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 |
|:------------------|:----|-------:|--------:|------:|--------:|-------:|--------:|-------:|---------:|
| Pittsburgh AGO    | A   |   9098 |  896142 |  4596 |  247167 |  69688 |  996145 |  83382 |  2139454 |
| Allegheny         | A   |      0 |       0 |     0 |       0 |      0 |       0 |      0 |        0 |
| Armstrong         | A   |   1149 |  257086 |  1149 |  255131 |  20682 |  347468 |  22980 |   859685 |
| Beaver            | A   |  13748 |  894954 |  1239 |  482835 |  49840 | 1339724 |  64827 |  2717513 |
| Bedford           | A   |      0 |  182066 |     0 |   88063 |      0 |  250475 |      0 |   520604 |
| Blair             | A   |      0 |  143282 |  1622 |  148505 |   1622 |  300414 |   3244 |   592201 |
| Butler            | A   |      0 |  629530 |  2937 |  358118 |  33240 |  599861 |  36177 |  1587509 |
| Cambria           | A   |   7466 |  483801 | 18352 | 1096892 | 104155 | 1260292 | 129973 |  2840985 |
| Clarion           | A   |      0 |   66156 |     0 |       0 |      0 |   51044 |      0 |   117200 |
| Clearfield        | A   |      0 |   23912 |     0 |       0 |      0 |   27863 |      0 |    51775 |
| Crawford          | A   |   5489 |  693736 |  7152 |  218867 |  34376 |  802849 |  47017 |  1715452 |
| Elk               | A   |   6830 |  310035 |  3271 |  116956 |  17104 |  416607 |  27205 |   843598 |
| Erie              | A   |   1653 |  103573 |  5057 |  278070 |  33217 |  293159 |  39927 |   674802 |
| Fayette           | A   |   2641 |  434198 |  4596 | 1022527 |  36790 |  975237 |  44027 |  2431962 |
| Forest            | A   |      0 |     532 |     0 |    4596 |      0 |    4245 |      0 |     9373 |
| Fulton            | A   |   1254 |   36341 |     0 |       0 |   9934 |   34771 |  11188 |    71112 |
| Greene            | A   |      0 |   67718 |     0 |   24342 |      0 |   37058 |      0 |   129118 |
| Huntingdon        | A   |      0 |   43942 |     0 |    4376 |      0 |   54763 |      0 |   103081 |
| Indiana           | A   |   4656 |  716785 |  3222 |  376878 |  54411 |  883944 |  62289 |  1977607 |
| Jefferson         | A   |      0 |   31880 |     0 |       0 |      0 |    1303 |      0 |    33183 |
| Lawrence          | A   |      0 |  327845 |  7140 |  247802 |  27801 |  372729 |  34941 |   948376 |
| McKean            | A   |   4338 |  250615 |     0 |   88039 |  31591 |  306930 |  35929 |   645584 |
| Mercer            | A   |   3069 |  411101 |    90 |  324331 |   1764 |  546569 |   4923 |  1282001 |
| Somerset          | A   |   3083 |  299948 |     0 |   56937 |  11611 |  277520 |  14694 |   634405 |
| Venango           | A   |   1852 |  194861 |     0 |   14487 |  36128 |  287835 |  37980 |   497183 |
| Warren            | A   |  18102 |  785314 |   408 |  115611 |  56091 |  701517 |  74601 |  1602442 |
| Washington        | A   |   2848 |  405367 |  4418 |  398239 |  53815 |  717798 |  61081 |  1521404 |
| Westmoreland      | A   |   9922 |  906551 |  6253 |  969015 |  67172 | 1880595 |  83347 |  3756161 |
| PSSH              | A   |      0 |       0 |     0 |   36299 |      0 |   12836 |      0 |    49135 |
| HVH               | A   |      0 |    2367 |     0 |  220099 |      0 |  176269 |      0 |   398735 |
| SWVC              | A   |      0 |   54903 |     0 |   84272 |      0 |  189907 |      0 |   329082 |
| Philadelphia AGO  | B   |   6233 |  618713 |  1149 |    9192 |   7979 |  463524 |  15361 |  1091429 |
| Adams             | B   |   8766 |  492501 |     0 |   22936 |  48044 |  375254 |  56810 |   890691 |
| Berks             | B   |  55422 | 3090019 |     0 |   80491 | 102616 | 1995194 | 158038 |  5165704 |
| Bradford          | B   |  21546 | 2332255 |     0 |   60883 |  97747 | 1706139 | 119293 |  4099277 |
| Bucks             | B   |  15578 | 1375534 |  2937 |   88454 |  66388 | 1553375 |  84903 |  3017363 |
| Cameron           | B   |      0 |   62144 |     0 |    6608 |      0 |  112682 |      0 |   181434 |
| Carbon            | B   |  35452 | 1663347 |  1788 |  269529 |  20954 | 1249932 |  58194 |  3182808 |
