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 |
|:--------|:--------------------------------------------|----:|----:|---------:|----------:|
| Adams   | DRS System Retirees                         |   1 |   1 |    12    | 1         |
| Asotin  | Children, Youth and Families, Department of |  15 |   1 |    48    | 0.0666667 |
| Asotin  | Department of Social and Health Services    |  19 |   2 |    17    | 0.105263  |
| Asotin  | State Parks And Recreation Commission       |   2 |   1 |   240    | 0.5       |
| Asotin  | Transportation, Department of               |  10 |   1 |    60    | 0.1       |
| Benton  | Agriculture, Department of                  |  13 |   1 |   420    | 0.0769231 |
| Benton  | Attorney General, Office of the             |  13 |   2 |   660    | 0.153846  |
| Benton  | Children, Youth and Families, Department of | 113 |  12 |  1188    | 0.106195  |
| Benton  | Columbia Basin College                      |  11 |   2 |  2616    | 0.181818  |
| Benton  | Corrections, Department of                  |  70 |   4 |   192    | 0.0571429 |
| Benton  | Department of Fish and Wildlife             |   2 |   1 |   240    | 0.5       |
| Benton  | Department of Social and Health Services    | 222 |  37 |  3520    | 0.166667  |
| Benton  | DRS System Retirees                         |   8 |   5 |  1296    | 0.625     |
| Benton  | Ecology, Department of                      |  78 |  16 |  3086    | 0.205128  |
| Benton  | Employment Security Department              |  23 |   3 |  1812    | 0.130435  |
| Benton  | Health, Department of                       |  21 |   2 |  1260    | 0.0952381 |
| Benton  | Labor and Industries, Department of         |  56 |   6 |   480    | 0.107143  |
| Benton  | Licensing, Department of                    |  17 |   8 |   314    | 0.470588  |
| Benton  | Revenue, Department of                      |  17 |   5 |   445    | 0.294118  |
| Benton  | State Auditor, Office of the                |  13 |   1 |   840    | 0.0769231 |
| Benton  | Transportation, Department of               |  38 |   3 |   449    | 0.0789474 |
| Benton  | Washington State Patrol                     |  59 |   5 |   204    | 0.0847458 |
| Benton  | Washington State University                 |  57 |   3 |   600    | 0.0526316 |
| Chelan  | Administrative Office of the Courts         |   3 |   1 |   420    | 0.333333  |
| Chelan  | Attorney General, Office of the             |  11 |   2 |   564    | 0.181818  |
| Chelan  | Children, Youth and Families, Department of |  51 |   6 |   595    | 0.117647  |
| Chelan  | Corrections, Department of                  |  21 |   1 |   240    | 0.047619  |
| Chelan  | Department of Fish and Wildlife             |  63 |   2 |    65    | 0.031746  |
| Chelan  | Department of Social and Health Services    |  64 |  14 |  1716    | 0.21875   |
| Chelan  | DRS System Retirees                         |   2 |   1 |    48    | 0.5       |
| Chelan  | Ecology, Department of                      |   4 |   1 |    96    | 0.25      |
| Chelan  | Licensing, Department of                    |  11 |   1 |     5    | 0.0909091 |
| Chelan  | Liquor and Cannabis Board                   |   9 |   1 |   240    | 0.111111  |
| Chelan  | Revenue, Department of                      |  13 |   3 |   415.8  | 0.230769  |
| Chelan  | State Auditor, Office of the                |  17 |   5 |  1145    | 0.294118  |
| Chelan  | Transportation, Department of               | 181 |  12 |  4633    | 0.0662983 |
| Chelan  | Washington State Patrol                     |  51 |   6 |  1565    | 0.117647  |
| Chelan  | Washington State University                 |   5 |   1 |   600    | 0.2       |
| Chelan  | Wenatchee Valley College                    |  35 |   2 |   660    | 0.0571429 |
| Clallam | Attorney General, Office of the             |   7 |   1 |   120    | 0.142857  |
| Clallam | Children, Youth and Families, Department of |  37 |   4 |   324    | 0.108108  |
| Clallam | Corrections, Department of                  | 411 |  32 |  8931.25 | 0.0778589 |
| Clallam | Department of Fish and Wildlife             |  40 |   2 |   180    | 0.05      |
| Clallam | Department of Social and Health Services    |  47 |   5 |  1080    | 0.106383  |
| Clallam | DRS System Retirees                         |   7 |   5 |  1434    | 0.714286  |
| Clallam | Employment Security Department              |  12 |   2 |   384    | 0.166667  |
| Clallam | Natural Resources, Department of            | 119 |   5 |  1176    | 0.0420168 |
| Clallam | Peninsula College                           |  46 |   1 |   360    | 0.0217391 |
| Clallam | Revenue, Department of                      |  10 |   2 |   292.8  | 0.2       |
| Clallam | Transportation, Department of               |  54 |   1 |   144    | 0.0185185 |
| Clallam | Washington State Patrol                     |  20 |   3 |   108    | 0.15      |
| Clark   | Attorney General, Office of the             |  22 |   5 |  1980    | 0.227273  |
| Clark   | Blind, Department of Services for the       |   8 |   1 |   120    | 0.125     |
| Clark   | Center for Childhood Deafness               | 173 |   7 |   936    | 0.0404624 |
| Clark   | Children, Youth and Families, Department of | 175 |  12 |  1825    | 0.0685714 |
| Clark   | Clark College                               | 211 |  31 |  4932    | 0.146919  |
| Clark   | Corrections, Department of                  | 229 |  32 |  6691    | 0.139738  |
| Clark   | Department of Fish and Wildlife             | 113 |  11 |  1345    | 0.0973451 |
| Clark   | Department of Social and Health Services    | 411 |  73 | 10041    | 0.177616  |
| Clark   | DRS System Retirees                         |  10 |  10 |  4380    | 1         |
| Clark   | Eastern Washington University               |   2 |   1 |    36    | 0.5       |
| Clark   | Ecology, Department of                      |  17 |   4 |    74    | 0.235294  |
| Clark   | Employment Security Department              |  30 |   3 |   312    | 0.1       |
| Clark   | Enterprise Services, Department of          |   1 |   1 |   180    | 1         |
| Clark   | Health Care Authority                       |   1 |   1 |   120    | 1         |
| Clark   | Labor and Industries, Department of         |  59 |   7 |   799    | 0.118644  |
| Clark   | Licensing, Department of                    |  27 |   1 |    60    | 0.037037  |



label: F=D/C
labeled_formulas: F=D/C
output: {"Arithmetic-Relationship": ["F=D/C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_486866___xlsx_55e6010978fb5336f9ddd8e1de342cde24d0c285.xlsx___line_453