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 |
|-----:|------:|------:|------:|-------:|---------:|
| 1989 | 32752 | 104.7 |  77.2 |  181.9 | 0.575591 |
| 1988 | 32478 | 106.3 |  88.8 |  195.1 | 0.544849 |
| 1989 | 32568 |  84.2 |  66.2 |  150.4 | 0.55984  |
| 1989 | 32660 |  92   |  78.2 |  170.2 | 0.540541 |
| 1989 | 32752 |  78.9 |  71.9 |  150.8 | 0.52321  |
| 1989 | 32843 |  80.9 |  84.2 |  165.1 | 0.490006 |
| 1990 | 32933 |  67.3 |  62.2 |  129.5 | 0.519691 |
| 1990 | 33025 |  88.3 |  73.8 |  162.1 | 0.544725 |
| 1990 | 33117 |  78.8 |  64.9 |  143.7 | 0.548365 |
| 1990 | 33208 |  84.2 |  82.6 |  166.8 | 0.504796 |
| 1991 | 33298 |  68   |  58.6 |  126.6 | 0.537125 |
| 1991 | 33390 |  93.8 |  70.8 |  164.6 | 0.569866 |
| 1991 | 33482 |  87.9 |  65.5 |  153.4 | 0.573012 |
| 1991 | 33573 |  88.1 |  76.1 |  164.2 | 0.536541 |
| 1992 | 33664 |  69.3 |  56   |  125.3 | 0.553073 |
| 1992 | 33756 |  87.4 |  73.6 |  161   | 0.542857 |
| 1992 | 33848 |  86.5 |  74.4 |  160.9 | 0.537601 |
| 1992 | 33939 |  91.6 |  83   |  174.6 | 0.524628 |
| 1993 | 34029 |  74.2 |  48.8 |  123   | 0.603252 |
| 1993 | 34121 |  95.8 |  77.5 |  173.3 | 0.552799 |
| 1993 | 34213 | 110.4 |  77.1 |  187.5 | 0.5888   |
| 1993 | 34304 | 119   |  89.9 |  208.9 | 0.569651 |
| 1994 | 34394 | 100.9 |  74.7 |  175.6 | 0.574601 |
| 1994 | 34486 | 123.4 |  97.2 |  220.6 | 0.559383 |
| 1994 | 34578 | 127.5 |  98.6 |  226.1 | 0.56391  |
| 1994 | 34669 | 126.4 | 105.8 |  232.2 | 0.544358 |
| 1995 | 34759 | 106.3 |  84   |  190.3 | 0.558592 |
| 1995 | 34851 | 135.3 | 109.3 |  244.6 | 0.553148 |
| 1995 | 34943 | 125   | 102.1 |  227.1 | 0.550418 |
| 1995 | 35034 | 128.9 | 100.4 |  229.3 | 0.562146 |
| 1996 | 35125 | 118.6 | 100.4 |  219   | 0.541553 |
| 1996 | 35217 | 147   | 137.9 |  284.9 | 0.515971 |
| 1996 | 35309 | 162.8 | 111.4 |  274.2 | 0.593727 |
| 1996 | 35400 | 173.1 | 118.5 |  291.6 | 0.593621 |
| 1997 | 35490 | 144.2 |  91.4 |  235.6 | 0.612054 |
| 1997 | 35582 | 211.6 | 135.6 |  347.2 | 0.609447 |
| 1997 | 35674 | 182.7 | 119.1 |  301.8 | 0.605368 |
| 1997 | 35765 | 162.3 | 119.7 |  282   | 0.575532 |
| 1998 | 35855 | 142   |  78.4 |  220.4 | 0.644283 |
| 1998 | 35947 | 173.4 |  89.2 |  262.6 | 0.66032  |
| 1998 | 36039 | 154.1 |  81.8 |  235.9 | 0.653243 |
| 1998 | 36130 | 157.3 |  82.3 |  239.6 | 0.656511 |
| 1999 | 36220 | 102.3 |  65   |  167.3 | 0.611476 |
