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 |
|:---------------------------------------|-----:|-----:|-----:|-----:|
| New South Wales                        | 57.4 | 62.4 | 66   |  8.6 |
| Greater Sydney                         | 59.7 | 64.9 | 68.6 |  8.9 |
| Central Coast                          | 53.7 | 58.6 | 63.6 |  9.9 |
| Sydney - Baulkham Hills and Hawkesbury | 70.6 | 74.4 | 77.9 |  7.3 |
| Sydney - Blacktown                     | 49.4 | 55.8 | 61.4 | 12   |
| Sydney - City and Inner South          | 59.8 | 70.6 | 73.5 | 13.7 |
| Sydney - Eastern Suburbs               | 69.1 | 74.8 | 78   |  8.9 |
| Sydney - Inner South West              | 52.4 | 57.9 | 62.5 | 10.1 |
| Sydney - Inner West                    | 68.5 | 73.7 | 76.1 |  7.6 |
| Sydney - North Sydney and Hornsby      | 77.9 | 81.5 | 83.4 |  5.5 |
| Sydney - Northern Beaches              | 71.3 | 76.2 | 79.3 |  8   |
| Sydney - Outer South West              | 50.5 | 55.5 | 60.5 | 10   |
| Sydney - Outer West and Blue Mountains | 55   | 58.7 | 62.8 |  7.8 |
| Sydney - Parramatta                    | 52.8 | 58.7 | 62.7 |  9.9 |
| Sydney - Ryde                          | 71.9 | 77.1 | 79.7 |  7.8 |
| Sydney - South West                    | 42.2 | 46.1 | 50.2 |  8   |
| Sydney - Sutherland                    | 66.7 | 71.2 | 75.1 |  8.4 |
| Rest of New South Wales                | 53.3 | 57.8 | 61   |  7.7 |
| Capital Region                         | 56.3 | 60.8 | 63.2 |  6.9 |
| Central West                           | 52.2 | 55.9 | 58.3 |  6.1 |
| Coffs Harbour - Grafton                | 51.6 | 56.4 | 59.4 |  7.8 |
| Far West and Orana                     | 48.6 | 52.5 | 54.4 |  5.8 |
| Hunter Valley exc Newcastle            | 50.4 | 54.9 | 58.1 |  7.7 |
| Illawarra                              | 55.4 | 60.7 | 65.5 | 10.1 |
| Mid North Coast                        | 49.5 | 53.9 | 57.1 |  7.6 |
| Murray                                 | 54.6 | 57.8 | 60.2 |  5.6 |
| New England and North West             | 52.6 | 55.8 | 57.6 |  5   |
| Newcastle and Lake Macquarie           | 55.6 | 61.4 | 66.4 | 10.8 |
| Richmond - Tweed                       | 54.1 | 59.2 | 62.1 |  8   |
| Riverina                               | 52.9 | 56.5 | 58.3 |  5.4 |
| Southern Highlands and Shoalhaven      | 54.7 | 58.9 | 62.2 |  7.5 |
| Victoria                               | 58.1 | 63.4 | 67.2 |  9.1 |
| Greater Melbourne                      | 59.4 | 65   | 68.9 |  9.5 |
| Melbourne - Inner                      | 69   | 75.6 | 77.1 |  8.1 |
| Melbourne - Inner East                 | 73.7 | 77.7 | 79.5 |  5.8 |
| Melbourne - Inner South                | 70.3 | 75.5 | 78.8 |  8.5 |
| Melbourne - North East                 | 56.4 | 62.7 | 67.4 | 11   |
| Melbourne - North West                 | 49.1 | 55.1 | 60.8 | 11.7 |
| Melbourne - Outer East                 | 61.2 | 66.8 | 71.2 | 10   |
| Melbourne - South East                 | 52.9 | 58.9 | 63.6 | 10.7 |
| Melbourne - West                       | 48.5 | 55.5 | 61.2 | 12.7 |
| Mornington Peninsula                   | 55.3 | 61.1 | 66.1 | 10.8 |
