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 |
|:-------------------------------------|-----------------:|----------:|-----------------:|----------:|-----------------:|----------:|---------:|----------:|----------:|
| Advertising                          |  73531.4         |  17028.7  |  90560.1         |  26112.6  |  64447.5         | 0.414244  | 0.520907 | 0.334787  | 0.436228  |
| Aerospace/Defense                    | 278122           |  23308.7  | 301430           |  75070.2  | 226360           | 0.255041  | 0.561067 | 0.204514  | 0.489772  |
| Air Transport                        | 434730           | 167878    | 602608           |  71585.7  | 531022           | 0.61104   | 0.680918 | 0.580597  | 0.652836  |
| Apparel                              | 235765           |  70956.5  | 306721           |  70251.5  | 236470           | 0.27676   | 0.454286 | 0.227811  | 0.390911  |
| Auto & Truck                         |      1.19954e+06 |  20363.7  |      1.21991e+06 | 300270    | 919636           | 0.568793  | 0.541761 | 0.498594  | 0.471253  |
| Auto Parts                           | 202040           |  13139.6  | 215179           |  92394.9  | 122784           | 0.335284  | 0.335399 | 0.223493  | 0.223583  |
| Beverage (Alcoholic)                 | 263884           |  10600.7  | 274485           |  54209.1  | 220276           | 0.220319  | 0.450566 | 0.184851  | 0.3969    |
| Beverage (Soft)                      | 121460           |   4399.58 | 125859           |  22574    | 103285           | 0.178863  | 0.542645 | 0.151647  | 0.493332  |
| Broadcasting                         | 105078           |  10341.4  | 115419           |  16242.8  |  99176.2         | 0.504094  | 0.512356 | 0.466228  | 0.474463  |
| Building Materials                   | 119490           |  11487.9  | 130978           |  33342.8  |  97635           | 0.29028   | 0.408845 | 0.23365   | 0.34017   |
| Business & Consumer Services         | 201701           |  29070.6  | 230772           |  56060.6  | 174711           | 0.251262  | 0.525994 | 0.202589  | 0.456554  |
| Cable TV                             | 368207           |  12371.1  | 380579           |  28599.3  | 351979           | 0.450803  | 0.633254 | 0.431545  | 0.61493   |
| Chemical (Basic)                     | 276447           |  10376.9  | 286824           |  86800.1  | 200024           | 0.333316  | 0.366132 | 0.258524  | 0.287148  |
| Chemical (Diversified)               | 103523           |   5965.07 | 109488           |  20510    |  88978.2         | 0.422743  | 0.387555 | 0.373099  | 0.339612  |
| Chemical (Specialty)                 | 328767           |  20257.1  | 349024           |  83748.4  | 265275           | 0.246136  | 0.378135 | 0.198818  | 0.31608   |
| Coal & Related Energy                |  98171.1         |   1506.99 |  99678           |  52257.5  |  47420.6         | 0.3988    | 0.329719 | 0.239877  | 0.189641  |
| Computer Services                    | 226080           |  30500.5  | 256580           |  86648.4  | 169932           | 0.226854  | 0.447162 | 0.162709  | 0.34883   |
| Computers/Peripherals                | 328505           |  22961.2  | 351466           | 171711    | 179755           | 0.159906  | 0.395376 | 0.0887135 | 0.250623  |
| Construction Supplies                | 471447           |  20885.1  | 492332           | 162383    | 329949           | 0.367656  | 0.425976 | 0.280395  | 0.332144  |
| Diversified                          |      1.1066e+06  |  61536.1  |      1.16813e+06 | 302583    | 865552           | 0.461277  | 0.424007 | 0.388173  | 0.35294   |
| Drugs (Biotechnology)                | 150330           |  10614.4  | 160945           |  98613.4  |  62331.3         | 0.115571  | 0.453616 | 0.0481699 | 0.243301  |
