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 | 32660 |   527 |   479 | 0.523857 |  1006 |
| 1989 | 32752 |   594 |   452 | 0.567878 |  1046 |
| 1989 | 32843 |   576 |   548 | 0.512456 |  1124 |
| 1990 | 32933 |   465 |   431 | 0.518973 |   896 |
| 1990 | 33025 |   469 |   570 | 0.451396 |  1039 |
| 1990 | 33117 |   513 |   631 | 0.448427 |  1144 |
| 1990 | 33208 |   490 |   770 | 0.388889 |  1260 |
| 1991 | 33298 |   457 |   612 | 0.427502 |  1069 |
| 1991 | 33390 |   473 |   677 | 0.411304 |  1150 |
| 1991 | 33482 |   444 |   596 | 0.426923 |  1040 |
| 1991 | 33573 |   506 |   640 | 0.441536 |  1146 |
| 1992 | 33664 |   428 |   465 | 0.479283 |   893 |
| 1992 | 33756 |   556 |   632 | 0.468013 |  1188 |
| 1992 | 33848 |   672 |   593 | 0.531225 |  1265 |
| 1992 | 33939 |   840 |   602 | 0.582524 |  1442 |
| 1993 | 34029 |   732 |   574 | 0.56049  |  1306 |
| 1993 | 34121 |   800 |   735 | 0.521173 |  1535 |
| 1993 | 34213 |   763 |   582 | 0.567286 |  1345 |
| 1993 | 34304 |   980 |   637 | 0.606061 |  1617 |
| 1994 | 34394 |   671 |   606 | 0.52545  |  1277 |
| 1994 | 34486 |   772 |   640 | 0.546742 |  1412 |
| 1994 | 34578 |   662 |   668 | 0.497744 |  1330 |
| 1994 | 34669 |  1152 |   719 | 0.615714 |  1871 |
| 1995 | 34759 |   989 |   558 | 0.639302 |  1547 |
| 1995 | 34851 |   859 |   831 | 0.508284 |  1690 |
| 1995 | 34943 |   976 |   695 | 0.584081 |  1671 |
| 1995 | 35034 |  1205 |   806 | 0.599204 |  2011 |
| 1996 | 35125 |   901 |   813 | 0.525671 |  1714 |
| 1996 | 35217 |  1079 |  1191 | 0.47533  |  2270 |
| 1996 | 35309 |   815 |  1194 | 0.405674 |  2009 |
| 1996 | 35400 |   983 |  1375 | 0.416879 |  2358 |
| 1997 | 35490 |   995 |  1241 | 0.444991 |  2236 |
| 1997 | 35582 |  1107 |  1276 | 0.46454  |  2383 |
| 1997 | 35674 |  1145 |  1417 | 0.446916 |  2562 |
| 1997 | 35765 |  1455 |  1655 | 0.467846 |  3110 |
| 1998 | 35855 |  1439 |  1207 | 0.54384  |  2646 |
| 1998 | 35947 |  1539 |  1503 | 0.505917 |  3042 |
| 1998 | 36039 |  1132 |  1510 | 0.428463 |  2642 |
| 1998 | 36130 |   736 |  1760 | 0.294872 |  2496 |
| 1999 | 36220 |   818 |  1177 | 0.410025 |  1995 |
| 1999 | 36312 |   681 |  1251 | 0.352484 |  1932 |
| 1999 | 36404 |   683 |  1238 | 0.355544 |  1921 |
| 1999 | 36495 |   488 |   861 | 0.361749 |  1349 |
| 2000 | 36586 |   356 |   699 | 0.337441 |  1055 |
| 2000 | 36678 |   641 |   706 | 0.475872 |  1347 |
| 2000 | 36770 |   405 |   715 | 0.361607 |  1120 |
| 2000 | 36861 |   472 |   925 | 0.337867 |  1397 |
| 2001 | 36951 |   690 |   757 | 0.476849 |  1447 |
| 2001 | 37043 |   778 |   987 | 0.440793 |  1765 |
| 2001 | 37135 |   805 |  1010 | 0.443526 |  1815 |
| 2001 | 37226 |   749 |  1234 | 0.377711 |  1983 |
| 2002 | 37316 |   532 |  1165 | 0.313494 |  1697 |
| 2002 | 37408 |   731 |  1370 | 0.34793  |  2101 |
| 2002 | 37500 |   707 |  1368 | 0.340723 |  2075 |
| 2002 | 37591 |   882 |  1632 | 0.350835 |  2514 |
| 2003 | 37681 |   928 |  1131 | 0.450704 |  2059 |
| 2003 | 37773 |  1093 |  1474 | 0.425789 |  2567 |
| 2003 | 37865 |  1295 |  1169 | 0.525568 |  2464 |
| 2003 | 37956 |  1364 |  1502 | 0.475925 |  2866 |
| 2004 | 38047 |   992 |  1106 | 0.472831 |  2098 |
| 2004 | 38139 |  1170 |  1197 | 0.494297 |  2367 |
