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 |
|:---------------------|---------:|----------:|---------:|
| Bayswater            |  865.512 |  47.1309  |  912.643 |
| Eraring              |  862.346 |  47.7966  |  910.143 |
| Liddell              |  930     |  50.5917  |  980.592 |
| Mount Piper          |  862.302 |  46.2162  |  908.518 |
| Vales Point          |  860     |  48.3051  |  908.305 |
| Callide B            |  920     |  11.3435  |  931.343 |
| Callide Power Plant  |  895.323 |  11.589   |  906.912 |
| Gladstone            |  960     |  11.7614  |  971.761 |
| Kogan Creek          |  820     |  11.04    |  831.04  |
| Millmerran           |  830.135 |  11.4634  |  841.598 |
| Stanwell             |  860.94  |  11.25    |  872.19  |
| Tarong               |  860.022 |  11.4365  |  871.459 |
| Tarong North         |  832.965 |  10.7908  |  843.756 |
| Loy Yang A           | 1150     |   4.81765 | 1154.82  |
| Loy Yang B           | 1136.04  |   4.98045 | 1141.02  |
| Yallourn             | 1310     |   5.51489 | 1315.51  |
| Colongra             |  640     | 142.56    |  782.56  |
| Smithfield           |  480.969 | 106.771   |  587.74  |
| Tallawarra           |  358.14  |  89.3952  |  447.535 |
| Uranquinty           |  581.712 | 142.56    |  724.272 |
| Barcaldine           |  999.957 |  99.2829  | 1099.24  |
| Braemar              |  570.478 |  92.664   |  663.142 |
| Condamine            |  454.324 |  56.745   |  511.069 |
| Darling Downs        |  420.205 |  57.3809  |  477.585 |
| Oakey                |  760     |  85.2736  |  845.274 |
| Roma                 |  663.854 |  92.664   |  756.518 |
| Swanbank E           |  370     |  57.9523  |  427.952 |
| Yabulu               |  450     |  59.2122  |  509.212 |
| Yabulu Steam Turbine |  450     |  59.2122  |  509.212 |
| Yarwun               |  532.313 |  80.9365  |  613.249 |
| Somerton             |  760     |  57.915   |  817.915 |
| Bairnsdale           |  524.327 |  40.8812  |  565.208 |
| Jeeralang A          |  819.934 |  59.4707  |  879.405 |
| Jeeralang B          |  819.934 |  59.4707  |  879.405 |
| Laverton North       |  745.381 |  44.7987  |  790.18  |
| Mortlake             |  530     |  43.4363  |  573.436 |
| Newport              |  530     |  40.0541  |  570.054 |
| Valley Power         |  813.631 |  57.915   |  871.546 |
| Hallett GT           | 1020     | 154.44    | 1174.44  |
| Dry Creek            | 1200     | 142.56    | 1342.56  |
| Ladbroke Grove       |  530     | 123.552   |  653.552 |
| Mintaro              |  820     | 132.377   |  952.377 |
| Osborne              |  460     |  84.6857  |  544.686 |
| Pelican Point        |  397.267 |  76.44    |  473.707 |
| Quarantine           |  688.809 | 111.15    |  799.959 |
| Torrens Island A     |  590     | 118.56    |  708.56  |
| Torrens Island B     |  570     | 111.15    |  681.15  |
| Bell Bay Three       |  617.723 |  46.9614  |  664.684 |
| Tamar Valley GT      |  652.976 |  49.6414  |  702.617 |
| Tamar Valley ST      |  410.383 |  28.3725  |  438.755 |
| Hunter Valley GT     |  887.181 |  45.8229  |  933.004 |
| Mackay GT            | 1000     |  45.8229  | 1045.82  |
| Mount Stuart         |  955.865 |  42.768   |  998.633 |
| Angaston1            |  940.2   |  73.4     | 1013.6   |
| Lonsdale1            | 1442     |  49.8     | 1491.8   |
| Port Lincoln         | 1400     |  45.8585  | 1445.86  |
| Port Lincoln 3       | 1400     |  45.8585  | 1445.86  |
| Port Stanvac1        | 1442     |  49.8     | 1491.8   |
| Snuggery             | 1400     |  48.3508  | 1448.35  |
| Tailem Bend          |  940.2   |  73.4     | 1013.6   |
| All hydro            |    0     |   0       |    0     |
| All wind             |    0     |   0       |    0     |
| All solar            |    0     |   0       |    0     |



label: E=C+D
labeled_formulas: E=C+D
output: {"Arithmetic-Relationship": ["E=C+D"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_48846___xlsx_3a79510745e0d834fa5845d6908444ba3f2c75c6.xlsx___line_274