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 |
|:----|:-------------------------------------------------|--------:|---------:|-----------------:|---------:|
| 00C | NHS Darlington CCG                               |  145159 |  2336.71 | 142822           |  4937.51 |
| 00D | NHS Durham Dales, Easington and Sedgefield CCG   |  440432 |  6948.83 | 433483           | 14986    |
| 00K | NHS Hartlepool and Stockton-on-Tees CCG          |  397063 |  6277.41 | 390786           | 13509.9  |
| 00J | NHS North Durham CCG                             |  340109 |  6210.49 | 333899           | 11543.2  |
| 99C | NHS North Tyneside CCG                           |  307314 |  4807.4  | 302507           | 10458    |
| 00L | NHS Northumberland CCG                           |  448361 |  7093.77 | 441267           | 15255.1  |
| 00M | NHS South Tees CCG                               |  413341 |  6891.93 | 406449           | 14051.4  |
| 00N | NHS South Tyneside CCG                           |  242525 |  4267.4  | 238258           |  8236.81 |
| 00P | NHS Sunderland CCG                               |  447097 |  7309.76 | 439787           | 15203.9  |
| 00Q | NHS Blackburn with Darwen CCG                    |  217854 |  3564.09 | 214290           |  7408.22 |
| 00R | NHS Blackpool CCG                                |  250764 |  4213.43 | 246551           |  8523.5  |
| 00T | NHS Bolton CCG                                   |  387501 |  6481.35 | 381020           | 13172.2  |
| 00V | NHS Bury CCG                                     |  246199 |  3807.91 | 242391           |  8379.7  |
| 00W | NHS Central Manchester CCG                       |  254455 |  4412.21 | 250043           |  8644.23 |
| 00X | NHS Chorley and South Ribble CCG                 |  232421 |  3707.02 | 228714           |  7906.87 |
| 01H | NHS Cumbria CCG                                  |  719217 | 11803.9  | 707413           | 24456    |
| 01A | NHS East Lancashire CCG                          |  527178 |  8104.34 | 519074           | 17944.9  |
| 01C | NHS Eastern Cheshire CCG                         |  244843 |  3551.92 | 241291           |  8341.68 |
| 02M | NHS Fylde and Wyre CCG                           |  213918 |  3622.17 | 210296           |  7270.14 |
| 01E | NHS Greater Preston CCG                          |  264303 |  4462.36 | 259841           |  8982.95 |
| 01F | NHS Halton CCG                                   |  191317 |  2979.95 | 188337           |  6511    |
| 01D | NHS Heywood, Middleton and Rochdale CCG          |  305780 |  5167.72 | 300612           | 10392.5  |
| 01J | NHS Knowsley CCG                                 |  261616 |  4555.52 | 257060           |  8886.84 |
| 01K | NHS Lancashire North CCG                         |  209468 |  3401.53 | 206066           |  7123.93 |
| 99A | NHS Liverpool CCG                                |  769414 | 13787.5  | 755626           | 26122.8  |
| 01M | NHS North Manchester CCG                         |  280587 |  4157.46 | 276430           |  9556.45 |
| 00Y | NHS Oldham CCG                                   |  321901 |  5232.98 | 316668           | 10947.5  |
| 01G | NHS Salford CCG                                  |  365891 |  6143.63 | 359747           | 12436.8  |
| 01R | NHS South Cheshire CCG                           |  219961 |  3211.68 | 216749           |  7493.24 |
| 01N | NHS South Manchester CCG                         |  233982 |  3860.79 | 230121           |  7955.52 |
| 01T | NHS South Sefton CCG                             |  237180 |  4125.75 | 233054           |  8056.92 |
| 01V | NHS Southport and Formby CCG                     |  177793 |  2984.03 | 174809           |  6043.32 |
| 01X | NHS St Helens CCG                                |  284973 |  4489.31 | 280484           |  9696.6  |
| 01W | NHS Stockport CCG                                |  391056 |  5982.99 | 385073           | 13312.4  |
