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 |        L |
|-----:|------:|-----:|-----:|------:|-----:|------:|-----:|-----:|-------:|------:|---------:|
| 1989 | 32752 | 12.1 |  5.1 |  35.3 |  4.6 | 104.7 |  2.5 | 17.5 |  181.9 |  77.2 | 0.575591 |
| 1988 | 32478 | 15.7 |  6.6 |  36   |  6.5 | 106.3 |  3   | 21.1 |  195.1 |  88.8 | 0.544849 |
| 1989 | 32568 | 11   |  4.1 |  32   |  3   |  84.2 |  3.4 | 12.6 |  150.4 |  66.2 | 0.55984  |
| 1989 | 32660 | 11.8 |  5.9 |  36.5 |  2.5 |  92   |  4.2 | 17.4 |  170.2 |  78.2 | 0.540541 |
| 1989 | 32752 | 11.3 |  5.2 |  33.1 |  2.3 |  78.9 |  3.2 | 17   |  150.8 |  71.9 | 0.52321  |
| 1989 | 32843 | 13.2 |  6.3 |  38.6 |  3.3 |  80.9 |  3.3 | 19.4 |  165.1 |  84.2 | 0.490006 |
| 1990 | 32933 | 14.2 |  4.9 |  29.2 |  2.2 |  67.3 |  2.8 |  8.9 |  129.5 |  62.2 | 0.519691 |
| 1990 | 33025 | 16.4 |  4.5 |  27.6 |  5.3 |  88.3 |  2.5 | 17.4 |  162.1 |  73.8 | 0.544725 |
| 1990 | 33117 | 12.3 |  3   |  30.8 |  3.8 |  78.8 |  1.7 | 13.5 |  143.7 |  64.9 | 0.548365 |
| 1990 | 33208 | 18   |  2.6 |  38.3 |  4   |  84.2 |  3.1 | 16.6 |  166.8 |  82.6 | 0.504796 |
| 1991 | 33298 | 14.2 |  2.7 |  25.9 |  3.6 |  68   |  3.2 |  8.8 |  126.6 |  58.6 | 0.537125 |
| 1991 | 33390 | 16   |  4.5 |  29.1 |  4.2 |  93.8 |  1.9 | 15   |  164.6 |  70.8 | 0.569866 |
| 1991 | 33482 | 14.1 |  2.7 |  26.7 |  4.8 |  87.9 |  2.6 | 14.5 |  153.4 |  65.5 | 0.573012 |
| 1991 | 33573 | 17.8 |  2.5 |  31.5 |  6.6 |  88.1 |  1.9 | 15.7 |  164.2 |  76.1 | 0.536541 |
| 1992 | 33664 | 15.5 |  3.7 |  20.8 |  3.3 |  69.3 |  1.9 | 10.8 |  125.3 |  56   | 0.553073 |
| 1992 | 33756 | 15.9 |  3.7 |  31   |  4.9 |  87.4 |  1.4 | 16.7 |  161   |  73.6 | 0.542857 |
| 1992 | 33848 | 15.4 |  3   |  33   |  5.5 |  86.5 |  1.1 | 16.4 |  160.9 |  74.4 | 0.537601 |
| 1992 | 33939 | 20.3 |  3.4 |  34.5 |  5.9 |  91.6 |  1.7 | 17.2 |  174.6 |  83   | 0.524628 |
| 1993 | 34029 |  9.1 |  2.8 |  20.2 |  3.8 |  74.2 |  2.2 | 10.6 |  123   |  48.8 | 0.603252 |
| 1993 | 34121 | 16.1 |  3   |  30.2 |  6.1 |  95.8 |  2.8 | 19.3 |  173.3 |  77.5 | 0.552799 |
| 1993 | 34213 | 14.4 |  3.5 |  33.1 |  5.6 | 110.4 |  1.7 | 18.9 |  187.5 |  77.1 | 0.5888   |
| 1993 | 34304 | 18.4 |  4.6 |  39.6 |  6.4 | 119   |  2   | 18.9 |  208.9 |  89.9 | 0.569651 |
| 1994 | 34394 | 15.8 |  6.3 |  30.2 |  6.9 | 100.9 |  3.4 | 12.1 |  175.6 |  74.7 | 0.574601 |
| 1994 | 34486 | 25   |  6.3 |  37   |  5.8 | 123.4 |  3.1 | 19.9 |  220.6 |  97.2 | 0.559383 |
