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 |  1006 | 0.523857 |
| 1989 | 32752 |   594 |   452 |  1046 | 0.567878 |
| 1989 | 32843 |   576 |   548 |  1124 | 0.512456 |
| 1990 | 32933 |   465 |   431 |   896 | 0.518973 |
| 1990 | 33025 |   469 |   570 |  1039 | 0.451396 |
| 1990 | 33117 |   513 |   631 |  1144 | 0.448427 |
| 1990 | 33208 |   490 |   770 |  1260 | 0.388889 |
| 1991 | 33298 |   457 |   612 |  1069 | 0.427502 |
| 1991 | 33390 |   473 |   677 |  1150 | 0.411304 |
| 1991 | 33482 |   444 |   596 |  1040 | 0.426923 |
| 1991 | 33573 |   506 |   640 |  1146 | 0.441536 |
| 1992 | 33664 |   428 |   465 |   893 | 0.479283 |
| 1992 | 33756 |   556 |   632 |  1188 | 0.468013 |
| 1992 | 33848 |   672 |   593 |  1265 | 0.531225 |
| 1992 | 33939 |   840 |   602 |  1442 | 0.582524 |
| 1993 | 34029 |   732 |   574 |  1306 | 0.56049  |
| 1993 | 34121 |   800 |   735 |  1535 | 0.521173 |
| 1993 | 34213 |   763 |   582 |  1345 | 0.567286 |
| 1993 | 34304 |   980 |   637 |  1617 | 0.606061 |
| 1994 | 34394 |   671 |   606 |  1277 | 0.52545  |
| 1994 | 34486 |   772 |   640 |  1412 | 0.546742 |
| 1994 | 34578 |   662 |   668 |  1330 | 0.497744 |
| 1994 | 34669 |  1152 |   719 |  1871 | 0.615714 |
| 1995 | 34759 |   989 |   558 |  1547 | 0.639302 |
| 1995 | 34851 |   859 |   831 |  1690 | 0.508284 |
| 1995 | 34943 |   976 |   695 |  1671 | 0.584081 |
| 1995 | 35034 |  1205 |   806 |  2011 | 0.599204 |
| 1996 | 35125 |   901 |   813 |  1714 | 0.525671 |
| 1996 | 35217 |  1079 |  1191 |  2270 | 0.47533  |
| 1996 | 35309 |   815 |  1194 |  2009 | 0.405674 |
| 1996 | 35400 |   983 |  1375 |  2358 | 0.416879 |
| 1997 | 35490 |   995 |  1241 |  2236 | 0.444991 |
| 1997 | 35582 |  1107 |  1276 |  2383 | 0.46454  |
| 1997 | 35674 |  1145 |  1417 |  2562 | 0.446916 |
| 1997 | 35765 |  1455 |  1655 |  3110 | 0.467846 |
| 1998 | 35855 |  1439 |  1207 |  2646 | 0.54384  |
| 1998 | 35947 |  1539 |  1503 |  3042 | 0.505917 |
| 1998 | 36039 |  1132 |  1510 |  2642 | 0.428463 |
| 1998 | 36130 |   736 |  1760 |  2496 | 0.294872 |
| 1999 | 36220 |   818 |  1177 |  1995 | 0.410025 |
| 1999 | 36312 |   681 |  1251 |  1932 | 0.352484 |
| 1999 | 36404 |   683 |  1238 |  1921 | 0.355544 |
| 1999 | 36495 |   488 |   861 |  1349 | 0.361749 |
| 2000 | 36586 |   356 |   699 |  1055 | 0.337441 |
| 2000 | 36678 |   641 |   706 |  1347 | 0.475872 |
| 2000 | 36770 |   405 |   715 |  1120 | 0.361607 |
| 2000 | 36861 |   472 |   925 |  1397 | 0.337867 |
| 2001 | 36951 |   690 |   757 |  1447 | 0.476849 |
| 2001 | 37043 |   778 |   987 |  1765 | 0.440793 |
| 2001 | 37135 |   805 |  1010 |  1815 | 0.443526 |
| 2001 | 37226 |   749 |  1234 |  1983 | 0.377711 |
| 2002 | 37316 |   532 |  1165 |  1697 | 0.313494 |
| 2002 | 37408 |   731 |  1370 |  2101 | 0.34793  |
| 2002 | 37500 |   707 |  1368 |  2075 | 0.340723 |
| 2002 | 37591 |   882 |  1632 |  2514 | 0.350835 |
| 2003 | 37681 |   928 |  1131 |  2059 | 0.450704 |
| 2003 | 37773 |  1093 |  1474 |  2567 | 0.425789 |
| 2003 | 37865 |  1295 |  1169 |  2464 | 0.525568 |
| 2003 | 37956 |  1364 |  1502 |  2866 | 0.475925 |
| 2004 | 38047 |   992 |  1106 |  2098 | 0.472831 |
| 2004 | 38139 |  1170 |  1197 |  2367 | 0.494297 |
| 2004 | 38231 |  1282 |  1231 |  2513 | 0.510147 |
| 2004 | 38322 |  1380 |  1375 |  2755 | 0.500907 |
| 2005 | 38412 |  1174 |  1188 |  2362 | 0.497036 |
