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 |   F |   G |
|----:|-----:|----:|-----:|----:|----:|----:|
|   1 | 1951 | 196 | 1755 | 127 |   0 |   0 |
|   2 |  975 |  98 |  877 |  63 |   1 |   1 |
|   3 |  650 |  65 |  585 |  42 |   1 |   1 |
|   4 |  487 |  49 |  438 |  31 |   3 |   3 |
|   5 |  390 |  39 |  351 |  25 |   1 |   2 |
|   6 |  325 |  33 |  292 |  21 |   1 |   1 |
|   7 |  278 |  28 |  250 |  18 |   5 |   1 |
|   8 |  243 |  25 |  218 |  15 |   7 |   7 |
|   9 |  216 |  22 |  194 |  14 |   7 |   1 |
|  10 |  195 |  20 |  175 |  12 |   1 |   7 |
|  11 |  177 |  18 |  159 |  11 |   4 |   6 |
|  12 |  162 |  17 |  145 |  10 |   7 |   7 |
|  13 |  150 |  15 |  135 |   9 |   1 |  10 |
|  14 |  139 |  14 |  125 |   9 |   5 |   1 |
|  15 |  130 |  13 |  117 |   8 |   1 |   7 |
|  16 |  121 |  13 |  108 |   7 |  15 |  15 |
|  17 |  114 |  12 |  102 |   7 |  13 |   8 |
|  18 |  108 |  11 |   97 |   7 |   7 |   1 |
|  19 |  102 |  11 |   91 |   6 |  13 |  13 |
|  20 |   97 |  10 |   87 |   6 |  11 |   7 |
|  21 |   92 |  10 |   82 |   6 |  19 |   1 |
|  22 |   88 |   9 |   79 |   5 |  15 |  17 |
|  23 |   84 |   9 |   75 |   5 |  19 |  12 |
|  24 |   81 |   9 |   72 |   5 |   7 |   7 |
|  25 |   78 |   8 |   70 |   5 |   1 |   2 |
|  26 |   75 |   8 |   67 |   4 |   1 |  23 |
|  27 |   72 |   8 |   64 |   4 |   7 |  19 |
|  28 |   69 |   7 |   62 |   4 |  19 |  15 |
|  29 |   67 |   7 |   60 |   4 |   8 |  11 |
|  30 |   65 |   7 |   58 |   4 |   1 |   7 |
|  31 |   62 |   7 |   55 |   4 |  29 |   3 |
|  32 |   60 |   6 |   54 |   3 |  31 |  31 |
|  33 |   59 |   6 |   53 |   3 |   4 |  28 |
|  34 |   57 |   6 |   51 |   3 |  13 |  25 |
|  35 |   55 |   6 |   49 |   3 |  26 |  22 |
|  36 |   54 |   6 |   48 |   3 |   7 |  19 |
|  37 |   52 |   6 |   46 |   3 |  27 |  16 |
|  38 |   51 |   6 |   45 |   3 |  13 |  13 |
|  39 |   50 |   5 |   45 |   3 |   1 |  10 |
|  40 |   48 |   5 |   43 |   3 |  31 |   7 |
|  41 |   47 |   5 |   42 |   3 |  24 |   4 |
|  42 |   46 |   5 |   41 |   3 |  19 |   1 |
|  43 |   45 |   5 |   40 |   2 |  16 |  41 |
|  44 |   44 |   5 |   39 |   2 |  15 |  39 |
|  45 |   43 |   5 |   38 |   2 |  16 |  37 |
|  46 |   42 |   5 |   37 |   2 |  19 |  35 |
|  47 |   41 |   5 |   36 |   2 |  24 |  33 |
|  48 |   40 |   4 |   36 |   2 |  31 |  31 |
|  49 |   39 |   4 |   35 |   2 |  40 |  29 |
|  50 |   39 |   4 |   35 |   2 |   1 |  27 |
|  51 |   38 |   4 |   34 |   2 |  13 |  25 |
|  52 |   37 |   4 |   33 |   2 |  27 |  23 |
|  53 |   36 |   4 |   32 |   2 |  43 |  21 |
|  54 |   36 |   4 |   32 |   2 |   7 |  19 |
|  55 |   35 |   4 |   31 |   2 |  26 |  17 |
|  56 |   34 |   4 |   30 |   2 |  47 |  15 |
|  57 |   34 |   4 |   30 |   2 |  13 |  13 |
|  58 |   33 |   4 |   29 |   2 |  37 |  11 |
|  59 |   33 |   4 |   29 |   2 |   4 |   9 |
|  60 |   32 |   4 |   28 |   2 |  31 |   7 |
|  61 |   31 |   4 |   27 |   2 |  60 |   5 |
|  62 |   31 |   4 |   27 |   2 |  29 |   3 |
|  63 |   30 |   3 |   27 |   2 |  61 |   1 |
|  64 |   30 |   3 |   27 |   1 |  31 |  63 |
