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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 [88] had the largest ratio of [1.19999999999999996]

# 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 9 8 0.96 10 0.800
2 A 7 6 0.93 10 0.600
3 A 8 7 1.06 8 0.875
4 A 4 3 0.95 6 0.500
5 A 9 8 1.00 10 0.800
6 A 6 5 1.06 10 0.500
7 A 8 7 1.09 10 0.700
8 A 11 10 1.14 10 1.000
9 C 10 9 1.09 14 0.643
10 C 9 8 1.09 15 0.533
11 A 9 8 0.93 21 0.381
12 A 8 7 0.92 21 0.333
13 A 7 6 0.93 21 0.286
14 A 6 5 0.96 19 0.263
15 A 1 1 1.00 10 0.100
16 C 11 10 1.09 21 0.476
17 A 6 5 0.91 21 0.238
18 A 5 4 0.92 21 0.190
19 A 7 6 0.93 21 0.286
20 A 7 6 0.93 21 0.286
21 A 9 8 0.93 21 0.381
22 A 10 9 0.88 23 0.391
23 A 9 8 0.89 23 0.348
24 A 8 7 0.89 23 0.304
25 A 7 6 0.94 21 0.286
26 A 5 4 1.03 12 0.333
27 C 12 11 1.09 23 0.478
28 A 9 8 0.84 23 0.348
29 A 6 5 0.88 23 0.217
30 A 11 10 0.83 23 0.435
31 A 18 17 1.14 23 0.739
32 A 15 14 1.05 23 0.609
33 A 11 10 0.99 23 0.435
34 A 9 8 0.94 21 0.381
35 A 5 4 0.96 12 0.333
36 C 13 12 1.08 23 0.522
37 A 10 9 0.82 23 0.391
38 C 13 12 0.95 23 0.522
39 A 14 13 0.84 23 0.565
40 A 13 12 1.08 23 0.522
41 A 14 13 1.01 23 0.565
42 A 10 9 0.94 21 0.429
43 A 7 6 0.97 12 0.500
44 C 14 13 1.10 23 0.565
45 A 11 10 0.82 23 0.435
46 C 14 13 0.99 23 0.565
47 A 15 14 0.83 23 0.609
48 A 7 6 0.79 23 0.261
49 A 7 6 0.82 23 0.261
50 A 7 6 0.82 23 0.261
51 C 15 14 0.99 21 0.667
52 C 12 11 1.05 12 0.917
53 N/A 4 0 1.00 23 0.000
54 A 5 4 0.82 23 0.174
55 A 5 4 0.85 23 0.174
56 A 5 4 0.85 23 0.174
57 A 12 11 0.94 21 0.524
58 A 11 10 0.94 12 0.833
59 N/A 4 0 1.00 23 0.000
60 A 9 8 1.19 23 0.348
61 C 18 17 1.15 23 0.739
62 C 19 18 1.12 23 0.783
63 C 18 17 0.98 21 0.810
64 C 14 13 1.00 12 1.083
65 N/A 4 0 1.00 23 0.000
66 A 7 6 1.16 23 0.261
67 A 15 14 1.07 23 0.609
68 A 16 15 1.06 23 0.652
69 A 15 14 0.94 21 0.667
70 A 13 12 0.98 12 1.000
71 N/A 4 0 1.00 23 0.000
72 A 8 7 0.92 25 0.280
73 A 8 7 0.91 25 0.280
74 A 8 7 0.93 25 0.280
75 A 8 7 0.95 23 0.304
76 A 10 9 1.00 14 0.643
77 N/A 4 0 1.00 25 0.000
78 C 21 20 1.24 25 0.800
79 C 18 17 1.21 25 0.680
80 C 16 15 1.02 23 0.652
81 C 12 11 1.03 14 0.786
82 N/A 4 0 1.00 25 0.000
83 A 13 12 1.18 25 0.480
84 A 17 16 1.14 25 0.640
85 A 11 10 0.96 23 0.435
86 A 12 11 0.98 14 0.786
87 N/A 4 0 1.00 25 0.000
88 C 31 30 1.37 25 1.200
89 C 19 18 0.99 23 0.783
90 C 14 13 1.00 14 0.929
91 N/A 4 0 1.00 25 0.000
92 A 7 6 0.92 25 0.240
93 A 7 6 0.94 25 0.240
