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      | M        |
|:---------------|--------:|-------:|---------:|------:|------:|-----:|----:|----:|------:|--------:|:-------|:---------|
| Adams          |  101457 |   8253 | 0.999395 |  1902 |  1630 |  221 |  46 |   5 |  6356 |  268541 | 27938  | 929689   |
| Allegheny      | 1232953 | 107859 | 0.998833 | 33583 | 27702 | 4881 | 874 | 126 | 74402 | 3471659 | 696023 | 34733320 |
| Armstrong      |   68110 |   4828 | 0.999793 |  1339 |  1177 |  146 |  15 |   1 |  3490 |  145391 | 14471  | 481380   |
| Beaver         |  170060 |  11919 | 0.999497 |  3430 |  2957 |  397 |  70 |   6 |  8495 |  328168 | 49161  | 1828830  |
| Bedford        |   49133 |   4286 | 0.999534 |  1043 |   909 |  117 |  15 |   2 |  3245 |  143345 | 13299  | 422255   |
| Berks          |  413652 |  31995 | 0.999313 |  8246 |  6881 | 1115 | 228 |  22 | 23771 | 1094034 | 148933 | 6330830  |
| Blair          |  126379 |   9263 | 0.999568 |  3212 |  2709 |  417 |  82 |   4 |  6055 |  284408 | 52021  | 1811723  |
| Bradford       |   62356 |   4970 | 0.999196 |  1394 |  1233 |  140 |  17 |   4 |  3580 |  146554 | 19556  | 764360   |
| Bucks          |  626456 |  68765 | 0.999666 | 18930 | 16410 | 2148 | 349 |  23 | 49858 | 2794921 | 245793 | 10719264 |
| Butler         |  185369 |  16229 | 0.999261 |  4766 |  3998 |  639 | 117 |  12 | 11475 |  554838 | 79977  | 3463915  |
| Cambria        |  138900 |   9523 | 0.99958  |  3337 |  2864 |  408 |  61 |   4 |  6190 |  237131 | 48133  | 1607354  |
| Cameron        |    4894 |    355 | 1        |   113 |    96 |   15 |   2 |   0 |   242 |    7632 | 1579   | 52623    |
| Carbon         |   64690 |   4412 | 0.999547 |  1134 |  1022 |   94 |  16 |   2 |  3280 |  133239 | 13291  | 372813   |
| Centre         |  157847 |  12538 | 0.999841 |  3252 |  2704 |  491 |  55 |   2 |  9288 |  444869 | 44783  | 1555623  |
| Chester        |  509500 |  53869 | 0.999128 | 13950 | 11851 | 1757 | 295 |  47 | 39966 | 2349802 | 239228 | 14905982 |
| Clarion        |   39092 |   3380 | 1        |   937 |   821 |  102 |  14 |   0 |  2443 |  111653 | 10918  | 320656   |
| Clearfield     |   81589 |   6182 | 0.999515 |  2004 |  1722 |  250 |  29 |   3 |  4181 |  169866 | 26252  | 872511   |
| Clinton        |   39834 |   2617 | 0.999618 |   759 |   647 |   93 |  18 |   1 |  1859 |   72585 | 10950  | 368101   |
| Columbia       |   67139 |   4549 | 0.998902 |  1373 |  1167 |  162 |  39 |   5 |  3181 |  133867 | 22851  | 792800   |
| Crawford       |   87411 |   7409 | 0.99973  |  2031 |  1748 |  248 |  33 |   2 |  5380 |  223296 | 27581  | 872794   |
| Cumberland     |  241268 |  20456 | 0.998828 |  5733 |  4697 |  861 | 151 |  24 | 14747 |  713608 | 114225 | 4768149  |
| Dauphin        |  271017 |  21901 | 0.998723 |  6728 |  5515 |  996 | 189 |  28 | 15201 |  668961 | 142209 | 6450162  |