| 1999 | 36312 | 109.4 |  85.6 |  195   | 0.561026 |
| 1999 | 36404 | 107.9 |  72.2 |  180.1 | 0.599112 |
| 1999 | 36495 | 108.8 |  68.1 |  176.9 | 0.615037 |
| 2000 | 36586 |  85   |  51.7 |  136.7 | 0.6218   |
| 2000 | 36678 | 113.3 |  69.4 |  182.7 | 0.620142 |
| 2000 | 36770 | 104.4 |  65.4 |  169.8 | 0.614841 |
| 2000 | 36861 | 118   |  69.2 |  187.2 | 0.630342 |
| 2001 | 36951 |  90.8 |  52.7 |  143.5 | 0.632753 |
| 2001 | 37043 | 110.9 |  71.9 |  182.8 | 0.606674 |
| 2001 | 37135 | 103.3 |  64.1 |  167.4 | 0.617085 |
| 2001 | 37226 | 103.5 |  67.2 |  170.7 | 0.606327 |
| 2002 | 37316 |  82.5 |  51.7 |  134.2 | 0.614754 |
| 2002 | 37408 |  91.8 |  76.5 |  168.3 | 0.545455 |
| 2002 | 37500 | 110.1 |  72.8 |  182.9 | 0.601968 |
| 2002 | 37591 | 111.1 |  81.7 |  192.8 | 0.576245 |
| 2003 | 37681 |  90.8 |  62.6 |  153.4 | 0.591917 |
| 2003 | 37773 | 111.6 |  92.1 |  203.7 | 0.547865 |
| 2003 | 37865 | 108.5 |  71.2 |  179.7 | 0.603784 |
| 2003 | 37956 | 122   |  77.5 |  199.5 | 0.611529 |
| 2004 | 38047 |  96.5 |  70.8 |  167.3 | 0.576808 |
| 2004 | 38139 | 138.8 | 101.4 |  240.2 | 0.577852 |
| 2004 | 38231 | 147.9 | 103.2 |  251.1 | 0.589008 |
| 2004 | 38322 | 156.7 | 104.1 |  260.8 | 0.600844 |
| 2005 | 38412 | 134.4 |  91.4 |  225.8 | 0.595217 |
| 2005 | 38504 | 167   | 123.7 |  290.7 | 0.574475 |
| 2005 | 38596 | 154.4 | 137.6 |  292   | 0.528767 |
| 2005 | 38687 | 158   | 169.6 |  327.6 | 0.482295 |
| 2006 | 38777 | 121.5 | 142.2 |  263.7 | 0.460751 |
| 2006 | 38869 | 156.3 | 201.1 |  357.4 | 0.437325 |
| 2006 | 38961 | 190.2 | 204.4 |  394.6 | 0.482007 |
| 2006 | 39052 | 217.3 | 230.9 |  448.2 | 0.484828 |
| 2007 | 39142 | 179.9 | 189.4 |  369.3 | 0.487138 |
| 2007 | 39234 | 251.8 | 250.7 |  502.5 | 0.501095 |
| 2007 | 39326 | 293.3 | 270.1 |  563.4 | 0.520589 |
| 2007 | 39417 | 313.8 | 312.1 |  625.9 | 0.501358 |
| 2008 | 39508 | 271.4 | 272.6 |  544   | 0.498897 |
| 2008 | 39600 | 381.2 | 346.9 |  728.1 | 0.523554 |
| 2008 | 39692 | 383.8 | 303.9 |  687.7 | 0.558092 |
| 2008 | 39783 | 364   | 284.5 |  648.5 | 0.561295 |
| 2009 | 39873 | 224.2 | 179.3 |  403.5 | 0.555638 |
| 2009 | 39965 | 274.8 | 208.7 |  483.5 | 0.568356 |
| 2009 | 40057 | 298.9 | 258.5 |  557.4 | 0.53624  |
| 2009 | 40148 | 321.7 | 257.1 |  578.8 | 0.555805 |
| 2010 | 40238 | 257.1 | 202.2 |  459.3 | 0.559765 |
| 2010 | 40330 | 366.3 | 270.8 |  637.1 | 0.574949 |
