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 |
|-----:|------:|------:|------:|------:|---------:|----------:|
| 2000 | 36770 |  1081 | 11791 | 12872 | 0.374653 | 0.0839807 |
| 2000 | 36861 |  1591 | 11915 | 13506 | 0.296669 | 0.117799  |
| 2001 | 36951 |  1672 |  9907 | 11579 | 0.412679 | 0.144399  |
| 2001 | 37043 |  1640 | 11820 | 13460 | 0.47439  | 0.121842  |
| 2001 | 37135 |  1676 | 10818 | 12494 | 0.48031  | 0.134144  |
| 2001 | 37226 |  1727 | 12315 | 14042 | 0.4337   | 0.122988  |
| 2002 | 37316 |  1450 | 10621 | 12071 | 0.366897 | 0.120123  |
| 2002 | 37408 |  1849 | 12498 | 14347 | 0.395349 | 0.128877  |
| 2002 | 37500 |  1673 | 12296 | 13969 | 0.422594 | 0.119765  |
| 2002 | 37591 |  2071 | 14857 | 16928 | 0.425881 | 0.122342  |
| 2003 | 37681 |  1918 | 12071 | 13989 | 0.483837 | 0.137108  |
| 2003 | 37773 |  2320 | 13591 | 15911 | 0.471121 | 0.145811  |
| 2003 | 37865 |  2484 | 12879 | 15363 | 0.521337 | 0.161687  |
| 2003 | 37956 |  2875 | 13842 | 16717 | 0.474435 | 0.171981  |
| 2004 | 38047 |  2113 | 11325 | 13438 | 0.469475 | 0.157241  |
| 2004 | 38139 |  2573 | 13851 | 16424 | 0.454722 | 0.156661  |
| 2004 | 38231 |  2570 | 12940 | 15510 | 0.498833 | 0.1657    |
| 2004 | 38322 |  3043 | 15867 | 18910 | 0.4535   | 0.16092   |
| 2005 | 38412 |  2681 | 13036 | 15717 | 0.437896 | 0.17058   |
| 2005 | 38504 |  2949 | 16493 | 19442 | 0.498135 | 0.151682  |
| 2005 | 38596 |  3636 | 15600 | 19236 | 0.512926 | 0.189021  |
| 2005 | 38687 |  4480 | 19026 | 23506 | 0.57433  | 0.19059   |
| 2006 | 38777 |  4308 | 15672 | 19980 | 0.60376  | 0.215616  |
| 2006 | 38869 |  5747 | 18026 | 23773 | 0.64364  | 0.241745  |
| 2006 | 38961 |  4567 | 16687 | 21254 | 0.629735 | 0.214877  |
| 2006 | 39052 |  5618 | 17895 | 23513 | 0.654147 | 0.238932  |
| 2007 | 39142 |  5301 | 16700 | 22001 | 0.623845 | 0.240944  |
| 2007 | 39234 |  6613 | 20806 | 27419 | 0.602147 | 0.241183  |
| 2007 | 39326 |  5661 | 17857 | 23518 | 0.647589 | 0.240709  |
| 2007 | 39417 |  6798 | 21062 | 27860 | 0.635334 | 0.244006  |
| 2008 | 39508 |  6178 | 17014 | 23192 | 0.698932 | 0.266385  |
| 2008 | 39600 |  7343 | 22254 | 29597 | 0.687321 | 0.248099  |
| 2008 | 39692 |  7629 | 20069 | 27698 | 0.716083 | 0.275435  |
| 2008 | 39783 |  9494 | 24775 | 34269 | 0.706762 | 0.277043  |
| 2009 | 39873 |  7379 | 19497 | 26876 | 0.725573 | 0.274557  |
| 2009 | 39965 |  9564 | 23163 | 32727 | 0.614701 | 0.292236  |
| 2009 | 40057 |  7254 | 19268 | 26522 | 0.70306  | 0.273509  |
| 2009 | 40148 |  8191 | 24161 | 32352 | 0.657429 | 0.253184  |
| 2010 | 40238 |  7368 | 18320 | 25688 | 0.724077 | 0.286827  |
| 2010 | 40330 |  8594 | 21913 | 30507 | 0.710728 | 0.281706  |
| 2010 | 40422 |  8532 | 20069 | 28601 | 0.756212 | 0.298311  |
| 2010 | 40513 |  9284 | 24316 | 33600 | 0.732551 | 0.27631   |
