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 | K                                                                                                                                                         |
|:------------|------:|:----------|------:|------:|----:|----:|----:|---------:|----:|:----------------------------------------------------------------------------------------------------------------------------------------------------------|
| 2013 - 2014 | 41334 | ---       | 41381 | 41382 | 0.4 | 0.1 | 0.5 | 0.725    |   4 | ---                                                                                                                                                       |
| 2013 - 2014 | 41365 | ---       | 41407 | 41418 | 0.4 | 0.2 | 0.6 | 0.733333 |   4 | ---                                                                                                                                                       |
| 2013 - 2014 | 41395 | ---       | 41439 | 41452 | 0.2 | 0.1 | 0.3 | 0.725    |   4 | ---                                                                                                                                                       |
| 2013 - 2014 | 41426 | ---       | 41460 | 41471 | 0.2 | 0.1 | 0.3 | 0.725    |   4 | ---                                                                                                                                                       |
| 2013 - 2014 | 41456 | EW1302275 | 41501 | 41508 | 0.4 | 0.1 | 0.5 | 0.733333 |   4 | ---                                                                                                                                                       |
| 2013 - 2014 | 41518 | EW1302885 | 41562 | 41564 | 0.7 | 0.5 | 1.2 | 0.708333 |   4 | ---                                                                                                                                                       |
| 2013 - 2014 | 41548 | EW1303107 | 41586 | 41592 | 0.8 | 0.7 | 1.5 | 0.716667 |   4 | ---                                                                                                                                                       |
| 2013 - 2014 | 41579 | EW1303436 | 41619 | 41620 | 0.9 | 0.7 | 1.6 | 0.758333 |   4 | ---                                                                                                                                                       |
| 2013 - 2014 | 41609 | EW1400002 | 41654 | 41655 | 0.8 | 0.3 | 1.1 | 0.766667 |   4 | ---                                                                                                                                                       |
| 2013 - 2014 | 41640 | EW1400343 | 41680 | 41683 | 0.4 | 0.2 | 0.6 | 0.758333 |   4 | ---                                                                                                                                                       |
| 2014 - 2015 | 41699 | EW1400964 | 41737 | 41739 | 0.8 | 0.3 | 1.1 | 0.841667 |   4 | ---                                                                                                                                                       |
| 2014 - 2015 | 41730 | EW1401264 | 41767 | 41781 | 0.3 | 0.7 | 1   | 0.875    |   4 | ---                                                                                                                                                       |
| 2014 - 2015 | 41760 | EW1401618 | 41801 | 41823 | 0.5 | 0.5 | 1   | 0.933333 |   4 | Results reported late due to issue with COC documentation                                                                                                 |
| 2014 - 2015 | 41791 | EW1401917 | 41829 | 41837 | 0.2 | 0.3 | 0.5 | 0.95     |   4 | ---                                                                                                                                                       |
| 2014 - 2015 | 41821 | EW1402286 | 41858 | 41866 | 0.3 | 0.5 | 0.8 | 0.975    |   4 | ---                                                                                                                                                       |
| 2014 - 2015 | 41852 | EW1402628 | 41893 | 41907 | 0.5 | 0.5 | 1   | 1        |   4 | ---                                                                                                                                                       |
| 2014 - 2015 | 41883 | EW1403015 | 41922 | 41935 | 0.2 | 0.6 | 0.8 | 0.966667 |   4 | ---                                                                                                                                                       |
| 2014 - 2015 | 41913 | EW1403247 | 41950 | 41964 | 0.6 | 0.7 | 1.3 | 0.95     |   4 | ---                                                                                                                                                       |
| 2014 - 2015 | 41944 | EW1403683 | 41988 | 41992 | 1.3 | 1   | 2.3 | 1.00833  |   4 | ---                                                                                                                                                       |
| 2014 - 2015 | 41974 | EW1500019 | 42020 | 42033 | 1   | 0.6 | 1.6 | 1.05     |   4 | ---                                                                                                                                                       |
| 2014 - 2015 | 42005 | EW1500424 | 42048 | 42061 | 0.3 | 0.7 | 1   | 1.08333  |   4 | ---                                                                                                                                                       |
