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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 [114] had the largest ratio of [1.26086999999999994]

# 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 4 0.90 19 0.211
2 A 5 4 0.93 19 0.211
3 A 5 4 0.97 17 0.235
4 A 5 4 1.00 17 0.235
5 A 5 4 0.89 19 0.211
6 A 5 4 0.85 19 0.211
7 A 5 4 0.84 19 0.211
8 A 3 3 1.00 19 0.158
9 A 3 3 1.00 19 0.158
10 A 9 9 1.23 19 0.474
11 A 3 3 1.00 19 0.158
12 A 3 3 1.05 19 0.158
13 A 3 3 1.04 19 0.158
14 A 5 4 0.91 21 0.190
15 A 5 4 0.90 21 0.190
16 A 5 4 0.92 19 0.211
17 A 4 3 1.00 21 0.143
18 A 5 4 0.86 21 0.190
19 A 3 3 1.06 21 0.143
20 A 9 9 1.07 21 0.429
21 A 3 3 0.89 21 0.143
22 A 2 2 1.00 12 0.167
23 A 3 3 1.05 21 0.143
24 A 3 3 1.04 21 0.143
25 A 5 4 0.89 21 0.190
26 A 5 4 0.89 21 0.190
27 A 5 4 0.90 19 0.211
28 A 5 4 0.88 21 0.190
29 A 18 17 1.04 21 0.810
30 A 3 3 1.03 21 0.143
31 A 3 3 0.93 21 0.143
32 A 3 3 1.00 12 0.250
33 A 3 3 1.04 21 0.143
34 A 5 4 0.88 21 0.190
35 A 5 4 0.88 21 0.190
36 A 5 4 0.89 19 0.211
37 A 5 4 0.88 21 0.190
38 A 3 3 0.88 21 0.143
39 A 3 3 1.04 21 0.143
40 A 3 3 1.00 12 0.250
41 A 3 3 1.03 21 0.143
42 A 3 3 1.03 21 0.143
43 A 3 3 1.02 21 0.143
44 A 15 14 1.05 21 0.667
45 A 13 12 1.04 21 0.571
46 A 11 10 1.02 21 0.476
47 A 9 8 1.57 19 0.421
48 A 6 5 1.06 19 0.263
49 A 8 7 1.00 21 0.333
50 A 9 8 0.92 21 0.381
51 A 10 9 0.84 21 0.429
52 A 10 9 0.80 21 0.429
53 A 9 8 0.81 21 0.381
54 A 9 8 0.84 21 0.381
55 A 8 7 0.96 21 0.333
56 A 2 2 1.00 12 0.167
57 A 7 6 1.00 21 0.286
58 A 9 8 1.00 21 0.381
59 A 11 10 1.02 21 0.476
60 A 13 12 1.04 21 0.571
61 A 5 4 0.87 21 0.190
62 A 5 4 0.87 21 0.190
63 A 5 4 0.88 21 0.190
64 A 5 4 0.90 19 0.211
65 A 5 4 0.96 19 0.211
66 A 5 4 0.94 21 0.190
67 A 5 4 0.91 21 0.190
68 A 5 4 0.89 21 0.190
69 A 5 4 0.87 21 0.190
70 A 5 4 0.86 21 0.190
71 A 5 4 0.85 21 0.190
72 A 5 4 0.87 21 0.190
73 A 5 4 0.87 21 0.190
74 A 5 4 0.89 19 0.211
75 A 5 4 0.93 19 0.211
76 A 5 4 0.91 21 0.190
77 A 5 4 0.90 21 0.190
78 A 5 4 0.89 21 0.190
79 A 5 4 0.87 21 0.190
80 A 5 4 0.86 21 0.190
81 A 5 4 0.86 21 0.190
82 A 5 4 0.86 21 0.190
83 A 5 4 0.87 21 0.190
84 A 5 4 0.88 19 0.211
85 A 5 4 0.89 21 0.190
86 A 5 4 0.88 21 0.190
87 A 3 3 1.03 21 0.143
88 A 3 3 1.04 21 0.143
89 A 3 3 0.88 21 0.143
90 A 3 3 1.03 21 0.143
91 A 6 6 1.20 23 0.261
92 A 9 8 1.06 23 0.348
93 A 9 8 1.11 23 0.348
94 A 14 13 1.07 23 0.565
95 A 8 8 1.17 23 0.348
96 A 7 7 1.06 23 0.304
97 A 12 11 1.11 23 0.478
98 A 17 16 1.06 23 0.696
99 A 10 10 1.40 23 0.435
100 A 9 9 1.11 23 0.391
101 A 15 14 1.12 23 0.609
102 A 22 21 1.21 23 0.913
103 A 8 7 1.61 23 0.304
