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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 [26] had the largest ratio of [.608696000000000015]

# 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 1.39 34 0.059
2 A 2 2 1.12 34 0.059
3 A 2 2 1.00 32 0.062
4 A 2 2 1.00 34 0.059
5 A 2 2 1.00 34 0.059
6 A 2 2 1.00 34 0.059
7 A 6 6 1.26 35 0.171
8 A 6 6 0.71 36 0.167
9 A 6 6 0.74 36 0.167
10 A 6 6 0.80 36 0.167
11 A 8 7 0.88 36 0.194
12 A 10 9 0.92 36 0.250
13 A 13 12 0.78 36 0.333
14 A 6 6 1.08 34 0.176
15 A 2 2 1.00 23 0.087
16 A 2 2 1.00 23 0.087
17 A 2 2 1.00 21 0.095
18 A 5 5 0.99 23 0.217
19 A 6 6 1.04 23 0.261
20 C 7 6 0.46 25 0.240
21 A 6 5 1.26 23 0.217
22 A 2 2 1.00 23 0.087
23 A 2 2 1.00 23 0.087
24 A 2 2 1.00 21 0.095
25 C 6 6 2.49 23 0.261
26 C 14 14 2.49 23 0.609
27 C 8 7 2.78 25 0.280
28 C 7 6 2.44 23 0.261
29 A 2 2 1.53 36 0.056
30 A 2 2 1.37 36 0.056
31 A 2 2 1.11 36 0.056
32 A 2 2 1.00 34 0.059
33 A 2 2 1.00 36 0.056
34 A 2 2 1.00 36 0.056
35 A 2 2 1.00 36 0.056
36 A 8 7 0.98 38 0.184
37 A 8 7 1.12 38 0.184
38 A 9 8 1.19 38 0.211
39 A 11 10 1.18 38 0.263
40 A 14 13 1.01 38 0.342
41 A 9 8 1.54 36 0.222
42 A 2 2 1.00 25 0.080
43 A 2 2 1.00 25 0.080
44 A 2 2 1.00 23 0.087
45 A 7 6 1.00 25 0.240
46 A 9 8 1.05 25 0.320
47 C 9 8 0.35 27 0.296
48 A 8 7 1.34 25 0.280
49 A 2 2 1.00 25 0.080
50 A 2 2 1.00 25 0.080
51 A 2 2 1.00 23 0.087
52 C 8 7 2.43 25 0.280
53 C 10 9 1.84 25 0.360
54 C 9 8 3.03 25 0.320
55 A 3 3 1.00 40 0.075
56 A 3 3 1.00 38 0.079
57 A 3 3 1.00 40 0.075
58 A 3 3 1.00 40 0.075
59 A 3 3 1.00 40 0.075
60 A 3 3 0.60 42 0.071
61 A 3 3 0.60 42 0.071
62 A 3 3 0.59 42 0.071
63 A 3 3 0.60 42 0.071
64 A 3 3 0.60 42 0.071
65 A 3 3 1.11 20 0.150
66 A 3 3 0.68 40 0.075
67 A 2 2 1.77 38 0.053
68 A 2 2 1.32 38 0.053
69 A 2 2 1.05 38 0.053
70 A 2 2 1.00 36 0.056
71 A 11 10 0.97 38 0.263
72 A 11 10 0.99 38 0.263
73 A 15 14 1.05 38 0.368
74 A 11 10 1.23 43 0.233
75 A 9 8 1.23 43 0.186
76 A 7 6 1.25 43 0.140
77 A 7 6 1.21 43 0.140
78 A 9 8 1.20 43 0.186
79 A 11 10 1.20 43 0.233
80 A 6 5 1.22 41 0.122
81 A 6 5 0.81 34 0.147
82 A 6 5 1.13 35 0.143
83 A 6 5 0.93 34 0.147
84 A 6 5 1.29 35 0.143
85 A 2 2 1.00 34 0.059
86 A 2 2 1.00 34 0.059
87 A 2 2 1.00 32 0.062
88 A 2 2 1.00 34 0.059