| Delaware       |  561844 |  51427 | 0.999242 | 12628 | 10877 | 1461 | 251 |  39 | 38838 | 1988648 | 210571 | 11493212 |
| Elk            |   31455 |   2486 | 0.999598 |   881 |   742 |  114 |  24 |   1 |  1606 |   63198 | 13828  | 501680   |
| Erie           |  279760 |  20019 | 0.999451 |  6229 |  5117 |  936 | 165 |  11 | 13801 |  567293 | 113617 | 4095591  |
| Fayette        |  134799 |   8820 | 0.999433 |  2679 |  2328 |  304 |  42 |   5 |  6146 |  248152 | 35252  | 1118157  |
| Forest         |    7602 |    411 | 1        |   101 |    94 |    5 |   2 |   0 |   310 |   11416 | 1068   | 33347    |
| Franklin       |  152191 |  11758 | 0.999235 |  3022 |  2564 |  385 |  64 |   9 |  8745 |  361978 | 47802  | 1708891  |
| Fulton         |   14694 |   1223 | 0.999183 |   274 |   248 |   20 |   5 |   1 |   950 |   44037 | i      | D        |
| Greene         |   37882 |   2310 | 0.998271 |   756 |   626 |  107 |  19 |   4 |  1558 |   63054 | 14579  | 719090   |
| Huntingdon     |   45871 |   3311 | 0.999698 |   821 |   735 |   73 |  12 |   1 |  2491 |  103099 | 9809   | 293240   |
| Indiana        |   88246 |   6870 | 0.999854 |  1902 |  1632 |  227 |  42 |   1 |  4969 |  222978 | 25453  | 989309   |
| Jefferson      |   44977 |   4120 | 1        |  1159 |  1017 |  121 |  21 |   0 |  2961 |  127214 | 13465  | 448075   |
| Juniata        |   24790 |   2228 | 0.999551 |   460 |   407 |   47 |   5 |   1 |  1769 |   86999 | 5385   | 153982   |
| Lackawanna     |  213834 |  17012 | 0.999119 |  5402 |  4554 |  683 | 150 |  15 | 11625 |  576849 | 96226  | 3214779  |
| Lancaster      |  530122 |  52086 | 0.999328 | 12266 | 10262 | 1663 | 306 |  35 | 39855 | 2035456 | 213446 | 8334452  |
| Lawrence       |   89306 |   6799 | 0.999706 |  1975 |  1719 |  217 |  37 |   2 |  4826 |  204911 | 26783  | 899815   |
| Lebanon        |  135707 |  10592 | 0.999057 |  2634 |  2239 |  323 |  62 |  10 |  7968 |  360912 | 43681  | 1520099  |
| Lehigh         |  355768 |  29533 | 0.998985 |  8437 |  7020 | 1163 | 224 |  30 | 21126 |  899722 | 165363 | 7868210  |
| Luzerne        |  319862 |  23588 | 0.998814 |  7175 |  6075 |  875 | 197 |  28 | 16441 |  798224 | 129227 | 4696258  |
| Lycoming       |  116732 |   9051 | 0.999669 |  2850 |  2385 |  384 |  78 |   3 |  6204 |  268633 | 46696  | 1683525  |
| McKean         |   42788 |   3190 | 0.999373 |  1062 |   942 |   92 |  26 |   2 |  2130 |   84932 | 14014  | 514601   |
| Mercer         |  115313 |   9138 | 0.999344 |  2806 |  2372 |  364 |  64 |   6 |  6338 |  271416 | 45046  | 1472459  |
| Mifflin        |   46701 |   3555 | 0.999438 |   948 |   820 |  108 |  18 |   2 |  2609 |  112255 | 13983  | 477151   |
| Monroe         |  167130 |  13164 | 0.999317 |  3360 |  2981 |  324 |  46 |   9 |  9813 |  444597 | 44388  | 1545699  |
