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 |      O |      P |      Q |      R |      S |     T |     U |     V |     W |     X |
|:--------------|:---------|:----------------------|:--------------------------------|-------:|--------:|---------:|-------:|-------:|-------:|-------:|-------:|-------:|-------:|-------:|-------:|-------:|-------:|-------:|------:|------:|------:|------:|------:|
| Eastern Cape  | District | Eastern CapeDistrict  | DC10: Cacadu                    |  45969 |  8072.2 |  54041.2 |  40361 |  36272 |  38575 |  42359 |  39786 |  32411 |  31370 |  29412 |  26466 |  22845 |  18530 |  14683 | 10894 |  8999 |  5422 |  3275 |  2956 |
| Eastern Cape  | District | Eastern CapeDistrict  | DC12: Amathole                  | 104030 | 19623.6 | 123654   |  98118 |  96434 | 106473 |  76240 |  54717 |  43185 |  41923 |  40604 |  41290 |  41992 |  36517 |  31241 | 24456 | 23432 | 14262 |  9849 |  7875 |
| Eastern Cape  | District | Eastern CapeDistrict  | DC13: Chris Hani                |  94664 | 18467.2 | 113131   |  92336 |  86257 |  91126 |  66057 |  51709 |  40128 |  39100 |  36743 |  36578 |  36906 |  32155 |  27299 | 19414 | 19449 | 11510 |  7685 |  6346 |
| Eastern Cape  | District | Eastern CapeDistrict  | DC14: Joe Gqabi                 |  40967 |  7913.4 |  48880.4 |  39567 |  38758 |  40407 |  32025 |  24637 |  19771 |  18007 |  15421 |  14868 |  14393 |  13115 |  11475 |  8147 |  7114 |  5455 |  3213 |  2426 |
| Eastern Cape  | District | Eastern CapeDistrict  | DC15: O.R.Tambo                 | 181935 | 34934.6 | 216870   | 174673 | 175859 | 188498 | 129395 |  92504 |  69657 |  60864 |  51974 |  48407 |  45725 |  37456 |  31912 | 21359 | 22190 | 14802 | 10766 |  6968 |
| Eastern Cape  | District | Eastern CapeDistrict  | DC44: Alfred Nzo                | 111741 | 21505.6 | 133247   | 107528 | 108435 | 106594 |  70273 |  49925 |  37650 |  33541 |  28542 |  27623 |  26744 |  22722 |  20513 | 15018 | 12788 |  9997 |  7178 |  4532 |
| Eastern Cape  | Metro    | Eastern CapeMetro     | BUF: Buffalo City               |  77503 | 13137.6 |  90640.6 |  65688 |  56124 |  68031 |  76571 |  70425 |  58381 |  52514 |  48131 |  43962 |  39469 |  31530 |  21685 | 15825 | 13186 |  7628 |  4764 |  3781 |
| Eastern Cape  | Metro    | Eastern CapeMetro     | NMA: Nelson Mandela Bay         | 110406 | 19544.2 | 129950   |  97721 |  86143 | 100811 | 115451 | 106603 |  87405 |  82085 |  76509 |  69414 |  62732 |  50381 |  37822 | 25357 | 18793 | 12160 |  6997 |  5326 |
| Free State    | District | Free StateDistrict    | DC16: Xhariep                   |  16284 |  3037   |  19321   |  15185 |  13515 |  13792 |  13821 |  12415 |  10408 |   9292 |   8390 |   7317 |   6331 |   5607 |   4628 |  3105 |  2641 |  1727 |   945 |   855 |
| Free State    | District | Free StateDistrict    | DC18: Lejweleputswa             |  68396 | 11681.2 |  80077.2 |  58406 |  54615 |  57625 |  63861 |  57346 |  46315 |  40051 |  37747 |  37498 |  32375 |  24583 |  17193 | 11796 |  8512 |  5889 |  3015 |  2403 |
| Free State    | District | Free StateDistrict    | DC19: Thabo Mofutsanyane        |  84251 | 15729.2 |  99980.2 |  78646 |  71637 |  77058 |  72533 |  63403 |  51267 |  44071 |  39185 |  35954 |  30622 |  26502 |  20599 | 14146 | 10532 |  7459 |  4578 |  3794 |
| Free State    | District | Free StateDistrict    | DC20: Fezile Dabi               |  51617 |  8927.8 |  60544.8 |  44639 |  40903 |  43467 |  47617 |  45199 |  38389 |  33024 |  29208 |  26711 |  22931 |  19483 |  15178 | 10864 |  7870 |  5260 |  3136 |  2539 |
