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 |
|-----:|------:|------:|------:|-------:|---------:|
| 1994 | 34578 |  99.1 |  81.4 |  180.5 | 0.54903  |
| 1994 | 34669 |  91   |  86.4 |  177.4 | 0.512965 |
| 1995 | 34759 |  65.6 |  53.8 |  119.4 | 0.549414 |
| 1995 | 34851 |  89.2 | 106.2 |  195.4 | 0.456499 |
| 1995 | 34943 |  88.5 | 104.6 |  193.1 | 0.458312 |
| 1995 | 35034 |  75.7 | 115.9 |  191.6 | 0.395094 |
| 1996 | 35125 |  74.6 |  64.4 |  139   | 0.536691 |
| 1996 | 35217 |  80.3 |  84.6 |  164.9 | 0.486962 |
| 1996 | 35309 | 130.7 |  72.1 |  202.8 | 0.644477 |
| 1996 | 35400 | 132.6 | 108.6 |  241.2 | 0.549751 |
| 1997 | 35490 |  78.6 |  83.6 |  162.2 | 0.484587 |
| 1997 | 35582 |  97.2 | 105.2 |  202.4 | 0.480237 |
| 1997 | 35674 |  46.8 |  77.4 |  124.2 | 0.376812 |
| 1997 | 35765 | 106.9 | 108.8 |  215.7 | 0.495596 |
| 1998 | 35855 | 165   |  91   |  256   | 0.644531 |
| 1998 | 35947 | 145.2 | 177.1 |  322.3 | 0.450512 |
| 1998 | 36039 |  90.8 |  94.9 |  185.7 | 0.488961 |
| 1998 | 36130 | 148.5 | 100.3 |  248.8 | 0.596865 |
| 1999 | 36220 | 164.1 |  62.3 |  226.4 | 0.724823 |
| 1999 | 36312 | 127.2 |  63.6 |  190.8 | 0.666667 |
| 1999 | 36404 | 112   |  85.2 |  197.2 | 0.567951 |
| 1999 | 36495 |  96.9 |  82.3 |  179.2 | 0.540737 |
| 2000 | 36586 | 121.2 |  38.8 |  160   | 0.7575   |
| 2000 | 36678 | 113.9 |  50.4 |  164.3 | 0.693244 |
| 2000 | 36770 | 148.8 |  69.5 |  218.3 | 0.681631 |
| 2000 | 36861 | 166.3 |  75.4 |  241.7 | 0.688043 |
| 2001 | 36951 | 216.4 |  82.4 |  298.8 | 0.72423  |
| 2001 | 37043 | 156   | 110   |  266   | 0.586466 |
| 2001 | 37135 | 136.3 |  95.4 |  231.7 | 0.588261 |
| 2001 | 37226 | 141.7 | 125.7 |  267.4 | 0.529918 |
| 2002 | 37316 | 119.7 |  83.3 |  203   | 0.589655 |
| 2002 | 37408 |  82   |  98.5 |  180.5 | 0.454294 |
| 2002 | 37500 |  85.3 | 132.7 |  218   | 0.391284 |
| 2002 | 37591 | 170.2 | 100.2 |  270.4 | 0.629438 |
| 2003 | 37681 | 191.5 |  75   |  266.5 | 0.718574 |
| 2003 | 37773 | 151.3 |  88.8 |  240.1 | 0.630154 |
| 2003 | 37865 | 177.9 |  52.8 |  230.7 | 0.771131 |
| 2003 | 37956 | 188.2 |  99.9 |  288.1 | 0.653245 |
| 2004 | 38047 | 106.9 |  61.9 |  168.8 | 0.633294 |
| 2004 | 38139 | 197.5 |  58.9 |  256.4 | 0.770281 |
| 2004 | 38231 | 129.7 |  80.8 |  210.5 | 0.616152 |
| 2004 | 38322 | 113.1 | 173.5 |  286.6 | 0.394627 |
| 2005 | 38412 | 154.3 | 114.9 |  269.2 | 0.57318  |
| 2005 | 38504 | 129.4 | 149.1 |  278.5 | 0.464632 |
| 2005 | 38596 | 135.1 | 146.9 |  282   | 0.479078 |
| 2005 | 38687 | 152.8 | 173.7 |  326.5 | 0.467994 |
| 2006 | 38777 | 137   | 136.6 |  273.6 | 0.500731 |
| 2006 | 38869 | 168.7 | 211.2 |  379.9 | 0.444064 |
| 2006 | 38961 | 289.9 | 198.7 |  488.6 | 0.593328 |
| 2006 | 39052 | 346.1 | 198.4 |  544.5 | 0.635629 |
| 2007 | 39142 | 319.5 | 140.8 |  460.3 | 0.694113 |
| 2007 | 39234 | 525.4 | 206.7 |  732.1 | 0.717662 |
| 2007 | 39326 | 546.5 | 151.8 |  698.3 | 0.782615 |
| 2007 | 39417 | 512.7 | 257.3 |  770   | 0.665844 |
