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 |
|:------|:----|:--------|-------------:|----------:|----------:|-------------:|
| ANH21 | ANH | 2020-21 |  1.06716     |  494.854  |  0.794906 |  1.86207     |
| ANH22 | ANH | 2021-22 |  1.29271     |  569.163  |  0.750179 |  2.04289     |
| ANH23 | ANH | 2022-23 |  0.0223865   |  614.483  |  0.556026 |  0.578413    |
| ANH24 | ANH | 2023-24 |  0.0224123   |  601.174  |  0.365067 |  0.387479    |
| ANH25 | ANH | 2024-25 |  0.0224326   |  466.572  |  0.410842 |  0.433275    |
| NES21 | NES | 2020-21 |  0.372       |  348.078  |  0        |  0.372       |
| NES22 | NES | 2021-22 |  0.369       |  368.717  |  0        |  0.369       |
| NES23 | NES | 2022-23 |  0.245       |  360.499  |  0        |  0.245       |
| NES24 | NES | 2023-24 |  0.122       |  337.229  |  0        |  0.122       |
| NES25 | NES | 2024-25 |  0.122       |  311.733  |  0        |  0.122       |
| NWT21 | NWT | 2020-21 |  0.0417306   |  546.914  |  0        |  0.0417306   |
| NWT22 | NWT | 2021-22 |  0.310004    |  511.026  |  0        |  0.310004    |
| NWT23 | NWT | 2022-23 |  0.00842264  |  491.883  |  0        |  0.00842264  |
| NWT24 | NWT | 2023-24 |  0.000431808 |  466.262  |  0        |  0.000431808 |
| NWT25 | NWT | 2024-25 |  0.00411107  |  461.418  |  0        |  0.00411107  |
| SRN21 | SRN | 2020-21 |  0.988       |  238.969  |  0        |  0.988       |
| SRN22 | SRN | 2021-22 |  0.988       |  240.008  |  0        |  0.988       |
| SRN23 | SRN | 2022-23 |  0.988       |  219.66   |  0        |  0.988       |
| SRN24 | SRN | 2023-24 |  0.988       |  201.802  |  0        |  0.988       |
| SRN25 | SRN | 2024-25 |  0.988       |  217.626  |  0        |  0.988       |
| SWB21 | SWB | 2020-21 |  0.38        |  164.926  |  0.025    |  0.405       |
| SWB22 | SWB | 2021-22 |  0.38        |  179.669  |  0.025    |  0.405       |
| SWB23 | SWB | 2022-23 |  0.38        |  192.194  |  0.025    |  0.405       |
| SWB24 | SWB | 2023-24 |  0.38        |  181.702  |  0.025    |  0.405       |
| SWB25 | SWB | 2024-25 |  0.38        |  175.761  |  0.025    |  0.405       |
| TMS21 | TMS | 2020-21 |  0.233084    | 1009.84   |  0.480995 |  0.714079    |
| TMS22 | TMS | 2021-22 |  1.1777      | 1101.9    |  0.480995 |  1.6587      |
| TMS23 | TMS | 2022-23 |  0.951397    | 1077.42   |  0.480995 |  1.43239     |
| TMS24 | TMS | 2023-24 |  0           | 1033.97   |  0.480995 |  0.480995    |
| TMS25 | TMS | 2024-25 |  0           |  997.919  |  0.480995 |  0.480995    |
| WSH21 | WSH | 2020-21 |  0.146       |  338.873  |  0        |  0.146       |
| WSH22 | WSH | 2021-22 |  0.146       |  347.164  |  0        |  0.146       |
| WSH23 | WSH | 2022-23 |  0.118       |  338.818  |  0        |  0.118       |
| WSH24 | WSH | 2023-24 |  0.121       |  324.732  |  0        |  0.121       |
| WSH25 | WSH | 2024-25 |  0.115       |  316.383  |  0        |  0.115       |
| WSX21 | WSX | 2020-21 |  0.23551     |  134.266  |  0        |  0.23551     |
| WSX22 | WSX | 2021-22 |  0.0595694   |  125.599  |  0        |  0.0595694   |
| WSX23 | WSX | 2022-23 |  0.459917    |  144.289  |  0        |  0.459917    |
| WSX24 | WSX | 2023-24 |  0.0285297   |  125.345  |  0        |  0.0285297   |
| WSX25 | WSX | 2024-25 |  0.0285297   |  120.554  |  0        |  0.0285297   |
| YKY21 | YKY | 2020-21 |  2.474       |  385.797  |  0        |  2.474       |
| YKY22 | YKY | 2021-22 |  1.419       |  385.065  |  0        |  1.419       |
| YKY23 | YKY | 2022-23 |  2.232       |  393.66   |  0        |  2.232       |