| 01Y | NHS Tameside and Glossop CCG                     |  336879 |  6099.86 | 330779           | 11435.4  |
| 02A | NHS Trafford CCG                                 |  293510 |  4409.35 | 289101           |  9994.5  |
| 02D | NHS Vale Royal CCG                               |  127900 |  2100.56 | 125799           |  4349.01 |
| 02E | NHS Warrington CCG                               |  267772 |  3840.68 | 263931           |  9124.37 |
| 02F | NHS West Cheshire CCG                            |  327677 |  4740.35 | 322937           | 11164.2  |
| 02G | NHS West Lancashire CCG                          |  146593 |  2430.95 | 144162           |  4983.83 |
| 02H | NHS Wigan Borough CCG                            |  443480 |  7423.74 | 436056           | 15074.9  |
| 12F | NHS Wirral CCG                                   |  486512 |  8394.23 | 478118           | 16529    |
| 02N | NHS Airedale, Wharfedale and Craven CCG          |  201599 |  3142.08 | 198457           |  6860.86 |
| 02P | NHS Barnsley CCG                                 |  367042 |  5774.04 | 361268           | 12489.4  |
| 02Q | NHS Bassetlaw CCG                                |  153110 |  2342.28 | 150768           |  5212.19 |
| 02W | NHS Bradford City CCG                            |  130715 |  1686.37 | 129029           |  4460.65 |
| 02R | NHS Bradford Districts CCG                       |  431625 |  6814.55 | 424810           | 14686.1  |
| 02T | NHS Calderdale CCG                               |  277214 |  4292.38 | 272922           |  9435.18 |
| 02X | NHS Doncaster CCG                                |  438087 |  7039.81 | 431047           | 14901.7  |
| 02Y | NHS East Riding of Yorkshire CCG                 |  376501 |  6314.06 | 370187           | 12797.7  |
| 03A | NHS Greater Huddersfield CCG                     |  290258 |  4859.59 | 285398           |  9866.51 |
| 03D | NHS Hambleton, Richmondshire and Whitby CCG      |  184053 |  2856.51 | 181196           |  6264.15 |
| 03E | NHS Harrogate and Rural District CCG             |  189853 |  2954.31 | 186899           |  6461.28 |
| 03F | NHS Hull CCG                                     |  381963 |  6774.35 | 375189           | 12970.6  |
| 02V | NHS Leeds North CCG                              |  250872 |  4025.76 | 246846           |  8533.72 |
| 03G | NHS Leeds South and East CCG                     |  364573 |  4936.51 | 359636           | 12433    |
| 03C | NHS Leeds West CCG                               |  409259 |  6474    | 402785           | 13924.7  |
| 03H | NHS North East Lincolnshire CCG                  |  221217 |  3635.4  | 217582           |  7522.02 |
| 03J | NHS North Kirklees CCG                           |  237139 |  3812.11 | 233327           |  8066.35 |
| 03K | NHS North Lincolnshire CCG                       |  217072 |  3547.78 | 213524           |  7381.75 |
| 03L | NHS Rotherham CCG                                |  353184 |  6272.4  | 346912           | 11993.1  |
| 03M | NHS Scarborough and Ryedale CCG                  |  158111 |  2073.32 | 156038           |  5394.38 |
| 03N | NHS Sheffield CCG                                |  737037 | 12613.3  | 724424           | 25044.1  |
| 03Q | NHS Vale of York CCG                             |  394029 |  6209.43 | 387820           | 13407.3  |
| 03R | NHS Wakefield CCG                                |  488812 |  7687.88 | 481124           | 16632.9  |
| 13P | NHS Birmingham CrossCity CCG                     |  896349 | 17347.7  | 879001           | 30388    |
| 04X | NHS Birmingham South and Central CCG             |  341043 |  4787.2  | 336256           | 11624.7  |
| 04Y | NHS Cannock Chase CCG                            |  164232 |  2581.03 | 161651           |  5588.44 |
| 05A | NHS Coventry and Rugby CCG                       |  578866 |  9167.89 | 569698           | 19695    |
