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 |
|:----------------------------|-----:|-----:|----:|----:|---------:|-----:|----------:|-----:|-----------:|----:|
| Argentina                   |  455 |  675 |   0 |   0 | 0.815385 |  371 | 0.164835  |   75 | 0.0197802  |   9 |
| Australia                   | 1219 | 1462 |   0 |   0 | 0.861362 | 1050 | 0.133716  |  163 | 0.00492207 |   6 |
| Austria                     |    9 |   15 |   0 |   0 | 0.777778 |    7 | 0.111111  |    1 | 0.111111   |   1 |
| Belarus                     |    1 |    1 |   0 |   0 | 1        |    1 | 0         |    0 | 0          |   0 |
| Belgium                     |  500 |  784 |   0 |   0 | 0.812    |  406 | 0.188     |   94 | 0          |   0 |
| British Virgin Islands      |    1 |    1 |   0 |   0 | 1        |    1 | 0         |    0 | 0          |   0 |
| Bulgaria                    |    2 |    4 |   0 |   0 | 1        |    2 | 0         |    0 | 0          |   0 |
| Chile                       |  204 |  292 |   0 |   0 | 0.843137 |  172 | 0.151961  |   31 | 0.00490196 |   1 |
| China                       |    3 |   42 |   0 |   0 | 1        |    3 | 0         |    0 | 0          |   0 |
| Colombia                    |   97 |  170 |   0 |   0 | 0.865979 |   84 | 0.113402  |   11 | 0.0206186  |   2 |
| Costa Rica                  |   48 |   61 |   0 |   0 | 0.895833 |   43 | 0.104167  |    5 | 0          |   0 |
| Czech Republic              |   34 |   62 |   0 |   0 | 0.764706 |   26 | 0.117647  |    4 | 0.117647   |   4 |
| Denmark                     |  107 |  256 |   0 |   0 | 0.831776 |   89 | 0.158879  |   17 | 0.00934579 |   1 |
| Dominican Republic          |    7 |   79 |   0 |   0 | 1        |    7 | 0         |    0 | 0          |   0 |
| Ecuador                     |   17 |   18 |   0 |   0 | 1        |   17 | 0         |    0 | 0          |   0 |
| El Salvador                 |    9 |   15 |   0 |   0 | 1        |    9 | 0         |    0 | 0          |   0 |
| Estonia                     |    3 |    6 |   0 |   0 | 1        |    3 | 0         |    0 | 0          |   0 |
| Finland                     |   29 |   48 |   0 |   0 | 0.862069 |   25 | 0.137931  |    4 | 0          |   0 |
| France                      | 4379 | 7926 |   0 |   0 | 0.821877 | 3599 | 0.169902  |  744 | 0.00822106 |  36 |
| French Polynesia            |    1 |    1 |   0 |   0 | 1        |    1 | 0         |    0 | 0          |   0 |
| French Southern Territories |    1 |    1 |   0 |   0 | 0        |    0 | 1         |    1 | 0          |   0 |
| Germany                     | 5185 | 9670 |   0 |   0 | 0.832787 | 4318 | 0.159306  |  826 | 0.00790743 |  41 |
| Greece                      |   10 |   64 |   0 |   0 | 0.9      |    9 | 0.1       |    1 | 0          |   0 |
| Hong Kong                   |  597 |  597 |   0 |   0 | 0.839196 |  501 | 0.160804  |   96 | 0          |   0 |
| Hungary                     |   70 |  127 |   0 |   0 | 0.828571 |   58 | 0.157143  |   11 | 0.0142857  |   1 |
| Iceland                     |    6 |    7 |   0 |   0 | 0.833333 |    5 | 0.166667  |    1 | 0          |   0 |
| India                       |  278 |  413 |   0 |   0 | 0.805755 |  224 | 0.161871  |   45 | 0.0323741  |   9 |
| Israel                      |   34 |   66 |   0 |   0 | 0.735294 |   25 | 0.0882353 |    3 | 0.176471   |   6 |
| Italy                       |  852 | 1172 |   0 |   0 | 0.78169  |  666 | 0.188967  |  161 | 0.0293427  |  25 |
| Japan                       |  476 |  574 |   0 |   0 | 0.792017 |  377 | 0.134454  |   64 | 0.0735294  |  35 |
| Korea                       |  126 |  222 |   0 |   0 | 0.865079 |  109 | 0.119048  |   15 | 0.015873   |   2 |
| Latvia                      |    1 |    1 |   0 |   0 | 1        |    1 | 0         |    0 | 0          |   0 |