| 1994 | 34578 | 18.4 |  6.7 |  45   |  4.6 | 127.5 |  2.8 | 21.1 |  226.1 |  98.6 | 0.56391  |
| 1994 | 34669 | 18.3 |  6.5 |  53.7 |  5.1 | 126.4 |  2.9 | 19.3 |  232.2 | 105.8 | 0.544358 |
| 1995 | 34759 | 19.7 |  9.3 |  32.4 |  4.6 | 106.3 |  4   | 14.1 |  190.3 |  84   | 0.558592 |
| 1995 | 34851 | 22.7 |  8.7 |  44.9 |  6.6 | 135.3 |  5.2 | 21.3 |  244.6 | 109.3 | 0.553148 |
| 1995 | 34943 | 20.5 |  8.2 |  43.8 |  5.6 | 125   |  2.5 | 21.6 |  227.1 | 102.1 | 0.550418 |
| 1995 | 35034 | 17.7 | 11.5 |  39.4 |  6.6 | 128.9 |  5.6 | 19.5 |  229.3 | 100.4 | 0.562146 |
| 1996 | 35125 | 19.2 | 10.1 |  40.9 |  5.1 | 118.6 |  6   | 19   |  219   | 100.4 | 0.541553 |
| 1996 | 35217 | 23   | 12.8 |  56.9 |  6.8 | 147   |  4.7 | 33.7 |  284.9 | 137.9 | 0.515971 |
| 1996 | 35309 | 21.1 | 14.9 |  38.3 |  5.4 | 162.8 |  4.2 | 27.5 |  274.2 | 111.4 | 0.593727 |
| 1996 | 35400 | 20.6 | 14.1 |  45.1 |  8   | 173.1 |  5.7 | 25   |  291.6 | 118.5 | 0.593621 |
| 1997 | 35490 | 22   |  9.6 |  31.6 |  7.2 | 144.2 |  6   | 14.8 |  235.6 |  91.4 | 0.612054 |
| 1997 | 35582 | 30.4 | 13.2 |  45.7 | 14.5 | 211.6 | 10.1 | 21.6 |  347.2 | 135.6 | 0.609447 |
| 1997 | 35674 | 23.3 |  9.5 |  41.9 | 12.5 | 182.7 |  9.7 | 22.1 |  301.8 | 119.1 | 0.605368 |
| 1997 | 35765 | 26.1 | 13.4 |  41.7 | 11.4 | 162.3 |  3.8 | 23.4 |  282   | 119.7 | 0.575532 |
| 1998 | 35855 | 20.8 | 10.6 |  21.5 |  9.2 | 142   |  3.7 | 12.6 |  220.4 |  78.4 | 0.644283 |
| 1998 | 35947 | 18   |  9.6 |  28.2 | 12   | 173.4 |  3.5 | 17.8 |  262.6 |  89.2 | 0.66032  |
| 1998 | 36039 | 14.2 |  9   |  22.2 | 12.6 | 154.1 |  2.4 | 21.2 |  235.9 |  81.8 | 0.653243 |
| 1998 | 36130 | 18.4 | 11   |  25   |  8.9 | 157.3 |  3   | 16   |  239.6 |  82.3 | 0.656511 |
| 1999 | 36220 | 15.6 | 10.3 |  20.2 |  7.6 | 102.3 |  3.8 |  7.6 |  167.3 |  65   | 0.611476 |
| 1999 | 36312 | 17.4 |  6.7 |  26.4 | 12.8 | 109.4 |  2.6 | 19.6 |  195   |  85.6 | 0.561026 |
| 1999 | 36404 | 14.6 |  8.2 |  21   |  6.5 | 107.9 |  2.7 | 19.2 |  180.1 |  72.2 | 0.599112 |
| 1999 | 36495 | 14.8 |  8.1 |  21.3 |  6.7 | 108.8 |  2.3 | 14.8 |  176.9 |  68.1 | 0.615037 |
| 2000 | 36586 | 12.1 |  7.5 |  17.1 |  3.8 |  85   |  2.4 |  8.8 |  136.7 |  51.7 | 0.6218   |
| 2000 | 36678 | 14.6 | 10   |  23.1 |  5.6 | 113.3 |  1.3 | 14.7 |  182.7 |  69.4 | 0.620142 |
| 2000 | 36770 | 13.6 |  8.6 |  21.8 |  5.5 | 104.4 |  1.7 | 14.2 |  169.8 |  65.4 | 0.614841 |
