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 |            N |
|:---------------------------------------|-----:|-----------------:|-----------------:|-----------------:|-----------------:|------------------:|----------:|----------:|----------------:|----------:|----------:|----------:|-------------:|
| Advertising                            |  314 | 177751           | 111848           | 137032           | 158679           |  -65902.7         |  25184.5  |  21646.9  |  -19071.3       | -0.370759 | 0.225168  | 0.157969  | -0.107292    |
| Aerospace/Defense                      |  234 |      1.21994e+06 | 674526           | 785600           | 953949           | -545415           | 111073    | 168349    | -265992         | -0.447083 | 0.164669  | 0.214294  | -0.218037    |
| Air Transport                          |  162 | 558882           | 315549           | 336511           | 398229           | -243333           |  20961.3  |  61718.6  | -160653         | -0.435392 | 0.066428  | 0.183408  | -0.287454    |
| Apparel                                | 1143 |      1.06537e+06 | 755184           | 853394           |      1.01208e+06 | -310190           |  98209.2  | 158683    |  -53297         | -0.291156 | 0.130047  | 0.185944  | -0.0500265   |
| Auto & Truck                           |  138 |      1.20335e+06 | 809726           | 999074           |      1.39597e+06 | -393621           | 189348    | 396898    |  192625         | -0.327105 | 0.233842  | 0.397266  |  0.160074    |
| Auto Parts                             |  690 | 537184           | 358569           | 427688           | 543636           | -178616           |  69119.2  | 115949    |    6451.99      | -0.332503 | 0.192764  | 0.271105  |  0.0120107   |
| Bank (Money Center)                    |  629 |      6.848e+06   |      4.65442e+06 |      4.74394e+06 |      5.339e+06   |      -2.19358e+06 |  89518.6  | 595062    |      -1.509e+06 | -0.320324 | 0.019233  | 0.125436  | -0.220356    |
| Banks (Regional)                       |  814 |      1.01088e+06 | 656561           | 711527           | 820676           | -354319           |  54966.5  | 109149    | -190204         | -0.350506 | 0.0837189 | 0.153401  | -0.188157    |
| Beverage (Alcoholic)                   |  220 |      1.14975e+06 | 875336           |      1.0153e+06  |      1.25922e+06 | -274419           | 139961    | 243926    |  109468         | -0.238676 | 0.159894  | 0.24025   |  0.0952099   |
| Beverage (Soft)                        |  102 | 703895           | 481835           | 574008           | 619801           | -222060           |  92172.9  |  45793.1  |  -84094.1       | -0.315473 | 0.191296  | 0.0797778 | -0.11947     |
| Broadcasting                           |  140 | 165360           |  94506.5         | 111969           | 124942           |  -70853           |  17462.1  |  12973.8  |  -40417.1       | -0.428479 | 0.184772  | 0.11587   | -0.24442     |
| Brokerage & Investment Banking         |  555 | 826525           | 635427           | 687960           | 914623           | -191098           |  52533.1  | 226663    |   88097.8       | -0.231207 | 0.0826737 | 0.329471  |  0.106588    |
| Building Materials                     |  420 | 441515           | 298406           | 364628           | 471307           | -143109           |  66221.4  | 106679    |   29791.7       | -0.324132 | 0.221917  | 0.292571  |  0.0674759   |
| Business & Consumer Services           |  853 | 908878           | 591898           | 749435           | 887683           | -316980           | 157537    | 138248    |  -21195         | -0.348759 | 0.266155  | 0.18447   | -0.02332     |
| Cable TV                               |   58 | 544753           | 388771           | 461273           | 529078           | -155982           |  72502.2  |  67804.2  |  -15675.9       | -0.286336 | 0.186491  | 0.146994  | -0.0287762   |