| 2010 | 40422 | 384.6 | 284.8 |  669.4 | 0.574544 |
| 2010 | 40513 | 393.7 | 330.7 |  724.4 | 0.543484 |
| 2011 | 40603 | 362.2 | 287.9 |  650.1 | 0.557145 |
| 2011 | 40695 | 449.6 | 457.8 |  907.4 | 0.495482 |
| 2011 | 40787 | 481.6 | 501.8 |  983.4 | 0.48973  |
| 2011 | 40878 | 531.9 | 500.5 | 1032.4 | 0.515207 |
| 2012 | 40969 | 490.1 | 386   |  876.1 | 0.559411 |
| 2012 | 41061 | 603.2 | 457.9 | 1061.1 | 0.568467 |
| 2012 | 41153 | 488.6 | 406.1 |  894.7 | 0.546105 |
| 2012 | 41244 | 470.7 | 353.2 |  823.9 | 0.571307 |
| 2013 | 41334 | 421.8 | 250.4 |  672.2 | 0.627492 |
| 2013 | 41426 | 382.3 | 282.3 |  664.6 | 0.575233 |
| 2013 | 41518 | 395.8 | 242.6 |  638.4 | 0.619987 |
| 2013 | 41609 | 308.3 | 239.1 |  547.4 | 0.563208 |
| 2014 | 41699 | 206.2 | 201.8 |  408   | 0.505392 |
| 2014 | 41791 | 309.7 | 205.3 |  515   | 0.601359 |
| 2014 | 41883 | 267.1 | 190.6 |  457.7 | 0.58357  |
| 2014 | 41974 | 262.3 | 196.9 |  459.2 | 0.571211 |
| 2015 | 42064 | 183.2 | 134.5 |  317.7 | 0.576645 |
| 2015 | 42156 | 204.8 | 139.3 |  344.1 | 0.595176 |
| 2015 | 42248 | 233.1 | 160.9 |  394   | 0.591624 |
| 2015 | 42339 | 222.6 | 160.2 |  382.8 | 0.581505 |
| 2016 | 42430 | 187.1 | 103.3 |  290.4 | 0.644284 |
| 2016 | 42522 | 228.2 | 125.7 |  353.9 | 0.644815 |
| 2016 | 42614 | 248.8 | 130.7 |  379.5 | 0.655599 |
| 2016 | 42705 | 263.5 | 139.6 |  403.1 | 0.653684 |
| 2017 | 42795 | 225   | 112.6 |  337.6 | 0.666469 |
| 2017 | 42887 | 291   | 153.9 |  444.9 | 0.65408  |
| 2017 | 42979 | 294.2 | 181   |  475.2 | 0.619108 |
| 2017 | 43070 | 298.5 | 197.6 |  496.1 | 0.601693 |
| 2018 | 43160 | 261   | 177.7 |  438.7 | 0.59494  |
| 2018 | 43252 | 349.8 | 218   |  567.8 | 0.616062 |
| 2018 | 43344 | 361   | 223.4 |  584.4 | 0.617728 |
| 2018 | 43435 | 346.3 | 246.4 |  592.7 | 0.584275 |
| 2019 | 43525 | 319.5 | 186.2 |  505.7 | 0.631798 |
| 2019 | 43617 | 415.1 | 249.7 |  664.8 | 0.624398 |
| 2019 | 43709 | 459.7 | 265.1 |  724.8 | 0.634244 |
| 2019 | 43800 | 453.9 | 299.2 |  753.1 | 0.602709 |
| 2020 | 43891 | 367.1 | 243.5 |  610.6 | 0.601212 |
| 2020 | 43983 | 412.4 | 270.9 |  683.3 | 0.603542 |
| 2020 | 44075 | 483.3 | 261.6 |  744.9 | 0.648812 |
| 2020 | 44166 | 480.3 | 273.7 |  754   | 0.637003 |



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_44289___xlsx_f8b21cedc02571be18d14c0f61c587edf8640b6d.xlsx___line_660