| 2015 - 2016 | 42036 | EW1500773 | 42075 | 42075 | 0.5 | 0.6 | 1.1 | 1.125    |   4 | ---                                                                                                                                                       |
| 2015 - 2016 | 42064 | EW1501097 | 42109 | 42117 | 0.5 | 0.5 | 1   | 1.11667  |   4 | ---                                                                                                                                                       |
| 2015 - 2016 | 42095 | EW1510118 | 42139 | 42145 | 0.6 | 0.6 | 1.2 | 1.13333  |   4 | ---                                                                                                                                                       |
| 2015 - 2016 | 42125 | EW1510476 | 42159 | 41808 | 0.4 | 0.3 | 0.7 | 1.10833  |   4 | ---                                                                                                                                                       |
| 2015 - 2016 | 42156 | EW1510800 | 42194 | 42201 | 0.2 | 0.2 | 0.4 | 1.1      |   4 | ---                                                                                                                                                       |
| 2015 - 2016 | 42186 | EW1511126 | 42226 | 42229 | 0.7 | 0.5 | 1.2 | 1.13333  |   4 | ---                                                                                                                                                       |
| 2015 - 2016 | 42217 | EW1511518 | 42255 | 42258 | 0.6 | 0.4 | 1   | 1.13333  |   4 | ---                                                                                                                                                       |
| 2015 - 2016 | 42248 | EW1511934 | 42286 | 42299 | 0.4 | 0.4 | 0.8 | 1.13333  |   4 | ---                                                                                                                                                       |
| 2015 - 2016 | 42278 | EW1512357 | 42314 | 42328 | 0.7 | 0.5 | 1.2 | 1.125    |   4 | ---                                                                                                                                                       |
| 2015 - 2016 | 42309 | EW1512763 | 42342 | 42348 | 1   | 0.5 | 1.5 | 1.05833  |   4 | ---                                                                                                                                                       |
| 2015 - 2016 | 42339 | EW1600024 | 42381 | 42390 | 1.2 | 0.7 | 1.9 | 1.08333  |   4 | ---                                                                                                                                                       |
| 2015 - 2016 | 42370 | EW1600375 | 42405 | 42418 | 1.4 | 0.7 | 2.1 | 1.175    |   4 | ---                                                                                                                                                       |
| 2016 - 2017 | 42401 | EW1600892 | 42440 | 42446 | 0.8 | 0.4 | 1.2 | 1.18333  |   4 | ---                                                                                                                                                       |
| 2016 - 2017 | 42430 | EW1601256 | 42467 | 42474 | 2.5 | 0.6 | 3.1 | 1.35833  |   4 | ---                                                                                                                                                       |
| 2016 - 2017 | 42461 | EW1601758 | 42134 | 42502 | 0.5 | 0.2 | 0.7 | 1.31667  |   4 | ---                                                                                                                                                       |
| 2016 - 2017 | 42491 | EW1602097 | 42529 | 42558 | 1.2 | 0.3 | 1.5 | 1.38333  |   4 | ---                                                                                                                                                       |
| 2016 - 2017 | 42522 | EW1602562 | 42564 | 42573 | 0.8 | 0.9 | 1.7 | 1.49167  |   4 | ---                                                                                                                                                       |
| 2016 - 2017 | 42522 | EW1602884 | 42587 | 42600 | 0.7 | 0.7 | 1.4 | 1.50833  |   4 | ---                                                                                                                                                       |
| 2016 - 2017 | 42583 | EW1603249 | 42620 | 42628 | 0.4 | 0.2 | 0.6 | 1.475    |   4 | ---                                                                                                                                                       |
| 2016 - 2017 | 42614 | EW1603770 | 42660 | 42670 | 0.8 | 0.7 | 1.5 | 1.53333  |   4 | ---                                                                                                                                                       |
| 2016 - 2017 | 42644 | EW1604119 | 42682 | 42698 | 0.8 | 0.3 | 1.1 | 1.525    |   4 | ---                                                                                                                                                       |
| 2016 - 2017 | 42675 | EW1604548 | 42716 | 42726 | 0.5 | 0.7 | 1.2 | 1.5      |   4 | ---                                                                                                                                                       |
| 2016 - 2017 | 42705 | EW1700052 | 42748 | 42754 | 1   | 0.5 | 1.5 | 1.46667  |   4 | ---                                                                                                                                                       |
