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 |
|:----------------------------------------------------|----:|-----:|---------:|
| Aberystwyth University                              |  17 |   26 | 0.653846 |
| Anglia Ruskin University                            |   6 |   15 | 0.4      |
| Aston University                                    |  89 |  128 | 0.695312 |
| Bangor University                                   |  43 |   59 | 0.728814 |
| Birkbeck College                                    |   5 |    6 | 0.833333 |
| Birmingham City University                          |   2 |    4 | 0.5      |
| Bournemouth University                              |   3 |   13 | 0.230769 |
| Brunel University London                            |  52 |   83 | 0.626506 |
| Cardiff Metropolitan University                     |   5 |    7 | 0.714286 |
| Cardiff University                                  | 204 |  266 | 0.766917 |
| City University of London                           |  30 |   52 | 0.576923 |
| Coventry University                                 |  35 |   60 | 0.583333 |
| Cranfield University                                |  86 |  144 | 0.597222 |
| De Montfort University                              |  31 |   76 | 0.407895 |
| Edinburgh Napier University                         |  16 |   26 | 0.615385 |
| Glasgow Caledonian University                       |  15 |   19 | 0.789474 |
| Glasgow School of Art                               |   4 |    7 | 0.571429 |
| Glyndŵr University                                  |   1 |    1 | 1        |
| Harper Adams University                             |   2 |    2 | 1        |
| Heriot-Watt University                              |  69 |   96 | 0.71875  |
| Imperial College of Science Technology and Medicine | 697 | 1004 | 0.694223 |
| Keele University                                    |  24 |   34 | 0.705882 |
| King's College London                               | 250 |  337 | 0.74184  |
| Kingston University                                 |   4 |   19 | 0.210526 |
| Leeds Beckett University                            |   1 |    4 | 0.25     |
| Liverpool John Moores University                    |  10 |   34 | 0.294118 |
| Liverpool School of Tropical Medicine               |  10 |   13 | 0.769231 |
| London Business School                              |   1 |    1 | 1        |
| London Metropolitan University                      |   2 |    6 | 0.333333 |
| London School of Hygiene and Tropical Medicine      |  23 |   29 | 0.793103 |
| London South Bank University                        |  37 |   54 | 0.685185 |
| Loughborough University                             |  61 |  107 | 0.570093 |
| Medway School of Pharmacy                           |   1 |    1 | 1        |
| Middlesex University                                |   6 |    8 | 0.75     |
| Newcastle University                                | 120 |  165 | 0.727273 |
| Oxford Brookes University                           |  13 |   17 | 0.764706 |
| Queen Margaret University Edinburgh                 |   1 |    1 | 1        |
| Queen Mary University of London                     | 139 |  193 | 0.720207 |
| Roehampton University                               |   2 |    2 | 1        |
| Royal College of Art                                |  34 |   58 | 0.586207 |
| Royal Holloway and Bedford New College              |  36 |   47 | 0.765957 |
| Sheffield Hallam University                         |  49 |   75 | 0.653333 |
| SRUC                                                |   3 |    3 | 1        |
| St George's University of London                    |  23 |   39 | 0.589744 |
| Staffordshire University                            |  11 |   25 | 0.44     |
| Swansea University                                  |  62 |  118 | 0.525424 |
| Teesside University                                 |   8 |   11 | 0.727273 |
| The Institute of Cancer Research                    | 111 |  121 | 0.917355 |
| The Manchester Metropolitan University              |  15 |   32 | 0.46875  |
| The Nottingham Trent University                     |  55 |   78 | 0.705128 |
| The Open University                                 |  12 |   17 | 0.705882 |
| The Queen's University of Belfast                   | 171 |  250 | 0.684    |
| The Robert Gordon University                        |  23 |   31 | 0.741935 |
| The Royal Veterinary College                        |  12 |   30 | 0.4      |
| The University of Aberdeen                          | 126 |  158 | 0.797468 |
| The University of Bath                              |  84 |  127 | 0.661417 |
| The University of Birmingham                        | 157 |  226 | 0.69469  |
| The University of Bolton                            |   9 |   36 | 0.25     |
