Task: Arithmetic-Relationship (source dataset: Auto-Relate)

You are given a table with numerical values in multiple columns. Your task is to analyze the data and identify semantic relationships, expressed in arithmetic relationships, that exist between columns.

These relationships may involve any combination of the following operations: addition (+), subtraction (−), multiplication (*), and division (/). The expressions can involve two or more columns and may be nested (e.g., B = (A + C) / D).

Please only identify arithmetic relationships that hold semantically based on the data, and do not return relationships that are likely spurious, e.g., (A = B * 0), where A is an all 0 column. Please only return minimal atomic relationships, e.g., if A = B + C and D = E + F, then there is no need to return A = B + C + E + F - D.

No explanation, return all the formula(s) in JSON format: {"Arithmetic-Relationship": [<list-of-formulas>]}. If no relationship is found, return {"Arithmetic-Relationship": []}.

Input Table:
|   A |   B |   C |   D |   E |
|----:|----:|----:|----:|----:|
|   1 |   0 |   1 |   1 |   0 |
|   2 |   1 |   1 |   1 |   0 |
|   3 |   0 |   0 |   0 |   0 |
|   4 |   2 |   2 |   2 |   0 |
|   5 |   1 |   1 |   1 |   0 |
|   6 |   0 |   0 |   0 |   0 |
|   7 |   2 |   2 |   2 |   0 |
|   8 |   3 |   3 |   2 |   1 |
|   9 |   2 |   3 |   2 |   1 |
|  10 |   0 |   1 |   1 |   0 |
|  11 |   1 |   1 |   1 |   0 |
|  12 |   3 |   3 |   2 |   1 |
|  13 |   0 |   1 |   1 |   0 |
|  14 |   1 |   1 |   1 |   0 |
|  15 |   3 |   3 |   2 |   1 |
|  16 |   3 |   4 |   2 |   2 |
|  17 |   1 |   3 |   2 |   1 |
|  18 |   0 |   1 |   1 |   0 |
|  19 |   1 |   1 |   1 |   0 |
|  20 |   1 |   1 |   1 |   0 |
|  21 |   0 |   0 |   0 |   0 |
|  22 |   1 |   1 |   1 |   0 |
|  23 |   4 |   4 |   2 |   2 |
|  24 |   0 |   2 |   2 |   0 |
|  25 |   4 |   4 |   2 |   2 |
|  26 |   4 |   6 |   2 |   4 |
|  27 |   2 |   6 |   2 |   4 |
|  28 |   1 |   5 |   2 |   3 |
|  29 |   1 |   4 |   2 |   2 |
|  30 |   1 |   3 |   2 |   1 |
|  31 |   1 |   2 |   2 |   0 |
|  32 |   1 |   1 |   1 |   0 |
|  33 |   1 |   1 |   1 |   0 |
|  34 |   1 |   1 |   1 |   0 |
|  35 |   2 |   2 |   2 |   0 |
|  36 |   0 |   0 |   0 |   0 |
|  37 |   3 |   3 |   2 |   1 |
|  38 |   1 |   2 |   2 |   0 |
|  39 |   1 |   1 |   1 |   0 |
|  40 |   2 |   2 |   2 |   0 |
|  41 |   0 |   0 |   0 |   0 |
|  42 |   1 |   1 |   1 |   0 |
|  43 |   3 |   3 |   2 |   1 |
|  44 |   1 |   2 |   2 |   0 |
|  45 |   3 |   3 |   2 |   1 |
|  46 |   1 |   2 |   2 |   0 |
|  47 |   1 |   1 |   1 |   0 |
|  48 |   1 |   1 |   1 |   0 |
|  49 |   1 |   1 |   1 |   0 |
|  50 |   3 |   3 |   2 |   1 |
|  51 |   1 |   2 |   2 |   0 |
|  52 |   1 |   1 |   1 |   0 |
|  53 |   5 |   5 |   2 |   3 |
|  54 |   2 |   5 |   2 |   3 |
|  55 |   0 |   3 |   2 |   1 |
|  56 |   1 |   2 |   2 |   0 |
|  57 |   1 |   1 |   1 |   0 |
|  58 |   1 |   1 |   1 |   0 |
