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 |   G |   H |   I | J             |
|:-----------------------------|-------------:|---------:|-----------:|------------:|----:|----:|----:|----:|:--------------|
| Guildhall School Music/Drama | -58.2208     | 1.45867  | -61.0798   | -55.3619    |   0 |   1 |   0 |   0 | Other         |
| Cons Dance/Drama             | -56.4183     | 0.96824  | -58.3161   | -54.5206    |   0 |   1 |   0 |   0 | Other         |
| L'pool Inst Perf Arts        | -33.8341     | 1.61284  | -36.9952   | -30.6729    |   0 |   1 |   0 |   0 | Other         |
| Central Sch Speech/Drama     | -24.4717     | 1.97665  | -28.3459   | -20.5974    |   0 |   1 |   0 |   0 | Other         |
| Trinity Cons Music/Dance     | -24.1376     | 1.714    | -27.497    | -20.7782    |   0 |   1 |   0 |   0 | Other         |
| Glasgow School of Art        | -20.9858     | 1.93742  | -24.7831   | -17.1885    |   0 |   1 |   0 |   0 | Other         |
| Glyndwr                      | -19.9607     | 1.4804   | -22.8623   | -17.0591    |   0 |   1 |   0 |   0 | Other         |
| Leeds City                   | -19.5492     | 1.827    | -23.1301   | -15.9683    |   0 |   1 |   0 |   0 | Other         |
| Wales Trinity St David       | -19.2035     | 0.955511 | -21.0763   | -17.3307    |   0 |   1 |   0 |   0 | Other         |
| Bolton                       | -18.7678     | 0.913149 | -20.5576   | -16.9781    |   0 |   1 |   0 |   0 | Other         |
| U Campus Suffolk             | -17.9186     | 1.00248  | -19.8835   | -15.9537    |   0 |   1 |   0 |   0 | Other         |
| Bangor                       | -15.6536     | 0.604393 | -16.8382   | -14.469     |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Royal Northern C Music       | -15.5911     | 2.34244  | -20.1822   | -10.9999    |   0 |   1 |   0 |   0 | Other         |
| Glamorgan                    | -15.5159     | 0.767446 | -17.0201   | -14.0117    |   0 |   0 |   1 |   0 | Post 1992 uni |
| Rose Bruford                 | -15.0264     | 1.76332  | -18.4825   | -11.5703    |   0 |   1 |   0 |   0 | Other         |
| Norwich UC Arts              | -14.1101     | 1.53667  | -17.122    | -11.0982    |   0 |   1 |   0 |   0 | Other         |
| St Mark & St John            | -11.2274     | 0.852628 | -12.8986   |  -9.55625   |   0 |   1 |   0 |   0 | Other         |
| UC Falmouth                  | -11.0636     | 1.07561  | -13.1717   |  -8.95536   |   0 |   1 |   0 |   0 | Other         |
| Derby                        | -10.5191     | 0.571571 | -11.6394   |  -9.39885   |   0 |   1 |   0 |   0 | Other         |
| UC Birmingham                | -10.3637     | 0.968654 | -12.2623   |  -8.46516   |   0 |   1 |   0 |   0 | Other         |
| West London                  |  -9.82543    | 1.24809  | -12.2717   |  -7.37917   |   0 |   0 |   1 |   0 | Post 1992 uni |
| Writtle C                    |  -9.38659    | 1.78196  | -12.8792   |  -5.89394   |   0 |   1 |   0 |   0 | Other         |
| Bishop Grosseteste           |  -8.43958    | 1.22602  | -10.8426   |  -6.03658   |   0 |   1 |   0 |   0 | Other         |
| Stirling                     |  -8.3407     | 1.36537  | -11.0168   |  -5.66458   |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Prifysgol Aberystwyth        |  -8.00093    | 0.632431 |  -9.2405   |  -6.76137   |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Staffordshire                |  -7.75571    | 0.575203 |  -8.88311  |  -6.62831   |   0 |   0 |   1 |   0 | Post 1992 uni |
| Teesside                     |  -7.66316    | 0.668854 |  -8.97411  |  -6.35221   |   0 |   0 |   1 |   0 | Post 1992 uni |