| The University of Bradford                          |  38 |   59 | 0.644068 |
| The University of Brighton                          |  21 |   27 | 0.777778 |
| The University of Bristol                           | 196 |  289 | 0.678201 |
| The University of Buckingham                        |   2 |    5 | 0.4      |
| The University of Cambridge                         | 656 |  873 | 0.751432 |
| The University of Central Lancashire                |  20 |   32 | 0.625    |
| The University of Chichester                        |   2 |    2 | 1        |
| The University of Dundee                            | 182 |  265 | 0.686792 |
| The University of East Anglia                       |  32 |   46 | 0.695652 |
| The University of East London                       |   4 |    8 | 0.5      |
| The University of Edinburgh                         | 250 |  363 | 0.688705 |
| The University of Essex                             |  11 |   13 | 0.846154 |
| The University of Exeter                            |  43 |   71 | 0.605634 |
| The University of Glasgow                           | 175 |  222 | 0.788288 |
| The University of Greenwich                         |  26 |   39 | 0.666667 |
| The University of Huddersfield                      |  10 |   20 | 0.5      |
| The University of Hull                              |  44 |   70 | 0.628571 |
| The University of Kent                              |  30 |   45 | 0.666667 |
| The University of Lancaster                         |  47 |   83 | 0.566265 |
| The University of Leeds                             | 175 |  227 | 0.770925 |
| The University of Leicester                         | 123 |  150 | 0.82     |
| The University of Lincoln                           |   8 |   15 | 0.533333 |
| The University of Liverpool                         | 127 |  177 | 0.717514 |
| The University of Manchester                        | 302 |  441 | 0.684807 |
| The University of Northampton                       |   3 |    3 | 1        |
| The University of Oxford                            | 930 | 1370 | 0.678832 |
| The University of Portsmouth                        |   7 |   11 | 0.636364 |
| The University of Reading                           |  34 |   51 | 0.666667 |
| The University of Salford                           |  16 |   29 | 0.551724 |
| The University of Sheffield                         | 214 |  353 | 0.606232 |
| The University of Southampton                       | 265 |  383 | 0.691906 |
| The University of St Andrews                        | 181 |  224 | 0.808036 |
| The University of Stirling                          |   3 |    4 | 0.75     |
| The University of Strathclyde                       | 133 |  193 | 0.689119 |
| The University of Sunderland                        |  14 |   17 | 0.823529 |
| The University of Surrey                            | 128 |  187 | 0.684492 |
| The University of Sussex                            |  36 |   62 | 0.580645 |
| The University of the West of Scotland              |   7 |   15 | 0.466667 |
| The University of Wales                             |   4 |    5 | 0.8      |
| The University of Warwick                           | 125 |  217 | 0.576037 |
| The University of West London                       |   1 |    1 | 1        |
| The University of Westminster                       |   3 |   11 | 0.272727 |
| The University of Wolverhampton                     |   9 |   23 | 0.391304 |
| The University of York                              | 120 |  172 | 0.697674 |
| University College London                           | 536 |  709 | 0.755994 |
| University of Abertay Dundee                        |  12 |   19 | 0.631579 |
| University of Chester                               |   2 |    4 | 0.5      |
| University of Derby                                 |   2 |    3 | 0.666667 |
| University of Durham                                |  97 |  126 | 0.769841 |
| University of Hertfordshire                         |  14 |   33 | 0.424242 |
| University of Northumbria at Newcastle              |  11 |   24 | 0.458333 |
| University of Nottingham                            | 241 |  329 | 0.732523 |
| University of Plymouth                              |  28 |   59 | 0.474576 |
| University of South Wales                           |   6 |   12 | 0.5      |
| University of the Arts London                       |   1 |    2 | 0.5      |
| University of the West of England Bristol           |  28 |   34 | 0.823529 |
| University of Ulster                                |  65 |  101 | 0.643564 |
| University of Wales Trinity Saint David             |   2 |    5 | 0.4      |



label: D=B/C
labeled_formulas: D=B/C
output: {"Arithmetic-Relationship": ["D=B/C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_305759___xlsx_f70dfa78b67926a583826fc880a1b81289bf7611.xlsx___line_591