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 |
|:-----------------------------|---------:|-----:|----:|----------:|-----:|
| Amber Valley                 |  2137000 |   73 |   0 |   9864488 |   73 |
| Ashfield                     |  1085500 |   29 |   0 |   4366057 |   29 |
| Birmingham                   |  8107697 |  232 |  86 |  38542084 |  318 |
| Blaby                        |  2959000 |   63 |   8 |  12341240 |   71 |
| Boston                       |  3621000 |  117 |  32 |  19624796 |  149 |
| Bromsgrove                   |  1387994 |   36 |   6 |   6121333 |   42 |
| Cannock Chase                |    49392 |    1 |   0 |    207999 |    1 |
| Charnwood                    |        0 |    0 | 112 |  10317739 |  112 |
| Coventry                     |  4315814 |  136 |  24 |  22087234 |  160 |
| Derby                        |        0 |    0 |  65 |   6926652 |   65 |
| Derbyshire Dales             |  2607600 |   61 |  33 |  13060229 |   94 |
| Dudley                       |  9225000 |  232 |   6 |  31312113 |  238 |
| East Lindsey                 |  2268654 |   66 |   0 |   8657836 |   66 |
| East Staffordshire           |  1235000 |   30 |   0 |   4203975 |   30 |
| Erewash                      |  3605000 |  101 |   0 |  13909377 |  101 |
| Harborough                   |   425000 |   12 |  30 |   5199822 |   42 |
| Herefordshire, County of     |  3468820 |  124 |  10 |  21108678 |  134 |
| High Peak                    |  1537302 |   60 |   0 |   8525734 |   60 |
| Hinckley and Bosworth        |  7168750 |  172 |  32 |  29715995 |  204 |
| Leicester                    |        0 |    0 |   9 |   1359264 |    9 |
| Lichfield                    |  4835053 |  131 |  87 |  30647612 |  218 |
| Lincoln                      |   248500 |    7 |   0 |    904783 |    7 |
| Malvern Hills                |  7737950 |  239 |  28 |  45016735 |  267 |
| Mansfield                    |   126000 |    6 |  10 |   1711164 |   16 |
| Melton                       |   180000 |    6 |  17 |   2330164 |   23 |
| Newark and Sherwood          |  5903636 |  140 |   2 |  19297931 |  142 |
| Newcastle-under-Lyme         |  3440500 |   87 |   0 |  11422485 |   87 |
| North Kesteven               |  4194000 |  115 |  35 |  18253333 |  150 |
| North Warwickshire           |  1755500 |   54 |   9 |   9160577 |   63 |
| North West Leicestershire    |  2100000 |   53 |  35 |  11569311 |   88 |
| Nottingham                   |  2526280 |  107 |   0 |  12919685 |  107 |
| Nuneaton and Bedworth        |   120000 |    4 | 109 |   9553283 |  113 |
| Oadby and Wigston            |    93000 |    3 |   0 |    613958 |    3 |
| Rugby                        |  1804000 |   58 |  20 |  10837843 |   78 |
| Rushcliffe                   |   834000 |   25 | 241 |  29321805 |  266 |
| Rutland                      |        0 |    0 |  16 |   1954698 |   16 |
| Sandwell                     | 11071000 |  284 |   0 |  43918087 |  284 |
| Shropshire                   | 12783953 |  300 |  14 |  44541643 |  314 |
| Solihull                     |  4202680 |  111 |  24 |  22078271 |  135 |
| South Derbyshire             |  2898000 |   76 |   6 |  11069920 |   82 |
| South Holland                |   627000 |   19 |   3 |   2980034 |   22 |
| South Kesteven               |   540000 |   46 |   3 |   6196163 |   49 |
| South Staffordshire          |  2170020 |   69 |  50 |  15689237 |  119 |
| Stafford                     |  7941000 |  216 |  31 |  30622758 |  247 |
| Staffordshire Moorlands      |  3834000 |   71 |   0 |  10905235 |   71 |
| Stoke-on-Trent               |  5229250 |  122 |   5 |  17776798 |  127 |
| Stratford-on-Avon            |  4988000 |  123 |  25 |  28234836 |  148 |