94 A 7 6 0.93 25 0.240
95 C 13 12 1.08 23 0.522
96 C 10 9 1.09 14 0.643
97 N/A 4 0 1.00 25 0.000
98 A 5 4 0.92 25 0.160
99 A 5 4 0.94 25 0.160
100 A 5 4 0.94 25 0.160
101 A 11 10 1.03 23 0.435
102 A 10 9 1.05 14 0.643
103 N/A 4 0 1.00 25 0.000
104 A 9 8 1.38 25 0.320
105 C 16 15 1.31 25 0.600
106 C 17 16 1.26 25 0.640
107 C 16 15 1.03 23 0.652
108 C 12 11 1.06 14 0.786
109 N/A 4 0 1.00 25 0.000
110 A 7 6 1.29 25 0.240
111 A 14 13 1.23 25 0.520
112 A 15 14 1.18 25 0.560
113 A 14 13 1.02 23 0.565
114 A 12 11 1.04 14 0.786
115 N/A 4 0 1.00 25 0.000
116 A 9 8 1.03 23 0.348
117 A 8 7 1.03 23 0.304
118 A 7 6 1.02 23 0.261
119 A 6 5 0.98 23 0.217
120 A 5 4 0.98 23 0.174
121 A 9 8 0.99 23 0.348
122 A 8 7 1.02 23 0.304
123 A 4 3 1.01 25 0.120
124 A 4 3 1.01 25 0.120
125 A 4 3 1.01 25 0.120
126 A 4 3 0.99 25 0.120
127 A 4 3 0.99 25 0.120
128 A 4 3 0.98 25 0.120
129 N/A 4 0 1.00 25 0.000
130 N/A 4 0 1.00 25 0.000
131 N/A 4 0 1.00 25 0.000
132 N/A 4 0 1.00 25 0.000
133 N/A 4 0 1.00 25 0.000
134 N/A 4 0 1.00 23 0.000
135 N/A 4 0 1.00 23 0.000
136 A 4 3 0.96 23 0.130
137 A 6 5 1.09 21 0.238
138 N/A 3 0 1.00 23 0.000
139 N/A 3 0 1.00 23 0.000
140 C 8 7 1.24 10 0.700
141 A 8 7 1.07 10 0.700
142 A 7 6 1.03 8 0.750
143 A 6 5 1.02 6 0.833
144 C 8 7 1.41 10 0.700
145 A 3 3 1.00 10 0.300
146 A 4 4 1.07 10 0.400
147 A 3 3 1.00 4 0.750
148 C 8 7 1.13 10 0.700
149 A 3 3 1.00 14 0.214
150 A 2 2 1.02 14 0.143
151 A 2 2 1.00 14 0.143
152 A 1 1 1.11 12 0.083
153 A 1 1 1.00 14 0.071
154 A 1 1 1.00 14 0.071
155 A 2 2 1.02 14 0.143
156 A 3 3 1.00 14 0.214
157 A 2 2 0.97 14 0.143
158 A 2 2 1.00 14 0.143
159 A 1 1 1.00 12 0.083
160 A 1 1 1.00 14 0.071
161 A 1 1 1.00 14 0.071
162 A 2 2 1.02 14 0.143
163 A 2 2 1.01 16 0.125
164 A 2 2 1.02 16 0.125
165 A 1 1 1.00 16 0.062
166 A 1 1 1.00 16 0.062
167 A 1 1 1.00 16 0.062
168 A 2 2 1.01 16 0.125
169 A 2 2 1.00 16 0.125
170 A 2 2 1.01 16 0.125
171 A 2 2 1.02 16 0.125
172 A 1 1 1.00 16 0.062
173 A 1 1 1.00 16 0.062
174 A 1 1 1.00 16 0.062
175 A 2 2 1.01 16 0.125
176 A 2 2 1.00 16 0.125
177 N/A 1 0 1.00 40 0.000
178 C 12 11 0.93 40 0.275
179 C 11 10 0.97 40 0.250
180 C 10 9 1.02 38 0.237
181 N/A 1 0 1.00 40 0.000
182 N/A 1 0 1.00 40 0.000
183 C 9 8 1.08 10 0.800
184 C 10 9 1.07 19 0.474
185 A 4 3 1.00 20 0.150
186 A 5 4 0.93 12 0.333
187 A 5 4 0.91 14 0.286
188 A 6 5 1.23 10 0.500
189 A 3 2 1.00 26 0.077
190 A 3 2 1.00 26 0.077

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