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:
|                B |                C |                D |                E |                F |                G |      H |
|-----------------:|-----------------:|-----------------:|-----------------:|-----------------:|-----------------:|-------:|
| 406902           | 503934           |  86509           |      0           |  86509           | 202258           |   8595 |
|  12877           |  21610           |   2035           |      0           |   2035           |   1672           |   1426 |
| 109396           | 109396           |   8300           |      0           |   8300           |  22184           |   1831 |
|  18188           |  24004           |   2101           |      0           |   2101           |   3599           |    362 |
| 375152           | 407060           |  24371           |      0           |  24371           |  45744           |   3159 |
|      1.51711e+06 |      1.73266e+06 | 269331           |      0           | 269331           | 462948           |  47840 |
| 405316           | 360795           |  33124           |  19267           |  52391           |  66610           |   8823 |
|  54625           |  51253           |   5489           |      0           |   5489           |   5133           |   5134 |
|  53019           |  51584           |  11120           |      0           |  11120           |  28114           |   3873 |
|  24065           | 166611           |   6784           |      0           |   6784           |  11734           |   1420 |
| 291316           | 281127           |  22895           |      0           |  22895           |  56798           |   5162 |
| 169815           | 168664           |  18363           |      0           |  18363           |  18375           |   5678 |
|      1.14065e+06 |      1.36272e+06 | 445836           |      0           | 445836           | 403824           |  25860 |
| 106040           |  93015           |  18032           |      0           |  18032           |  43831           |   1396 |
| 551450           | 605077           |  65411           |      0           |  65411           | 118391           |   6922 |
| 177462           | 180354           |  27523           |   1620           |  29143           |  29006           |   3564 |
|  96504           | 151714           |   3500           |      0           |   3500           |   5165           |    443 |
|      1.21929e+06 |      1.37238e+06 | 204733           |  45260           | 249993           | 212220           |  10778 |
| 161639           | 192567           |  34842           |      0           |  34842           |  42199           |   3636 |
|  47272           |  68021           |   9521           |      0           |   9521           |   5938           |   1378 |
|      1.06377e+06 |      1.02318e+06 | 152600           |  69892           | 222492           | 222621           |  26220 |
|  95183           |  92983           |  11420           |      0           |  11420           |  25921           |   3582 |
| 161728           | 194502           |  38295           |      0           |  38295           |  55218           |   3634 |
|  66284           | 153848           |  26000           |      0           |  26000           |  58000           |   4000 |
| 646922           | 715939           |  40500           |      0           |  40500           |  76207           |  12047 |
| 176056           | 163904           |  37260           |   4879           |  42139           |  52756           |   4393 |
|      2.3834e+06  |      2.1704e+06  | 298326           | 221582           | 519908           | 591435           |  74295 |
| 205011           | 383947           |  45730           |  12908           |  58638           |  47363           |   6161 |
| 201865           | 289361           |  48000           |   4380           |  52380           |  60925           |   4356 |
|  50234           |  63500           |   7606           |      0           |   7606           |  10875           |   2379 |
| 843159           | 990220           |  90143           |  57712           | 147855           | 209735           |  38752 |
|      1.13095e+06 |      1.52184e+06 | 221665           |      0           | 221665           | 300815           |  14002 |
|   6305           |   6494           |    642           |      0           |    642           |   1144           |      0 |
|  32057           |  47492           |   7395           |      0           |   7395           |   3230           |   1437 |
|      4.30697e+07 |      4.22936e+07 |      4.05221e+06 |      1.35953e+06 |      5.41174e+06 |      8.79066e+06 | 505064 |
|  91731           | 112186           |  13926           |    500           |  14426           |  14878           |   1790 |
| 108782           | 109493           |  16205           |      0           |  16205           |  19075           |   2704 |
| 183972           | 205106           |  38164           |      0           |  38164           |  80961           |   3646 |
|      1.0579e+07  |      1.00959e+07 | 777282           | 763750           |      1.54103e+06 |      2.23722e+06 | 113301 |
| 217807           | 257772           |  21000           |      0           |  21000           |  50560           |   4295 |
| 195308           | 182686           |  64864           |      0           |  64864           |  43768           |   3698 |
|  62145           |  64137           |   7658           |      0           |   7658           |   8482           |   4237 |
| 236384           | 247259           |  45136           |      0           |  45136           |  66207           |   5534 |
| 166219           | 154722           |  26208           |      0           |  26208           |  33736           |   2454 |
|  32025           |  46645           |   5640           |   5640           |  11280           |  13852           |   1801 |
| 717864           | 888787           |  73100           |      0           |  73100           | 286400           |  26212 |
| 281309           | 328446           |  97157           |   1381           |  98538           |  86690           |  13340 |
| 510380           | 950303           | 223961           |      0           | 223961           |  81971           |  20334 |
| 258783           | 263684           |  64537           |      0           |  64537           |  94576           |  11087 |