| 2016 - 2017 | 42736 | EW1700458 | 42779 | 42782 | 0.6 | 0.5 | 1.1 | 1.38333  |   4 | ---                                                                                                                                                       |
| 2017 - 2018 | 42767 | EW1700935 | 42821 | 42824 | 1.1 | 0.6 | 1.7 | 1.425    |   4 | ---                                                                                                                                                       |
| 2017 - 2018 | 42795 | EW1701462 | 42832 | 42838 | 0.3 | 0.5 | 0.8 | 1.23333  |   4 | ---                                                                                                                                                       |
| 2017 - 2018 | 42826 | EW1701914 | 42864 | 42880 | 0.4 | 0.3 | 0.7 | 1.23333  |   4 | ---                                                                                                                                                       |
| 2017 - 2018 | 42856 | EW1702380 | 42922 | 42900 | 0.2 | 0.1 | 0.3 | 1.13333  |   4 | ---                                                                                                                                                       |
| 2017 - 2018 | 42917 | EW1703247 | 42954 | 42964 | 0.4 | 0.1 | 0.5 | 0.933333 |   4 | ---                                                                                                                                                       |
| 2017 - 2018 | 42948 | EW1703638 | 42984 | 42993 | 0.4 | 0.2 | 0.6 | 0.933333 |   4 | ---                                                                                                                                                       |
| 2017 - 2018 | 42979 | EW1704084 | 43014 | 43020 | 0.4 | 0.4 | 0.8 | 0.875    |   4 | ---                                                                                                                                                       |
| 2017 - 2018 | 43009 | EW1704426 | 43042 | 43048 | 0.7 | 0.5 | 1.2 | 0.883333 |   4 | ---                                                                                                                                                       |
| 2017 - 2018 | 43040 | EW1704973 | 43077 | 43090 | 0.5 | 0.6 | 1.1 | 0.875    |   4 | ---                                                                                                                                                       |
| 2017 - 2018 | 43070 | EW1800117 | 43122 | 43159 | 0.8 | 0.5 | 1.3 | 0.858333 |   4 | ---                                                                                                                                                       |
| 2017 - 2018 | 43101 | EW1800369 | 43137 | 43159 | 0.4 | 0.4 | 0.8 | 0.833333 |   4 | ---                                                                                                                                                       |
| 2018 - 2019 | 43132 | EW1800830 | 43166 | 43173 | 0.5 | 0.3 | 0.8 | 0.758333 |   4 | ---                                                                                                                                                       |
| 2018 - 2019 | 43160 | EW1801350 | 43188 | 43216 | 0.5 | 0.1 | 0.6 | 0.741667 |   4 | ---                                                                                                                                                       |
| 2018 - 2019 | 43191 | EW1801757 | 43224 | 43235 | 0.5 | 0.3 | 0.8 | 0.75     |   4 | ---                                                                                                                                                       |
| 2018 - 2019 | 43221 | EW1802206 | 43258 | 43272 | 0.4 | 0.2 | 0.6 | 0.775    |   4 | ---                                                                                                                                                       |
| 2018 - 2019 | 43252 | EW1802654 | 43287 | 43299 | 0.4 | 0.2 | 0.6 | 0.808333 |   4 | ---                                                                                                                                                       |
| 2018 - 2019 | 43282 | EW1803051 | 43320 | 43341 | 0.3 | 0.1 | 0.4 | 0.8      |   4 | ---                                                                                                                                                       |
| 2018 - 2019 | 43313 | EW1803477 | 43348 | 43355 | 0.5 | 0.7 | 1.2 | 0.85     |   4 | ---                                                                                                                                                       |
| 2018 - 2019 | 43344 | EW1803931 | 43383 | 43383 | 0.4 | 0.1 | 0.5 | 0.825    |   4 | ---                                                                                                                                                       |
| 2018 - 2019 | 43374 | EW1804416 | 43410 | 43425 | 0.3 | 0.2 | 0.5 | 0.766667 |   4 | ---                                                                                                                                                       |
| 2018 - 2019 | 43405 | EW1804934 | 43439 | 43453 | 1.1 | 0.4 | 1.5 | 0.8      |   4 | ---                                                                                                                                                       |
| 2018 - 2019 | 43435 | EW1900063 | 43481 | 43495 | 0.7 | 0.3 | 1   | 0.775    |   4 | ---                                                                                                                                                       |
