 0.85 21 0.286
105 A 7 7 0.75 21 0.333
106 A 6 5 0.78 21 0.238
107 A 6 5 0.74 19 0.263
108 A 6 5 1.08 21 0.238
109 A 6 5 1.10 21 0.238
110 A 4 3 1.10 21 0.143
111 A 4 3 1.14 19 0.158
112 A 4 3 1.10 18 0.167
113 A 4 3 1.12 21 0.143
114 A 4 3 1.10 21 0.143
115 A 4 3 1.11 21 0.143
116 A 4 3 1.12 21 0.143
117 A 7 6 0.86 19 0.316
118 A 4 3 1.10 21 0.143
119 A 4 3 1.07 21 0.143
120 A 4 3 1.07 21 0.143
121 A 4 3 1.07 18 0.167
122 A 4 3 1.07 21 0.143
123 A 4 3 1.09 21 0.143
124 A 7 6 0.88 21 0.286
125 A 9 8 0.91 19 0.421
126 A 4 3 1.08 21 0.143
127 A 4 3 1.05 21 0.143
128 A 4 3 1.05 21 0.143
129 A 4 3 1.05 18 0.167
130 A 15 14 0.85 23 0.609
131 A 13 12 0.85 23 0.522
132 A 11 10 0.86 21 0.476
133 N/A 1 0 1.00 23 0.000
134 N/A 1 0 1.00 23 0.000
135 N/A 1 0 1.00 23 0.000
136 N/A 1 0 1.00 20 0.000
137 N/A 1 0 1.00 23 0.000
138 A 11 11 0.82 23 0.478
139 A 12 12 0.83 23 0.522
140 A 15 14 0.85 23 0.609
141 A 13 12 0.86 21 0.571
142 N/A 1 0 1.00 23 0.000
143 N/A 1 0 1.00 23 0.000
144 N/A 1 0 1.00 23 0.000
145 N/A 1 0 1.00 20 0.000
146 N/A 1 0 1.00 23 0.000
147 N/A 1 0 1.00 23 0.000
148 A 12 12 0.83 23 0.522
149 A 13 13 0.83 23 0.565
150 A 13 12 0.86 23 0.522
151 A 11 10 0.86 23 0.435
152 A 10 9 0.90 21 0.429
153 N/A 1 0 1.00 23 0.000
154 N/A 1 0 1.00 23 0.000
155 N/A 1 0 1.00 23 0.000
156 N/A 1 0 1.00 20 0.000
157 A 10 10 0.84 23 0.435
158 A 11 11 0.83 23 0.478
159 A 11 10 0.87 23 0.435
160 A 9 8 0.91 23 0.348
161 A 6 5 1.00 21 0.238
162 N/A 1 0 1.00 23 0.000
163 N/A 1 0 1.00 23 0.000
164 N/A 1 0 1.00 23 0.000
165 N/A 1 0 1.00 23 0.000
166 A 4 4 1.00 20 0.200
167 A 11 11 0.86 23 0.478
168 A 11 10 0.84 23 0.435
169 A 8 7 0.88 23 0.304
170 A 7 6 0.88 21 0.286
171 N/A 1 0 1.00 23 0.000
172 N/A 1 0 1.00 23 0.000
173 N/A 1 0 1.00 23 0.000
174 N/A 1 0 1.00 23 0.000
175 A 8 8 0.83 23 0.348
176 A 10 10 0.84 20 0.500
177 A 7 7 0.88 23 0.304
178 A 6 6 0.88 23 0.261
179 A 4 4 0.89 21 0.190
180 N/A 1 0 1.00 23 0.000
181 N/A 1 0 1.00 23 0.000
182 N/A 1 0 1.00 25 0.000
183 N/A 1 0 1.00 25 0.000
184 N/A 1 0 1.00 25 0.000
185 N/A 1 0 1.00 25 0.000
186 A 7 6 0.51 26 0.231
187 A 9 8 0.53 26 0.308
188 A 8 7 0.71 26 0.269
189 N/A 1 0 1.00 26 0.000
190 N/A 1 0 1.00 26 0.000

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