| Free State    | Metro    | Free StateMetro       | MAN: Mangaung                   |  75348 | 13129.2 |  88477.2 |  65646 |  59827 |  70956 |  84646 |  73305 |  59360 |  52542 |  46847 |  39511 |  33071 |  26249 |  20435 | 14190 | 10528 |  7123 |  4080 |  3766 |
| Gauteng       | District | GautengDistrict       | DC42: Sedibeng                  |  89564 | 14753   | 104317   |  73765 |  69081 |  79777 |  97956 |  90754 |  77192 |  67780 |  58754 |  52800 |  46343 |  37891 |  27974 | 18431 | 12981 |  7861 |  4263 |  3317 |
| Gauteng       | District | GautengDistrict       | DC48: West Rand                 |  78288 | 12415.4 |  90703.4 |  62077 |  57771 |  62415 |  86684 |  91426 |  76944 |  66284 |  58277 |  53384 |  43814 |  30926 |  19816 | 12710 |  9022 |  5415 |  3344 |  2396 |
| Gauteng       | Metro    | GautengMetro          | EKU: Ekurhuleni                 | 316977 | 47860.6 | 364838   | 239303 | 216183 | 238705 | 346727 | 387047 | 321232 | 264302 | 211951 | 176239 | 143422 | 111814 |  78014 | 50080 | 34423 | 20715 | 12352 |  8985 |
| Gauteng       | Metro    | GautengMetro          | JHB: City of Johannesburg       | 432722 | 63693   | 496415   | 318465 | 277624 | 315116 | 502412 | 572807 | 472034 | 377866 | 293746 | 236477 | 192933 | 151531 | 107684 | 67906 | 48797 | 31049 | 19589 | 16068 |
| Gauteng       | Metro    | GautengMetro          | TSH: City of Tshwane            | 273866 | 42378.2 | 316244   | 211891 | 191352 | 228577 | 340844 | 338813 | 277369 | 235789 | 197126 | 164191 | 136340 | 106239 |  76187 | 52501 | 37686 | 24315 | 15912 | 12490 |
| KwaZulu-Natal | District | KwaZulu-NatalDistrict | DC21: Ugu                       |  88077 | 15310.2 | 103387   |  76551 |  75875 |  82887 |  69602 |  61061 |  44346 |  38646 |  32253 |  32221 |  27574 |  23436 |  22055 | 15822 | 13386 |  8511 |  6186 |  3997 |
| KwaZulu-Natal | District | KwaZulu-NatalDistrict | DC22: UMgungundlovu             | 103802 | 18380.2 | 122182   |  91901 |  92400 | 104342 | 112396 | 101418 |  78137 |  70114 |  55616 |  48340 |  39904 |  35625 |  29669 | 18704 | 14211 |  9367 |  6760 |  5056 |
| KwaZulu-Natal | District | KwaZulu-NatalDistrict | DC23: Uthukela                  |  89609 | 15877.8 | 105487   |  79389 |  77210 |  76801 |  63491 |  56285 |  41867 |  34994 |  28937 |  27315 |  23203 |  20690 |  17785 | 10559 |  8630 |  5243 |  3794 |  3043 |
| KwaZulu-Natal | District | KwaZulu-NatalDistrict | DC27: Umkhanyakude              |  90186 | 16054.4 | 106240   |  80272 |  81472 |  81127 |  62461 |  48313 |  34508 |  28447 |  24271 |  22219 |  18843 |  14200 |  11476 |  7641 |  7741 |  5020 |  4537 |  3111 |
| KwaZulu-Natal | District | KwaZulu-NatalDistrict | DC28: Uthungulu                 | 114234 | 20036.2 | 134270   | 100181 | 101186 | 107354 |  97505 |  83623 |  59985 |  48889 |  38852 |  36482 |  31502 |  25424 |  21255 | 12737 | 11236 |  6995 |  5710 |  4369 |
| KwaZulu-Natal | District | KwaZulu-NatalDistrict | DC43: Sisonke                   |  63490 | 11312.6 |  74802.6 |  56563 |  54826 |  56593 |  44020 |  35274 |  26352 |  22658 |  19506 |  18205 |  15841 |  13725 |  11606 |  7905 |  5734 |  4067 |  3003 |  2051 |
| KwaZulu-Natal | District | KwaZulu-NatalDistrict | DC24: Umzinyathi                |  72800 | 13291.2 |  86091.2 |  66456 |  65851 |  64937 |  45266 |  35991 |  26812 |  23015 |  19698 |  19591 |  15795 |  15049 |  12914 |  8879 |  6958 |  4105 |  3608 |  3114 |
| KwaZulu-Natal | District | KwaZulu-NatalDistrict | DC25: Amajuba                   |  58621 | 11153.6 |  69774.6 |  55768 |  53985 |  57112 |  52394 |  44056 |  33145 |  27957 |  22859 |  20896 |  19263 |  17171 |  13340 |  8559 |  6514 |  3884 |  2445 |  1868 |