| Chemical (Basic)                       |  792 | 715790           | 529298           | 618023           | 759573           | -186491           |  88724.9  | 141550    |   43783.3       | -0.260539 | 0.167627  | 0.229036  |  0.0611679   |
| Chemical (Diversified)                 |   73 | 211995           | 139677           | 163139           | 196993           |  -72317.8         |  23462    |  33854.3  |  -15001.5       | -0.34113  | 0.167973  | 0.207518  | -0.0707637   |
| Chemical (Specialty)                   |  821 |      1.32268e+06 | 965209           |      1.17263e+06 |      1.42089e+06 | -357474           | 207423    | 248257    |   98206.4       | -0.270264 | 0.214899  | 0.211709  |  0.0742479   |
| Coal & Related Energy                  |  220 | 171943           | 139357           | 150244           | 164475           |  -32585.3         |  10887    |  14230.7  |   -7467.6       | -0.189512 | 0.0781226 | 0.0947171 | -0.0434307   |
| Computer Services                      |  944 |      1.09775e+06 | 769876           | 944821           |      1.11009e+06 | -327875           | 174944    | 165268    |   12337.4       | -0.298679 | 0.227237  | 0.17492   |  0.0112388   |
| Computers/Peripherals                  |  330 |      2.21606e+06 |      1.56522e+06 |      2.01617e+06 |      2.72678e+06 | -650846           | 450956    | 710605    |  510715         | -0.293695 | 0.288111  | 0.352452  |  0.230461    |
| Construction Supplies                  |  736 |      1.0384e+06  | 750689           | 872102           |      1.07091e+06 | -287707           | 121413    | 198805    |   32510.9       | -0.277069 | 0.161736  | 0.227961  |  0.0313087   |
| Diversified                            |  322 |      1.71813e+06 |      1.18553e+06 |      1.31763e+06 |      1.54094e+06 | -532598           | 132099    | 223316    | -177183         | -0.309987 | 0.111426  | 0.169483  | -0.103126    |
| Drugs (Biotechnology)                  | 1019 |      1.40722e+06 |      1.1337e+06  |      1.54241e+06 |      1.70364e+06 | -273517           | 408705    | 161235    |  296423         | -0.194367 | 0.360504  | 0.104534  |  0.210644    |
| Drugs (Pharmaceutical)                 | 1254 |      3.56736e+06 |      2.83989e+06 |      3.46322e+06 |      3.74594e+06 | -727466           | 623331    | 282718    |  178582         | -0.203923 | 0.219491  | 0.0816345 |  0.0500602   |
| Education                              |  226 | 194250           | 151244           | 176752           | 232982           |  -43005.9         |  25508.1  |  56230.1  |   38732.3       | -0.221395 | 0.168655  | 0.31813   |  0.199394    |
| Electrical Equipment                   |  894 | 895482           | 678481           | 773193           |      1.0243e+06  | -217000           |  94712.1  | 251109    |  128821         | -0.242328 | 0.139594  | 0.324769  |  0.143857    |
| Electronics (Consumer & Office)        |  141 | 216546           | 161121           | 187647           | 237522           |  -55425           |  26526    |  49874.3  |   20975.2       | -0.25595  | 0.164633  | 0.265788  |  0.0968624   |
| Electronics (General)                  | 1324 |      1.44603e+06 |      1.08665e+06 |      1.26621e+06 |      1.57495e+06 | -359385           | 179562    | 308734    |  128911         | -0.248531 | 0.165244  | 0.243825  |  0.0891481   |
| Engineering/Construction               | 1182 | 749677           | 549516           | 606083           | 689964           | -200161           |  56567.5  |  83881.3  |  -59712.3       | -0.266997 | 0.102941  | 0.138399  | -0.0796507   |
| Entertainment                          |  658 |      1.11613e+06 | 843839           |      1.08381e+06 |      1.304e+06   | -272293           | 239970    | 220195    |  187871         | -0.243961 | 0.284379  | 0.203167  |  0.168324    |