| 05C | NHS Dudley CCG                                   |  404961 |  7281.06 | 397680           | 13748.2  |
| 05D | NHS East Staffordshire CCG                       |  155647 |  2405.78 | 153241           |  5297.7  |
| 05F | NHS Herefordshire CCG                            |  225205 |  4105.86 | 221099           |  7643.62 |
| 05G | NHS North Staffordshire CCG                      |  275390 |  4140.02 | 271250           |  9377.39 |
| 05J | NHS Redditch and Bromsgrove CCG                  |  197525 |  3477.12 | 194048           |  6708.43 |
| 05L | NHS Sandwell and West Birmingham CCG             |  665595 | 12592.4  | 653003           | 22575    |
| 05N | NHS Shropshire CCG                               |  376852 |  6498.7  | 370353           | 12803.5  |
| 05P | NHS Solihull CCG                                 |  291565 |  4058.03 | 287507           |  9939.41 |
| 05Q | NHS South East Staffs and Seisdon Peninsular CCG |  247038 |  4312.49 | 242726           |  8391.27 |
| 05R | NHS South Warwickshire CCG                       |  320006 |  4919.53 | 315086           | 10892.9  |
| 05T | NHS South Worcestershire CCG                     |  336569 |  5729.08 | 330840           | 11437.5  |
| 05V | NHS Stafford and Surrounds CCG                   |  168275 |  2918.05 | 165357           |  5716.56 |
| 05W | NHS Stoke-on-Trent CCG                           |  379130 |  6366.99 | 372763           | 12886.8  |
| 05X | NHS Telford and Wrekin CCG                       |  205369 |  3610.13 | 201759           |  6975.01 |
| 05Y | NHS Walsall CCG                                  |  372632 |  6675.88 | 365956           | 12651.5  |
| 05H | NHS Warwickshire North CCG                       |  229147 |  3563.15 | 225584           |  7798.66 |
| 06A | NHS Wolverhampton CCG                            |  337458 |  6417.83 | 331040           | 11444.4  |
| 06D | NHS Wyre Forest CCG                              |  136178 |  1912.11 | 134266           |  4641.71 |
| 03V | NHS Corby CCG                                    |   93236 |  1160.36 |  92075.6         |  3183.15 |
| 03W | NHS East Leicestershire and Rutland CCG          |  357473 |  5451.13 | 352022           | 12169.8  |
| 03X | NHS Erewash CCG                                  |  125700 |  2077.22 | 123623           |  4273.76 |
| 03Y | NHS Hardwick CCG                                 |  143412 |  2381.72 | 141030           |  4875.56 |
| 04C | NHS Leicester City CCG                           |  427456 |  7337.56 | 420118           | 14523.9  |
| 03T | NHS Lincolnshire East CCG                        |  333513 |  4960.97 | 328552           | 11358.4  |
| 04D | NHS Lincolnshire West CCG                        |  279084 |  4977.07 | 274107           |  9476.15 |
| 04E | NHS Mansfield and Ashfield CCG                   |  252380 |  4003.13 | 248377           |  8586.64 |
| 04F | NHS Milton Keynes CCG                            |  295638 |  4320.44 | 291318           | 10071.1  |
| 04G | NHS Nene CCG                                     |  757879 | 11224.3  | 746655           | 25812.6  |
| 04H | NHS Newark and Sherwood CCG                      |  163905 |  2420.3  | 161485           |  5582.69 |
| 04J | NHS North Derbyshire CCG                         |  390444 |  5909.93 | 384534           | 13293.7  |
| 04K | NHS Nottingham City CCG                          |  420223 |  7227    | 412996           | 14277.7  |
| 04L | NHS Nottingham North and East CCG                |  182127 |  3052.9  | 179074           |  6190.77 |
| 04M | NHS Nottingham West CCG                          |  117187 |  2293.79 | 114893           |  3971.97 |
| 04N | NHS Rushcliffe CCG                               |  136589 |  2332.57 | 134256           |  4641.38 |
| 99D | NHS South Lincolnshire CCG                       |  198948 |  3098.75 | 195849           |  6770.71 |
| 04Q | NHS South West Lincolnshire CCG                  |  157312 |  2666.29 | 154646           |  5346.26 |