| London South Bank            |  -7.58808    | 1.03569  |  -9.61804  |  -5.55812   |   0 |   0 |   1 |   0 | Post 1992 uni |
| Chester                      |  -7.57365    | 0.535458 |  -8.62315  |  -6.52415   |   0 |   1 |   0 |   0 | Other         |
| London Met                   |  -7.13359    | 0.856587 |  -8.8125   |  -5.45468   |   0 |   0 |   1 |   0 | Post 1992 uni |
| Worcester                    |  -6.87809    | 0.738394 |  -8.32535  |  -5.43084   |   0 |   1 |   0 |   0 | Other         |
| Bradford                     |  -6.67139    | 0.886652 |  -8.40923  |  -4.93355   |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Chichester                   |  -6.44667    | 0.938926 |  -8.28696  |  -4.60637   |   0 |   1 |   0 |   0 | Other         |
| Winchester                   |  -6.29471    | 0.72791  |  -7.72141  |  -4.868     |   0 |   1 |   0 |   0 | Other         |
| Cardiff Met                  |  -6.28565    | 0.789711 |  -7.83349  |  -4.73782   |   0 |   1 |   0 |   0 | Other         |
| Sunderland                   |  -6.00381    | 0.720834 |  -7.41664  |  -4.59097   |   0 |   0 |   1 |   0 | Post 1992 uni |
| Middlesex                    |  -5.71454    | 0.806593 |  -7.29546  |  -4.13362   |   0 |   0 |   1 |   0 | Post 1992 uni |
| Bedfordshire                 |  -5.70054    | 0.750995 |  -7.17249  |  -4.22859   |   0 |   1 |   0 |   0 | Other         |
| Cental Lancashire            |  -5.67147    | 0.495361 |  -6.64238  |  -4.70056   |   0 |   0 |   1 |   0 | Post 1992 uni |
| Plymouth                     |  -5.39848    | 0.477382 |  -6.33415  |  -4.46281   |   0 |   0 |   1 |   0 | Post 1992 uni |
| De Montfort                  |  -5.24154    | 0.547596 |  -6.31483  |  -4.16825   |   0 |   0 |   1 |   0 | Post 1992 uni |
| L'pool Hope                  |  -5.01939    | 0.781582 |  -6.55129  |  -3.48749   |   0 |   1 |   0 |   0 | Other         |
| SOAS                         |  -4.95668    | 1.33866  |  -7.58045  |  -2.33291   |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Wolverhampton                |  -4.95416    | 0.632732 |  -6.19431  |  -3.714     |   0 |   0 |   1 |   0 | Post 1992 uni |
| Anglia Ruskin                |  -4.83104    | 0.570592 |  -5.9494   |  -3.71268   |   0 |   0 |   1 |   0 | Post 1992 uni |
| Northampton                  |  -4.75653    | 0.592641 |  -5.91811  |  -3.59495   |   0 |   1 |   0 |   0 | Other         |
| York St John UC              |  -4.65606    | 0.680591 |  -5.99002  |  -3.32211   |   0 |   1 |   0 |   0 | Other         |
| Swansea                      |  -4.65082    | 0.630945 |  -5.88747  |  -3.41416   |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Arts Inst Bournemouth        |  -4.43021    | 1.75694  |  -7.87381  |  -0.986612  |   0 |   1 |   0 |   0 | Other         |
| Huddersfield                 |  -4.30808    | 0.619747 |  -5.52279  |  -3.09338   |   0 |   0 |   1 |   0 | Post 1992 uni |
| Lincoln                      |  -4.14937    | 0.542418 |  -5.21251  |  -3.08623   |   0 |   1 |   0 |   0 | Other         |
| Sussex                       |  -4.12119    | 0.62883  |  -5.3537   |  -2.88869   |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Cumbria                      |  -3.97166    | 0.700443 |  -5.34453  |  -2.59879   |   0 |   1 |   0 |   0 | Other         |
| Manchester Met               |  -3.87536    | 0.422415 |  -4.70329  |  -3.04742   |   0 |   0 |   1 |   0 | Post 1992 uni |
| U Creative Arts              |  -3.77288    | 1.341    |  -6.40123  |  -1.14452   |   0 |   1 |   0 |   0 | Other         |
| Queen Margaret               |  -3.56102    | 2.15597  |  -7.78673  |   0.664685  |   0 |   1 |   0 |   0 | Other         |