| Tamworth                     |        0 |    0 |  19 |   2487073 |   19 |
| Telford and Wrekin           | 13989903 |  310 |  39 |  51293277 |  349 |
| Walsall                      |  2520000 |   79 |  23 |  11876728 |  102 |
| Warwick                      |  3130300 |  104 |  60 |  27263127 |  164 |
| West Lindsey                 |  3370000 |   89 |   0 |  12161907 |   89 |
| Wolverhampton                |  3959000 |   91 |  42 |  13550456 |  133 |
| Worcester                    |  2441700 |   68 |   2 |  10319722 |   70 |
| Wychavon                     |  3624670 |  114 |  95 |  30441056 |  209 |
| Wyre Forest                  |  4894000 |  154 |   0 |  22784791 |  154 |
| Barnsley                     |  3215204 |   80 |  45 |  12734299 |  125 |
| Bassetlaw                    |  1526000 |   39 |   0 |   5137991 |   39 |
| Bolsover                     |  1449366 |   43 |   0 |   5497900 |   43 |
| Bradford                     |  6758994 |  190 |  34 |  25926114 |  224 |
| Calderdale                   |  7147900 |  152 |   0 |  24631539 |  152 |
| County Durham                | 28923308 |  870 |  71 | 113926005 |  941 |
| Craven                       |  5380844 |  153 |  12 |  23793295 |  165 |
| Darlington                   |  4588336 |  143 |   8 |  19723807 |  151 |
| Doncaster                    | 13873250 |  377 |   1 |  49954705 |  378 |
| East Riding of Yorkshire     |   520000 |   15 |  64 |   7114946 |   79 |
| Gateshead                    |  7550140 |  188 |   0 |  27476674 |  188 |
| Hambleton                    |  5085000 |  152 |  41 |  23230690 |  193 |
| Harrogate                    |  3013000 |   85 | 158 |  29605199 |  243 |
| Hartlepool                   |  2238803 |   75 |   0 |   7043061 |   75 |
| Kingston upon Hull, city of  |  7629500 |  155 |  20 |  22615184 |  175 |
| Kirklees                     |  4308750 |   94 |   0 |  12976643 |   94 |
| Leeds                        |  7238970 |  203 |   9 |  29195491 |  212 |
| Middlesbrough                |  8055000 |  202 |   8 |  24087352 |  210 |
| Newcastle upon Tyne          | 14449301 |  528 |  71 |  69026153 |  599 |
| North East Derbyshire        |  1378000 |   38 |   4 |   6075124 |   42 |
| North East Lincolnshire      |  5718750 |  150 |  19 |  20980526 |  169 |
| North Lincolnshire           |  3602000 |   92 |   2 |  11815219 |   94 |
| North Tyneside               |  2571000 |   93 |  66 |  17638532 |  159 |
| Northumberland               |  6705000 |  184 |  99 |  36660294 |  283 |
| Redcar and Cleveland         |  6452000 |  169 |  45 |  26624827 |  214 |
| Richmondshire                |  2266000 |   78 |  20 |  12569774 |   98 |
| Rotherham                    |  6885000 |  230 |   0 |  26572130 |  230 |
| Ryedale                      |  2363400 |   62 |   0 |   8349939 |   62 |
| Scarborough                  |  9682000 |  222 |   0 |  31093948 |  222 |
| Selby                        |  1364000 |   41 |  41 |   8150419 |   82 |
| Sheffield                    |    96000 |    2 |   0 |    365925 |    2 |
| South Tyneside               |  2504000 |   66 |   4 |  11190321 |   70 |
| Stockton-on-Tees             |  6512360 |  142 |  70 |  23840605 |  212 |
| Sunderland                   |  8237000 |  278 |  34 |  37870457 |  312 |
| Wakefield                    | 12570000 |  376 |  30 |  48906843 |  406 |
| York                         |  3724715 |   78 |   0 |  17038104 |   78 |
| Allerdale                    |  1110000 |   26 |  32 |   7313088 |   58 |
| Blackburn with Darwen        |   975000 |   25 |   0 |   3757881 |   25 |
| Blackpool                    |  1716000 |   44 |   0 |   5885640 |   44 |