| 2008 | 39508 | 498.7 | 210.7 |  709.4 | 0.702988 |
| 2008 | 39600 | 616.9 | 240.3 |  857.2 | 0.719669 |
| 2008 | 39692 | 539.5 | 241.8 |  781.3 | 0.690516 |
| 2008 | 39783 | 798.9 | 214.5 | 1013.4 | 0.788336 |
| 2009 | 39873 | 789.4 | 209.2 |  998.6 | 0.790507 |
| 2009 | 39965 | 817.4 | 200   | 1017.4 | 0.80342  |
| 2009 | 40057 | 603.9 | 193.8 |  797.7 | 0.757052 |
| 2009 | 40148 | 541.7 | 285.3 |  827   | 0.655018 |
| 2010 | 40238 | 646.7 | 216.8 |  863.5 | 0.748929 |
| 2010 | 40330 | 692.3 | 313.6 | 1005.9 | 0.688239 |
| 2010 | 40422 | 597.1 | 253.3 |  850.4 | 0.70214  |
| 2010 | 40513 | 559.2 | 290.4 |  849.6 | 0.658192 |
| 2011 | 40603 | 607   | 159.1 |  766.1 | 0.792325 |
| 2011 | 40695 | 639   | 210.3 |  849.3 | 0.752384 |
| 2011 | 40787 | 487.9 | 292.3 |  780.2 | 0.625352 |
| 2011 | 40878 | 611.9 | 285.1 |  897   | 0.682163 |
| 2012 | 40969 | 393.2 | 202.8 |  596   | 0.659732 |
| 2012 | 41061 | 624.2 | 299.6 |  923.8 | 0.675687 |
| 2012 | 41153 | 753.9 | 330.1 | 1084   | 0.69548  |
| 2012 | 41244 | 985.3 | 413.3 | 1398.6 | 0.70449  |
| 2013 | 41334 | 713.4 | 296.3 | 1009.7 | 0.706546 |
| 2013 | 41426 | 841.2 | 459.9 | 1301.1 | 0.64653  |
| 2013 | 41518 | 752.2 | 363.1 | 1115.3 | 0.674437 |
| 2013 | 41609 | 677.4 | 425.9 | 1103.3 | 0.613976 |
| 2014 | 41699 | 737.1 | 335   | 1072.1 | 0.687529 |
| 2014 | 41791 | 823.9 | 709.9 | 1533.8 | 0.537163 |
| 2014 | 41883 | 591.5 | 388.4 |  979.9 | 0.603633 |
| 2014 | 41974 | 605.4 | 547.7 | 1153.1 | 0.52502  |
| 2015 | 42064 | 439.3 | 521.3 |  960.6 | 0.457318 |
| 2015 | 42156 | 432.7 | 265.1 |  697.8 | 0.620092 |
| 2015 | 42248 | 407.5 | 175.4 |  582.9 | 0.699091 |
| 2015 | 42339 | 337.6 | 144.4 |  482   | 0.700415 |
| 2016 | 42430 | 340.1 |  87.8 |  427.9 | 0.794812 |
| 2016 | 42522 | 212.2 |  71.2 |  283.4 | 0.748765 |
| 2016 | 42614 | 229.8 | 125.4 |  355.2 | 0.646959 |
| 2016 | 42705 | 213.9 | 121.3 |  335.2 | 0.638126 |
| 2017 | 42795 | 100   | 250   |  350   | 0.285714 |
| 2017 | 42887 | 107.8 | 227.8 |  335.6 | 0.321216 |
| 2017 | 42979 | 157.2 | 126.3 |  283.5 | 0.554497 |
| 2017 | 43070 | 127.5 | 117.6 |  245.1 | 0.520196 |
| 2018 | 43160 |  75.2 | 108.1 |  183.3 | 0.410256 |
| 2018 | 43252 | 202.4 | 113.7 |  316.1 | 0.640304 |
| 2018 | 43344 | 193.1 | 114.8 |  307.9 | 0.627152 |
| 2018 | 43435 | 201.6 | 150.8 |  352.4 | 0.572077 |
| 2019 | 43525 |  82   | 140.5 |  222.5 | 0.368539 |
| 2019 | 43617 | 257.6 | 120.1 |  377.7 | 0.682023 |
| 2019 | 43709 | 219.6 | 150.7 |  370.3 | 0.593033 |
| 2019 | 43800 | 190.1 | 224.1 |  414.2 | 0.458957 |
| 2020 | 43891 | 104.5 | 136.9 |  241.4 | 0.432891 |
| 2020 | 43983 |  81.3 | 155.6 |  236.9 | 0.343183 |
| 2020 | 44075 |  78.5 | 145.5 |  224   | 0.350446 |
| 2020 | 44166 | 114.9 | 139.9 |  254.8 | 0.450942 |



label: D=E-C
F=C/E
labeled_formulas: D=E-C
F=C/E
output: {"Arithmetic-Relationship": ["D=E-C", "F=C/E"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_44298___xlsx_f8b21cedc02571be18d14c0f61c587edf8640b6d.xlsx___line_664