| 2004 | 38231 |  1282 |  1231 | 0.510147 |  2513 |
| 2004 | 38322 |  1380 |  1375 | 0.500907 |  2755 |
| 2005 | 38412 |  1174 |  1188 | 0.497036 |  2362 |
| 2005 | 38504 |  1469 |  1744 | 0.457205 |  3213 |
| 2005 | 38596 |  1865 |  1837 | 0.503782 |  3702 |
| 2005 | 38687 |  2573 |  2393 | 0.518123 |  4966 |
| 2006 | 38777 |  2601 |  2277 | 0.53321  |  4878 |
| 2006 | 38869 |  3699 |  2414 | 0.605104 |  6113 |
| 2006 | 38961 |  2876 |  2070 | 0.58148  |  4946 |
| 2006 | 39052 |  3675 |  2564 | 0.589037 |  6239 |
| 2007 | 39142 |  3307 |  2184 | 0.602258 |  5491 |
| 2007 | 39234 |  3982 |  2963 | 0.573362 |  6945 |
| 2007 | 39326 |  3666 |  2500 | 0.594551 |  6166 |
| 2007 | 39417 |  4319 |  3215 | 0.573268 |  7534 |
| 2008 | 39508 |  4318 |  2404 | 0.642368 |  6722 |
| 2008 | 39600 |  5047 |  3732 | 0.574895 |  8779 |
| 2008 | 39692 |  5463 |  3109 | 0.637308 |  8572 |
| 2008 | 39783 |  6710 |  4332 | 0.60768  | 11042 |
| 2009 | 39873 |  5354 |  3736 | 0.588999 |  9090 |
| 2009 | 39965 |  5879 |  3394 | 0.633991 |  9273 |
| 2009 | 40057 |  5100 |  2861 | 0.640623 |  7961 |
| 2009 | 40148 |  5385 |  3941 | 0.577418 |  9326 |
| 2010 | 40238 |  5335 |  2753 | 0.659619 |  8088 |
| 2010 | 40330 |  6108 |  3702 | 0.62263  |  9810 |
| 2010 | 40422 |  6452 |  3968 | 0.619194 | 10420 |
| 2010 | 40513 |  6801 |  4742 | 0.589188 | 11543 |
| 2011 | 40603 |  6577 |  3948 | 0.624893 | 10525 |
| 2011 | 40695 |  8463 |  5896 | 0.589386 | 14359 |
| 2011 | 40787 |  9539 |  7759 | 0.551451 | 17298 |
| 2011 | 40878 | 10452 |  9488 | 0.524173 | 19940 |
| 2012 | 40969 | 10922 |  8690 | 0.556904 | 19612 |
| 2012 | 41061 | 14158 | 10989 | 0.56301  | 25147 |
| 2012 | 41153 | 12757 | 10919 | 0.538816 | 23676 |
| 2012 | 41244 | 13203 | 12842 | 0.50693  | 26045 |
| 2013 | 41334 |  9733 | 10901 | 0.471697 | 20634 |
| 2013 | 41426 | 12507 | 11847 | 0.51355  | 24354 |
| 2013 | 41518 | 12245 | 11958 | 0.505929 | 24203 |
| 2013 | 41609 | 12301 | 12406 | 0.497875 | 24707 |
| 2014 | 41699 | 10246 |  8846 | 0.536665 | 19092 |
| 2014 | 41791 | 11967 | 10423 | 0.53448  | 22390 |
| 2014 | 41883 | 11785 |  9022 | 0.566396 | 20807 |
| 2014 | 41974 | 12213 |  9044 | 0.57454  | 21257 |
| 2015 | 42064 | 10737 |  6074 | 0.638689 | 16811 |
| 2015 | 42156 | 11255 |  5987 | 0.652767 | 17242 |
| 2015 | 42248 |  9813 |  5075 | 0.659121 | 14888 |
| 2015 | 42339 | 10579 |  5648 | 0.651938 | 16227 |
| 2016 | 42430 |  7824 |  3576 | 0.686316 | 11400 |
| 2016 | 42522 |  6995 |  3879 | 0.643278 | 10874 |
| 2016 | 42614 |  5869 |  4200 | 0.582878 | 10069 |
| 2016 | 42705 |  6192 |  4390 | 0.585145 | 10582 |
| 2017 | 42795 |  4820 |  3771 | 0.561052 |  8591 |
| 2017 | 42887 |  5349 |  4159 | 0.562579 |  9508 |
| 2017 | 42979 |  5055 |  4310 | 0.539776 |  9365 |
| 2017 | 43070 |  5234 |  4639 | 0.530133 |  9873 |
| 2018 | 43160 |  4268 |  3907 | 0.52208  |  8175 |
| 2018 | 43252 |  4616 |  4359 | 0.514318 |  8975 |
| 2018 | 43344 |  4249 |  4173 | 0.504512 |  8422 |
| 2018 | 43435 |  4658 |  4342 | 0.517556 |  9000 |



label: D=F-C
E=C/F
labeled_formulas: D=F-C
E=C/F
output: {"Arithmetic-Relationship": ["D=F-C", "E=C/F"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_411662___xlsx_c4665848f0183df8581213262be6a915f20b1735.xlsx___line_579