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:
| B                                        |            C |            D |            E |           F |
|:-----------------------------------------|-------------:|-------------:|-------------:|------------:|
| Vector Limited                           | 172.113      | 179.893      |   7.78005    |  0.0452031  |
| Powerco Limited                          |  92.2086     |  81.2842     | -10.9244     | -0.118475   |
| Meridian Energy Limited                  |  80.9379     |  66.6268     | -14.311      | -0.176815   |
| Orion New Zealand Limited                |  61.5961     |  53.4972     |  -8.09888    | -0.131484   |
| Wellington Electricity Lines Limited     |  54.3737     |  46.2681     |  -8.10561    | -0.149072   |
| NZ Aluminium Smelters Limited            |  58.323      |  44.7041     | -13.6189     | -0.233508   |
| Contact Energy Limited                   |  24.5609     |  29.817      |   5.25609    |  0.214002   |
| Unison Networks Limited                  |  29.8381     |  26.9805     |  -2.85755    | -0.0957685  |
| Aurora Energy Limited                    |  22.115      |  25.3736     |   3.25861    |  0.147348   |
| Powernet Ltd                             |  24.3208     |  22.3199     |  -2.00089    | -0.0822708  |
| WEL Networks Limited                     |  19.9396     |  19.9988     |   0.0591737  |  0.00296765 |
| Northpower Limited                       |  16.3387     |  18.2548     |   1.91614    |  0.117276   |
| Genesis Energy Ltd                       |  10.2628     |  14.5336     |   4.27081    |  0.416143   |
| Alpine Energy Ltd                        |  12.3078     |  12.6147     |   0.306925   |  0.0249375  |
| Mainpower New Zealand Limited            |  12.3142     |  12.1192     |  -0.195076   | -0.0158415  |
| Mercury NZ Limited                       |   3.4791     |  12.1086     |   8.62953    |  2.48039    |
| Counties Power Ltd                       |  10.9639     |  11.3085     |   0.344598   |  0.0314303  |
| Network Tasman Limited                   |  11.8171     |  10.7079     |  -1.1092     | -0.0938643  |
| EA Networks                              |   4.55698    |  10.6543     |   6.09731    |  1.33802    |
| New Zealand Steel Limited                |   3.12971    |   9.97704    |   6.84734    |  2.18785    |
| Electra Limited                          |   7.50899    |   9.01908    |   1.51008    |  0.201103   |
| Horizon Energy Distribution Ltd          |   3.48821    |   7.68744    |   4.19923    |  1.20383    |
| Waipa Networks Limited                   |   7.69076    |   6.29223    |  -1.39853    | -0.181845   |
| The Lines Company Ltd                    |   4.73732    |   6.08608    |   1.34875    |  0.284708   |
| Top Energy Ltd                           |   4.92926    |   5.87884    |   0.949579   |  0.192641   |
| Marlborough Lines Limited                |   6.65786    |   5.44867    |  -1.20919    | -0.181618   |
| Network Waitaki Limited                  |   4.23118    |   5.27887    |   1.04769    |  0.247612   |
| Pan Pac Forest Product Limited           |   2.77409    |   4.19828    |   1.42419    |  0.513389   |
| Eastland Network Limited                 |   5.49494    |   4.00828    |  -1.48666    | -0.27055    |
| Westpower Limited                        |   2.04222    |   4.05686    |   2.01464    |  0.986497   |
| Norske Skog Tasman Limited               |   1.16603    |   3.82314    |   2.65711    |  2.27875    |
| Winstone Pulp International              |   3.34664    |   3.52447    |   0.177828   |  0.0531364  |
| KiwiRail Holdings Limited                |   2.84988    |   3.54282    |   0.692944   |  0.243148   |
| Nga Awa Purua Joint Venture              |   0.426895   |   2.46533    |   2.03843    |  4.77502    |
| Centralines Limited                      |   2.65462    |   2.20335    |  -0.451277   | -0.169997   |
| Trustpower Limited                       |   4.48509    |   1.97555    |  -2.50953    | -0.559528   |
| Scanpower Limited                        |   1.91857    |   1.70381    |  -0.214753   | -0.111934   |
| Ngatamariki Geothermal Ltd               |   0.260192   |   1.37385    |   1.11366    |  4.28014    |
| Buller Electricity Ltd                   |   0.550022   |   1.63561    |   1.08559    |  1.97373    |
| OMV New Zealand Production Ltd           |   1.24727    |   1.10072    |  -0.14655    | -0.117497   |
| Todd Generation Taranaki Limited         |   0.0649186  |   0.978331   |   0.913413   | 14.0701     |
| Nelson Electricity Ltd                   |   1.03561    |   0.935732   |  -0.0998782  | -0.0964439  |
| Whareroa Cogeneration Limited            |   0.16673    |   0.880669   |   0.713939   |  4.282      |
| Methanex New Zealand Ltd                 |   0.748327   |   0.856873   |   0.108546   |  0.145052   |
| Daiken Southland Limited                 |   0.79045    |   0.844241   |   0.0537909  |  0.068051   |
| Nova Energy Limited                      |   0.276678   |   0.71233    |   0.435652   |  1.57458    |
| Beach Energy Resources NZ (Holdings) Ltd |   0.884247   |   0.70153    |  -0.182717   | -0.206635   |
| Southern Generation GP Limited           |   0.241378   |   0.22926    |  -0.0121178  | -0.0502025  |
| MEL (West Wind) Limited                  |   0.115793   |   0.62467    |   0.508877   |  4.39473    |
| Mercury SPV Limited                      |   0.0801909  |   0.573981   |   0.49379    |  6.15768    |
| Waverley Wind Farm                       |   0.0733771  |   0.362538   |   0.289161   |  3.94076    |
| Tararua Wind Power                       |   0.0667613  |   0.342342   |   0.27558    |  4.12785    |
| MEL (Te Apiti) Limited                   |   0.0723059  |   0.265146   |   0.19284    |  2.667      |
| Southdown Cogeneration Ltd               |   0.0635376  |   0.154535   |   0.0909972  |  1.43218    |
| Southpark Utilities Limited              |   0.0438741  |   0.0480051  |   0.00413105 |  0.094157   |
| GTL Energy New Zealand Ltd               |   0.00514803 |   0.00949985 |   0.00435182 |  0.845336   |



label: E=D-C
labeled_formulas: E=D-C
output: {"Arithmetic-Relationship": ["E=D-C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_777080___xlsx_f42da3c86361dc19c0857ce64164b882e3d3d070.xlsx___line_622