| Lithuania                   |    6 |   20 |   0 |   0 | 0.5      |    3 | 0.166667  |    1 | 0.333333   |   2 |
| Luxembourg                  |   55 |  121 |   0 |   0 | 0.781818 |   43 | 0.218182  |   12 | 0          |   0 |
| Malta                       |   29 |   34 |   0 |   0 | 0.827586 |   24 | 0.172414  |    5 | 0          |   0 |
| Mexico                      |  340 |  770 |   0 |   0 | 0.85     |  289 | 0.147059  |   50 | 0.00294118 |   1 |
| Moldova                     |    1 |    2 |   0 |   0 | 1        |    1 | 0         |    0 | 0          |   0 |
| Monaco                      |    2 |    2 |   0 |   0 | 0.5      |    1 | 0         |    0 | 0.5        |   1 |
| Netherlands                 |  411 |  714 |   0 |   0 | 0.781022 |  321 | 0.216545  |   89 | 0.00243309 |   1 |
| New Zealand                 |   34 |   43 |   0 |   0 | 0.823529 |   28 | 0.117647  |    4 | 0.0588235  |   2 |
| Norway                      |   74 |  131 |   0 |   0 | 0.837838 |   62 | 0.162162  |   12 | 0          |   0 |
| Panama                      |   10 |   18 |   0 |   0 | 0.9      |    9 | 0.1       |    1 | 0          |   0 |
| Peru                        |   29 |   77 |   0 |   0 | 0.931034 |   27 | 0.0689655 |    2 | 0          |   0 |
| Poland                      |   55 |   76 |   0 |   0 | 0.727273 |   40 | 0.254545  |   14 | 0.0181818  |   1 |
| Portugal                    |  334 |  411 |   0 |   0 | 0.817365 |  273 | 0.182635  |   61 | 0          |   0 |
| Qatar                       |    1 |    1 |   0 |   0 | 1        |    1 | 0         |    0 | 0          |   0 |
| Russian Federation          |    3 |    6 |   0 |   0 | 1        |    3 | 0         |    0 | 0          |   0 |
| Singapore                   |   66 |   92 |   0 |   0 | 0.909091 |   60 | 0.0909091 |    6 | 0          |   0 |
| Slovakia                    |   15 |   18 |   0 |   0 | 0.933333 |   14 | 0         |    0 | 0.0666667  |   1 |
| Spain                       |  927 | 1478 |   0 |   0 | 0.79288  |  735 | 0.201726  |  187 | 0.00539374 |   5 |
| Sweden                      |  281 |  825 |   0 |   0 | 0.875445 |  246 | 0.103203  |   29 | 0.0213523  |   6 |
| Switzerland                 |   43 |   80 |   0 |   0 | 0.627907 |   27 | 0.255814  |   11 | 0.116279   |   5 |
| Taiwan                      |  802 | 1516 |   0 |   0 | 0.855362 |  686 | 0.142145  |  114 | 0.00249377 |   2 |
| Thailand                    |   44 |   56 |   0 |   0 | 0.840909 |   37 | 0.159091  |    7 | 0          |   0 |
| Trinidad and Tobago         |    1 |    2 |   0 |   0 | 1        |    1 | 0         |    0 | 0          |   0 |
| Turkey                      | 6226 | 7333 |   0 |   0 | 0.750723 | 4674 | 0.248795  | 1549 | 0.00048185 |   3 |
| Ukraine                     |    5 |   32 |   0 |   0 | 0.8      |    4 | 0.2       |    1 | 0          |   0 |
| United Kingdom              | 4404 | 6723 |   0 |   0 | 0.781789 | 3443 | 0.196866  |  867 | 0.0213442  |  94 |
| Uruguay                     |    1 |    1 |   0 |   0 | 1        |    1 | 0         |    0 | 0          |   0 |
| Venezuala                   |   15 |   28 |   0 |   0 | 0.933333 |   14 | 0         |    0 | 0.0666667  |   1 |



labeled_formulas: E=C*D
E=D*F
E=D*G
E=D*H
E=D*I
E=D*J
E=D*K
E=(B+C)*D
E=(B*D)*F
E=(B*D)*G
E=(B*D)*H
E=(B*D)*I
E=(B*D)*J
E=(B*D)*K
G=(B+D)*F
I=(B+D)*H
K=(B+D)*J
G=(B+E)*F
I=(B+E)*H
K=(B+E)*J
K=(B-G)-I
E=(C*D)*F
E=(C*D)*G
E=(C*D)*H
E=(C*D)*I
E=(C*D)*J
E=(C*D)*K
E=(D*F)*H
E=(D*F)*I
E=(D*F)*J
E=(D*F)*K
E=(D*G)*H
E=(D*G)*I
E=(D*G)*J
E=(D*G)*K
E=(D*H)*I
E=(D*H)*J
E=(D*H)*K
E=(D*I)*J
E=(D*I)*K
E=(D*J)*K
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_720567___xlsx_091f90dc70cae62066cff573dc2891733087cd4d.xlsx___line_38