| YKY24 | YKY | 2023-24 |  1.536       |  376.679  |  0        |  1.536       |
| YKY25 | YKY | 2024-25 |  0.308       |  345.664  |  0        |  0.308       |
| AFW21 | AFW | 2020-21 |  0.0864683   |  287.61   |  0        |  0.0864683   |
| AFW22 | AFW | 2021-22 |  0.0746805   |  290.692  |  0        |  0.0746805   |
| AFW23 | AFW | 2022-23 |  0.0718172   |  281.391  |  0        |  0.0718172   |
| AFW24 | AFW | 2023-24 |  0.0717941   |  264.46   |  0        |  0.0717941   |
| AFW25 | AFW | 2024-25 |  0.0643421   |  241.872  |  0        |  0.0643421   |
| BRL21 | BRL | 2020-21 |  0.11        |   91.388  |  0        |  0.11        |
| BRL22 | BRL | 2021-22 |  0.11        |   89.27   |  0        |  0.11        |
| BRL23 | BRL | 2022-23 |  0.11        |   89.474  | -0.001    |  0.109       |
| BRL24 | BRL | 2023-24 |  0.11        |   89.114  | -0.001    |  0.109       |
| BRL25 | BRL | 2024-25 |  0.11        |   89.552  | -0.001    |  0.109       |
| PRT21 | PRT | 2020-21 |  0           |   45.14   |  0        |  0           |
| PRT22 | PRT | 2021-22 |  0           |   38.365  |  0        |  0           |
| PRT23 | PRT | 2022-23 |  0           |   39.048  |  0        |  0           |
| PRT24 | PRT | 2023-24 |  0           |   51.654  |  0        |  0           |
| PRT25 | PRT | 2024-25 |  0           |   53.923  |  0        |  0           |
| SES21 | SES | 2020-21 |  0           |   52.777  |  0.017    |  0.017       |
| SES22 | SES | 2021-22 |  0           |   57.544  |  0.017    |  0.017       |
| SES23 | SES | 2022-23 |  0           |   52.131  |  0.017    |  0.017       |
| SES24 | SES | 2023-24 |  0           |   46.371  |  0.016    |  0.016       |
| SES25 | SES | 2024-25 |  0           |   45.346  |  0.016    |  0.016       |
| SEW21 | SEW | 2020-21 |  2.60254     |  172.073  |  0        |  2.60254     |
| SEW22 | SEW | 2021-22 |  4.16274     |  199.614  |  0        |  4.16274     |
| SEW23 | SEW | 2022-23 |  5.38144     |  208.204  |  0        |  5.38144     |
| SEW24 | SEW | 2023-24 |  9.96239     |  186.195  |  0        |  9.96239     |
| SEW25 | SEW | 2024-25 | 12.7967      |  194.588  |  0        | 12.7967      |
| SSC21 | SSC | 2020-21 |  0.127209    |  113.258  |  0        |  0.127209    |
| SSC22 | SSC | 2021-22 |  0.121103    |  115.482  |  0        |  0.121103    |
| SSC23 | SSC | 2022-23 |  0           |  116.387  |  0        |  0           |
| SSC24 | SSC | 2023-24 |  0           |   93.9133 |  0        |  0           |
| SSC25 | SSC | 2024-25 |  0           |   96.8046 |  0        |  0           |
| SVE21 | SVE | 2020-21 |  0.32        |  575.066  |  0        |  0.32        |
| SVE22 | SVE | 2021-22 |  0.32        |  631.129  |  0        |  0.32        |
| SVE23 | SVE | 2022-23 |  0.32        |  643.435  |  0        |  0.32        |
| SVE24 | SVE | 2023-24 |  0.32        |  635.412  |  0        |  0.32        |
| SVE25 | SVE | 2024-25 |  0.32        |  630.764  |  0        |  0.32        |
| HDD21 | HDD | 2020-21 |  0           |   27.46   |  0.01005  |  0.01005     |
| HDD22 | HDD | 2021-22 |  0           |   27.121  |  0.01005  |  0.01005     |
| HDD23 | HDD | 2022-23 |  0           |   26.327  |  0.01005  |  0.01005     |
| HDD24 | HDD | 2023-24 |  0           |   25.742  |  0.01005  |  0.01005     |
| HDD25 | HDD | 2024-25 |  0           |   26.044  |  0.01005  |  0.01005     |



label: G=D+F
labeled_formulas: G=D+F
output: {"Arithmetic-Relationship": ["G=D+F"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_42350___xlsx_8e383faf11472ad28f6da85f42655ff8bcfd635a.xlsx___line_476