| Bolton                       |  1740000 |   57 |  14 |   8777248 |   71 |
| Burnley                      |  1283000 |   43 |   0 |   4169261 |   43 |
| Bury                         |   646000 |   24 |   0 |   3063064 |   24 |
| Carlisle                     |  3126000 |   91 |   2 |  10704931 |   93 |
| Cheshire East                | 12907000 |  361 |  88 |  65360010 |  449 |
| Cheshire West and Chester    | 10657200 |  313 |  54 |  55390740 |  367 |
| Chorley                      |   972000 |   22 | 102 |   9513619 |  124 |
| Copeland                     |  1192000 |   36 |   0 |   4943926 |   36 |
| Eden                         |   680000 |   22 |   0 |   3137473 |   22 |
| Fylde                        |  1454000 |   42 | 163 |  19575201 |  205 |
| Halton                       |  8489857 |  228 |  11 |  33597343 |  239 |
| Hyndburn                     |   525000 |   15 |   0 |   2021185 |   15 |
| Knowsley                     | 14613947 |  401 |   0 |  57101370 |  401 |
| Lancaster                    |   624000 |   16 |  52 |   6708026 |   68 |
| Liverpool                    | 31335723 |  866 |   6 | 122074160 |  872 |
| Manchester                   | 38835437 | 1092 |  22 | 164470318 | 1114 |
| Oldham                       |  7610000 |  216 |  18 |  30115834 |  234 |
| Pendle                       |  1481000 |   45 |   0 |   5716602 |   45 |
| Preston                      |  8057000 |  190 | 189 |  40635172 |  379 |
| Ribble Valley                |   110000 |    5 |  27 |   2940025 |   32 |
| Rochdale                     | 14771465 |  308 |   0 |  46054021 |  308 |
| Rossendale                   |  1200000 |   30 |   6 |   4611959 |   36 |
| Salford                      | 10094044 |  329 |  72 |  54781675 |  401 |
| Sefton                       |  7376142 |  245 |  13 |  35281770 |  258 |
| South Lakeland               |  7128540 |  165 |  95 |  36648843 |  260 |
| South Ribble                 |   935000 |   34 |  24 |   7904448 |   58 |
| St. Helens                   | 20077686 |  526 |  12 |  63958877 |  538 |
| Stockport                    |  8398448 |  269 |  53 |  45945713 |  322 |
| Tameside                     |  5687916 |  192 |   0 |  24527941 |  192 |
| Trafford                     |  3436500 |  139 |  12 |  21144519 |  151 |
| Warrington                   |  5250000 |  175 |  33 |  29010441 |  208 |
| West Lancashire              |  1830000 |   50 |   5 |   8810210 |   55 |
| Wigan                        |  9681000 |  305 |  25 |  38064625 |  330 |
| Wirral                       | 15983352 |  445 |   0 |  64217391 |  445 |
| Wyre                         |  4310000 |   72 |  77 |  20689329 |  149 |
| Adur                         |  1500000 |   50 |  32 |  22935370 |   82 |
| Arun                         |   897900 |   62 | 160 |  39861257 |  222 |
| Ashford                      |  2005000 |   55 | 204 |  49310571 |  259 |
| Aylesbury Vale               |  6275000 |  186 | 163 |  65808583 |  349 |
| Babergh                      |   887914 |   21 |  29 |   6919792 |   50 |
| Basildon                     |  2223875 |   98 |  29 |  26638111 |  127 |
| Bedford                      |   670000 |   19 | 206 |  33378544 |  225 |
| Braintree                    |  3451616 |   85 |  83 |  33066421 |  168 |
| Breckland                    |  1753557 |   69 |  72 |  16780118 |  141 |
| Brentwood                    |        0 |    0 |  34 |   6520691 |   34 |
| Brighton and Hove            |  2547440 |   77 |  28 |  22010415 |  105 |
| Broadland                    |   168000 |    8 |  97 |  10235738 |  105 |
| Broxbourne                   |  6860000 |  145 |  80 |  59091364 |  225 |