|  65 |   30 |   3 |   27 |   1 |   1 |  62 |
|  66 |   29 |   3 |   26 |   1 |  37 |  61 |
|  67 |   29 |   3 |   26 |   1 |   8 |  60 |
|  68 |   28 |   3 |   25 |   1 |  47 |  59 |
|  69 |   28 |   3 |   25 |   1 |  19 |  58 |
|  70 |   27 |   3 |   24 |   1 |  61 |  57 |
|  71 |   27 |   3 |   24 |   1 |  34 |  56 |
|  72 |   27 |   3 |   24 |   1 |   7 |  55 |
|  73 |   26 |   3 |   23 |   1 |  53 |  54 |
|  74 |   26 |   3 |   23 |   1 |  27 |  53 |
|  75 |   26 |   3 |   23 |   1 |   1 |  52 |
|  76 |   25 |   3 |   22 |   1 |  51 |  51 |
|  77 |   25 |   3 |   22 |   1 |  26 |  50 |
|  78 |   25 |   3 |   22 |   1 |   1 |  49 |
|  79 |   24 |   3 |   21 |   1 |  55 |  48 |
|  80 |   24 |   3 |   21 |   1 |  31 |  47 |
|  81 |   24 |   3 |   21 |   1 |   7 |  46 |
|  82 |   23 |   3 |   20 |   1 |  65 |  45 |
|  83 |   23 |   3 |   20 |   1 |  42 |  44 |
|  84 |   23 |   3 |   20 |   1 |  19 |  43 |
|  85 |   22 |   3 |   19 |   1 |  81 |  42 |
|  86 |   22 |   3 |   19 |   1 |  59 |  41 |
|  87 |   22 |   3 |   19 |   1 |  37 |  40 |
|  88 |   22 |   3 |   19 |   1 |  15 |  39 |
|  89 |   21 |   3 |   18 |   1 |  82 |  38 |
|  90 |   21 |   3 |   18 |   1 |  61 |  37 |
|  91 |   21 |   3 |   18 |   1 |  40 |  36 |
|  92 |   21 |   3 |   18 |   1 |  19 |  35 |
|  93 |   20 |   2 |   18 |   1 |  91 |  34 |
|  94 |   20 |   2 |   18 |   1 |  71 |  33 |
|  95 |   20 |   2 |   18 |   1 |  51 |  32 |
|  96 |   20 |   2 |   18 |   1 |  31 |  31 |
|  97 |   20 |   2 |   18 |   1 |  11 |  30 |
|  98 |   19 |   2 |   17 |   1 |  89 |  29 |
|  99 |   19 |   2 |   17 |   1 |  70 |  28 |
| 100 |   19 |   2 |   17 |   1 |  51 |  27 |
| 101 |   19 |   2 |   17 |   1 |  32 |  26 |
| 102 |   19 |   2 |   17 |   1 |  13 |  25 |
| 103 |   18 |   2 |   16 |   1 |  97 |  24 |
| 104 |   18 |   2 |   16 |   1 |  79 |  23 |
| 105 |   18 |   2 |   16 |   1 |  61 |  22 |
| 106 |   18 |   2 |   16 |   1 |  43 |  21 |
| 107 |   18 |   2 |   16 |   1 |  25 |  20 |
| 108 |   18 |   2 |   16 |   1 |   7 |  19 |
| 109 |   17 |   2 |   15 |   1 |  98 |  18 |
| 110 |   17 |   2 |   15 |   1 |  81 |  17 |
| 111 |   17 |   2 |   15 |   1 |  64 |  16 |
| 112 |   17 |   2 |   15 |   1 |  47 |  15 |
| 113 |   17 |   2 |   15 |   1 |  30 |  14 |
| 114 |   17 |   2 |   15 |   1 |  13 |  13 |
| 115 |   16 |   2 |   14 |   1 | 111 |  12 |
| 116 |   16 |   2 |   14 |   1 |  95 |  11 |
| 117 |   16 |   2 |   14 |   1 |  79 |  10 |
| 118 |   16 |   2 |   14 |   1 |  63 |   9 |
| 119 |   16 |   2 |   14 |   1 |  47 |   8 |
| 120 |   16 |   2 |   14 |   1 |  31 |   7 |
| 121 |   16 |   2 |   14 |   1 |  15 |   6 |
| 122 |   15 |   2 |   13 |   1 | 121 |   5 |
| 123 |   15 |   2 |   13 |   1 | 106 |   4 |
| 124 |   15 |   2 |   13 |   1 |  91 |   3 |
| 125 |   15 |   2 |   13 |   1 |  76 |   2 |
| 126 |   15 |   2 |   13 |   1 |  61 |   1 |
| 127 |   15 |   2 |   13 |   1 |  46 |   0 |
| 128 |   15 |   2 |   13 |   0 |  31 | 127 |
| 129 |   15 |   2 |   13 |   0 |  16 | 127 |
| 130 |   15 |   2 |   13 |   0 |   1 | 127 |