| Environmental & Waste Services         |  314 | 273323           | 213748           | 238605           | 266711           |  -59575.6         |  24857.7  |  28105.3  |   -6612.61      | -0.217968 | 0.116295  | 0.11779   | -0.0241934   |
| Farming/Agriculture                    |  410 | 315828           | 238367           | 272870           | 352993           |  -77460.9         |  34503.1  |  80123    |   37165.2       | -0.245263 | 0.144748  | 0.293631  |  0.117675    |
| Financial Svcs. (Non-bank & Insurance) | 1032 |      1.64952e+06 |      1.03867e+06 |      1.24251e+06 |      1.47609e+06 | -610846           | 203833    | 233584    | -173428         | -0.370317 | 0.196243  | 0.187994  | -0.105139    |
| Food Processing                        | 1249 |      1.79845e+06 |      1.50715e+06 |      1.70891e+06 |      1.96596e+06 | -291293           | 201752    | 257051    |  167510         | -0.161969 | 0.133863  | 0.150418  |  0.0931415   |
| Food Wholesalers                       |  148 |  93453.7         |  50334.3         |  64161.4         |  74741           |  -43119.3         |  13827.1  |  10579.6  |  -18712.7       | -0.461398 | 0.274704  | 0.16489   | -0.200235    |
| Furn/Home Furnishings                  |  332 | 330783           | 253254           | 292458           | 374659           |  -77528.5         |  39204    |  82201    |   43876.6       | -0.234379 | 0.154801  | 0.281069  |  0.132645    |
| Green & Renewable Energy               |  210 | 224460           | 179494           | 199072           | 232552           |  -44966           |  19577.3  |  33480.9  |    8092.13      | -0.200329 | 0.109069  | 0.168185  |  0.0360515   |
| Healthcare Products                    |  729 |      1.83361e+06 |      1.35175e+06 |      1.79734e+06 |      2.05134e+06 | -481858           | 445588    | 254001    |  217731         | -0.262792 | 0.329638  | 0.14132   |  0.118745    |
| Healthcare Support Services            |  395 |      1.08332e+06 | 764207           |      1.00285e+06 |      1.09919e+06 | -319109           | 238638    |  96345.1  |   15873.8       | -0.294567 | 0.312268  | 0.0960718 |  0.014653    |
| Heathcare Information and Technology   |  376 | 771669           | 606754           | 826490           |      1.00798e+06 | -164915           | 219737    | 181491    |  236313         | -0.213712 | 0.362152  | 0.219592  |  0.306236    |
| Homebuilding                           |  159 | 246953           | 126995           | 177474           | 221990           | -119957           |  50479.1  |  44516.4  |  -24962         | -0.485751 | 0.397489  | 0.250833  | -0.10108     |
| Hospitals/Healthcare Facilities        |  205 | 251674           | 163146           | 198924           | 253718           |  -88528.5         |  35778.4  |  54793.8  |    2043.72      | -0.351758 | 0.219303  | 0.275451  |  0.00812048  |
| Hotel/Gaming                           |  641 | 701122           | 380649           | 486548           | 571304           | -320473           | 105899    |  84756.4  | -129818         | -0.457086 | 0.278206  | 0.1742    | -0.185158    |
| Household Products                     |  533 |      1.47483e+06 |      1.19125e+06 |      1.33445e+06 |      1.55299e+06 | -283574           | 143195    | 218542    |   78163.1       | -0.192276 | 0.120206  | 0.16377   |  0.0529982   |
| Information Services                   |  216 |      1.68807e+06 |      1.09082e+06 |      1.49786e+06 |      1.67903e+06 | -597245           | 407037    | 181170    |   -9037.93      | -0.353804 | 0.373147  | 0.120952  | -0.00535401  |
| Insurance (General)                    |  223 | 834359           | 508644           | 583483           | 691628           | -325715           |  74839.2  | 108145    | -142731         | -0.390377 | 0.147135  | 0.185343  | -0.171067    |