| 2000 | 36861 | 15.8 |  7.3 |  21.4 |  6.8 | 118   |  2.6 | 15.3 |  187.2 |  69.2 | 0.630342 |
| 2001 | 36951 | 12.7 |  8.4 |  17.1 |  4.9 |  90.8 |  2.5 |  7.2 |  143.5 |  52.7 | 0.632753 |
| 2001 | 37043 | 15.1 |  8.4 |  22.8 | 12.4 | 110.9 |  2.3 | 10.9 |  182.8 |  71.9 | 0.606674 |
| 2001 | 37135 | 12.5 |  7.2 |  21.6 |  6.9 | 103.3 |  0.9 | 15   |  167.4 |  64.1 | 0.617085 |
| 2001 | 37226 | 12.6 |  7.1 |  25   |  8   | 103.5 |  1.2 | 13.3 |  170.7 |  67.2 | 0.606327 |
| 2002 | 37316 | 10.5 |  8.4 |  17.3 |  7.3 |  82.5 |  1   |  7.2 |  134.2 |  51.7 | 0.614754 |
| 2002 | 37408 | 12.6 | 11.2 |  28.7 |  9.9 |  91.8 |  0.9 | 13   |  168.3 |  76.5 | 0.545455 |
| 2002 | 37500 | 15.4 | 10.7 |  23.2 |  9.7 | 110.1 |  1.1 | 12.8 |  182.9 |  72.8 | 0.601968 |
| 2002 | 37591 | 13.7 |  8.9 |  31.9 | 10   | 111.1 |  1   | 16.2 |  192.8 |  81.7 | 0.576245 |
| 2003 | 37681 | 13.2 | 12.1 |  23.5 |  6   |  90.8 |  1.2 |  6.6 |  153.4 |  62.6 | 0.591917 |
| 2003 | 37773 | 16.5 | 14.5 |  35.7 | 11   | 111.6 |  1   | 13.4 |  203.7 |  92.1 | 0.547865 |
| 2003 | 37865 | 10.4 | 12.9 |  26   |  9.3 | 108.5 |  1.2 | 11.2 |  179.7 |  71.2 | 0.603784 |
| 2003 | 37956 | 14.8 | 10.6 |  31.2 |  9.6 | 122   |  1   | 10.3 |  199.5 |  77.5 | 0.611529 |
| 2004 | 38047 | 10.6 | 17.4 |  26   |  7.1 |  96.5 |  1.7 |  7.9 |  167.3 |  70.8 | 0.576808 |
| 2004 | 38139 | 14.7 | 12.6 |  42   | 15.7 | 138.8 |  3.6 | 13.1 |  240.2 | 101.4 | 0.577852 |
| 2004 | 38231 | 17.2 | 14.5 |  40.9 | 15.5 | 147.9 |  1.3 | 13.8 |  251.1 | 103.2 | 0.589008 |
| 2004 | 38322 | 17.2 |  7.9 |  45.2 | 17.2 | 156.7 |  1.6 | 14.9 |  260.8 | 104.1 | 0.600844 |
| 2005 | 38412 | 18   | 13.8 |  33.4 | 14   | 134.4 |  2.5 |  9.6 |  225.8 |  91.4 | 0.595217 |
| 2005 | 38504 | 21.2 | 15.3 |  46.9 | 20.1 | 167   |  2.9 | 17.3 |  290.7 | 123.7 | 0.574475 |
| 2005 | 38596 | 22.7 | 15.7 |  45.9 | 25.8 | 154.4 |  3.6 | 24.1 |  292   | 137.6 | 0.528767 |
| 2005 | 38687 | 29.4 | 20.7 |  58.7 | 39.5 | 158   |  3.7 | 17.6 |  327.6 | 169.6 | 0.482295 |
| 2006 | 38777 | 29.8 | 17.8 |  49   | 24.7 | 121.5 |  8.4 | 12.6 |  263.7 | 142.2 | 0.460751 |
| 2006 | 38869 | 32.2 | 20   |  65.2 | 56.5 | 156.3 |  6.9 | 20.5 |  357.4 | 201.1 | 0.437325 |
| 2006 | 38961 | 35.3 | 22.3 |  64.2 | 51.1 | 190.2 |  6.6 | 25   |  394.6 | 204.4 | 0.482007 |
| 2006 | 39052 | 43   | 22.1 |  73.7 | 59.1 | 217.3 |  5.9 | 27.3 |  448.2 | 230.9 | 0.484828 |