| 04R | NHS Southern Derbyshire CCG                      |  664254 | 11179.5  | 653075           | 22577.4  |
| 04V | NHS West Leicestershire CCG                      |  412525 |  6438.09 | 406087           | 14038.8  |
| 99E | NHS Basildon and Brentwood CCG                   |  332716 |  4937.38 | 327779           | 11331.6  |
| 06F | NHS Bedfordshire CCG                             |  530054 |  6932.13 | 523122           | 18084.9  |
| 06H | NHS Cambridgeshire and Peterborough CCG          |  985993 | 15136.4  | 970857           | 33563.5  |
| 99F | NHS Castle Point and Rochford CCG                |  227460 |  3347.59 | 224112           |  7747.79 |
| 06K | NHS East and North Hertfordshire CCG             |  695482 |  9229.64 | 686252           | 23724.4  |
| 06M | NHS Great Yarmouth and Waveney CCG               |  319346 |  4566.01 | 314780           | 10882.3  |
| 06N | NHS Herts Valleys CCG                            |  733574 |  9730.95 | 723843           | 25024    |
| 06L | NHS Ipswich and East Suffolk CCG                 |  458011 |  8191.88 | 449819           | 15550.7  |
| 06P | NHS Luton CCG                                    |  262417 |  3674.63 | 258742           |  8944.98 |
| 06Q | NHS Mid Essex CCG                                |  440637 |  7408.68 | 433228           | 14977.1  |
| 06T | NHS North East Essex CCG                         |  443893 |  6174.2  | 437719           | 15132.4  |
| 06V | NHS North Norfolk CCG                            |  226799 |  3761.37 | 223038           |  7710.64 |
| 06W | NHS Norwich CCG                                  |  237872 |  4369.63 | 233502           |  8072.41 |
| 06Y | NHS South Norfolk CCG                            |  265067 |  5331.83 | 259735           |  8979.31 |
| 99G | NHS Southend CCG                                 |  238020 |  3841.9  | 234178           |  8095.77 |
| 07G | NHS Thurrock CCG                                 |  200344 |  3050.23 | 197294           |  6820.64 |
| 07H | NHS West Essex CCG                               |  371640 |  5731.8  | 365908           | 12649.8  |
| 07J | NHS West Norfolk CCG                             |  234389 |  3841.08 | 230548           |  7970.27 |
| 07K | NHS West Suffolk CCG                             |  292859 |  4627.57 | 288231           |  9964.45 |
| 07L | NHS Barking and Dagenham CCG                     |  262332 |  4257.15 | 258075           |  8921.91 |
| 07M | NHS Barnet CCG                                   |  457630 |  6748.92 | 450881           | 15587.4  |
| 07N | NHS Bexley CCG                                   |  293260 |  4328.55 | 288931           |  9988.65 |
| 07P | NHS Brent CCG                                    |  406569 |  6261.91 | 400307           | 13839    |
| 07Q | NHS Bromley CCG                                  |  421490 |  5550.5  | 415940           | 14379.4  |
| 07R | NHS Camden CCG                                   |  354671 |  5994.86 | 348676           | 12054.1  |
| 09A | NHS Central London (Westminster) CCG             |  267044 |  4425.66 | 262618           |  9078.98 |
| 07T | NHS City and Hackney CCG                         |  369643 |  6778.31 | 362865           | 12544.6  |
| 07V | NHS Croydon CCG                                  |  467031 |  6533.74 | 460497           | 15919.9  |
| 07W | NHS Ealing CCG                                   |  475508 |  6609.41 | 468899           | 16210.3  |
| 07X | NHS Enfield CCG                                  |  385869 |  6054.89 | 379814           | 13130.6  |
| 08A | NHS Greenwich CCG                                |  359356 |  6202.41 | 353154           | 12208.9  |
| 08C | NHS Hammersmith and Fulham CCG                   |  259170 |  4281.95 | 254888           |  8811.74 |
| 08D | NHS Haringey CCG                                 |  344095 |  5353.49 | 338742           | 11710.6  |