| Rest of Victoria                       | 54.2 | 58.5 | 61.4 |  7.2 |
| Ballarat                               | 54   | 59.1 | 62.7 |  8.7 |
| Bendigo                                | 55.4 | 60.3 | 63   |  7.6 |
| Geelong                                | 56   | 61.9 | 66.7 | 10.7 |
| Hume                                   | 55.8 | 59.9 | 62.2 |  6.4 |
| Latrobe - Gippsland                    | 52.8 | 56.9 | 59.2 |  6.4 |
| North West                             | 52.3 | 54.7 | 55.9 |  3.6 |
| Shepparton                             | 51.4 | 54   | 57   |  5.6 |
| Warrnambool and South West             | 55.6 | 59.2 | 60.8 |  5.2 |
| Queensland                             | 54.7 | 59.7 | 63.4 |  8.7 |
| Greater Brisbane                       | 57.6 | 63   | 66.8 |  9.2 |
| Brisbane - East                        | 57   | 63.1 | 67.8 | 10.8 |
| Brisbane - North                       | 58.8 | 65.4 | 70.9 | 12.1 |
| Brisbane - South                       | 63.3 | 68.9 | 72.8 |  9.5 |
| Brisbane - West                        | 73.7 | 78.1 | 80.8 |  7.1 |
| Brisbane Inner City                    | 70.1 | 76.4 | 77.9 |  7.8 |
| Ipswich                                | 46.4 | 51.6 | 55.6 |  9.2 |
| Logan - Beaudesert                     | 47   | 51.7 | 56   |  9   |
| Moreton Bay - North                    | 47   | 52   | 56.7 |  9.7 |
| Moreton Bay - South                    | 58.9 | 65   | 69.1 | 10.2 |
| Rest of Queensland                     | 52.1 | 56.6 | 60.3 |  8.2 |
| Cairns                                 | 52.8 | 56.5 | 59.5 |  6.7 |
| Darling Downs - Maranoa                | 49.9 | 52.6 | 55   |  5.1 |
| Central Queensland                     | 49.2 | 53   | 55.8 |  6.6 |
| Gold Coast                             | 55.8 | 61.1 | 65.5 |  9.7 |
| Mackay - Isaac - Whitsunday            | 48.5 | 53.4 | 55.6 |  7.1 |
| Queensland - Outback                   | 46   | 48.8 | 51.1 |  5.1 |
| Far North                              | 41.7 | 44.6 | 46   |  4.3 |
| Outback - North                        | 45.9 | 49.1 | 52.9 |  7   |
| Outback - South                        | 52.3 | 54.4 | 57.3 |  5   |
| Sunshine Coast                         | 56.8 | 62.6 | 67.1 | 10.3 |
| Toowoomba                              | 53.9 | 58.7 | 62.6 |  8.7 |
| Townsville                             | 53.2 | 56.9 | 60.2 |  7   |
| Wide Bay                               | 45.1 | 49.2 | 52.4 |  7.3 |
| South Australia                        | 54.9 | 59.4 | 63   |  8.1 |
| Greater Adelaide                       | 56.5 | 61.4 | 65.3 |  8.8 |
| Adelaide - Central and Hills           | 68.6 | 72.7 | 75.6 |  7   |
| Adelaide - North                       | 47.3 | 52.5 | 56.9 |  9.6 |
| Adelaide - South                       | 59.4 | 64   | 68   |  8.6 |
| Adelaide - West                        | 52.8 | 59.2 | 64   | 11.2 |
| Rest of South Australia                | 49.4 | 52.6 | 54.8 |  5.4 |
| Barossa - Yorke - Mid North            | 50.4 | 53.8 | 56.3 |  5.9 |
| South Australia - Outback              | 48.4 | 51.7 | 53.1 |  4.7 |