| 2007 | 39142 | 32.3 | 16.9 |  54.4 | 66.5 | 179.9 |  3   | 16.4 |  369.3 | 189.4 | 0.487138 |
| 2007 | 39234 | 33.5 | 21.2 |  80   | 84.1 | 251.8 |  8.4 | 23.5 |  502.5 | 250.7 | 0.501095 |
| 2007 | 39326 | 38   | 17.7 |  84.9 | 87.2 | 293.3 |  9   | 33.4 |  563.4 | 270.1 | 0.520589 |
| 2007 | 39417 | 48.3 | 25.3 |  99.9 | 93.5 | 313.8 |  7   | 38.2 |  625.9 | 312.1 | 0.501358 |
| 2008 | 39508 | 52.3 | 23.6 |  86.3 | 79.3 | 271.4 |  8.2 | 22.9 |  544   | 272.6 | 0.498897 |
| 2008 | 39600 | 51.3 | 27.1 | 126.8 | 95.2 | 381.2 |  8.3 | 38.2 |  728.1 | 346.9 | 0.523554 |
| 2008 | 39692 | 49.2 | 22.4 | 109.5 | 75   | 383.8 |  7.3 | 40.6 |  687.7 | 303.9 | 0.558092 |
| 2008 | 39783 | 49.6 | 19.5 |  94.9 | 68   | 364   |  7   | 45.5 |  648.5 | 284.5 | 0.561295 |
| 2009 | 39873 | 40.2 | 10.3 |  68.6 | 36   | 224.2 |  3.3 | 20.9 |  403.5 | 179.3 | 0.555638 |
| 2009 | 39965 | 36.3 | 10   |  78.6 | 41.8 | 274.8 |  2.7 | 39.2 |  483.5 | 208.7 | 0.568356 |
| 2009 | 40057 | 38.7 | 15   | 103.8 | 48.2 | 298.9 |  3.5 | 49.2 |  557.4 | 258.5 | 0.53624  |
| 2009 | 40148 | 28.4 | 24   | 123.5 | 37.6 | 321.7 |  4.4 | 39.1 |  578.8 | 257.1 | 0.555805 |
| 2010 | 40238 | 32.6 | 24.2 |  80.6 | 34   | 257.1 |  5.7 | 25   |  459.3 | 202.2 | 0.559765 |
| 2010 | 40330 | 30.7 | 20.2 | 128.7 | 48.1 | 366.3 |  7.1 | 36.1 |  637.1 | 270.8 | 0.574949 |
| 2010 | 40422 | 31.5 | 12.4 | 129.8 | 47.4 | 384.6 |  8   | 55.8 |  669.4 | 284.8 | 0.574544 |
| 2010 | 40513 | 36.9 | 12.5 | 161.8 | 59.5 | 393.7 | 10.2 | 49.8 |  724.4 | 330.7 | 0.543484 |
| 2011 | 40603 | 39   | 13.1 | 129.1 | 62.6 | 362.2 |  9.4 | 34.7 |  650.1 | 287.9 | 0.557145 |
| 2011 | 40695 | 45.8 | 19.4 | 242.8 | 85.2 | 449.6 |  9.6 | 55   |  907.4 | 457.8 | 0.495482 |
| 2011 | 40787 | 63.6 | 19.4 | 263   | 74.7 | 481.6 |  9.6 | 71.6 |  983.4 | 501.8 | 0.48973  |
| 2011 | 40878 | 63.4 | 13.1 | 256.6 | 90.3 | 531.9 | 10.1 | 67.1 | 1032.4 | 500.5 | 0.515207 |
| 2012 | 40969 | 58.8 | 13.2 | 199.1 | 73.4 | 490.1 | 10   | 31.6 |  876.1 | 386   | 0.559411 |
| 2012 | 41061 | 56.4 | 12.8 | 248.8 | 90   | 603.2 |  9.7 | 40.1 | 1061.1 | 457.9 | 0.568467 |
| 2012 | 41153 | 49.2 | 10.2 | 207   | 81.4 | 488.6 | 10.9 | 47.4 |  894.7 | 406.1 | 0.546105 |
| 2012 | 41244 | 45.4 |  7.9 | 189.5 | 66.8 | 470.7 | 10.1 | 33.5 |  823.9 | 353.2 | 0.571307 |
| 2013 | 41334 | 44.7 | 10.9 | 125.6 | 37.6 | 421.8 |  9.8 | 21.8 |  672.2 | 250.4 | 0.627492 |