| Insurance (Life)                       |  136 |      1.20003e+06 | 785409           | 868062           |      1.07702e+06 | -414623           |  82652.1  | 208960    | -123011         | -0.34551  | 0.105234  | 0.24072   | -0.102506    |
| Insurance (Prop/Cas.)                  |  221 | 656546           | 433989           | 484877           | 556264           | -222557           |  50888    |  71387.1  | -100282         | -0.338982 | 0.117256  | 0.147227  | -0.152742    |
| Investments & Asset Management         | 1081 | 873820           | 535966           | 670593           | 783195           | -337854           | 134627    | 112602    |  -90625         | -0.38664  | 0.251185  | 0.167915  | -0.103711    |
| Machinery                              | 1303 |      1.17947e+06 | 820650           |      1.01948e+06 |      1.25051e+06 | -358821           | 198832    | 231028    |   71038.2       | -0.304222 | 0.242286  | 0.226613  |  0.0602289   |
| Metals & Mining                        | 1455 | 843662           | 545009           | 693305           | 874596           | -298654           | 148297    | 181291    |   30934         | -0.353997 | 0.2721    | 0.261488  |  0.0366663   |
| Office Equipment & Services            |  138 |  46458.5         |  31810.7         |  36616.6         |  43907.3         |  -14647.9         |   4805.89 |   7290.78 |   -2551.21      | -0.315289 | 0.151078  | 0.199112  | -0.0549136   |
| Oil/Gas (Integrated)                   |   50 |      3.67932e+06 |      2.61736e+06 |      3.0989e+06  |      3.17318e+06 |      -1.06196e+06 | 481533    |  74287.1  | -506137         | -0.288629 | 0.183976  | 0.0239721 | -0.137563    |
| Oil/Gas (Production and Exploration)   |  716 | 694262           | 319661           | 475380           | 510217           | -374601           | 155718    |  34837.1  | -184045         | -0.539567 | 0.487134  | 0.0732826 | -0.265095    |
| Oil/Gas Distribution                   |  199 | 645242           | 355860           | 470198           | 498102           | -289382           | 114337    |  27904.5  | -147140         | -0.448486 | 0.321298  | 0.0593463 | -0.228039    |
| Oilfield Svcs/Equip.                   |  488 | 744236           | 419396           | 545532           | 662094           | -324840           | 126137    | 116562    |  -82141.2       | -0.436474 | 0.300758  | 0.213666  | -0.11037     |
| Packaging & Container                  |  397 | 280532           | 201272           | 233918           | 281017           |  -79260.2         |  32646.5  |  47098.4  |     484.732     | -0.282535 | 0.162201  | 0.201346  |  0.0017279   |
| Paper/Forest Products                  |  275 | 170560           | 121987           | 141526           | 170957           |  -48572.7         |  19539    |  29430.6  |     397.008     | -0.284784 | 0.160173  | 0.207952  |  0.00232768  |
| Power                                  |  559 |      2.21274e+06 |      1.59794e+06 |      1.80272e+06 |      2.01661e+06 | -614802           | 204781    | 213888    | -196134         | -0.277846 | 0.128153  | 0.118647  | -0.0886382   |
| Precious Metals                        |  796 | 420064           | 298000           | 484265           | 589203           | -122064           | 186265    | 104938    |  169139         | -0.290584 | 0.625048  | 0.216696  |  0.40265     |
| Publishing & Newspapers                |  343 | 147021           | 107972           | 114178           | 134220           |  -39049.5         |   6205.98 |  20042.4  |  -12801.1       | -0.265604 | 0.0574778 | 0.175537  | -0.0870697   |
| R.E.I.T.                               |  808 |      2.22142e+06 |      1.3366e+06  |      1.60158e+06 |      1.78866e+06 | -884816           | 264979    | 187083    | -432754         | -0.398312 | 0.198248  | 0.116811  | -0.19481     |