| Eyre Peninsula and South West          | 50.5 | 53.5 | 55.3 |  4.8 |
| Outback - North and East               | 44.2 | 48.1 | 48.6 |  4.4 |
| South Australia - South East           | 49.3 | 52.4 | 54.7 |  5.4 |
| Western Australia                      | 57.2 | 61.6 | 64.6 |  7.4 |
| Greater Perth                          | 58.9 | 63.8 | 66.9 |  8   |
| Mandurah                               | 47.1 | 52.2 | 57   |  9.9 |
| Perth - Inner                          | 72.7 | 77.2 | 78.6 |  5.9 |
| Perth - North East                     | 55   | 59.3 | 62.8 |  7.8 |
| Perth - North West                     | 60.4 | 65.2 | 68.6 |  8.2 |
| Perth - South East                     | 56.4 | 61.6 | 64.9 |  8.5 |
| Perth - South West                     | 58.4 | 63.7 | 66.6 |  8.2 |
| Rest of Western Australia              | 51.7 | 54.4 | 56.3 |  4.6 |
| Bunbury                                | 53.2 | 57.3 | 59.5 |  6.3 |
| Western Australia - Wheat Belt         | 54.9 | 56.5 | 56.6 |  1.7 |
| Western Australia - Outback (North)    | 47.1 | 50.8 | 54.3 |  7.2 |
| Kimberley                              | 45.2 | 48   | 51.2 |  6   |
| East Pilbara                           | 43.5 | 50.6 | 52.5 |  9   |
| West Pilbara                           | 52.3 | 53.5 | 58   |  5.7 |
| Western Australia - Outback (South)    | 49.7 | 52   | 53.5 |  3.8 |
| Esperance                              | 54.5 | 56.5 | 54.9 |  0.4 |
| Gascoyne                               | 51.9 | 52.6 | 55.1 |  3.2 |
| Goldfields                             | 46.9 | 49.3 | 51.5 |  4.6 |
| Mid West                               | 49.9 | 52.8 | 54.3 |  4.4 |
| Tasmania                               | 51.6 | 56.5 | 59   |  7.4 |
| Greater Hobart                         | 56.1 | 60.8 | 63.6 |  7.5 |
| Rest of Tasmania                       | 48.3 | 53.3 | 55.3 |  7   |
| Launceston and North East              | 50.3 | 55.3 | 56.8 |  6.5 |
| South East                             | 46.6 | 51.8 | 55.1 |  8.5 |
| West and North West                    | 46.4 | 51.3 | 53.6 |  7.2 |
| Northern Territory                     | 50.9 | 55.5 | 56.4 |  5.5 |
| Greater Darwin                         | 58.1 | 61.5 | 64.4 |  6.3 |
| Rest of Northern Territory             | 41.3 | 46.9 | 43.8 |  2.5 |
| Northern Territory - Outback           | 41.3 | 46.9 | 43.8 |  2.5 |
| Alice Springs                          | 48.2 | 53.2 | 52.5 |  4.3 |
| Barkly                                 | 33.7 | 38.3 | 40.6 |  6.9 |
| Daly - Tiwi - West Arnhem              | 30.7 | 38.6 | 31.2 |  0.5 |
| East Arnhem                            | 36.3 | 43.1 | 36.1 | -0.2 |
| Katherine                              | 40.3 | 45.8 | 42.5 |  2.2 |
| Australian Capital Territory           | 71.9 | 76   | 77.4 |  5.5 |
| Australian Capital Cities              | 59.2 | 64.4 | 68.1 |  8.9 |
| Australian Rest of States              | 52.4 | 56.7 | 59.8 |  7.4 |



label: E=D-B
labeled_formulas: E=D-B
output: {"Arithmetic-Relationship": ["E=D-B"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_393632___xlsx_5e7793da209622211ca8ea6a98da5e132ca5b15e.xlsx___line_421