| Drugs (Pharmaceutical)               | 622636           |  28302    | 650938           | 199544    | 451394           | 0.17495   | 0.40111  | 0.128195  | 0.317146  |
| Education                            |  22246.3         |   8079.42 |  30325.7         |  10851.6  |  19474.1         | 0.152025  | 0.430359 | 0.103241  | 0.326667  |
| Electrical Equipment                 | 192803           |  57786.1  | 250589           |  89850.3  | 160739           | 0.248756  | 0.39689  | 0.175189  | 0.296823  |
| Electronics (Consumer & Office)      |  76829.8         |   4493.23 |  81323           |  38840.1  |  42482.9         | 0.318873  | 0.388133 | 0.196505  | 0.248899  |
| Electronics (General)                | 244709           |  11058.5  | 255767           | 178607    |  77159.7         | 0.170256  | 0.296159 | 0.0582935 | 0.112641  |
| Engineering/Construction             | 667478           |  25819.8  | 693298           | 275096    | 418202           | 0.537687  | 0.5023   | 0.412301  | 0.378412  |
| Entertainment                        | 150266           |  32497.5  | 182763           |  67367    | 115396           | 0.167783  | 0.388183 | 0.112922  | 0.286024  |
| Environmental & Waste Services       |  87203.4         |   5120.03 |  92323.4         |  19154    |  73169.4         | 0.277288  | 0.521574 | 0.233174  | 0.463522  |
| Farming/Agriculture                  | 183877           |   6222.86 | 190100           |  27206.6  | 162893           | 0.416244  | 0.518327 | 0.379266  | 0.479733  |
| Food Processing                      | 465317           |  28560.8  | 493878           |  96032.4  | 397845           | 0.239956  | 0.43001  | 0.202758  | 0.378003  |
| Food Wholesalers                     |  63271.5         |  10674.6  |  73946.1         |  10637.8  |  63308.3         | 0.550523  | 0.607425 | 0.511864  | 0.569836  |
| Furn/Home Furnishings                |  70506.5         |   8846.4  |  79352.9         |  54993.9  |  24359           | 0.218606  | 0.394926 | 0.0790872 | 0.166914  |
| Green & Renewable Energy             | 154938           |   3341.85 | 158279           |  14053.7  | 144226           | 0.443359  | 0.569964 | 0.420548  | 0.54704   |
| Healthcare Products                  | 204145           |  12322    | 216467           |  66262.4  | 150204           | 0.125363  | 0.361932 | 0.0904596 | 0.282432  |
| Healthcare Support Services          | 377965           |  60594.5  | 438559           |  85008.2  | 353551           | 0.321876  | 0.514328 | 0.276752  | 0.460547  |
| Heathcare Information and Technology |  77897.3         |   7188.46 |  85085.7         |  23418.1  |  61667.6         | 0.115509  | 0.400035 | 0.0864665 | 0.325805  |
| Homebuilding                         |  81615.2         |  17987.9  |  99603.1         |  34257.9  |  65345.2         | 0.379838  | 0.405994 | 0.286642  | 0.309585  |
| Hospitals/Healthcare Facilities      | 167106           |  33340.5  | 200447           |  13406.3  | 187041           | 0.507335  | 0.732794 | 0.490031  | 0.719023  |
| Hotel/Gaming                         | 345381           |  56428.4  | 401809           |  71554.9  | 330254           | 0.456026  | 0.557591 | 0.407945  | 0.508818  |
| Household Products                   | 182181           |  17981.1  | 200162           |  53883.6  | 146279           | 0.137907  | 0.461634 | 0.104668  | 0.385237  |
| Information Services                 | 172750           |   9322.35 | 182072           |  55428.4  | 126644           | 0.118125  | 0.431973 | 0.0852293 | 0.345963  |
| Investments & Asset Management       | 738027           |  23999.6  | 762026           | 190594    | 571432           | 0.533378  | 0.553452 | 0.461545  | 0.481706  |
| Machinery                            | 246127           |  25131.8  | 271259           | 114422    | 156837           | 0.221379  | 0.358898 | 0.141181  | 0.244527  |