| UEA                          |  -3.32081    | 0.527448 |  -4.3546   |  -2.28701   |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Buckingham New               |  -3.11405    | 0.954642 |  -4.98515  |  -1.24296   |   0 |   1 |   0 |   0 | Other         |
| Hull                         |  -3.109      | 0.52125  |  -4.13065  |  -2.08735   |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Greenwich                    |  -2.98729    | 0.715071 |  -4.38883  |  -1.58575   |   0 |   0 |   1 |   0 | Post 1992 uni |
| L'pool John Moores           |  -2.92876    | 0.54604  |  -3.999    |  -1.85852   |   0 |   0 |   1 |   0 | Post 1992 uni |
| Bath Spa                     |  -2.8543     | 0.677258 |  -4.18172  |  -1.52687   |   0 |   1 |   0 |   0 | Other         |
| Aberdeen                     |  -2.78687    | 1.38468  |  -5.50086  |  -0.0728933 |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Essex                        |  -2.77098    | 0.549225 |  -3.84746  |  -1.6945    |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Gloucestershire              |  -2.67024    | 0.617164 |  -3.87988  |  -1.4606    |   0 |   1 |   0 |   0 | Other         |
| East London                  |  -2.63897    | 1.00284  |  -4.60453  |  -0.673409  |   0 |   0 |   1 |   0 | Post 1992 uni |
| Leeds Met                    |  -2.41596    | 0.504344 |  -3.40447  |  -1.42745   |   0 |   1 |   0 |   0 | Other         |
| U West England               |  -2.04888    | 0.479776 |  -2.98924  |  -1.10852   |   0 |   0 |   1 |   0 | Post 1992 uni |
| Edge Hill                    |  -1.55297    | 0.744416 |  -3.01203  |  -0.093918  |   0 |   1 |   0 |   0 | Other         |
| Herriot-Watt                 |  -1.20332    | 2.02618  |  -5.17463  |   2.76799   |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Salford                      |  -0.736034   | 0.633439 |  -1.97757  |   0.505506  |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Portsmouth                   |  -0.565092   | 0.539665 |  -1.62283  |   0.492651  |   0 |   0 |   1 |   0 | Post 1992 uni |
| Roehampton                   |  -0.563398   | 0.699996 |  -1.93539  |   0.808595  |   0 |   1 |   0 |   0 | Other         |
| Canterbury Christchuch       |  -0.253874   | 0.63287  |  -1.4943   |   0.98655   |   0 |   1 |   0 |   0 | Other         |
| Keele                        |  -0.192033   | 0.61711  |  -1.40157  |   1.0175    |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Newman                       |  -0.00635621 | 1.06805  |  -2.09973  |   2.08702   |   0 |   1 |   0 |   0 | Other         |
| Kent                         |   0.0570428  | 0.575585 |  -1.0711   |   1.18519   |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Nottingham Trent             |   0.061159   | 0.456678 |  -0.83393  |   0.956248  |   0 |   0 |   1 |   0 | Post 1992 uni |
| Coventry                     |   0.132875   | 0.609972 |  -1.06267  |   1.32842   |   0 |   0 |   1 |   0 | Post 1992 uni |
| Sheffield Hallam             |   0.135438   | 0.520453 |  -0.88465  |   1.15553   |   0 |   0 |   1 |   0 | Post 1992 uni |
| S'ton Solent                 |   0.244644   | 0.805241 |  -1.33363  |   1.82292   |   0 |   1 |   0 |   0 | Other         |
| Leicester                    |   0.716125   | 0.643503 |  -0.545141 |   1.97739   |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Royal Agricultural C         |   0.783647   | 1.77288  |  -2.69119  |   4.25848   |   0 |   1 |   0 |   0 | Other         |
| U Arts London                |   0.847192   | 0.992502 |  -1.09811  |   2.7925    |   0 |   1 |   0 |   0 | Other         |
| Leeds Trinity                |   1.51649    | 0.926217 |  -0.298896 |   3.33188   |   0 |   1 |   0 |   0 | Other         |