| Centre            | B   |  13740 | 1246092 |  1344 |   75620 |  68982 |  712165 |  84066 |  2033877 |
| Chester           | B   |   2336 |  152054 |     0 |   12639 |   5710 |  242220 |   8046 |   406913 |
| Clinton           | B   |  23403 | 2720862 |     0 |   60685 |  48478 | 2045165 |  71881 |  4826712 |
| Columbia          | B   |   9856 |  943531 |     0 |  166424 |  33194 |  839208 |  43050 |  1949163 |
| Cumberland        | B   |  33856 | 4510829 |  2120 |  378354 |  93678 | 2675824 | 129654 |  7565007 |
| Dauphin           | B   |   7057 |  807200 |   870 |  217062 |  34363 |  674148 |  42290 |  1698410 |
| Delaware          | B   |   6337 |  168427 |     0 |   29483 |  31685 |  249494 |  38022 |   447404 |
| Ft Indiantown Gap | B   |  26884 | 1379346 |     0 |       0 |  35089 |  821175 |  61973 |  2200521 |
| Franklin          | B   |  42184 | 4178925 |     0 |  127484 |  68052 | 2583786 | 110236 |  6890195 |
| Juniata           | B   |   7220 |  144898 |     0 |   17963 |  28912 |  200492 |  36132 |   363353 |
| Lackawanna        | B   |  37587 | 1943429 |  3269 |  204050 | 183717 | 1620722 | 224573 |  3768201 |
| Lancaster         | B   |  22280 | 1659392 |  4657 |  328886 |  68922 | 1527281 |  95859 |  3515559 |
| Lebanon           | B   |      0 |   91971 |     0 |       0 |      0 |    4154 |      0 |    96125 |
| Lehigh            | B   |  16214 | 1536274 |     0 |  228379 |  65130 |  945867 |  81344 |  2710520 |
| Luzerne           | B   |  30304 | 1152662 |  3657 |  280813 |  97970 | 1101860 | 131931 |  2535335 |
| Lycoming          | B   |  13296 | 5821370 |  1428 |  240527 |  87625 | 4291573 | 102349 | 10353470 |
| Mifflin           | B   |  15172 |  832349 |     0 |     363 |  21708 |  456848 |  36880 |  1289560 |
| Monroe            | B   | 108630 | 2110161 |  1927 |  150013 | 367882 | 1572937 | 478439 |  3833111 |
| Montgomery        | B   |   6149 |  943302 |  2459 |  188357 |  16516 |  902758 |  25124 |  2034417 |
| Montour           | B   |  12554 |  589610 |  1254 |   34285 |  66654 |  530431 |  80462 |  1154326 |
| Northampton       | B   |  18304 | 1514602 |     0 |  104241 |  83908 | 1548308 | 102212 |  3167151 |
| Northumberland    | B   |  16505 | 1171980 |     0 |   67659 |  55052 | 1225283 |  71557 |  2464922 |
| Perry             | B   |  18542 |  863161 |  1655 |   19538 |  27424 |  465130 |  47621 |  1347829 |
| Philadelphia      | B   |   6187 |  286510 |  2120 |    6343 |  32388 |  279199 |  40695 |   572052 |
| Pike              | B   |   8785 |  744431 |     0 |    5364 |  29531 |  776500 |  38316 |  1526295 |
| Potter            | B   |  12557 |   98523 |     0 |       0 |  23646 |   60514 |  36203 |   159037 |
| Schuylkill        | B   |      0 |  270216 |     0 |   31839 |      0 |  452890 |      0 |   754945 |
| Snyder            | B   |  13750 |  137927 |  1149 |    4485 |  32289 |  111121 |  47188 |   253533 |
| Sullivan          | B   |      0 |   69796 |     0 |       0 |      0 |   68914 |      0 |   138710 |
| Susquehanna       | B   |   3754 |  286858 |     0 |   65492 |   5295 |  408836 |   9049 |   761186 |
| Tioga             | B   |  44762 | 2606351 |     0 |   30672 | 114922 | 1376664 | 159684 |  4013687 |
| Union             | B   |      0 |  266578 |     0 |   16044 |      0 |   80642 |      0 |   363264 |
| Wayne             | B   |      0 |       0 |     0 |       0 |      0 |       0 |      0 |        0 |
| Wyoming           | B   |      0 |    1862 |     0 |   15201 |      0 |    5350 |      0 |    22413 |
| York              | B   |  33679 | 3766968 |  3576 |  178368 | 121922 | 2645137 | 159177 |  6590473 |
| DVH               | B   |      0 |       0 |     0 |   56649 |      0 |   52020 |      0 |   108669 |
| GMVC              | B   |    836 |     836 |     0 |     614 |   4180 |    4180 |   5016 |     5630 |
| SEVC              | B   |      0 |    2394 |     0 |   60925 |      0 |   69811 |      0 |   133130 |



label: I=C+E+G
labeled_formulas: I=C+E+G
output: {"Arithmetic-Relationship": ["I=C+E+G"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_597740___xlsx_cb60ea3c2d91e1110a716c7f18619e9fc1a130f4.xlsx___line_728