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                  |
|:----------------------------------------|----:|-----------------:|:-------------------|
| Grand Total                             | 406 |      1.32125e+07 | 32543.187906403939 |
| National Lottery Community Fund         |  43 |      8.16121e+06 | 189795.46767441861 |
| National Lottery Heritage Fund          |  10 |      1.3889e+06  | 138890             |
| Arts Council                            |  22 | 468352           | 21288.727272727272 |
| Sport England                           |  20 | 676709           | 33835.449999999997 |
| Leeds Community Foundation              |   1 |    720           | 720                |
| BBC Children in Need                    |   1 | 120132           | 120132             |
| Liz & Terry Bramall Foundation          |  35 | 519680           | 14848              |
| Esmée Fairbairn Foundation              |   1 | 454835           | 454835             |
| The Tudor Trust                         |   0 |      0           | #DIV/0!            |
| Lloyds Bank Foundation                  |   1 |  60000           | 60000              |
| The Henry Smith Charity                 |   0 |      0           | #DIV/0!            |
| Comic Relief                            |   0 |      0           | #DIV/0!            |
| Power to Change                         |   1 | 119000           | 119000             |
| Garfield Weston Foundation              |   0 |      0           | #DIV/0!            |
| Two Ridings Community Foundation        |  97 | 667199           | 6878.344742268041  |
| Cooperative Group                       |  41 |  79685.7         | 1943.5546341463412 |
| South Yorkshire's Community Foundation  |   0 |      0           | #DIV/0!            |
| Paul Hamlyn Foundation                  |   0 |      0           | #DIV/0!            |
| The Brelms Trust                        |   7 |  47302           | 6757.4285714285716 |
| Lankelly Chase Foundation               |   0 |      0           | #DIV/0!            |
| Charles & Elsie Sykes Trust             |  77 | 303675           | 3943.8311688311687 |
| Pears Foundation                        |   0 |      0           | #DIV/0!            |
| The Clothworkers Foundation             |   1 |  25000           | 25000              |
| Nationwide Foundation                   |   0 |      0           | #DIV/0!            |
| Sir George Martin Trust                 |  35 |  45970           | 1313.4285714285713 |
| Wolfson Foundation                      |   0 |      0           | #DIV/0!            |
| NESTA                                   |   0 |      0           | #DIV/0!            |
| Joseph Rowntree Foundation              |   0 |      0           | #DIV/0!            |
| Scurrah Wainwright Charity              |   0 |      0           | #DIV/0!            |
| Allen Lane Foundation                   |   0 |      0           | #DIV/0!            |
| True Colours Trust                      |   0 |      0           | #DIV/0!            |
| The Jospeh Rank Trust                   |   1 |  45000           | 45000              |
| LandAid                                 |   0 |      0           | #DIV/0!            |
| The Dulverton Trust                     |   0 |      0           | #DIV/0!            |
| National Churches Trust                 |   0 |      0           | #DIV/0!            |
| AB Charitable Trust                     |   0 |      0           | #DIV/0!            |
| The Talbot Trusts                       |   0 |      0           | #DIV/0!            |
| Samworth Foundation                     |   0 |      0           | #DIV/0!            |
| The Wharfedale Foundation               |   1 |   1500           | 1500               |
| Masonic Charitable Foundation           |   1 |   2431           | 2431               |
| Barrow Cadbury Trust                    |   1 |  15000           | 15000              |
| The Craven Trust and the Beamsley Trust |   1 |    623           | 623                |
| Seafarers UK                            |   0 |      0           | #DIV/0!            |
| Metis Trust                             |   1 |     25           | 25                 |
| Tarn Moor Estate                        |   0 |      0           | #DIV/0!            |
| Leeds Building Society Foundation       |   5 |   4390           | 878                |
| The HBJ Trust                           |   0 |      0           | #DIV/0!            |
| Tuixen Foundation                       |   0 |      0           | #DIV/0!            |
| Woodward Charitable Trust               |   1 |    500           | 500                |
| Tedworth Charitable Trust               |   0 |      0           | #DIV/0!            |
| R S Macdonald Charitable Trust          |   0 |      0           | #DIV/0!            |
| Mollie Croysdale Charitable Trust       |   0 |      0           | #DIV/0!            |
| Three Guineas Trust                     |   1 |   4700           | 4700               |
| Indigo Trust                            |   0 |      0           | #DIV/0!            |



label: D=C/B
labeled_formulas: D=C/B
output: {"Arithmetic-Relationship": ["D=C/B"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_410988___xlsx_4ae75bb02b09782887a2062563030b362ff7bc5c.xlsx___line_166