|  59 |   3 |   3 |   2 |   1 |
|  60 |   1 |   2 |   2 |   0 |
|  61 |   1 |   1 |   1 |   0 |
|  62 |   2 |   2 |   2 |   0 |
|  63 |   3 |   3 |   2 |   1 |
|  64 |   5 |   6 |   2 |   4 |
|  65 |   2 |   6 |   2 |   4 |
|  66 |   0 |   4 |   2 |   2 |
|  67 |   4 |   6 |   2 |   4 |
|  68 |   3 |   7 |   2 |   5 |
|  69 |   2 |   7 |   2 |   5 |
|  70 |   2 |   7 |   2 |   5 |
|  71 |   1 |   6 |   2 |   4 |
|  72 |   1 |   5 |   2 |   3 |
|  73 |   3 |   6 |   2 |   4 |
|  74 |   0 |   4 |   2 |   2 |
|  75 |   1 |   3 |   2 |   1 |
|  76 |   3 |   4 |   2 |   2 |
|  77 |   1 |   3 |   2 |   1 |
|  78 |   0 |   1 |   1 |   0 |
|  79 |   0 |   0 |   0 |   0 |
|  80 |   2 |   2 |   2 |   0 |
|  81 |   1 |   1 |   1 |   0 |
|  82 |   0 |   0 |   0 |   0 |
|  83 |   2 |   2 |   2 |   0 |
|  84 |   2 |   2 |   2 |   0 |
|  85 |   0 |   0 |   0 |   0 |
|  86 |   0 |   0 |   0 |   0 |
|  87 |   3 |   3 |   2 |   1 |
|  88 |   2 |   3 |   2 |   1 |
|  89 |   2 |   3 |   2 |   1 |
|  90 |   0 |   1 |   1 |   0 |
|  91 |   0 |   0 |   0 |   0 |
|  92 |   4 |   4 |   2 |   2 |
|  93 |   0 |   2 |   2 |   0 |
|  94 |   1 |   1 |   1 |   0 |
|  95 |   1 |   1 |   1 |   0 |
|  96 |   3 |   3 |   2 |   1 |
|  97 |   0 |   1 |   1 |   0 |
|  98 |   3 |   3 |   2 |   1 |
|  99 |   1 |   2 |   2 |   0 |
| 100 |   3 |   3 |   2 |   1 |
| 101 |   1 |   2 |   2 |   0 |
| 102 |   1 |   1 |   1 |   0 |
| 103 |   2 |   2 |   2 |   0 |
| 104 |   0 |   0 |   0 |   0 |
| 105 |   2 |   2 |   2 |   0 |
| 106 |   3 |   3 |   2 |   1 |
| 107 |   0 |   1 |   1 |   0 |
| 108 |   0 |   0 |   0 |   0 |
| 109 |   1 |   1 |   1 |   0 |
| 110 |   0 |   0 |   0 |   0 |
| 111 |   0 |   0 |   0 |   0 |
| 112 |   1 |   1 |   1 |   0 |
| 113 |   4 |   4 |   2 |   2 |
| 114 |   0 |   2 |   2 |   0 |
| 115 |   0 |   0 |   0 |   0 |
| 116 |   1 |   1 |   1 |   0 |
| 117 |   3 |   3 |   2 |   1 |
| 118 |   2 |   3 |   2 |   1 |
| 119 |   1 |   2 |   2 |   0 |
| 120 |   2 |   2 |   2 |   0 |
| 121 |   2 |   2 |   2 |   0 |
| 122 |   2 |   2 |   2 |   0 |
| 123 |   4 |   4 |   2 |   2 |
| 124 |   0 |   2 |   2 |   0 |
| 125 |   1 |   1 |   1 |   0 |
| 126 |   2 |   2 |   2 |   0 |
| 127 |   0 |   0 |   0 |   0 |
| 128 |   1 |   1 |   1 |   0 |
| 129 |   1 |   1 |   1 |   0 |
| 130 |   0 |   0 |   0 |   0 |
| 131 |   1 |   1 |   1 |   0 |
| 132 |   5 |   5 |   2 |   3 |
| 133 |   1 |   4 |   2 |   2 |
| 134 |   0 |   2 |   2 |   0 |
| 135 |   4 |   4 |   2 |   2 |
| 136 |   4 |   6 |   2 |   4 |
| 137 |   2 |   6 |   2 |   4 |
| 138 |   2 |   6 |   2 |   4 |
| 139 |   1 |   5 |   2 |   3 |
| 140 |   4 |   7 |   2 |   5 |
| 141 |   0 |   5 |   2 |   3 |
| 142 |   4 |   7 |   2 |   5 |
| 143 |   1 |   6 |   2 |   4 |
| 144 |   1 |   5 |   2 |   3 |
| 145 |   0 |   3 |   2 |   1 |
| 146 |   4 |   5 |   2 |   3 |
| 147 |   1 |   4 |   2 |   2 |
| 148 |   2 |   4 |   2 |   2 |
| 149 |   3 |   5 |   2 |   3 |
| 150 |   4 |   7 |   2 |   5 |
| 151 |   2 |   7 |   2 |   5 |