| 192305           | 265623           |  49835           |      0           |  49835           |  70497           |   3699 |
| 203488           | 258099           |  45804           |      0           |  45804           |  59130           |   4270 |
|  47094           |  58490           |   7696           |      0           |   7696           |   5369           |   1246 |
| 679450           | 799054           |  66041           |      0           |  66041           |  97135           |  11252 |
| 740254           | 752177           |  18800           |      0           |  18800           |  82939           |  12924 |
| 648192           | 645276           | 162682           | 151494           | 314176           | 194256           |  12075 |
| 158485           | 182647           |  52000           |      0           |  52000           |  27105           |   8733 |
| 109925           | 123888           |  15730           |      0           |  15730           |  29186           |   3013 |
|  79645           | 108328           |  12300           |    623           |  12923           |  35050           |   1688 |
|      2.8482e+06  |      3.28472e+06 | 369243           | 470219           | 839462           | 751292           |  68043 |
|  34305           |  23620           |   4195           |      0           |   4195           |   3251           |    751 |
|      1.85504e+06 |      2.16394e+06 | 304900           |      0           | 304900           | 392711           |  31990 |
|      1.89218e+07 |      1.99319e+07 |      2.23177e+06 |      1.98947e+06 |      4.22124e+06 |      2.17214e+06 | 238087 |
| 189730           | 197312           |  43764           |    636           |  44400           |  39826           |  11978 |
|      1.64502e+06 |      1.92357e+06 | 203972           |  75208           | 279180           | 497016           |  27024 |
|  37444           |  22527           |   7100           |      0           |   7100           |   4136           |   2208 |
| 695013           | 797731           | 119469           |      0           | 119469           | 216861           |  27048 |
|  40739           |  65798           |   8269           |      0           |   8269           |  10854           |   1625 |
|   9507           |  11440           |    382           |      0           |    382           |   1758           |    407 |
|      1.22302e+06 |      1.3368e+06  | 225000           |      0           | 225000           | 170488           |  21947 |
| 623048           | 631917           |  60000           |      0           |  60000           | 123554           |   5320 |
|  24018           |  25662           |   2707           |      0           |   2707           |  10411           |    327 |
|  65330           |  66881           |  15534           |      0           |  15534           |  12096           |   5796 |
| 183866           | 260499           |  45000           |      0           |  45000           | 134913           |   4979 |
| 484751           | 551439           |  40241           |      0           |  40241           |  92004           |   6649 |
|  67875           |  56970           |  10578           |      0           |  10578           |  14592           |   1697 |
| 183327           | 209369           |  16094           |      0           |  16094           |  14500           |   2700 |
| 291912           | 289239           |  47065           |      0           |  47065           |  28426           |   4011 |
| 280903           | 278248           |  34883           |   4888           |  39771           |  75200           |   6500 |
| 287908           | 371071           |  54038           |      0           |  54038           |  82266           |  15159 |
| 106989           | 130734           |  18151           |      0           |  18151           |  24862           |   2267 |
| 733613           | 916356           | 117389           |      0           | 117389           | 129034           |  20552 |
| 378359           | 353740           |  62050           |      0           |  62050           |  23748           |  10301 |
|      2.66138e+06 |      3.15457e+06 | 323294           |      0           | 323294           | 624907           |  60034 |
| 186520           | 176400           |  28206           |      0           |  28206           |  36667           |   5415 |
|  62347           |  61688           |   1944           |      0           |   1944           |   5034           |   1080 |
| 179024           | 184254           |  23503           |      0           |  23503           |  38108           |   2692 |
| 299119           | 369410           |  83000           |      0           |  83000           |  59246           |   7614 |
|  39755           |  66809           |   8500           |      0           |   8500           |  11341           |    990 |
| 148862           | 175453           |  74963           |      0           |  74963           |  58753           |   6691 |
| 699776           | 763910           | 144278           |      0           | 144278           | 252371           |  16448 |
| 282608           | 300790           |  48892           |   7852           |  56744           |  50577           |   8167 |
| 423619           | 528756           |  31104           |      0           |  31104           |  41269           |   4933 |
|   8102           |  10724           |   1258           |      0           |   1258           |   3468           |    428 |
| 929819           |      1.02784e+06 | 193187           |  86729           | 279916           | 168972           |  15585 |
| 277192           | 326479           |  44659           |    366           |  45025           |  53196           |   3622 |
| 218097           | 229954           |  33702           |      0           |  33702           |  35829           |   5924 |
|  17500           |  33971           |   2811           |      0           |   2811           |   1872           |   1607 |
| 827875           | 979050           | 150000           |      0           | 150000           | 101150           |  21000 |
| 142693           | 152438           |   9134           |      0           |   9134           |  35548           |  15143 |
| 104518           | 104518           |  13878           |      0           |  13878           |  27469           |   3971 |