| Real Estate (Development)              |  830 | 820164           | 650725           | 674116           | 786452           | -169439           |  23391.4  | 112336    |  -33711.7       | -0.206591 | 0.0359467 | 0.166641  | -0.0411036   |
| Real Estate (General/Diversified)      |  371 | 476634           | 345779           | 372478           | 413504           | -130855           |  26698.7  |  41026.6  |  -63129.9       | -0.27454  | 0.0772133 | 0.110145  | -0.132449    |
| Real Estate (Operations & Services)    |  713 | 624979           | 412749           | 466174           | 538859           | -212231           |  53425    |  72685.3  |  -86120.4       | -0.33958  | 0.129437  | 0.155919  | -0.137797    |
| Recreation                             |  311 | 261971           | 184069           | 236658           | 273223           |  -77902.5         |  52589.1  |  36564.9  |   11251.5       | -0.29737  | 0.285703  | 0.154505  |  0.0429494   |
| Reinsurance                            |   35 | 180669           |  98289.9         | 115462           | 138178           |  -82379.1         |  17172.3  |  22716    |  -42490.7       | -0.455967 | 0.174711  | 0.196739  | -0.235186    |
| Restaurant/Dining                      |  362 | 676038           | 424284           | 551359           | 604496           | -251754           | 127075    |  53137.8  |  -71541.7       | -0.372396 | 0.299504  | 0.0963761 | -0.105825    |
| Retail (Automotive)                    |  183 | 194937           | 123132           | 178198           | 220553           |  -71805.1         |  55065.9  |  42354.5  |   25615.3       | -0.36835  | 0.44721   | 0.237682  |  0.131403    |
| Retail (Building Supply)               |   87 | 452206           | 269287           | 427570           | 525726           | -182919           | 158283    |  98155.9  |   73520         | -0.404503 | 0.587785  | 0.229567  |  0.162581    |
| Retail (Distributors)                  |  946 | 612777           | 421199           | 500822           | 602757           | -191577           |  79622.1  | 101936    |  -10019.2       | -0.312638 | 0.189037  | 0.203538  | -0.0163504   |
| Retail (General)                       |  212 |      1.06269e+06 | 889891           | 985938           |      1.1272e+06  | -172804           |  96047.2  | 141262    |   64505.9       | -0.162609 | 0.107931  | 0.143277  |  0.0607003   |
| Retail (Grocery and Food)              |  169 | 480225           | 397990           | 446521           | 496881           |  -82235.3         |  48531.4  |  50359.1  |   16655.2       | -0.171243 | 0.121941  | 0.112781  |  0.0346821   |
| Retail (Online)                        |  310 |      2.4578e+06  |      1.99168e+06 |      2.63574e+06 |      3.40884e+06 | -466120           | 644057    | 773105    |  951042         | -0.189649 | 0.323374  | 0.293316  |  0.386949    |
| Retail (Special Lines)                 |  467 | 815761           | 548366           | 661242           | 790135           | -267395           | 112876    | 128893    |  -25626         | -0.327786 | 0.205842  | 0.194925  | -0.0314137   |
| Rubber& Tires                          |   90 | 106644           |  78572.5         |  87439.6         | 102909           |  -28071.8         |   8867.1  |  15469.5  |   -3735.26      | -0.263228 | 0.112853  | 0.176916  | -0.0350254   |
| Semiconductor                          |  541 |      2.05914e+06 |      1.45714e+06 |      1.89425e+06 |      2.33096e+06 | -602008           | 437110    | 436716    |  271819         | -0.292358 | 0.299979  | 0.230549  |  0.132006    |
| Semiconductor Equip                    |  293 | 525578           | 340382           | 480971           | 594233           | -185196           | 140589    | 113262    |   68654.7       | -0.352366 | 0.413031  | 0.235486  |  0.130627    |