| KwaZulu-Natal | District | KwaZulu-NatalDistrict | DC26: Zululand                  | 112324 | 20522.8 | 132847   | 102614 | 102770 | 102252 |  79818 |  62875 |  43269 |  35304 |  29949 |  29084 |  25836 |  22492 |  17450 | 11008 | 10421 |  6629 |  5289 |  4191 |
| KwaZulu-Natal | District | KwaZulu-NatalDistrict | DC29: iLembe                    |  77018 | 12857.4 |  89875.4 |  64287 |  63520 |  67591 |  62709 |  56453 |  41643 |  35209 |  27994 |  25352 |  20914 |  17786 |  16274 | 10367 |  8157 |  4990 |  3765 |  2781 |
| KwaZulu-Natal | Metro    | KwaZulu-NatalMetro    | ETH: eThekwini                  | 327972 | 53709   | 381681   | 268545 | 269763 | 318539 | 412726 | 395581 | 299167 | 247382 | 199167 | 174931 | 145722 | 119972 |  97501 | 63492 | 44833 | 27566 | 17029 | 12473 |
| Limpopo       | District | LimpopoDistrict       | DC33: Mopani                    | 138761 | 23149.8 | 161911   | 115749 | 115006 | 129588 | 113916 |  89600 |  69610 |  61792 |  53224 |  48174 |  38722 |  31454 |  24789 | 19058 | 17407 | 10699 |  8369 |  6592 |
| Limpopo       | District | LimpopoDistrict       | DC34: Vhembe                    | 163902 | 28776.2 | 192678   | 143881 | 143810 | 159489 | 130759 |  99827 |  79930 |  70398 |  59696 |  54494 |  44753 |  35101 |  27521 | 21081 | 18216 | 16123 | 13799 | 11943 |
| Limpopo       | District | LimpopoDistrict       | DC35: Capricorn                 | 154877 | 27004.6 | 181882   | 135023 | 133401 | 147946 | 127354 | 100793 |  77094 |  68359 |  60471 |  56031 |  45172 |  39011 |  32989 | 25110 | 22055 | 14433 | 11075 | 10269 |
| Limpopo       | District | LimpopoDistrict       | DC36: Waterberg                 |  78220 | 12793.8 |  91013.8 |  63969 |  60752 |  65874 |  71146 |  67302 |  52196 |  44578 |  35960 |  33654 |  27393 |  21916 |  16844 | 12512 | 11204 |  6968 |  4913 |  3938 |
| Limpopo       | District | LimpopoDistrict       | DC47: Greater Sekhukhune        | 144404 | 25068.4 | 169472   | 125342 | 117916 | 124438 | 104390 |  84367 |  65009 |  55112 |  46373 |  43962 |  34954 |  31113 |  26804 | 23262 | 18776 | 11770 |  9739 |  9106 |
| Mpumalanga    | District | MpumalangaDistrict    | DC30: Gert Sibande              | 118795 | 21530   | 140325   | 107650 | 102981 | 108525 | 107728 |  99716 |  74466 |  64017 |  56010 |  51493 |  44395 |  35315 |  25027 | 16796 | 13022 |  7740 |  5273 |  4244 |
| Mpumalanga    | District | MpumalangaDistrict    | DC31: Nkangala                  | 140505 | 23830   | 164335   | 119150 | 113132 | 124098 | 136115 | 131404 | 102176 |  88764 |  76174 |  69396 |  58520 |  47828 |  35447 | 23668 | 17504 | 10280 |  7390 |  6577 |
| Mpumalanga    | District | MpumalangaDistrict    | DC32: Ehlanzeni                 | 202259 | 35194.2 | 237453   | 175971 | 180235 | 191655 | 183698 | 161976 | 120921 | 103126 |  84654 |  72949 |  53765 |  46218 |  33968 | 23752 | 21237 | 13194 | 10887 |  8150 |
| North West    | District | North WestDistrict    | DC37: Bojanala                  | 166076 | 24731.8 | 190808   | 123659 | 108618 | 122148 | 156882 | 162994 | 135236 | 111484 |  92693 |  83986 |  70396 |  54774 |  38796 | 28655 | 20574 | 13881 |  8916 |  7740 |
| North West    | District | North WestDistrict    | DC38: Ngaka Modiri Molema       | 103088 | 17974   | 121062   |  89870 |  87615 |  85908 |  78070 |  66643 |  54741 |  50808 |  45634 |  41246 |  36460 |  29944 |  22713 | 17828 | 13052 |  8459 |  5509 |  5110 |