| 2018 - 2019 | 43466 | EW1900341 | 43536 | 43537 | 0.9 | 0.5 | 1.4 | 0.825    |   4 | ---                                                                                                                                                       |
| 2019 - 2020 | 43497 | EW1900768 | 43528 | 43537 | 1.3 | 0.6 | 1.9 | 0.916667 |   4 | ---                                                                                                                                                       |
| 2019 - 2020 | 43525 | EW1901229 | 43557 | 43565 | 0.7 | 0.2 | 0.9 | 0.941667 |   4 | ---                                                                                                                                                       |
| 2019 - 2020 | 43586 | EW1902254 | 43616 | 43623 | 0.5 | 0.1 | 0.6 | 0.916667 |   4 | ---                                                                                                                                                       |
| 2019 - 2020 | 43617 | EW1902725 | 43650 | 43651 | 0.4 | 0.4 | 0.8 | 0.933333 |   4 | ---                                                                                                                                                       |
| 2019 - 2020 | 43647 | EW1903263 | 43682 | 43693 | 0.4 | 0.2 | 0.6 | 0.95     |   4 | ---                                                                                                                                                       |
| 2019 - 2020 | 43678 | EW1903742 | 43712 | 43721 | 0.7 | 0.2 | 0.9 | 0.925    |   4 | ---                                                                                                                                                       |
| 2019 - 2020 | 43709 | EW1904237 | 43747 | 43749 | 0.4 | 0.2 | 0.6 | 0.933333 |   4 | ---                                                                                                                                                       |
| 2019 - 2020 | 43739 | EW1904743 | 43777 | 43791 | 0.5 | 0.3 | 0.8 | 0.958333 |   4 | ---                                                                                                                                                       |
| 2019 - 2020 | 43770 | EW1905240 | 43805 | 43819 | 2.7 | 0.8 | 3.5 | 1.125    |   4 | Significant number of bushfires in regional and surrounding areas. multiple (5) PM10 spikes during the month. See AQI evidence                            |
| 2019 - 2020 | 43800 | EW2000006 | 43844 | 43847 | 1.1 | 0.8 | 1.9 | 1.2      |   4 | Significant number of bushfires in regional and surrounding areas. multiple (10) PM10 spikes during the month. See AQI evidence                           |
| 2019 - 2020 | 43831 | EW2000470 | 43872 | 43875 | 5.5 | 0.9 | 6.4 | 1.61667  |   4 | Ash content correlates with regional bushfire occurrences during the month. multiple (9) PM10 spikes during the month. See AQI evidence                   |
| 2020 - 2021 | 43862 | EW2001142 | 43899 | 43903 | 1.5 | 0.5 | 2   | 1.625    |   4 | ---                                                                                                                                                       |
| 2020 - 2021 | 43891 | EW2001710 | 43929 | 43945 | 0.7 | 0.3 | 1   | 1.63333  |   4 | ---                                                                                                                                                       |
| 2020 - 2021 | 43922 | EW2002139 | 43962 | 43973 | 0.4 | 0.4 | 0.8 | 1.65833  |   4 | ---                                                                                                                                                       |
| 2020 - 2021 | 43983 | EW2003042 | 44022 | 44029 | 0.1 | 0.1 | 0.2 | 1.575    |   4 | ---                                                                                                                                                       |
| 2020 - 2021 | 44013 | EW2003463 | 44050 | 44057 | 0.1 | 0.2 | 0.3 | 1.55     |   4 | ---                                                                                                                                                       |
| 2020 - 2021 | 44044 | EW2003993 | 44082 | 44085 | 0.3 | 0.2 | 0.5 | 1.51667  |   4 | Major weather events in the region responsible for increased PM10 concentrations & inferred 'insoluble solids content' during the month. See AQI evidence |
| 2020 - 2021 | 44075 | EW2004427 | 44113 | 44127 | 0.5 | 0.3 | 0.8 | 1.53333  |   4 | Increased vegetation content contributing to combustible solids                                                                                           |
| 2020 - 2021 | 44105 | EW2004934 | 44144 | 44155 | 0.5 | 0.3 | 0.8 | 1.53333  |   4 | Notable vegetation content contributing to combustible solids                                                                                             |
| 2020 - 2021 | 44136 | EW2005444 | 44175 | 44183 | 0.4 | 0.3 | 0.7 | 1.3      |   4 | ---                                                                                                                                                       |
| 2020 - 2021 | 44166 | EW2100086 | 44210 | 44211 | 0.4 | 0.7 | 1.1 | 1.23333  |   4 | Very high organics present (polysaccharide slime) contributing to 'Combustible Solids'                                                                    |
| 2020 - 2021 | 44197 | EW2100439 | 44235 | 44242 | 0.4 | 0.3 | 0.7 | 0.758333 |   4 | ---                                                                                                                                                       |



labeled_formulas: H=F+G
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_107853___xlsx_c165fd5489adedc1bd9c5e954dc102f31fee99a2.xlsx___line_666