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:
| B                                                     |        C |        D | E                      |       F |
|:------------------------------------------------------|---------:|---------:|:-----------------------|--------:|
| EUROPE                                                | 21486270 | 22161107 | 3.140782462474867E-2   |  674837 |
| - EUROPEAN UNION 27 countries                         | 18595985 | 18768153 | 9.2583425938448372E-3  |  172168 |
| - EUROPEAN UNION 15 countries                         | 14629947 | 14730310 | 6.860106875301808E-3   |  100363 |
| Double Counts Austria / Germany                       |        0 |        0 |                        |       0 |
| Double Counts Austria / Japan                         |        0 |        0 |                        |       0 |
| Double Counts Belgium / Germany                       |        0 |        0 |                        |       0 |
| Double Counts Italy / Germany                         |        0 |        0 |                        |       0 |
| Double Counts Portugal / World                        |    -8505 |   -11643 | 0.36895943562610234    |   -3138 |
| AUSTRIA                                               |   109730 |    99880 | -8.9765788754214926E-2 |   -9850 |
| BELGIUM                                               |   399427 |   379140 | -5.0790257043214382E-2 |  -20287 |
| FINLAND                                               |    48000 |    91598 | 0.90829166666666672    |   43598 |
| FRANCE *** AS OF 2011,  CARS AND LCV ONLY             |  2090279 |  2227000 | 6.5408014910928181E-2  |  136721 |
| GERMANY *** AS OF 2016, CARS ONLY                     |  5746808 |  5645581 | -1.7614473982774492E-2 | -101227 |
| ITALY                                                 |  1103305 |  1142210 | 3.5262234830803818E-2  |   38905 |
| NETHERLANDS *** AS OF 2013,  FIGURES ONCE A YEAR ONLY |    89889 |   157280 | 0.7497135355827742     |   67391 |
| PORTUGAL                                              |   143096 |   175544 | 0.2267568625258567     |   32448 |
| SPAIN                                                 |  2885922 |  2848335 | -1.3024260530949849E-2 |  -37587 |
| SWEDEN *** AS OF 2011, CARS ONLY                      |   205374 |   226000 | 0.10043140806528572    |   20626 |
| UNITED KINGDOM                                        |  1816622 |  1749385 | -3.7012102682891679E-2 |  -67237 |
| - EUROPEAN UNION New Members                          |  3966038 |  4037843 | 1.810497024990676E-2   |   71805 |
| Double Counts East Europe / World                     |  -125200 |  -123010 | -1.7492012779552701E-2 |    2190 |
| CZECH REPUBLIC                                        |  1349896 |  1419993 | 5.192770406016467E-2   |   70097 |
| HUNGARY                                               |   526500 |   505400 | -4.0075973409306798E-2 |  -21100 |
| POLAND                                                |   681834 |   689729 | 1.157906469903236E-2   |    7895 |
| ROMANIA                                               |   359306 |   359250 | -1.5585601131073989E-4 |     -56 |
| SLOVAKIA                                              |  1040000 |  1001520 | -3.7000000000000033E-2 |  -38480 |
| SLOVENIA                                              |   133702 |   189852 | 0.41996380009274348    |   56150 |
| - OTHER EUROPE                                        |  1404358 |  1697223 | 0.20854013008079142    |  292865 |
| SERBIA                                                |    80320 |    79912 | -5.0796812749004383E-3 |    -408 |
| CIS                                                   |  1324038 |  1617311 | 0.22149892978902419    |  293273 |
| Double Counts CIS / World                             |  -101090 |  -116270 | 0.1501632208922743     |  -15180 |
| Double Counts Ukraine / World                         |        0 |        0 |                        |       0 |
| RUSSIA                                                |  1303544 |  1551293 | 0.19005802642641911    |  247749 |
| AZERBAIDJAN                                           |      247 |        0 | -1                     |    -247 |
| BELARUS                                               |    17270 |    13428 | -0.22246670526925305   |   -3842 |
| KAZAKHSTAN                                            |    10651 |    19071 | 0.79053609989672324    |    8420 |
| UKRAINE                                               |     5264 |     9542 | 0.81268996960486328    |    4278 |
| UZBEKISTAN                                            |    88152 |   140247 | 0.59096787367274706    |   52095 |
| TURKEY                                                |  1485927 |  1695731 | 0.14119401558757594    |  209804 |
| AMERICA                                               | 20821670 | 20669537 | -7.3064744566597728E-3 | -152133 |
| - NAFTA                                               | 18151322 | 17458189 | -3.8186364607492473E-2 | -693133 |
| CANADA                                                |  2370656 |  2199789 | -7.2075830487426273E-2 | -170867 |
| MEXICO                                                |  3600365 |  4068415 | 0.13000070826152355    |  468050 |