| 152 |   0 |   5 |   2 |   3 |
| 153 |   2 |   5 |   2 |   3 |
| 154 |   1 |   4 |   2 |   2 |
| 155 |   1 |   3 |   2 |   1 |
| 156 |   4 |   5 |   2 |   3 |
| 157 |   2 |   5 |   2 |   3 |
| 158 |   3 |   6 |   2 |   4 |
| 159 |   3 |   7 |   2 |   5 |
| 160 |   4 |   9 |   2 |   7 |
| 161 |   2 |   9 |   2 |   7 |
| 162 |   1 |   8 |   2 |   6 |
| 163 |   0 |   6 |   2 |   4 |
| 164 |   3 |   7 |   2 |   5 |
| 165 |   3 |   8 |   2 |   6 |
| 166 |   1 |   7 |   2 |   5 |
| 167 |   1 |   6 |   2 |   4 |
| 168 |   3 |   7 |   2 |   5 |
| 169 |   2 |   7 |   2 |   5 |
| 170 |   1 |   6 |   2 |   4 |
| 171 |   3 |   7 |   2 |   5 |
| 172 |   5 |  10 |   2 |   8 |
| 173 |   0 |   8 |   2 |   6 |
| 174 |   4 |  10 |   2 |   8 |
| 175 |   2 |  10 |   2 |   8 |
| 176 |   1 |   9 |   2 |   7 |
| 177 |   4 |  11 |   2 |   9 |
| 178 |   1 |  10 |   2 |   8 |
| 179 |   1 |   9 |   2 |   7 |
| 180 |   3 |  10 |   2 |   8 |
| 181 |   2 |  10 |   2 |   8 |
| 182 |   1 |   9 |   2 |   7 |
| 183 |   2 |   9 |   2 |   7 |
| 184 |   3 |  10 |   2 |   8 |
| 185 |   0 |   8 |   2 |   6 |
| 186 |   0 |   6 |   2 |   4 |
| 187 |   3 |   7 |   2 |   5 |
| 188 |   2 |   7 |   2 |   5 |
| 189 |   2 |   7 |   2 |   5 |
| 190 |   5 |  10 |   2 |   8 |
| 191 |   0 |   8 |   2 |   6 |
| 192 |   2 |   8 |   2 |   6 |
| 193 |   0 |   6 |   2 |   4 |
| 194 |   5 |   9 |   2 |   7 |
| 195 |   4 |  11 |   2 |   9 |
| 196 |   2 |  11 |   2 |   9 |
| 197 |   0 |   9 |   2 |   7 |
| 198 |   1 |   8 |   2 |   6 |
| 199 |   0 |   6 |   2 |   4 |
| 200 |   2 |   6 |   2 |   4 |
| 201 |   4 |   8 |   2 |   6 |
| 202 |   0 |   6 |   2 |   4 |
| 203 |   2 |   6 |   2 |   4 |
| 204 |   4 |   8 |   2 |   6 |
| 205 |   0 |   6 |   2 |   4 |
| 206 |   1 |   5 |   2 |   3 |
| 207 |   1 |   4 |   2 |   2 |
| 208 |   0 |   2 |   2 |   0 |
| 209 |   1 |   1 |   1 |   0 |
| 210 |   0 |   0 |   0 |   0 |
| 211 |   2 |   2 |   2 |   0 |
| 212 |   1 |   1 |   1 |   0 |
| 213 |   0 |   0 |   0 |   0 |
| 214 |   0 |   0 |   0 |   0 |
| 215 |   0 |   0 |   0 |   0 |
| 216 |   0 |   0 |   0 |   0 |
| 217 |   5 |   5 |   2 |   3 |
| 218 |   3 |   6 |   2 |   4 |
| 219 |   2 |   6 |   2 |   4 |
| 220 |   2 |   6 |   2 |   4 |
| 221 |   3 |   7 |   2 |   5 |
| 222 |   3 |   8 |   2 |   6 |
| 223 |   0 |   6 |   2 |   4 |
| 224 |   1 |   5 |   2 |   3 |
| 225 |   1 |   4 |   2 |   2 |
| 226 |   1 |   3 |   2 |   1 |
| 227 |   2 |   3 |   2 |   1 |
| 228 |   3 |   4 |   2 |   2 |
| 229 |   0 |   2 |   2 |   0 |
| 230 |   2 |   2 |   2 |   0 |
| 231 |   3 |   3 |   2 |   1 |
| 232 |   0 |   1 |   1 |   0 |
| 233 |   1 |   1 |   1 |   0 |
| 234 |   2 |   2 |   2 |   0 |
| 235 |   4 |   4 |   2 |   2 |
| 236 |   2 |   4 |   2 |   2 |
| 237 |   1 |   3 |   2 |   1 |



label: E=C-D
labeled_formulas: E=C-D
output: {"Arithmetic-Relationship": ["E=C-D"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_58594___xlsx_bcc8b7374fcd3d0b13cd41d546101e36a2914396.xlsx___line_432