89 A 2 2 1.14 34 0.059
90 A 2 2 1.00 22 0.091
91 A 2 2 1.00 28 0.071
92 C 18 17 4.53 30 0.567
93 C 14 13 2.79 30 0.433
94 C 10 9 2.59 30 0.300
95 C 14 13 3.28 30 0.433
96 C 18 17 6.70 30 0.567
97 F 0 0 N/A 0.000 N/A
98 A 1 1 1.00 34 0.029
99 A 1 1 1.00 32 0.031
100 A 1 1 1.00 34 0.029
101 A 1 1 1.00 34 0.029
102 A 1 1 1.00 34 0.029
103 A 1 1 1.00 36 0.028
104 A 1 1 1.00 36 0.028
105 A 1 1 1.00 36 0.028
106 A 1 1 1.00 36 0.028
107 A 1 1 1.00 36 0.028
108 A 1 1 1.00 34 0.029
109 A 2 2 1.28 57 0.035
110 A 2 2 1.01 57 0.035
111 A 2 2 1.00 55 0.036
112 A 2 2 1.00 57 0.035
113 A 2 2 1.00 57 0.035
114 A 2 2 1.00 57 0.035
115 F 0 0 N/A 0.000 N/A
116 F 0 0 N/A 0.000 N/A
117 F 0 0 N/A 0.000 N/A
118 C 17 16 5.29 30 0.533
119 C 13 12 5.55 30 0.400
120 C 9 8 6.53 30 0.267
121 C 13 12 6.03 30 0.400
122 C 17 16 6.10 30 0.533
123 F 0 0 N/A 0.000 N/A
124 F 0 0 N/A 0.000 N/A
125 A 2 2 1.00 43 0.047
126 A 2 2 1.00 41 0.049
127 A 2 2 1.00 43 0.047
128 A 2 2 1.03 43 0.047
129 F 0 0 N/A 0.000 N/A
130 F 0 0 N/A 0.000 N/A
131 F 0 0 N/A 0.000 N/A
132 C 10 9 0.93 30 0.300
133 F 0 0 N/A 0.000 N/A
134 A 2 2 1.07 38 0.053
135 A 2 2 0.76 36 0.056
136 A 1 1 1.00 30 0.033
137 A 2 2 0.91 38 0.053
138 A 2 2 0.91 38 0.053
139 A 7 7 1.19 43 0.163
140 A 5 5 1.04 40 0.125
141 A 5 5 1.06 38 0.132
142 A 5 5 1.10 32 0.156
143 A 5 5 1.07 40 0.125
144 A 5 5 1.08 40 0.125
145 A 5 5 1.05 40 0.125
146 A 5 5 1.03 38 0.132
147 A 5 5 1.05 32 0.156
148 A 5 5 1.04 40 0.125
149 A 5 5 1.05 40 0.125
150 A 4 4 0.78 42 0.095
151 A 4 4 0.86 40 0.100
152 A 4 4 1.01 34 0.118
153 A 7 6 0.86 42 0.143
154 A 7 6 0.86 42 0.143
155 A 4 4 0.93 42 0.095
156 A 6 5 1.01 40 0.125
157 A 5 4 1.31 34 0.118
158 A 7 6 0.93 42 0.143
159 A 9 8 0.95 42 0.190
160 A 9 8 0.91 42 0.190
161 A 8 7 0.93 40 0.175
162 A 8 7 0.98 34 0.206
163 A 13 12 0.95 42 0.286
164 A 15 14 0.97 42 0.333
165 A 2 2 1.00 26 0.077
166 A 2 2 1.00 26 0.077
167 A 2 2 1.00 24 0.083
168 C 7 6 3.10 26 0.231
169 C 15 14 2.18 26 0.538
170 C 8 7 3.65 26 0.269
171 A 2 2 1.00 26 0.077
172 A 2 2 1.00 26 0.077
173 A 2 2 1.00 24 0.083
174 A 7 6 0.96 26 0.231
175 A 9 8 1.03 26 0.308
176 A 8 7 1.34 26 0.269
177 A 2 2 1.00 24 0.083
178 A 3 3 1.00 50 0.060

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