| Cambridge                    |   775570 |   37 | 171 |  35917687 |  208 |
| Canterbury                   |  1055758 |   35 |  71 |  23896922 |  106 |
| Castle Point                 |        0 |    0 |  11 |   1454516 |   11 |
| Central Bedfordshire         |  6243500 |  212 | 398 | 120623510 |  610 |
| Chelmsford                   |  1850000 |  115 | 305 |  76461037 |  420 |
| Chichester                   |   960000 |   32 | 225 |  50289147 |  257 |
| Chiltern                     |   823000 |   29 |   0 |   6421164 |   29 |
| Colchester                   |        0 |    0 | 138 |  19222245 |  138 |
| Corby                        |  3580935 |  117 |   0 |  18123678 |  117 |
| Crawley                      |   715000 |   25 |   0 |   5203560 |   25 |
| Dacorum                      |  1125000 |   30 | 132 |  23946961 |  162 |
| Dartford                     |   170000 |    6 | 468 |  97509231 |  474 |
| Daventry                     |    77000 |    2 |  99 |  11227694 |  101 |
| Dover                        |        0 |    0 | 107 |  16336179 |  107 |
| East Cambridgeshire          |  2677051 |   69 |  24 |  17024254 |   93 |
| East Hertfordshire           |  4883002 |  111 | 201 |  68115945 |  312 |
| East Northamptonshire        |  1332000 |   37 |   4 |   6440983 |   41 |
| Eastbourne                   |   375000 |   15 |   0 |   4906804 |   15 |
| Elmbridge                    |  1040000 |   28 |  61 |  24120911 |   89 |
| Epping Forest                |   900000 |   20 |   9 |   8176905 |   29 |
| Epsom and Ewell              |  1050000 |   33 |  36 |  19981781 |   69 |
| Fenland                      |   560000 |   14 |  37 |   6165436 |   51 |
| Forest Heath                 |   112500 |    5 |  42 |   6102219 |   47 |
| Gravesham                    |  1380000 |   46 |  71 |  30467978 |  117 |
| Great Yarmouth               |        0 |    0 |  22 |   2285916 |   22 |
| Guildford                    |    88000 |    1 |  48 |  11565492 |   49 |
| Harlow                       |        0 |    0 |  19 |   3689378 |   19 |
| Hastings                     |   480000 |   16 |   0 |   3201679 |   16 |
| Hertsmere                    |   550000 |   21 |  39 |  13855709 |   60 |
| Horsham                      |  1914835 |   60 | 414 |  87839321 |  474 |
| Huntingdonshire              |    75000 |    3 |  89 |  13232808 |   92 |
| Ipswich                      |   990000 |   22 |   0 |   4138446 |   22 |
| Kettering                    |        0 |    0 |  38 |   4130869 |   38 |
| King's Lynn and West Norfolk |    65000 |    4 |  24 |   2461652 |   28 |
| Lewes                        |  2782085 |  117 |  15 |  33203077 |  132 |
| Luton                        |  8042000 |  224 |  76 |  47029087 |  300 |
| Maidstone                    |  2710000 |   78 | 348 |  84009968 |  426 |
| Maldon                       |        0 |    0 |  69 |  11603854 |   69 |
| Medway                       |  2830000 |   91 | 219 |  74528423 |  310 |
| Mid Suffolk                  |   195500 |    5 |   0 |    834457 |    5 |
| Mid Sussex                   |  1710000 |   51 | 171 |  46020659 |  222 |
| Milton Keynes                |  4248000 |  114 | 542 |  97501426 |  656 |
| Mole Valley                  |        0 |    0 |  36 |   9406808 |   36 |
| North Hertfordshire          |  3245000 |   93 |  26 |  23139995 |  119 |
| North Norfolk                |  1698000 |   60 |  48 |  14084527 |  108 |
| Northampton                  |  2849000 |   81 |  62 |  20870408 |  143 |
| Norwich                      |  1440000 |   48 |   0 |   8306606 |   48 |
| Peterborough                 |  3555000 |  143 |  99 |  33194654 |  242 |