| North West    | District | North WestDistrict    | DC39: Dr Ruth Segomotsi Mompati |  60194 | 10929   |  71123   |  54645 |  48291 |  47856 |  39249 |  34284 |  28636 |  26301 |  22836 |  21906 |  19581 |  16851 |  13324 | 10715 |  7606 |  5261 |  3242 |  3037 |
| North West    | District | North WestDistrict    | DC40: Dr Kenneth Kaunda         |  74990 | 12826   |  87816   |  64130 |  59190 |  60620 |  69190 |  63740 |  53069 |  48146 |  43764 |  39981 |  34130 |  27008 |  19705 | 14493 | 10479 |  6615 |  3816 |  2868 |
| Northern Cape | District | Northern CapeDistrict | DC6: Namakwa                    |   9746 |  1957.8 |  11703.8 |   9789 |  10346 |  10190 |   8910 |   8816 |   7896 |   8038 |   8245 |   7770 |   6622 |   5668 |   4443 |  3557 |  2483 |  1550 |   945 |   828 |
| Northern Cape | District | Northern CapeDistrict | DC7: Pixley ka Seme             |  20198 |  3960.6 |  24158.6 |  19803 |  18851 |  17158 |  15514 |  14984 |  12674 |  11543 |  11251 |  10341 |   9019 |   7710 |   6017 |  4275 |  3001 |  1952 |  1025 |  1036 |
| Northern Cape | District | Northern CapeDistrict | DC8: Siyanda                    |  23304 |  4413.8 |  27717.8 |  22069 |  21939 |  22437 |  23934 |  22264 |  18937 |  16294 |  14780 |  12956 |  10877 |   8370 |   6468 |  4378 |  3347 |  2213 |  1091 |  1126 |
| Northern Cape | District | Northern CapeDistrict | DC9: Frances Baard              |  40979 |  7379.4 |  48358.4 |  36897 |  35127 |  35836 |  35848 |  34702 |  29721 |  25522 |  22722 |  20257 |  17959 |  14323 |  11033 |  7721 |  5673 |  3796 |  2191 |  1780 |
| Northern Cape | District | Northern CapeDistrict | DC45: John Taolo Gaetsewe       |  27691 |  5089.8 |  32780.8 |  25449 |  23185 |  22056 |  20425 |  19607 |  16769 |  13826 |  11426 |  10495 |   9503 |   7905 |   5660 |  3861 |  2739 |  1962 |  1234 |  1005 |
| Western Cape  | District | Western CapeDistrict  | DC1: West Coast                 |  36668 |  6372   |  43040   |  31860 |  31196 |  32431 |  37729 |  36832 |  29556 |  28855 |  28582 |  24805 |  20878 |  16298 |  12513 |  8944 |  6413 |  4158 |  2336 |  1714 |
| Western Cape  | District | Western CapeDistrict  | DC2: Cape Winelands             |  74012 | 12850.4 |  86862.4 |  64252 |  65212 |  72747 |  84093 |  74211 |  58571 |  56719 |  55901 |  48551 |  39824 |  30403 |  22579 | 15097 | 10861 |  7001 |  4161 |  3296 |
| Western Cape  | District | Western CapeDistrict  | DC3: Overberg                   |  22803 |  3939.2 |  26742.2 |  19696 |  19632 |  19863 |  22349 |  25324 |  20041 |  19053 |  18160 |  15756 |  13314 |  10674 |   9982 |  7935 |  6013 |  3757 |  2181 |  1642 |
| Western Cape  | District | Western CapeDistrict  | DC4: Eden                       |  53344 |  9579.4 |  62923.4 |  47897 |  47223 |  47552 |  48218 |  50139 |  42029 |  41617 |  40187 |  35230 |  29923 |  24726 |  21322 | 16455 | 12526 |  7844 |  4559 |  3473 |
| Western Cape  | District | Western CapeDistrict  | DC5: Central Karoo              |   7678 |  1406   |   9084   |   7030 |   6975 |   6159 |   5672 |   5343 |   4740 |   4773 |   4786 |   4278 |   3811 |   3047 |   2344 |  1637 |  1243 |   750 |   405 |   341 |
| Western Cape  | Metro    | Western CapeMetro     | CPT: City of Cape Town          | 370296 | 57885.4 | 428181   | 289427 | 268606 | 301370 | 385489 | 400698 | 326664 | 285622 | 247421 | 219245 | 184935 | 142949 | 109817 | 75143 | 56137 | 36430 | 22794 | 16983 |



label: G=F+E
labeled_formulas: G=F+E
output: {"Arithmetic-Relationship": ["G=F+E"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_167490___xlsx_482595f25e9ca4f0600682ef4276bebcb097eae8.xlsx___line_292