| 131 |   14 |   2 |   12 |   0 | 117 | 127 |
| 132 |   14 |   2 |   12 |   0 | 103 | 127 |
| 133 |   14 |   2 |   12 |   0 |  89 | 127 |
| 134 |   14 |   2 |   12 |   0 |  75 | 127 |
| 135 |   14 |   2 |   12 |   0 |  61 | 127 |
| 136 |   14 |   2 |   12 |   0 |  47 | 127 |
| 137 |   14 |   2 |   12 |   0 |  33 | 127 |
| 138 |   14 |   2 |   12 |   0 |  19 | 127 |
| 139 |   14 |   2 |   12 |   0 |   5 | 127 |
| 140 |   13 |   2 |   11 |   0 | 131 | 127 |
| 141 |   13 |   2 |   11 |   0 | 118 | 127 |
| 142 |   13 |   2 |   11 |   0 | 105 | 127 |
| 143 |   13 |   2 |   11 |   0 |  92 | 127 |
| 144 |   13 |   2 |   11 |   0 |  79 | 127 |
| 145 |   13 |   2 |   11 |   0 |  66 | 127 |
| 146 |   13 |   2 |   11 |   0 |  53 | 127 |
| 147 |   13 |   2 |   11 |   0 |  40 | 127 |
| 148 |   13 |   2 |   11 |   0 |  27 | 127 |
| 149 |   13 |   2 |   11 |   0 |  14 | 127 |
| 150 |   13 |   2 |   11 |   0 |   1 | 127 |
| 151 |   12 |   2 |   10 |   0 | 139 | 127 |
| 152 |   12 |   2 |   10 |   0 | 127 | 127 |
| 153 |   12 |   2 |   10 |   0 | 115 | 127 |
| 154 |   12 |   2 |   10 |   0 | 103 | 127 |
| 155 |   12 |   2 |   10 |   0 |  91 | 127 |
| 156 |   12 |   2 |   10 |   0 |  79 | 127 |
| 157 |   12 |   2 |   10 |   0 |  67 | 127 |
| 158 |   12 |   2 |   10 |   0 |  55 | 127 |
| 159 |   12 |   2 |   10 |   0 |  43 | 127 |
| 160 |   12 |   2 |   10 |   0 |  31 | 127 |
| 161 |   12 |   2 |   10 |   0 |  19 | 127 |
| 162 |   12 |   2 |   10 |   0 |   7 | 127 |
| 163 |   11 |   2 |    9 |   0 | 158 | 127 |
| 164 |   11 |   2 |    9 |   0 | 147 | 127 |
| 165 |   11 |   2 |    9 |   0 | 136 | 127 |
| 166 |   11 |   2 |    9 |   0 | 125 | 127 |
| 167 |   11 |   2 |    9 |   0 | 114 | 127 |
| 168 |   11 |   2 |    9 |   0 | 103 | 127 |
| 169 |   11 |   2 |    9 |   0 |  92 | 127 |
| 170 |   11 |   2 |    9 |   0 |  81 | 127 |
| 171 |   11 |   2 |    9 |   0 |  70 | 127 |
| 172 |   11 |   2 |    9 |   0 |  59 | 127 |
| 173 |   11 |   2 |    9 |   0 |  48 | 127 |
| 174 |   11 |   2 |    9 |   0 |  37 | 127 |
| 175 |   11 |   2 |    9 |   0 |  26 | 127 |
| 176 |   11 |   2 |    9 |   0 |  15 | 127 |
| 177 |   11 |   2 |    9 |   0 |   4 | 127 |
| 178 |   10 |   1 |    9 |   0 | 171 | 127 |
| 179 |   10 |   1 |    9 |   0 | 161 | 127 |
| 180 |   10 |   1 |    9 |   0 | 151 | 127 |
| 181 |   10 |   1 |    9 |   0 | 141 | 127 |
| 182 |   10 |   1 |    9 |   0 | 131 | 127 |
| 183 |   10 |   1 |    9 |   0 | 121 | 127 |
| 184 |   10 |   1 |    9 |   0 | 111 | 127 |
| 185 |   10 |   1 |    9 |   0 | 101 | 127 |
| 186 |   10 |   1 |    9 |   0 |  91 | 127 |
| 187 |   10 |   1 |    9 |   0 |  81 | 127 |
| 188 |   10 |   1 |    9 |   0 |  71 | 127 |
| 189 |   10 |   1 |    9 |   0 |  61 | 127 |
| 190 |   10 |   1 |    9 |   0 |  51 | 127 |
| 191 |   10 |   1 |    9 |   0 |  41 | 127 |
| 192 |   10 |   1 |    9 |   0 |  31 | 127 |



label: D=B-C
labeled_formulas: D=B-C
output: {"Arithmetic-Relationship": ["D=B-C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_306711___xlsx_e109c8959fa0625ef2d1543185721daebd5cbaec.xlsx___line_496