| 08E | NHS Harrow CCG                                   |  280748 |  4521.82 | 276226           |  9549.42 |
| 08F | NHS Havering CCG                                 |  342047 |  4689    | 337358           | 11662.8  |
| 08G | NHS Hillingdon CCG                               |  343399 |  4854.16 | 338545           | 11703.8  |
| 07Y | NHS Hounslow CCG                                 |  330098 |  4659.43 | 325439           | 11250.7  |
| 08H | NHS Islington CCG                                |  326996 |  5995.46 | 321001           | 11097.3  |
| 08J | NHS Kingston CCG                                 |  217326 |  2672.45 | 214654           |  7420.79 |
| 08K | NHS Lambeth CCG                                  |  451428 |  7035.32 | 444393           | 15363.1  |
| 08L | NHS Lewisham CCG                                 |  405174 |  6377.75 | 398796           | 13786.8  |
| 08R | NHS Merton CCG                                   |  237592 |  3487.13 | 234105           |  8093.24 |
| 08M | NHS Newham CCG                                   |  418341 |  6846.48 | 411495           | 14225.8  |
| 08N | NHS Redbridge CCG                                |  335688 |  5203.24 | 330485           | 11425.2  |
| 08P | NHS Richmond CCG                                 |  225963 |  3081.18 | 222882           |  7705.25 |
| 08Q | NHS Southwark CCG                                |  393667 |  7323.14 | 386344           | 13356.3  |
| 08T | NHS Sutton CCG                                   |  233743 |  3437.58 | 230305           |  7961.89 |
| 08V | NHS Tower Hamlets CCG                            |  353213 |  6830.4  | 346383           | 11974.8  |
| 08W | NHS Waltham Forest CCG                           |  338723 |  5076.03 | 333647           | 11534.5  |
| 08X | NHS Wandsworth CCG                               |  409092 |  6049.39 | 403043           | 13933.6  |
| 08Y | NHS West London (K&C & QPP) CCG                  |  353521 |  5785.06 | 347736           | 12021.6  |
| 09C | NHS Ashford CCG                                  |  142635 |  2346.08 | 140289           |  4849.93 |
| 10Y | NHS Aylesbury Vale CCG                           |  225169 |  3038.51 | 222130           |  7679.27 |
| 10G | NHS Bracknell and Ascot CCG                      |  153421 |  1956.62 | 151464           |  5236.28 |
| 09D | NHS Brighton and Hove CCG                        |  359388 |  5728.63 | 353659           | 12226.4  |
| 09E | NHS Canterbury and Coastal CCG                   |  256489 |  3902.74 | 252586           |  8732.16 |
| 10H | NHS Chiltern CCG                                 |  353943 |  4804.14 | 349139           | 12070.1  |
| 09G | NHS Coastal West Sussex CCG                      |  671769 |  9119.61 | 662649           | 22908.5  |
| 09H | NHS Crawley CCG                                  |  154166 |  2043.05 | 152123           |  5259.04 |
| 09J | NHS Dartford, Gravesham and Swanley CCG          |  306698 |  4857.4  | 301841           | 10434.9  |
| 09L | NHS East Surrey CCG                              |  209456 |  2894.32 | 206562           |  7141.05 |
| 09F | NHS Eastbourne, Hailsham and Seaford CCG         |  258836 |  4149.97 | 254686           |  8804.75 |
| 10K | NHS Fareham and Gosport CCG                      |  233744 |  3270.79 | 230473           |  7967.69 |
| 09N | NHS Guildford and Waverley CCG                   |  241562 |  3253.92 | 238308           |  8238.55 |
| 09P | NHS Hastings and Rother CCG                      |  269372 |  4092.26 | 265280           |  9170.99 |
| 99K | NHS High Weald Lewes Havens CCG                  |  199615 |  3813.36 | 195802           |  6769.06 |
| 09X | NHS Horsham and Mid Sussex CCG                   |  257608 |  4239.69 | 253368           |  8759.2  |
| 10L | NHS Isle of Wight CCG                            |  207027 |  3573.41 | 203454           |  7033.6  |