| Reigate and Banstead         |        0 |    0 |  55 |  11627837 |   55 |
| Rochford                     |  2616400 |   61 | 131 |  37314056 |  192 |
| Rother                       |  1500000 |   44 |  10 |  13280593 |   54 |
| Runnymede                    |        0 |    0 |  82 |  15696376 |   82 |
| Sevenoaks                    |  1198950 |   35 |  66 |  21057661 |  101 |
| Folkestone and Hythe         |        0 |    0 |  47 |   6568669 |   47 |
| South Bucks                  |        0 |    0 |  65 |  12759726 |   65 |
| South Cambridgeshire         |   602000 |   19 | 219 |  41663894 |  238 |
| South Norfolk                |   377000 |   14 | 145 |  16262734 |  159 |
| South Northamptonshire       |        0 |    0 | 365 |  65404576 |  365 |
| Southend-on-Sea              |  2630000 |   91 |  67 |  29183435 |  158 |
| Spelthorne                   |        0 |    0 |  25 |   6001852 |   25 |
| St Albans                    |   795000 |   27 |  47 |  15893721 |   74 |
| St Edmundsbury               |  3745560 |  102 |  38 |  21962569 |  140 |
| Stevenage                    |  6055000 |  200 | 178 |  81125410 |  378 |
| Suffolk Coastal              |   102000 |    4 |  48 |   5303967 |   52 |
| Surrey Heath                 |   400000 |   16 |  67 |  17417495 |   83 |
| Swale                        |  7100000 |  197 |  60 |  50153590 |  257 |
| Tandridge                    |  2237328 |   60 |  79 |  35206796 |  139 |
| Tendring                     |  1604373 |   41 |  14 |   9768827 |   55 |
| Thanet                       |   860350 |   22 |  24 |   8786513 |   46 |
| Three Rivers                 |   288000 |    8 |   0 |   1895187 |    8 |
| Thurrock                     |        0 |    0 | 179 |  29951477 |  179 |
| Tonbridge and Malling        |  1706835 |   43 | 163 |  39820668 |  206 |
| Tunbridge Wells              |  1187500 |   35 | 113 |  31218644 |  148 |
| Uttlesford                   |   925000 |   36 | 374 |  78387233 |  410 |
| Watford                      |  6050820 |  165 |  43 |  53361890 |  208 |
| Waveney                      |  1977438 |   65 |   6 |  10986209 |   71 |
| Waverley                     |   246000 |    6 | 104 |  27856793 |  110 |
| Wealden                      |  2995400 |   85 | 156 |  45557388 |  241 |
| Wellingborough               |  4289000 |  133 |   0 |  20584820 |  133 |
| Welwyn Hatfield              |   600000 |   20 | 429 | 113432227 |  449 |
| Worthing                     |  1050000 |   28 | 109 |  26990978 |  137 |
| Wycombe                      |  2125602 |   75 |  55 |  32838241 |  130 |
| Basingstoke and Deane        |  3859600 |  139 | 167 |  53845394 |  306 |
| Bath and North East Somerset |   932611 |   30 |  18 |   7364653 |   48 |
| Bournemouth                  |   264000 |   11 |   0 |   1944026 |   11 |
| Bracknell Forest             |   390000 |   10 |  90 |  20671530 |  100 |
| Bristol, City of             | 10316096 |  320 | 107 |  91988774 |  427 |
| Cheltenham                   |   105000 |    7 |  69 |  11740452 |   76 |
| Cherwell                     |  1602430 |   40 | 301 |  45862607 |  341 |
| Christchurch                 |  1580000 |   50 |  27 |  16167597 |   77 |
| Cornwall                     | 11122879 |  306 |  47 |  55007681 |  353 |
| Cotswold                     |   560000 |   14 | 202 |  30727012 |  216 |
| East Devon                   |   400000 |    8 |  44 |   5359045 |   52 |
| East Dorset                  |        0 |    0 |  48 |   5990786 |   48 |
| East Hampshire               |   510000 |   22 | 217 |  37345208 |  239 |
| Eastleigh                    |  4836000 |  121 | 138 |  56181199 |  259 |
