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 |
|:----|:--------------|------:|-----:|------:|-----:|------:|---------:|
| 601 | Appling       |   235 |   24 |   206 |    5 |   211 |  89.7872 |
| 602 | Atkinson      |    92 |   12 |    77 |    3 |    80 |  86.9565 |
| 603 | Bacon         |   134 |   17 |   114 |    3 |   117 |  87.3134 |
| 604 | Baker         |    20 |    4 |    16 |    0 |    16 |  80      |
| 605 | Baldwin       |   261 |   34 |   223 |    4 |   227 |  86.9732 |
| 606 | Banks         |   191 |   15 |   168 |    8 |   176 |  92.1466 |
| 607 | Barrow        |   725 |   37 |   652 |   36 |   688 |  94.8966 |
| 608 | Bartow        |   899 |   62 |   803 |   34 |   837 |  93.1034 |
| 609 | Ben Hill      |   158 |   24 |   125 |    9 |   134 |  84.8101 |
| 610 | Berrien       |   212 |   20 |   179 |   13 |   192 |  90.566  |
| 611 | Bibb          |  1136 |  155 |   934 |   47 |   981 |  86.3556 |
| 612 | Bleckley      |   129 |    5 |    93 |   31 |   124 |  96.124  |
| 613 | Brantley      |   215 |   10 |   191 |   14 |   205 |  95.3488 |
| 614 | Brooks        |   122 |    6 |   112 |    4 |   116 |  95.082  |
| 615 | Bryan         |   503 |   20 |   419 |   64 |   483 |  96.0239 |
| 616 | Bulloch       |   517 |   30 |   458 |   29 |   487 |  94.1973 |
| 617 | Burke         |   268 |   37 |   222 |    9 |   231 |  86.194  |
| 618 | Butts         |   221 |   14 |   199 |    8 |   207 |  93.6652 |
| 619 | Calhoun       |    27 |    1 |    26 |    0 |    26 |  96.2963 |
| 620 | Camden        |   586 |   29 |   514 |   43 |   557 |  95.0512 |
| 621 | Candler       |   113 |    8 |   102 |    3 |   105 |  92.9204 |
| 622 | Carroll       |   887 |   62 |   756 |   69 |   825 |  93.0101 |
| 623 | Catoosa       |   741 |   42 |   638 |   61 |   699 |  94.332  |
| 624 | Charlton      |    79 |    4 |    72 |    3 |    75 |  94.9367 |
| 625 | Chatham       |  1425 |   92 |  1250 |   83 |  1333 |  93.5439 |
| 626 | Chattahoochee |    91 |   17 |    71 |    3 |    74 |  81.3187 |
| 627 | Chattooga     |   175 |   14 |   157 |    4 |   161 |  92      |
| 628 | Cherokee      |  2375 |   44 |  2098 |  233 |  2331 |  98.1474 |
| 629 | Clarke        |   589 |   65 |   476 |   48 |   524 |  88.9643 |
| 631 | Clayton       |  2639 |  196 |  2349 |   94 |  2443 |  92.5729 |
| 632 | Clinch        |    87 |   13 |    73 |    1 |    74 |  85.0575 |
| 633 | Cobb          |  6615 |  159 |  5522 |  934 |  6456 |  97.5964 |
| 634 | Coffee        |   418 |   39 |   361 |   18 |   379 |  90.6699 |
| 635 | Colquitt      |   518 |   38 |   467 |   13 |   480 |  92.6641 |
| 636 | Columbia      |  1588 |   49 |  1360 |  179 |  1539 |  96.9144 |
| 637 | Cook          |   197 |   17 |   154 |   26 |   180 |  91.3706 |
| 638 | Coweta        |  1373 |   53 |  1224 |   96 |  1320 |  96.1398 |
| 639 | Crawford      |    80 |    7 |    72 |    1 |    73 |  91.25   |
| 640 | Crisp         |   199 |   32 |   160 |    7 |   167 |  83.9196 |
| 641 | Dade          |   151 |    7 |   137 |    7 |   144 |  95.3642 |
| 642 | Dawson        |   238 |   14 |   215 |    9 |   224 |  94.1176 |
| 643 | Decatur       |   310 |   25 |   280 |    5 |   285 |  91.9355 |
| 644 | DeKalb        |  5361 |  486 |  4595 |  280 |  4875 |  90.9345 |
| 645 | Dodge         |   201 |   21 |   152 |   28 |   180 |  89.5522 |