| 09W | NHS Medway CCG                                   |  349204 |  4652.57 | 344551           | 11911.5  |
| 10M | NHS Newbury and District CCG                     |  128530 |  1589.19 | 126941           |  4388.47 |
| 10N | NHS North and West Reading CCG                   |  123159 |  1582.02 | 121577           |  4203.04 |
| 99M | NHS North East Hampshire and Farnham CCG         |  254724 |  3417.06 | 251307           |  8687.93 |
| 10J | NHS North Hampshire CCG                          |  243438 |  3610.82 | 239827           |  8291.07 |
| 09Y | NHS North West Surrey CCG                        |  417545 |  5477.56 | 412067           | 14245.6  |
| 10Q | NHS Oxfordshire CCG                              |  729492 | 10464.5  | 719028           | 24857.5  |
| 10R | NHS Portsmouth CCG                               |  266636 |  4151.57 | 262484           |  9074.35 |
| 10T | NHS Slough CCG                                   |  171799 |  2403.3  | 169396           |  5856.18 |
| 10V | NHS South Eastern Hampshire CCG                  |  254412 |  3472.59 | 250939           |  8675.23 |
| 10A | NHS South Kent Coast CCG                         |  273420 |  3896.91 | 269523           |  9317.68 |
| 10W | NHS South Reading CCG                            |  132649 |  1819.53 | 130829           |  4522.91 |
| 10X | NHS Southampton CCG                              |  315236 |  5172.51 | 310063           | 10719.2  |
| 99H | NHS Surrey Downs CCG                             |  346003 |  4596.76 | 341406           | 11802.8  |
| 10C | NHS Surrey Heath CCG                             |  113095 |  1521.97 | 111573           |  3857.19 |
| 10D | NHS Swale CCG                                    |  138060 |  2114.91 | 135945           |  4699.76 |
| 10E | NHS Thanet CCG                                   |  205239 |  2633.91 | 202605           |  7004.26 |
| 11A | NHS West Hampshire CCG                           |  643645 |  9087.81 | 634557           | 21937.3  |
| 99J | NHS West Kent CCG                                |  540964 |  8989.71 | 531974           | 18390.9  |
| 11C | NHS Windsor, Ascot and Maidenhead CCG            |  165111 |  2141.14 | 162970           |  5634.03 |
| 11D | NHS Wokingham CCG                                |  168714 |  1872.41 | 166842           |  5767.88 |
| 11E | NHS Bath and North East Somerset CCG             |  223389 |  3402.47 | 219987           |  7605.16 |
| 11H | NHS Bristol CCG                                  |  560129 |  9457.26 | 550672           | 19037.3  |
| 11J | NHS Dorset CCG                                   | 1007441 | 16116.6  | 991324           | 34271.1  |
| 11M | NHS Gloucestershire CCG                          |  730181 | 11796.1  | 718385           | 24835.3  |
| 11N | NHS Kernow CCG                                   |  731171 | 13083.2  | 718088           | 24825    |
| 11T | NHS North Somerset CCG                           |  270796 |  4307.9  | 266488           |  9212.76 |
| 99P | NHS North, East, West Devon CCG                  | 1133470 | 19520.2  |      1.11395e+06 | 38510.4  |
| 11X | NHS Somerset CCG                                 |  693362 | 11644.9  | 681717           | 23567.6  |
| 99Q | NHS South Devon and Torbay CCG                   |  395173 |  7001.12 | 388172           | 13419.5  |
| 12A | NHS South Gloucestershire CCG                    |  279102 |  4359.65 | 274742           |  9498.12 |
| 12D | NHS Swindon CCG                                  |  257364 |  3669.92 | 253694           |  8770.46 |
| 99N | NHS Wiltshire CCG                                |  571678 |  8500.03 | 563178           | 19469.6  |
| 13T | NHS Newcastle Gateshead CCG                      |  700165 | 12281.6  | 687883           | 23780.8  |



label: E=C-D
labeled_formulas: E=C-D
output: {"Arithmetic-Relationship": ["E=C-D"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_484524___xlsx_e3c05d3fd444789b40b0530c469d188d59f3c02b.xlsx___line_669