104 A 9 8 1.02 23 0.348
105 A 7 6 1.00 23 0.261
106 A 21 20 1.87 23 0.870
107 A 10 9 1.10 23 0.391
108 A 11 10 1.09 23 0.435
109 A 11 10 1.07 23 0.435
110 A 19 18 1.82 23 0.783
111 A 12 11 1.66 23 0.478
112 A 13 12 1.05 23 0.522
113 A 14 13 1.08 23 0.565
114 A 30 29 1.97 23 1.261
115 A 16 15 1.02 23 0.652
116 A 9 9 1.07 23 0.391
117 A 7 6 1.70 23 0.261
118 A 7 6 1.70 23 0.261
119 A 12 11 1.07 23 0.478
120 A 9 9 1.06 23 0.391
121 A 7 6 1.70 23 0.261
122 A 7 6 1.70 23 0.261
123 A 3 3 1.00 23 0.130
124 A 3 3 1.00 23 0.130
125 A 3 3 1.00 21 0.143
126 A 7 6 1.00 23 0.261
127 A 3 3 1.03 23 0.130
128 A 3 3 1.02 23 0.130
129 A 6 5 1.41 23 0.217
130 A 8 7 1.02 21 0.333
131 A 5 4 1.04 19 0.211
132 A 4 3 1.00 19 0.158
133 A 5 4 0.98 21 0.190
134 A 8 7 1.00 21 0.333
135 A 12 11 1.10 21 0.524
136 A 9 8 1.03 21 0.381
137 A 4 4 1.00 12 0.333
138 A 6 5 1.10 21 0.238
139 A 6 5 1.10 21 0.238
140 A 6 5 1.13 19 0.263
141 A 5 4 0.84 17 0.235
142 A 5 4 1.00 17 0.235
143 A 5 4 0.89 19 0.211
144 A 5 4 0.85 19 0.211
145 A 3 3 1.00 19 0.158
146 A 3 3 1.00 19 0.158
147 A 3 3 1.00 19 0.158
148 A 3 3 1.05 19 0.158
149 A 3 3 1.04 19 0.158
150 A 7 6 1.11 21 0.286
151 A 7 6 0.90 19 0.316
152 A 5 4 0.93 19 0.211
153 A 5 4 0.89 21 0.190
154 A 5 4 0.88 21 0.190
155 A 3 3 1.04 21 0.143
156 A 3 3 1.06 21 0.143
157 A 3 3 1.00 21 0.143
158 A 3 3 1.05 21 0.143
159 A 3 3 1.05 21 0.143
160 A 7 6 1.05 21 0.286
161 A 7 6 0.99 19 0.316
162 A 5 4 0.91 19 0.211
163 A 5 4 0.90 21 0.190
164 A 5 4 0.89 21 0.190
165 A 3 3 1.04 21 0.143
166 A 3 3 1.03 21 0.143
167 A 3 3 1.00 21 0.143
168 A 3 3 1.04 21 0.143
169 A 3 3 1.07 21 0.143
170 A 10 9 1.08 21 0.429
171 A 8 7 1.15 21 0.333
172 A 8 7 1.01 19 0.368
173 A 6 5 1.00 19 0.263
174 A 5 4 0.93 21 0.190
175 A 5 4 0.92 21 0.190
176 A 17 16 1.04 21 0.762
177 A 11 10 1.06 21 0.476
178 A 13 12 1.16 21 0.571
179 A 13 12 1.10 21 0.571
180 A 20 19 1.12 21 0.905
181 A 9 8 1.04 21 0.381
182 A 7 6 1.14 21 0.286
183 A 7 6 1.17 19 0.316
184 A 5 4 0.94 19 0.211
185 A 5 4 0.92 21 0.190
186 A 5 4 0.92 21 0.190
187 A 3 3 1.00 21 0.143
188 A 3 3 1.00 21 0.143
189 A 15 14 1.40 21 0.667
190 A 16 15 1.12 21 0.714
191 A 23 22 1.19 21 1.048
192 A 9 8 0.98 21 0.381
193 A 7 6 1.10 21 0.286
194 A 7 6 1.09 19 0.316
195 A 5 4 0.92 19 0.211
196 A 5 4 0.92 21 0.190
197 A 5 4 0.92 21 0.190
198 A 3 3 1.00 21 0.143
199 A 3 3 1.00 21 0.143
200 A 17 16 1.23 21 0.762
201 A 18 17 1.24 21 0.810
202 A 26 25 1.23 21 1.190
203 A 3 3 1.00 23 0.130
204 A 3 3 1.00 23 0.130
205 A 3 3 1.00 21 0.143
206 F 0 0 N/A 0.000 N/A
207 F 0 0 N/A 0.000 N/A
208 N/A 2 0 1.00 23 0.000

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