| 2011 | 40603 |  8785 | 20158 | 28943 | 0.748662 | 0.303528  |
| 2011 | 40695 | 11054 | 25383 | 36437 | 0.765605 | 0.303373  |
| 2011 | 40787 | 12246 | 25266 | 37512 | 0.778948 | 0.326456  |
| 2011 | 40878 | 13673 | 28554 | 42227 | 0.764426 | 0.323798  |
| 2012 | 40969 | 13781 | 23752 | 37533 | 0.79254  | 0.36717   |
| 2012 | 41061 | 17379 | 28347 | 45726 | 0.814661 | 0.380068  |
| 2012 | 41153 | 15594 | 26627 | 42221 | 0.818071 | 0.369342  |
| 2012 | 41244 | 16372 | 29443 | 45815 | 0.806438 | 0.35735   |
| 2013 | 41334 | 12082 | 24339 | 36421 | 0.805579 | 0.331732  |
| 2013 | 41426 | 15182 | 28464 | 43646 | 0.823805 | 0.347844  |
| 2013 | 41518 | 14810 | 27776 | 42586 | 0.826806 | 0.347767  |
| 2013 | 41609 | 14913 | 29546 | 44459 | 0.824851 | 0.335433  |
| 2014 | 41699 | 12609 | 23198 | 35807 | 0.812594 | 0.352138  |
| 2014 | 41791 | 14636 | 28452 | 43088 | 0.817641 | 0.339677  |
| 2014 | 41883 | 14505 | 26788 | 41293 | 0.812478 | 0.35127   |
| 2014 | 41974 | 15181 | 28975 | 44156 | 0.804492 | 0.343804  |
| 2015 | 42064 | 12835 | 21608 | 34443 | 0.836541 | 0.372645  |
| 2015 | 42156 | 13707 | 26188 | 39895 | 0.821113 | 0.343577  |
| 2015 | 42248 | 12165 | 22389 | 34554 | 0.806658 | 0.352058  |
| 2015 | 42339 | 13162 | 25597 | 38759 | 0.803753 | 0.339586  |
| 2016 | 42430 |  9666 | 19984 | 29650 | 0.809435 | 0.326003  |
| 2016 | 42522 |  9149 | 24697 | 33846 | 0.764564 | 0.270313  |
| 2016 | 42614 |  7593 | 22491 | 30084 | 0.772949 | 0.252393  |
| 2016 | 42705 |  8193 | 25092 | 33285 | 0.755767 | 0.246147  |
| 2017 | 42795 |  6616 | 20504 | 27120 | 0.728537 | 0.243953  |
| 2017 | 42887 |  7434 | 25868 | 33302 | 0.719532 | 0.22323   |
| 2017 | 42979 |  7211 | 23758 | 30969 | 0.701012 | 0.232846  |
| 2017 | 43070 |  7546 | 27289 | 34835 | 0.693613 | 0.216621  |
| 2018 | 43160 |  6436 | 22037 | 28473 | 0.663145 | 0.226039  |
| 2018 | 43252 |  6793 | 28018 | 34811 | 0.679523 | 0.195139  |
| 2018 | 43344 |  6312 | 25721 | 32033 | 0.673162 | 0.197047  |
| 2018 | 43435 |  6865 | 29604 | 36469 | 0.678806 | 0.188242  |
| 2019 | 43525 |  5378 | 23893 | 29271 | 0.693566 | 0.183731  |
| 2019 | 43617 |  6612 | 29327 | 35939 | 0.654719 | 0.183978  |
| 2019 | 43709 |  6287 | 25705 | 31992 | 0.70447  | 0.196518  |
| 2019 | 43800 |  7025 | 28133 | 35158 | 0.675872 | 0.199812  |
| 2020 | 43891 |  6304 | 21762 | 28066 | 0.728426 | 0.224613  |
| 2020 | 43983 |  7248 | 25221 | 32469 | 0.716336 | 0.223228  |
| 2020 | 44075 |  6720 | 21577 | 28297 | 0.737202 | 0.237481  |
| 2020 | 44166 |  7388 | 25281 | 32669 | 0.713996 | 0.226147  |



label: D=E-C
G=C/E
labeled_formulas: D=E-C
G=C/E
output: {"Arithmetic-Relationship": ["D=E-C", "G=C/E"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_44287___xlsx_f8b21cedc02571be18d14c0f61c587edf8640b6d.xlsx___line_659