| Montgomery     |  813832 |  92118 | 0.99897  | 25988 | 21788 | 3417 | 688 |  95 | 66225 | 4058192 | 480721 | 27527260 |
| Montour        |   18535 |   1501 | 0.997342 |   458 |   372 |   61 |  21 |   4 |  1047 |   41634 | 14458  | 930050   |
| Northampton    |  299747 |  23350 | 0.999358 |  6208 |  5331 |  716 | 146 |  15 | 17157 |  813263 | 96900  | 3906925  |
| Northumberland |   94138 |   6116 | 0.99951  |  1657 |  1442 |  178 |  34 |   3 |  4462 |  207783 | 23134  | 796670   |
| Perry          |   45621 |   3598 | 0.999722 |   777 |   727 |   43 |   6 |   1 |  2822 |  115764 | 6249   | 159873   |
| Philadelphia   | 1556052 | 107492 | 0.998913 | 27239 | 22999 | 3428 | 695 | 117 | 80370 | 2946079 | 582474 | 31026403 |
| Pike           |   56614 |   4623 | 0.999784 |   888 |   828 |   49 |  10 |   1 |  3736 |  165501 | 7756   | 196692   |
| Potter         |   17491 |   1611 | 0.99938  |   349 |   314 |   27 |   7 |   1 |  1263 |   50598 | 4212   | 154621   |
| Schuylkill     |  146798 |   9443 | 0.999365 |  2804 |  2428 |  305 |  65 |   6 |  6645 |  311888 | 40381  | 1379300  |
| Snyder         |   40093 |   3746 | 0.999466 |   861 |   723 |  118 |  18 |   2 |  2887 |  133511 | 14441  | 384923   |
| Somerset       |   76722 |   6253 | 0.99984  |  1702 |  1523 |  148 |  30 |   1 |  4552 |  182600 | 18776  | 644743   |
| Sullivan       |    6352 |    644 | 1        |   160 |   149 |    9 |   2 |   0 |   484 |   21452 | 1233   | 29625    |
| Susquehanna    |   42334 |   4067 | 1        |   887 |   815 |   67 |   5 |   0 |  3180 |  159860 | 7097   | 219283   |
| Tioga          |   42458 |   3423 | 0.999416 |   890 |   780 |   87 |  21 |   2 |  2535 |  107534 | 11332  | 374747   |
| Union          |   44719 |   3535 | 0.999435 |   879 |   757 |  103 |  17 |   2 |  2658 |  131966 | 14919  | 498050   |
| Venango        |   53908 |   4108 | 0.999513 |  1205 |  1038 |  146 |  19 |   2 |  2905 |  108022 | 16494  | 540581   |
| Warren         |   40944 |   3123 | 0.99904  |   952 |   827 |  104 |  18 |   3 |  2174 |   92700 | 13988  | 498244   |
| Washington     |  208194 |  17128 | 0.999358 |  5037 |  4256 |  654 | 116 |  11 | 12102 |  631667 | 82272  | 4120663  |
| Wayne          |   51649 |   5150 | 0.999806 |  1311 |  1209 |   86 |  15 |   1 |  3840 |  179959 | 12236  | 380479   |
| Westmoreland   |  361080 |  29557 | 0.999391 |  8669 |  7470 | 1025 | 156 |  18 | 20906 |  916447 | 123087 | 4657193  |
| Wyoming        |   28142 |   2463 | 0.999189 |   646 |   574 |   60 |  10 |   2 |  1819 |   78674 | 11026  | 676092   |
| York           |  439393 |  33546 | 0.999196 |  8578 |  7080 | 1221 | 250 |  27 | 24995 | 1139831 | 159069 | 6263132  |



label: D=C/(E+J)
labeled_formulas: D=C/(E+J)
output: {"Arithmetic-Relationship": ["D=C/(E+J)"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_266556___xlsx_c86779bf830262a0497face4709cbeb3f05b813e.xlsx___line_598