| 646 | Dooly         |    57 |    6 |    48 |    3 |    51 |  89.4737 |
| 647 | Dougherty     |   714 |   78 |   624 |   12 |   636 |  89.0756 |
| 648 | Douglas       |  1458 |   79 |  1296 |   83 |  1379 |  94.5816 |
| 649 | Early         |   136 |   17 |   115 |    4 |   119 |  87.5    |
| 650 | Echols        |    57 |    4 |    49 |    4 |    53 |  92.9825 |
| 651 | Effingham     |   707 |   60 |   608 |   39 |   647 |  91.5134 |
| 652 | Elbert        |   176 |   18 |   153 |    5 |   158 |  89.7727 |
| 653 | Emanuel       |   242 |   37 |   199 |    6 |   205 |  84.7107 |
| 654 | Evans         |    87 |    6 |    80 |    1 |    81 |  93.1034 |
| 655 | Fannin        |   195 |    8 |   163 |   24 |   187 |  95.8974 |
| 656 | Fayette       |  1563 |   23 |  1287 |  253 |  1540 |  98.5285 |
| 657 | Floyd         |   633 |   27 |   566 |   40 |   606 |  95.7346 |
| 658 | Forsyth       |  2647 |   40 |  2218 |  389 |  2607 |  98.4889 |
| 659 | Franklin      |   207 |   14 |   177 |   16 |   193 |  93.2367 |
| 660 | Fulton        |  6135 |  238 |  4986 |  911 |  5897 |  96.1206 |
| 661 | Gilmer        |   267 |   29 |   219 |   19 |   238 |  89.1386 |
| 662 | Glascock      |    37 |    5 |    32 |    0 |    32 |  86.4865 |
| 663 | Glynn         |   601 |   33 |   540 |   28 |   568 |  94.5092 |
| 664 | Gordon        |   417 |   32 |   376 |    9 |   385 |  92.3261 |
| 665 | Grady         |   229 |   11 |   206 |   12 |   218 |  95.1965 |
| 666 | Greene        |    89 |    6 |    81 |    2 |    83 |  93.2584 |
| 667 | Gwinnett      | 10035 |  306 |  8171 | 1558 |  9729 |  96.9507 |
| 668 | Habersham     |   415 |   36 |   348 |   31 |   379 |  91.3253 |
| 669 | Hall          |  1416 |   73 |  1241 |  102 |  1343 |  94.8446 |
| 670 | Hancock       |    60 |    5 |    54 |    1 |    55 |  91.6667 |
| 671 | Haralson      |   182 |   16 |   159 |    7 |   166 |  91.2088 |
| 672 | Harris        |   345 |   16 |   305 |   24 |   329 |  95.3623 |
| 673 | Hart          |   237 |   32 |   194 |   11 |   205 |  86.4979 |
| 674 | Heard         |   121 |    5 |   109 |    7 |   116 |  95.8678 |
| 675 | Henry         |  2932 |  143 |  2540 |  249 |  2789 |  95.1228 |
| 676 | Houston       |  1706 |   97 |  1441 |  168 |  1609 |  94.3142 |
| 677 | Irwin         |    99 |    5 |    82 |   12 |    94 |  94.9495 |
| 678 | Jackson       |   417 |   24 |   351 |   42 |   393 |  94.2446 |
| 679 | Jasper        |   118 |   10 |   103 |    5 |   108 |  91.5254 |
| 680 | Jeff Davis    |   175 |   18 |   151 |    6 |   157 |  89.7143 |
| 681 | Jefferson     |   189 |   24 |   152 |   13 |   165 |  87.3016 |
| 682 | Jenkins       |    82 |   10 |    71 |    1 |    72 |  87.8049 |
| 683 | Johnson       |    74 |    5 |    69 |    0 |    69 |  93.2432 |
| 684 | Jones         |   311 |   18 |   280 |   13 |   293 |  94.2122 |
| 685 | Lamar         |   155 |   17 |   132 |    6 |   138 |  89.0323 |
| 686 | Lanier        |    86 |    5 |    80 |    1 |    81 |  94.186  |
| 687 | Laurens       |   387 |   18 |   345 |   24 |   369 |  95.3488 |
| 688 | Lee           |   413 |   17 |   366 |   30 |   396 |  95.8838 |
| 689 | Liberty       |   576 |   44 |   517 |   15 |   532 |  92.3611 |
| 690 | Lincoln       |    78 |    4 |    68 |    6 |    74 |  94.8718 |
| 691 | Long          |   159 |    9 |   138 |   12 |   150 |  94.3396 |
| 692 | Lowndes       |   665 |   38 |   585 |   42 |   627 |  94.2857 |