| 457077           | 359482           | 143502           |      0           | 143502           | 168748           |  21645 |
| 956093           |      1.21228e+06 | 101048           |  24079           | 125127           | 172341           |  10129 |
| 550328           | 616678           |  73338           |  10010           |  83348           |  73700           |  17600 |
| 124848           | 143665           |  19232           |      0           |  19232           |  37231           |   2902 |
|  18404           |  17794           |   2500           |      0           |   2500           |  12700           |   1600 |
| 154295           | 156511           |   7145           |      0           |   7145           |   6626           |   4114 |
| 356249           | 364465           |  53772           |      0           |  53772           |  72632           |   7466 |
| 188287           | 199533           |  17784           |      0           |  17784           |  26156           |   4259 |
|  22150           |  19029           |   4000           |      0           |   4000           |  11700           |   1055 |
| 664986           | 680902           | 159226           |  75982           | 235208           | 166297           |  10667 |
|      1.10038e+06 |      1.24409e+06 | 309968           | 105678           | 415646           | 311828           |  30075 |
|  73125           |  74135           |  13275           |      0           |  13275           |  17831           |   3146 |
| 279828           | 308230           |  24820           |      0           |  24820           |  44891           |   3283 |
| 418114           | 505730           |  63271           |      0           |  63271           | 314811           |   8615 |
|      2.31642e+06 |      2.76122e+06 | 175933           |      0           | 175933           | 277554           |  15001 |
|      1.67468e+07 |      1.79659e+07 |      1.90723e+06 |      1.37127e+06 |      3.2785e+06  |      7.25604e+06 | 134769 |
| 231436           | 236263           |  66729           |      0           |  66729           |  73234           |   6734 |
|      4.39329e+07 |      5.183e+07   |      5.87718e+06 |      4.15582e+06 |      1.0033e+07  |      1.49452e+07 | 602770 |
|      2.24636e+07 |      2.50403e+07 |      2.11422e+06 |      0           |      2.11422e+06 |      1.95791e+06 |  98271 |
| 270954           | 282660           |  31408           |      0           |  31408           |  30838           |   3478 |
|  43992           |  50360           |  13491           |      0           |  13491           |   6967           |   1285 |
|      2.083e+06   |      2.85459e+06 | 262261           | 323501           | 585762           | 396602           |  48911 |
|  80701           |  91808           |  10642           |      0           |  10642           |   9998           |    767 |
| 137293           | 147632           |  17853           |      0           |  17853           |  44952           |   2949 |
| 595674           | 711445           |  85360           |      0           |  85360           |  89812           |  14619 |
|  52918           |  48632           |  16675           |      0           |  16675           |  18041           |   4117 |
| 389459           | 269277           |  33672           |      0           |  33672           |  42202           |  10000 |
|  26896           |  37667           |   3000           |      0           |   3000           |   6829           |    877 |
|      1.26192e+07 |      1.32491e+07 |      2.0086e+06  |      3.96721e+06 |      5.9758e+06  |      3.60347e+06 | 211880 |
|      2.60176e+06 |      3.24009e+06 | 224588           |      0           | 224588           | 368889           |  49336 |
|  23621           |  26040           |   2000           |      0           |   2000           |   2667           |   2644 |
| 309608           | 490239           |  22247           |      0           |  22247           |  26326           |   6248 |
|  78619           | 101545           |  34263           |      0           |  34263           |  38870           |   3598 |
| 121861           | 160568           |  21101           |      0           |  21101           |  31197           |   6120 |
|  26488           |  27493           |   5600           |      0           |   5600           |   5988           |    386 |
| 250005           | 317279           |  54080           | 231176           | 285256           |  82184           |  12146 |
|      2.73027e+06 |      3.45259e+06 | 168000           |      0           | 168000           | 339053           |   9944 |
|      1.96972e+06 |      1.88234e+06 | 249439           |      0           | 249439           | 422974           |  40857 |
|  89123           |  87054           |   9531           |      0           |   9531           |  11789           |   1419 |
| 340793           | 439831           |  36000           |      0           |  36000           |  44806           |  21102 |
| 494673           | 427063           | 119051           |      0           | 119051           | 123418           |   4463 |
| 303390           | 332016           |  37000           |  45215           |  82215           |  88770           |   5309 |
| 475416           | 491757           | 114146           |      0           | 114146           | 150101           |  20213 |
|  29222           |  29328           |   1650           |      0           |   1650           |   3910           |   1035 |
| 592379           | 456178           | 130266           |      0           | 130266           | 146980           |  14425 |
|  55546           |  56333           |   8550           |      0           |   8550           |  25996           |   2500 |
|  19192           |  19457           |   1871           |      0           |   1871           |   1505           |    131 |
|  21739           |  34570           |   1306           |      0           |   1306           |   1778           |    195 |
| 307282           | 309074           |  47500           |      0           |  47500           |  68127           |  16404 |



label: F=D+E
labeled_formulas: F=D+E
output: {"Arithmetic-Relationship": ["F=D+E"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_450951___xlsx_fbe41b7b831f04421ec74fee97623c7b59728351.xlsx___line_1056