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:
|               BW |               BX |   BY |   BZ |   CA |
|-----------------:|-----------------:|-----:|-----:|-----:|
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|    210.605       |    210.605       |    0 |    0 |    0 |
|   2035.63        |   2035.63        |    0 |    0 |    0 |
|   5049.03        |   5049.03        |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|   4559.26        |   4559.26        |    0 |    0 |    0 |
|  89923.8         |  89923.8         |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|  66298           |  66298           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
| 168076           | 168076           |    0 |    0 |    0 |
| 275698           | 275698           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
| 163540           | 163540           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|  50730.9         |  50730.9         |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|    268.34        |    268.34        |    0 |    0 |    0 |
|  40075.8         |  40075.8         |    0 |    0 |    0 |
|   7799.28        |   7799.28        |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
| 109133           | 109133           |    0 |    0 |    0 |
|  21443.6         |  21443.6         |    0 |    0 |    0 |
|  91379.2         |  91379.2         |    0 |    0 |    0 |
| 184018           | 184018           |    0 |    0 |    0 |
|  32273.6         |  32273.6         |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
| 188780           | 188780           |    0 |    0 |    0 |
|    291.474       |    291.474       |    0 |    0 |    0 |
|  28774.6         |  28774.6         |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|   2316.97        |   2316.97        |    0 |    0 |    0 |
|   3181.24        |   3181.24        |    0 |    0 |    0 |
|  53213.4         |  53213.4         |    0 |    0 |    0 |
|  63882           |  63882           |    0 |    0 |    0 |
|    307.131       |    307.131       |    0 |    0 |    0 |
|  62867.7         |  62867.7         |    0 |    0 |    0 |
|  97269.4         |  97269.4         |    0 |    0 |    0 |
| 311834           | 311834           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
| 297392           | 297392           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
| 263689           | 263689           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|   2588.75        |   2588.75        |    0 |    0 |    0 |
|  23829.1         |  23829.1         |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|  47958.5         |  47958.5         |    0 |    0 |    0 |
|   2250.1         |   2250.1         |    0 |    0 |    0 |
|  15537.1         |  15537.1         |    0 |    0 |    0 |
|  21059.2         |  21059.2         |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|  12913.2         |  12913.2         |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
| 216995           | 216995           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|   3029.35        |   3029.35        |    0 |    0 |    0 |
|  49252.8         |  49252.8         |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
| 119255           | 119255           |    0 |    0 |    0 |
|  18459.7         |  18459.7         |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      1.34592e+06 |      1.34592e+06 |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|    785.715       |    785.715       |    0 |    0 |    0 |
|  27673.9         |  27673.9         |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|  10473.9         |  10473.9         |    0 |    0 |    0 |
|      0           |      0           |    0 |    0 |    0 |
|  76748.4         |  76748.4         |    0 |    0 |    0 |
|  88530           |  88530           |    0 |    0 |    0 |



labeled_formulas: BY=BW-BX
CA=BW-BX
BZ=BW*BY
CA=BW*BZ
BZ=BX*BY
BY=BX*CA
BY=(BW-BZ)-BX
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_109066___xlsx_ca4be097e796e7cbcb63584c4b41838172df9420.xlsx___line_788