| 2005 | 38504 |  1469 |  1744 |  3213 | 0.457205 |
| 2005 | 38596 |  1865 |  1837 |  3702 | 0.503782 |
| 2005 | 38687 |  2573 |  2393 |  4966 | 0.518123 |
| 2006 | 38777 |  2601 |  2277 |  4878 | 0.53321  |
| 2006 | 38869 |  3699 |  2414 |  6113 | 0.605104 |
| 2006 | 38961 |  2876 |  2070 |  4946 | 0.58148  |
| 2006 | 39052 |  3675 |  2564 |  6239 | 0.589037 |
| 2007 | 39142 |  3307 |  2184 |  5491 | 0.602258 |
| 2007 | 39234 |  3982 |  2963 |  6945 | 0.573362 |
| 2007 | 39326 |  3666 |  2500 |  6166 | 0.594551 |
| 2007 | 39417 |  4319 |  3215 |  7534 | 0.573268 |
| 2008 | 39508 |  4318 |  2404 |  6722 | 0.642368 |
| 2008 | 39600 |  5047 |  3732 |  8779 | 0.574895 |
| 2008 | 39692 |  5463 |  3109 |  8572 | 0.637308 |
| 2008 | 39783 |  6710 |  4332 | 11042 | 0.60768  |
| 2009 | 39873 |  5354 |  3736 |  9090 | 0.588999 |
| 2009 | 39965 |  5879 |  3394 |  9273 | 0.633991 |
| 2009 | 40057 |  5100 |  2861 |  7961 | 0.640623 |
| 2009 | 40148 |  5385 |  3941 |  9326 | 0.577418 |
| 2010 | 40238 |  5335 |  2753 |  8088 | 0.659619 |
| 2010 | 40330 |  6108 |  3702 |  9810 | 0.62263  |
| 2010 | 40422 |  6452 |  3968 | 10420 | 0.619194 |
| 2010 | 40513 |  6801 |  4742 | 11543 | 0.589188 |
| 2011 | 40603 |  6577 |  3948 | 10525 | 0.624893 |
| 2011 | 40695 |  8463 |  5896 | 14359 | 0.589386 |
| 2011 | 40787 |  9539 |  7759 | 17298 | 0.551451 |
| 2011 | 40878 | 10452 |  9488 | 19940 | 0.524173 |
| 2012 | 40969 | 10922 |  8690 | 19612 | 0.556904 |
| 2012 | 41061 | 14158 | 10989 | 25147 | 0.56301  |
| 2012 | 41153 | 12757 | 10919 | 23676 | 0.538816 |
| 2012 | 41244 | 13203 | 12842 | 26045 | 0.50693  |
| 2013 | 41334 |  9733 | 10901 | 20634 | 0.471697 |
| 2013 | 41426 | 12507 | 11847 | 24354 | 0.51355  |
| 2013 | 41518 | 12245 | 11958 | 24203 | 0.505929 |
| 2013 | 41609 | 12301 | 12406 | 24707 | 0.497875 |
| 2014 | 41699 | 10246 |  8846 | 19092 | 0.536665 |
| 2014 | 41791 | 11967 | 10423 | 22390 | 0.53448  |
| 2014 | 41883 | 11785 |  9022 | 20807 | 0.566396 |
| 2014 | 41974 | 12213 |  9044 | 21257 | 0.57454  |
| 2015 | 42064 | 10737 |  6074 | 16811 | 0.638689 |
| 2015 | 42156 | 11255 |  5987 | 17242 | 0.652767 |
| 2015 | 42248 |  9813 |  5075 | 14888 | 0.659121 |
| 2015 | 42339 | 10579 |  5648 | 16227 | 0.651938 |
| 2016 | 42430 |  7824 |  3576 | 11400 | 0.686316 |
| 2016 | 42522 |  6995 |  3879 | 10874 | 0.643278 |
| 2016 | 42614 |  5869 |  4200 | 10069 | 0.582878 |
| 2016 | 42705 |  6192 |  4390 | 10582 | 0.585145 |
| 2017 | 42795 |  4820 |  3771 |  8591 | 0.561052 |
| 2017 | 42887 |  5349 |  4159 |  9508 | 0.562579 |
| 2017 | 42979 |  5055 |  4310 |  9365 | 0.539776 |
| 2017 | 43070 |  5234 |  4639 |  9873 | 0.530133 |
| 2018 | 43160 |  4268 |  3907 |  8175 | 0.52208  |
| 2018 | 43252 |  4616 |  4359 |  8975 | 0.514318 |
| 2018 | 43344 |  4249 |  4173 |  8422 | 0.504512 |
| 2018 | 43435 |  4660 |  4363 |  9023 | 0.516458 |
| 2019 | 43525 |  3730 |  3575 |  7305 | 0.510609 |
| 2019 | 43617 |  4329 |  4275 |  8604 | 0.503138 |
| 2019 | 43709 |  4429 |  4208 |  8637 | 0.512794 |
| 2019 | 43800 |  4748 |  4598 |  9346 | 0.508025 |
| 2020 | 43891 |  4592 |  3399 |  7991 | 0.574646 |
| 2020 | 43983 |  5192 |  3989 |  9181 | 0.565516 |
| 2020 | 44075 |  4954 |  3653 |  8607 | 0.575578 |
| 2020 | 44166 |  5275 |  3995 |  9270 | 0.56904  |



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_44284___xlsx_f8b21cedc02571be18d14c0f61c587edf8640b6d.xlsx___line_658