| Shipbuilding & Marine                  |  345 | 263358           | 199442           | 234071           | 259927           |  -63915.9         |  34629.3  |  25856    |   -3430.71      | -0.242696 | 0.173631  | 0.110462  | -0.0130268   |
| Shoe                                   |   77 | 258915           | 168461           | 223002           | 258832           |  -90454.8         |  54540.9  |  35830.2  |     -83.733     | -0.34936  | 0.32376   | 0.160673  | -0.000323399 |
| Software (Entertainment)               |  297 |      2.53907e+06 |      1.84974e+06 |      2.47512e+06 |      2.82936e+06 | -689331           | 625382    | 354239    |  290290         | -0.27149  | 0.338093  | 0.14312   |  0.114329    |
| Software (Internet)                    |  134 | 226498           | 166495           | 286759           | 334677           |  -60002.1         | 120263    |  47917.8  |  108179         | -0.264913 | 0.722322  | 0.167102  |  0.477617    |
| Software (System & Application)        | 1344 |      3.77731e+06 |      2.79995e+06 |      3.70653e+06 |      4.2468e+06  | -977364           | 906578    | 540277    |  469491         | -0.258746 | 0.323784  | 0.145764  |  0.124292    |
| Steel                                  |  693 | 541660           | 377727           | 428726           | 532246           | -163933           |  50998.3  | 103521    |   -9413.58      | -0.302649 | 0.135014  | 0.241462  | -0.0173791   |
| Telecom (Wireless)                     |  105 |      1.05481e+06 | 829545           | 957862           |      1.05976e+06 | -225264           | 128316    | 101897    |    4948.92      | -0.213559 | 0.154683  | 0.10638   |  0.00469177  |
| Telecom. Equipment                     |  463 | 557292           | 454644           | 523394           | 574242           | -102648           |  68750.1  |  50847.3  |   16949.3       | -0.184191 | 0.151217  | 0.0971491 |  0.0304137   |
| Telecom. Services                      |  307 |      1.60881e+06 |      1.27805e+06 |      1.37889e+06 |      1.49143e+06 | -330755           | 100839    | 112537    | -117379         | -0.20559  | 0.0789002 | 0.0816139 | -0.0729604   |
| Tobacco                                |   52 | 488140           | 352129           | 406904           | 422641           | -136011           |  54775    |  15737.7  |  -65498.5       | -0.278632 | 0.155554  | 0.0386767 | -0.13418     |
| Transportation                         |  262 | 548154           | 415193           | 483871           | 650643           | -132961           |  68678.1  | 166772    |  102489         | -0.242561 | 0.165412  | 0.344662  |  0.186972    |
| Transportation (Railroads)             |   53 | 684052           | 505948           | 586344           | 634743           | -178104           |  80396    |  48398.7  |  -49309.4       | -0.260366 | 0.158902  | 0.0825432 | -0.0720842   |
| Trucking                               |  208 | 238580           | 148631           | 199082           | 218520           |  -89949.1         |  50451.2  |  19437.1  |  -20060.9       | -0.377018 | 0.339438  | 0.0976333 | -0.0840844   |
| Utility (General)                      |   53 | 624754           | 442208           | 502191           | 528395           | -182546           |  59983.3  |  26204    |  -96359         | -0.292189 | 0.135645  | 0.0521794 | -0.154235    |
| Utility (Water)                        |  100 | 143941           | 112617           | 123565           | 136381           |  -31323.5         |  10948.2  |  12815.2  |   -7560.1       | -0.217614 | 0.0972159 | 0.103712  | -0.0525223   |



label: G=D-C
H=E-D
I=F-E
J=F-C
K=G/C
L=H/D
M=I/E
N=J/C
labeled_formulas: G=D-C
H=E-D
I=F-E
J=F-C
K=G/C
L=H/D
M=I/E
N=J/C
output: {"Arithmetic-Relationship": ["G=D-C", "H=E-D", "I=F-E", "J=F-C", "K=G/C", "L=H/D", "M=I/E", "N=J/C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_637902___xlsx_d8c4f02e0673d67d84ed92aff04a596074e9446b.xlsx___line_479