| Goldsmiths                   |   1.60291    | 0.900901 |  -0.162853 |   3.36868   |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Birmingham City              |   1.79233    | 0.571623 |   0.671944 |   2.91271   |   0 |   0 |   1 |   0 | Post 1992 uni |
| Lancaster                    |   1.98403    | 0.579309 |   0.848584 |   3.11948   |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Kingston                     |   2.25204    | 0.648136 |   0.981691 |   3.52239   |   0 |   0 |   1 |   0 | Post 1992 uni |
| Northumbria                  |   2.26311    | 0.561835 |   1.16191  |   3.36431   |   0 |   0 |   1 |   0 | Post 1992 uni |
| City                         |   3.14665    | 0.937276 |   1.30958  |   4.98371   |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Royal Holloway               |   3.27132    | 0.796658 |   1.70987  |   4.83277   |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Hertfordshire                |   3.57578    | 0.563786 |   2.47076  |   4.6808    |   0 |   0 |   1 |   0 | Post 1992 uni |
| Brighton                     |   3.8826     | 0.61245  |   2.6822   |   5.083     |   0 |   0 |   1 |   0 | Post 1992 uni |
| Westminster                  |   4.65959    | 0.858293 |   2.97733  |   6.34184   |   0 |   0 |   1 |   0 | Post 1992 uni |
| St Mary's UC Twickeham       |   4.67516    | 0.915868 |   2.88006  |   6.47026   |   0 |   1 |   0 |   0 | Other         |
| Oxford Brookes               |   5.13972    | 0.557291 |   4.04743  |   6.23201   |   0 |   0 |   1 |   0 | Post 1992 uni |
| Bournemouth                  |   5.48813    | 0.648549 |   4.21697  |   6.75928   |   0 |   0 |   1 |   0 | Post 1992 uni |
| Royal Veterinary C           |   6.01423    | 3.11575  |  -0.092647 |  12.1211    |   0 |   1 |   0 |   0 | Other         |
| Reading                      |   6.74312    | 0.563358 |   5.63894  |   7.84731   |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Ravensbourne                 |   6.76067    | 1.75954  |   3.31198  |  10.2094    |   0 |   1 |   0 |   0 | Other         |
| Surrey                       |   6.9318     | 0.787978 |   5.38736  |   8.47624   |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Dundee                       |   8.71385    | 2.31506  |   4.17633  |  13.2514    |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Brunel                       |  11.5598     | 0.778413 |  10.0341   |  13.0855    |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Aston                        |  12.5745     | 1.00027  |  10.614    |  14.535     |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Heythrop College             |  13.1259     | 2.81322  |   7.61198  |  18.6398    |   0 |   1 |   0 |   0 | Other         |
| St George's Hospital         |  14.603      | 2.92944  |   8.86134  |  20.3447    |   0 |   1 |   0 |   0 | Other         |
| St Andrews                   |  14.8441     | 1.15905  |  12.5724   |  17.1159    |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Bath                         |  15.1489     | 1.04574  |  13.0993   |  17.1986    |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Loughborough                 |  17.1756     | 0.695948 |  15.8116   |  18.5397    |   0 |   0 |   0 |   1 | Pre 1992 uni  |
| Harper Adams                 |  21.9997     | 2.19877  |  17.6902   |  26.3093    |   0 |   1 |   0 |   0 | Other         |



labeled_formulas: F=G*H
F=G*I
F=H*I
F=(B*G)*H
F=(B*G)*I
F=(B*H)*I
F=(C*G)*H
F=(C*G)*I
F=(C*H)*I
F=(D*G)*H
F=(D*G)*I
F=(D*H)*I
F=(E*G)*H
F=(E*G)*I
F=(E*H)*I
F=(G+H)*I
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_595501___xlsx_d216e3f0abe4f7e0e87b8d0eec5ad915579c5ab5.xlsx___line_730