| 2013 | 41426 | 48   |  9.5 | 141.6 | 44.6 | 382.3 |  9.6 | 29   |  664.6 | 282.3 | 0.575233 |
| 2013 | 41518 | 35.9 |  7.8 | 130.9 | 26.4 | 395.8 |  9.3 | 32.3 |  638.4 | 242.6 | 0.619987 |
| 2013 | 41609 | 34.4 |  8.1 | 121.5 | 36.1 | 308.3 |  8.8 | 30.2 |  547.4 | 239.1 | 0.563208 |
| 2014 | 41699 | 40.7 |  7.9 | 100.2 | 24.8 | 206.2 |  6.4 | 21.4 |  408   | 201.8 | 0.505392 |
| 2014 | 41791 | 27.9 |  8.8 |  98.8 | 29.1 | 309.7 |  5.6 | 34.5 |  515   | 205.3 | 0.601359 |
| 2014 | 41883 | 34.6 |  5.6 |  87.6 | 25.3 | 267.1 |  7.5 | 27.3 |  457.7 | 190.6 | 0.58357  |
| 2014 | 41974 | 32.4 |  5.1 | 102.9 | 27.5 | 262.3 |  4.2 | 24.8 |  459.2 | 196.9 | 0.571211 |
| 2015 | 42064 | 29.7 |  5.8 |  52.9 | 22.2 | 183.2 |  4.4 | 19.4 |  317.7 | 134.5 | 0.576645 |
| 2015 | 42156 | 25.4 |  6.4 |  67.9 | 11.7 | 204.8 |  3.8 | 24.2 |  344.1 | 139.3 | 0.595176 |
| 2015 | 42248 | 29.4 |  6.4 |  76.6 | 11   | 233.1 |  3.9 | 33.4 |  394   | 160.9 | 0.591624 |
| 2015 | 42339 | 34.3 |  8.2 |  73.9 | 13   | 222.6 |  2.3 | 27.5 |  382.8 | 160.2 | 0.581505 |
| 2016 | 42430 | 28.7 |  6.2 |  37.1 |  7.7 | 187.1 |  3.8 | 19.4 |  290.4 | 103.3 | 0.644284 |
| 2016 | 42522 | 31.1 |  8.1 |  43.8 | 18.9 | 228.2 |  3.4 | 20.5 |  353.9 | 125.7 | 0.644815 |
| 2016 | 42614 | 31.9 |  7.9 |  55.1 | 10.4 | 248.8 |  3.2 | 22.1 |  379.5 | 130.7 | 0.655599 |
| 2016 | 42705 | 30.7 |  8.1 |  59.9 | 12.4 | 263.5 |  3.1 | 23.6 |  403.1 | 139.6 | 0.653684 |
| 2017 | 42795 | 36.7 | 11   |  34.5 | 11.9 | 225   |  3.4 | 11.9 |  337.6 | 112.6 | 0.666469 |
| 2017 | 42887 | 45.3 | 13.7 |  57.6 | 12.9 | 291   |  3.4 | 20.8 |  444.9 | 153.9 | 0.65408  |
| 2017 | 42979 | 42.1 | 16.7 |  76.5 | 10.6 | 294.2 |  7   | 28   |  475.2 | 181   | 0.619108 |
| 2017 | 43070 | 57.6 | 14.1 |  76.4 | 10.8 | 298.5 |  7.4 | 30.5 |  496.1 | 197.6 | 0.601693 |
| 2018 | 43160 | 61   | 18.4 |  56.8 | 14.1 | 261   |  4.7 | 22.5 |  438.7 | 177.7 | 0.59494  |
| 2018 | 43252 | 68.5 | 24.5 |  70.3 | 19.7 | 349.8 |  6.7 | 28.3 |  567.8 | 218   | 0.616062 |
| 2018 | 43344 | 56.7 | 22.4 |  86.1 | 20.4 | 361   |  5.3 | 32.5 |  584.4 | 223.4 | 0.617728 |
| 2018 | 43435 | 52.3 | 27.2 |  90.4 | 21.9 | 346.3 |  4.8 | 39.9 |  582.8 | 236.5 | 0.5942   |



label: K=J-G
L=G/J
labeled_formulas: K=J-G
L=G/J
output: {"Arithmetic-Relationship": ["K=J-G", "L=G/J"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_411668___xlsx_c4665848f0183df8581213262be6a915f20b1735.xlsx___line_581