| 693 | Lumpkin       |   222 |   11 |   184 |   27 |   211 |  95.045  |
| 694 | Macon         |    89 |   13 |    76 |    0 |    76 |  85.3933 |
| 695 | Madison       |   297 |   13 |   247 |   37 |   284 |  95.6229 |
| 696 | Marion        |    86 |   10 |    74 |    2 |    76 |  88.3721 |
| 697 | McDuffie      |   225 |   15 |   201 |    9 |   210 |  93.3333 |
| 698 | McIntosh      |   108 |   11 |    95 |    2 |    97 |  89.8148 |
| 699 | Meriwether    |   145 |    9 |   132 |    4 |   136 |  93.7931 |
| 700 | Miller        |    66 |   13 |    49 |    4 |    53 |  80.303  |
| 701 | Mitchell      |   108 |    5 |   102 |    1 |   103 |  95.3704 |
| 702 | Monroe        |   250 |    7 |   221 |   22 |   243 |  97.2    |
| 703 | Montgomery    |    83 |   13 |    67 |    3 |    70 |  84.3373 |
| 704 | Morgan        |   240 |   12 |   195 |   33 |   228 |  95      |
| 705 | Murray        |   421 |   35 |   377 |    9 |   386 |  91.6865 |
| 706 | Muscogee      |  1960 |  142 |  1652 |  166 |  1818 |  92.7551 |
| 707 | Newton        |  1069 |   76 |   972 |   21 |   993 |  92.8906 |
| 708 | Oconee        |   545 |   13 |   397 |  135 |   532 |  97.6147 |
| 709 | Oglethorpe    |   162 |    6 |   143 |   13 |   156 |  96.2963 |
| 710 | Paulding      |  1781 |  147 |  1520 |  114 |  1634 |  91.7462 |
| 711 | Peach         |   196 |   18 |   176 |    2 |   178 |  90.8163 |
| 712 | Pickens       |   275 |   24 |   242 |    9 |   251 |  91.2727 |
| 713 | Pierce        |   231 |   10 |   197 |   24 |   221 |  95.671  |
| 714 | Pike          |   207 |   10 |   191 |    6 |   197 |  95.1691 |
| 715 | Polk          |   424 |   32 |   375 |   17 |   392 |  92.4528 |
| 716 | Pulaski       |    90 |    8 |    76 |    6 |    82 |  91.1111 |
| 717 | Putnam        |   104 |    6 |    93 |    5 |    98 |  94.2308 |
| 718 | Quitman       |    18 |    1 |    17 |    0 |    17 |  94.4444 |
| 719 | Rabun         |   167 |    2 |   140 |   25 |   165 |  98.8024 |
| 720 | Randolph      |    65 |    8 |    57 |    0 |    57 |  87.6923 |
| 721 | Richmond      |  1667 |  173 |  1452 |   42 |  1494 |  89.6221 |
| 722 | Rockdale      |   691 |   18 |   604 |   69 |   673 |  97.3951 |
| 723 | Schley        |    85 |    9 |    73 |    3 |    76 |  89.4118 |
| 724 | Screven       |   152 |    9 |   138 |    5 |   143 |  94.0789 |
| 725 | Seminole      |    92 |    8 |    78 |    6 |    84 |  91.3043 |
| 726 | Spalding      |   551 |   49 |   483 |   19 |   502 |  91.1071 |
| 727 | Stephens      |   246 |   11 |   223 |   12 |   235 |  95.5285 |
| 728 | Stewart       |    34 |    7 |    25 |    2 |    27 |  79.4118 |
| 729 | Sumter        |   250 |   45 |   201 |    4 |   205 |  82      |
| 730 | Talbot        |    36 |   10 |    26 |    0 |    26 |  72.2222 |
| 731 | Taliaferro    |    12 |    0 |    11 |    1 |    12 | 100      |
| 732 | Tattnall      |   214 |   15 |   179 |   20 |   199 |  92.9907 |
| 733 | Taylor        |    98 |   13 |    83 |    2 |    85 |  86.7347 |
| 734 | Telfair       |    79 |   10 |    64 |    5 |    69 |  87.3418 |
| 735 | Terrell       |    93 |   12 |    79 |    2 |    81 |  87.0968 |
| 736 | Thomas        |   284 |   27 |   239 |   18 |   257 |  90.493  |
| 737 | Tift          |   487 |   57 |   393 |   37 |   430 |  88.2957 |
| 738 | Toombs        |   182 |   18 |   157 |    7 |   164 |  90.1099 |