| Exeter                       |  1800000 |   57 |  42 |  10700790 |   99 |
| Fareham                      |        0 |    0 |  45 |   6493203 |   45 |
| Forest of Dean               |   312000 |   12 |  22 |   3662236 |   34 |
| Gloucester                   |  3061946 |  103 |   0 |  13720805 |  103 |
| Gosport                      |   700000 |   14 |   0 |   3216189 |   14 |
| Hart                         |   576000 |   16 | 112 |  23482621 |  128 |
| Havant                       |  5020000 |  114 |  35 |  25564056 |  149 |
| Isle of Wight                |  6546057 |  168 |   0 |  28478480 |  168 |
| Mendip                       |  3570020 |   79 |   6 |  14373909 |   85 |
| Mid Devon                    |  1120000 |   28 |   0 |   4591000 |   28 |
| New Forest                   |  2123250 |   70 |  12 |  15694788 |   82 |
| North Devon                  |        0 |    0 |  31 |   2176746 |   31 |
| North Dorset                 |        0 |    0 |   9 |   1422584 |    9 |
| North Somerset               |   806299 |   40 |  18 |   9876898 |   58 |
| Oxford                       | 15641107 |  369 |   0 | 112515415 |  369 |
| Plymouth                     |  5757861 |  161 |  27 |  33319970 |  188 |
| Poole                        |  2380000 |   85 |   0 |  26296838 |   85 |
| Portsmouth                   |   410000 |   16 |  70 |  11980406 |   86 |
| Purbeck                      |        0 |    0 |  15 |   2146487 |   15 |
| Reading                      |  1260216 |   33 | 141 |  30665573 |  174 |
| Rushmoor                     |   488087 |   17 |  60 |  12224250 |   77 |
| Sedgemoor                    |   182000 |    5 |  16 |   1700693 |   21 |
| Slough                       |        0 |    0 |  10 |   2449915 |   10 |
| South Gloucestershire        |  4571842 |  159 |  55 |  31431638 |  214 |
| South Hams                   |        0 |    0 |  55 |   6094776 |   55 |
| South Oxfordshire            |  2386050 |   89 | 237 |  62380649 |  326 |
| South Somerset               |  3283496 |  120 |   9 |  22344411 |  129 |
| Southampton                  |  1720000 |   49 |  20 |  13673454 |   69 |
| Stroud                       |   970000 |   20 |  20 |   6028143 |   40 |
| Swindon                      |  1500000 |   50 |  32 |  17586236 |   82 |
| Taunton Deane                |  2160000 |   52 |   8 |  14055557 |   60 |
| Teignbridge                  |   270000 |    6 |  12 |   2142790 |   18 |
| Test Valley                  |        0 |    0 | 253 |  38452630 |  253 |
| Tewkesbury                   |   558000 |   15 | 257 |  35571141 |  272 |
| Torbay                       |  1680000 |   42 |   0 |   7246838 |   42 |
| Torridge                     |   790000 |   13 |  34 |   5048333 |   47 |
| Vale of White Horse          |        0 |    0 | 228 |  34676881 |  228 |
| West Berkshire               |   140000 |    4 | 114 |  20166034 |  118 |
| West Dorset                  |  6672812 |  192 |  55 |  45032568 |  247 |
| West Oxfordshire             |  1142033 |   36 |  79 |  20334536 |  115 |
| West Somerset                |   438000 |   12 |   0 |   1851778 |   12 |
| Weymouth and Portland        |  1600000 |   43 |  39 |  15677497 |   82 |
| Wiltshire                    |  8921510 |  264 | 445 | 110404723 |  709 |
| Winchester                   |   696940 |   21 | 161 |  38006593 |  182 |
| Windsor and Maidenhead       |  1460000 |   37 |  19 |  15353769 |   56 |
| Wokingham                    |  1121791 |   38 | 189 |  61158566 |  227 |



label: F=C+D
labeled_formulas: F=C+D
output: {"Arithmetic-Relationship": ["F=C+D"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_153250___xlsx_68d77a02ff1b25b23d720a8100fc1e2570331b81.xlsx___line_359