| Metals & Mining                      | 367086           |  10384.8  | 377471           | 106287    | 271184           | 0.381821  | 0.395652 | 0.307353  | 0.319883  |
| Office Equipment & Services          |  13944.7         |   1771.36 |  15716           |   6813.25 |   8902.8         | 0.308191  | 0.40629  | 0.201506  | 0.27936   |
| Oil/Gas (Integrated)                 | 849641           | 148374    | 998014           | 233135    | 764879           | 0.266301  | 0.313021 | 0.217632  | 0.258825  |
| Oil/Gas (Production and Exploration) | 386537           |  22284.6  | 408822           |  52345.6  | 356476           | 0.520528  | 0.386834 | 0.48629   | 0.354881  |
| Oil/Gas Distribution                 | 315769           |  11279.1  | 327048           |  18979.4  | 308069           | 0.4345    | 0.557305 | 0.419872  | 0.542509  |
| Oilfield Svcs/Equip.                 | 416802           |  43644.7  | 460447           |  82779.3  | 377667           | 0.492039  | 0.443384 | 0.442745  | 0.395172  |
| Packaging & Container                | 134456           |   7486.73 | 141942           |  17783.6  | 124159           | 0.390095  | 0.551747 | 0.358755  | 0.51846   |
| Paper/Forest Products                | 114487           |   3234.99 | 117722           |  20695.5  |  97026.5         | 0.457161  | 0.455372 | 0.409721  | 0.407978  |
| Power                                |      1.90447e+06 |  51028.3  |      1.9555e+06  | 166524    |      1.78897e+06 | 0.524757  | 0.557388 | 0.502526  | 0.535332  |
| Precious Metals                      |  78390.7         |   2202.51 |  80593.2         |  27929.1  |  52664.1         | 0.203058  | 0.279853 | 0.142733  | 0.202512  |
| Publishing & Newspapers              |  50587.2         |   9603.12 |  60190.3         |  28232    |  31958.4         | 0.334029  | 0.364156 | 0.210304  | 0.233178  |
| R.E.I.T.                             |      1.48121e+06 |  60156.6  |      1.54137e+06 |  66036.3  |      1.47533e+06 | 0.469955  | 0.563068 | 0.459063  | 0.552267  |
| Real Estate (Development)            |      1.25911e+06 |  13950.4  |      1.27306e+06 | 425476    | 847585           | 0.638319  | 0.562206 | 0.540235  | 0.460913  |
| Real Estate (General/Diversified)    | 452825           |  38525.4  | 491351           |  87431.6  | 403919           | 0.544293  | 0.41532  | 0.495423  | 0.368663  |
| Real Estate (Operations & Services)  | 402605           |  32818.1  | 435423           |  58894.9  | 376529           | 0.473763  | 0.42197  | 0.437733  | 0.386982  |
| Recreation                           |  66316.1         |   9192.16 |  75508.2         |  30226.1  |  45282.1         | 0.275706  | 0.455189 | 0.185852  | 0.333798  |
| Reinsurance                          |  40063.5         |   2072.83 |  42136.3         |  26947.7  |  15188.6         | 0.268885  | 0.208484 | 0.117052  | 0.0867127 |
| Restaurant/Dining                    | 203939           |  65791    | 269730           |  27171.7  | 242559           | 0.348186  | 0.846179 | 0.324492  | 0.831846  |
| Retail (Automotive)                  | 125118           |  25046.6  | 150164           |  15643.9  | 134520           | 0.485185  | 0.692668 | 0.457778  | 0.668766  |
| Retail (Building Supply)             |  93110.7         |  32557    | 125668           |  10590.4  | 115077           | 0.257839  | 0.739289 | 0.241355  | 0.721967  |
| Retail (Distributors)                | 528495           |  36531.2  | 565026           | 103876    | 461150           | 0.546297  | 0.54051  | 0.495643  | 0.489813  |
| Retail (General)                     | 383422           | 144145    | 527567           |  74388.3  | 453179           | 0.359796  | 0.589397 | 0.325581  | 0.55218   |