| 739 | Towns         |    86 |    4 |    79 |    3 |    82 |  95.3488 |
| 740 | Treutlen      |    67 |    9 |    55 |    3 |    58 |  86.5672 |
| 741 | Troup         |   707 |   33 |   650 |   24 |   674 |  95.3324 |
| 742 | Turner        |    78 |   11 |    65 |    2 |    67 |  85.8974 |
| 743 | Twiggs        |    65 |    5 |    58 |    2 |    60 |  92.3077 |
| 744 | Union         |   187 |    8 |   157 |   22 |   179 |  95.7219 |
| 745 | Upson         |   252 |   14 |   225 |   13 |   238 |  94.4444 |
| 746 | Walker        |   512 |   35 |   460 |   17 |   477 |  93.1641 |
| 747 | Walton        |   802 |   33 |   697 |   72 |   769 |  95.8853 |
| 748 | Ware          |   297 |   18 |   252 |   27 |   279 |  93.9394 |
| 749 | Warren        |    25 |    2 |    23 |    0 |    23 |  92      |
| 750 | Washington    |   208 |   16 |   188 |    4 |   192 |  92.3077 |
| 751 | Wayne         |   263 |   19 |   226 |   18 |   244 |  92.7757 |
| 752 | Webster       |    35 |    0 |    35 |    0 |    35 | 100      |
| 753 | Wheeler       |    70 |    9 |    56 |    5 |    61 |  87.1429 |
| 754 | White         |   259 |   20 |   215 |   24 |   239 |  92.278  |
| 755 | Whitfield     |   683 |   23 |   631 |   29 |   660 |  96.6325 |
| 756 | Wilcox        |    74 |    7 |    61 |    6 |    67 |  90.5405 |
| 757 | Wilkes        |    98 |    4 |    86 |    8 |    94 |  95.9184 |
| 758 | Wilkinson     |    94 |   15 |    77 |    2 |    79 |  84.0426 |
| 759 | Worth         |   193 |   17 |   168 |    8 |   176 |  91.1917 |
| 761 | Atlanta       |  1861 |  102 |  1638 |  121 |  1759 |  94.5191 |
| 763 | Bremen        |   145 |    3 |   118 |   24 |   142 |  97.931  |
| 764 | Buford        |   230 |    1 |   189 |   40 |   229 |  99.5652 |
| 765 | Calhoun       |   234 |    6 |   185 |   43 |   228 |  97.4359 |
| 766 | Carrollton    |   319 |   30 |   261 |   28 |   289 |  90.5956 |
| 767 | Cartersville  |   249 |    4 |   226 |   19 |   245 |  98.3936 |
| 769 | Chickamauga   |   114 |    4 |   101 |    9 |   110 |  96.4912 |
| 771 | Commerce      |    93 |    3 |    84 |    6 |    90 |  96.7742 |
| 772 | Dalton        |   408 |   21 |   350 |   37 |   387 |  94.8529 |
| 773 | Decatur       |   234 |   11 |   172 |   51 |   223 |  95.2991 |
| 774 | Dublin        |   119 |    3 |   110 |    6 |   116 |  97.479  |
| 776 | Gainesville   |   409 |   40 |   348 |   21 |   369 |  90.22   |
| 779 | Jefferson     |   208 |    3 |   173 |   32 |   205 |  98.5577 |
| 781 | Marietta      |   369 |    6 |   303 |   60 |   363 |  98.374  |
| 784 | Pelham        |    84 |   14 |    67 |    3 |    70 |  83.3333 |
| 785 | Rome          |   334 |   25 |   272 |   37 |   309 |  92.515  |
| 786 | Social Circle |   133 |   11 |   111 |   11 |   122 |  91.7293 |
| 789 | Thomasville   |   153 |   14 |   120 |   19 |   139 |  90.8497 |
| 791 | Trion         |    98 |    3 |    79 |   16 |    95 |  96.9388 |
| 792 | Valdosta      |   384 |   26 |   325 |   33 |   358 |  93.2292 |
| 793 | Vidalia       |   161 |   17 |   118 |   26 |   144 |  89.441  |
| ALL | Georgia       | 98398 | 5748 | 83925 | 8725 | 92650 |  94.1584 |



label: G=F+E
labeled_formulas: G=F+E
output: {"Arithmetic-Relationship": ["G=F+E"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_312331___xlsx_50334be47a3172c139be0a60ddf2ada8589f58cb.xlsx___line_317