| USA                                                   | 12180301 | 11189985 | -8.1304723093460485E-2 | -990316 |
| - SOUTH AMERICA                                       |  2670348 |  3211348 | 0.20259531716465418    |  541000 |
| Double counts South America / World                   |   -43370 |   -39950 | -7.8856352317269951E-2 |    3420 |
| ARGENTINA *** AS OF 2016, CARS AND LCV ONLY           |   472776 |   472158 | -1.3071729529418041E-3 |    -618 |
| BRAZIL                                                |  2156356 |  2699672 | 0.25196025146126155    |  543316 |
| CHILE                                                 |        0 |        0 |                        |       0 |
| COLOMBIA                                              |    79036 |    74994 | -5.1141252087656297E-2 |   -4042 |
| ECUADOR                                               |     2700 |     2700 | 0                      |       0 |
| PERU                                                  |        0 |        0 |                        |       0 |
| URUGUAY                                               |        0 |        0 |                        |       0 |
| VENEZUELA                                             |     2850 |     1774 | -0.37754385964912285   |   -1076 |
| ASIA-OCEANIA                                          | 51846421 | 53540607 | 3.267700966282705E-2   | 1694186 |
| Double Counts Asia / World                            |  -213830 |  -221410 | 3.5448720946546386E-2  |   -7580 |
| AUSTRALIA                                             |   161294 |    98632 | -0.38849554230163552   |  -62662 |
| BANGLADESH                                            |      580 |      580 | 0                      |       0 |
| CHINA                                                 | 28118794 | 29015434 | 3.1887569573574082E-2  |  896640 |
| INDIA                                                 |  4519341 |  4782896 | 5.8317130749815149E-2  |  263555 |
| INDONESIA                                             |  1177797 |  1216615 | 3.2958141343542247E-2  |   38818 |
| IRAN                                                  |  1282172 |  1515396 | 0.181897592522688      |  233224 |
| JAPAN                                                 |  9204813 |  9693746 | 5.3117102976453667E-2  |  488933 |
| MALAYSIA                                              |   545333 |   460140 | -0.15622197813079353   |  -85193 |
| PAKISTAN                                              |   214650 |   230250 | 7.267645003494061E-2   |   15600 |
| PHILIPPINES                                           |   116868 |   116868 | 0                      |       0 |
| SOUTH KOREA                                           |  4228509 |  4114913 | -2.686431553060431E-2  | -113596 |
| TAIWAN                                                |   309522 |   291563 | -5.8021723819308479E-2 |  -17959 |
| THAILAND                                              |  1944417 |  1988823 | 2.2837693766306399E-2  |   44406 |
| VIETNAM                                               |   236161 |   236161 | 0                      |       0 |
| AFRICA                                                |   903568 |   931283 | 3.0672843659802052E-2  |   27715 |
| Double Counts Egypt / World                           |        0 |        0 |                        |       0 |
| Double Counts South Africa / World                    |  -120720 |  -134140 | 0.11116633532140496    |  -13420 |
| ALGERIA                                               |    42008 |    60606 | 0.44272519520091413    |   18598 |
| BOTSWANA                                              |        0 |        0 |                        |       0 |
| EGYPT                                                 |    36230 |    36640 | 1.1316588462600086E-2  |     410 |
| KENYA                                                 |        0 |        0 |                        |       0 |
| LIBYA                                                 |        0 |        0 |                        |       0 |
| MOROCCO                                               |   345106 |   376286 | 9.034905217527367E-2   |   31180 |
| NIGERIA                                               |        0 |        0 |                        |       0 |
| SOUTH AFRICA                                          |   599004 |   589951 | -1.5113421613211275E-2 |   -9053 |
| SUDAN                                                 |        0 |        0 |                        |       0 |
| TUNISIA                                               |     1940 |     1940 | 0                      |       0 |
| ZIMBABWE                                              |        0 |        0 |                        |       0 |
| OTHERS                                                |        0 |        0 |                        |       0 |
| TOTAL                                                 | 95057929 | 97302534 | 2.3613022328731859E-2  | 2244605 |



label: F=D-C
labeled_formulas: F=D-C
output: {"Arithmetic-Relationship": ["F=D-C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_581466___xlsx_5ca840b7b61a66fb08ae62b923afecb6d8bf8943.xlsx___line_285