| Retail (Grocery and Food)            | 247974           | 113360    | 361334           |  56577.6  | 304757           | 0.468618  | 0.617064 | 0.42654   | 0.576108  |
| Retail (Online)                      | 152116           |  33231    | 185347           |  76674.8  | 108672           | 0.0831448 | 0.472023 | 0.0504858 | 0.34391   |
| Retail (Special Lines)               | 236332           | 154325    | 390658           |  70821.7  | 319836           | 0.384143  | 0.617383 | 0.338044  | 0.569161  |
| Rubber& Tires                        |  57608.4         |   4195.33 |  61803.7         |  13473.4  |  48330.3         | 0.420153  | 0.402449 | 0.361687  | 0.344981  |
| Semiconductor                        | 223222           |   9117.49 | 232340           | 125191    | 107149           | 0.120783  | 0.319263 | 0.0595794 | 0.177826  |
| Semiconductor Equip                  |  46718.2         |   2332.29 |  49050.5         |  32407.6  |  16642.9         | 0.108331  | 0.323182 | 0.0395907 | 0.139428  |
| Shipbuilding & Marine                | 249876           |  54451.2  | 304327           |  53951.2  | 250376           | 0.565545  | 0.516943 | 0.517133  | 0.468208  |
| Shoe                                 |  24169.3         |   9067.21 |  33236.5         |   9448.51 |  23788           | 0.147704  | 0.4399   | 0.110348  | 0.359845  |
| Software (Entertainment)             |  84834.2         |  28549.8  | 113384           |  86264    |  27120           | 0.0516273 | 0.210726 | 0.0128535 | 0.0600267 |
| Software (Internet)                  |  22994.1         |   2583.76 |  25577.9         |   8806.12 |  16771.7         | 0.126619  | 0.545372 | 0.0868098 | 0.440276  |
| Software (System & Application)      | 273825           |  33165.9  | 306991           | 130753    | 176238           | 0.0904724 | 0.430856 | 0.0540202 | 0.302939  |
| Steel                                | 365561           |  10088.4  | 375649           |  93149.9  | 282499           | 0.473127  | 0.389224 | 0.403097  | 0.323977  |
| Telecom (Wireless)                   | 639446           | 132038    | 771484           |  97876.8  | 673607           | 0.462011  | 0.543314 | 0.428514  | 0.509505  |
| Telecom. Equipment                   |  86649.3         |   7275.09 |  93924.4         |  48787.4  |  45136.9         | 0.161956  | 0.387695 | 0.0849795 | 0.233295  |
| Telecom. Services                    |      1.06859e+06 | 144281    |      1.21287e+06 |  93564.9  |      1.1193e+06  | 0.472821  | 0.569917 | 0.452864  | 0.550138  |
| Tobacco                              | 158857           |   2741.9  | 161599           |  22182.4  | 139416           | 0.284414  | 0.531102 | 0.255342  | 0.494229  |
| Transportation                       | 295989           |  38851.7  | 334840           |  60845.9  | 273995           | 0.429979  | 0.542206 | 0.381666  | 0.492171  |
| Transportation (Railroads)           | 259648           |  12991.5  | 272639           |  22503.1  | 250136           | 0.335879  | 0.493584 | 0.316943  | 0.472077  |
| Trucking                             | 145256           |  19719.6  | 164975           |  28628    | 136347           | 0.501891  | 0.598744 | 0.454371  | 0.552219  |
| Utility (General)                    | 483235           |  13584.5  | 496819           |  35428.7  | 461391           | 0.497756  | 0.594511 | 0.479272  | 0.576559  |
| Utility (Water)                      |  84274.9         |   1037.2  |  85312.1         |  13548    |  71764.1         | 0.403104  | 0.533471 | 0.362281  | 0.490289  |



label: D=B+C
F=D-E
labeled_formulas: D=B+C
F=D-E
output: {"Arithmetic-Relationship": ["D=B+C", "F=D-E"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_586733___xlsx_c4cd6edb4126ad878771b090ffc7bb1f586c6cdb.xlsx___line_678