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 |
|:---------|:---------|:-------------------|:--------|:-------------------|:-----------|-----:|-------:|---------:|----------:|
| Abby     | January  | 1040               | Coleman | Lisa Sullivan      | Individual | 19   | 1425   | 1311     |   114     |
| Bill     | March    | 1065               | Coleman | Sam's Services     | Corporate  | 22   | 1650   | 1848     |  -198     |
| Brenda   | April    | Financial Planning | Smith   | Betty Harrington   | Individual | 10.2 | 1020   | 1377     |  -357     |
| Jennifer | March    | 1065               | Coleman | Lisa Sullivan      | Individual | 18.4 |  630   |  705.6   |   -75.6   |
| Jennifer | January  | 1120               | Coleman | Sam's Services     | Corporate  | 32   | 2400   | 2208     |   192     |
| Jennifer | March    | 1040               | Coleman | Tony Davis         | Individual |  2.6 |  195   |  218.4   |   -23.4   |
| Jesseca  | March    | 1040               | Coleman | Betty Harrington   | Individual | 19   | 1900   | 2128     |  -228     |
| Jesseca  | March    | 1120               | Coleman | Course Concrete    | Corporate  | 17   | 1700   | 1904     |  -204     |
| John     | March    | 1040               | Coleman | Mindy Simmon       | Individual | 16   | 1600   | 1792     |  -192     |
| Jesseca  | January  | 1040               | Coleman | Molly Francis      | Individual |  3.5 |  350   |  322     |    28     |
| Jesseca  | January  | 1040               | Coleman | Robert Kennedy     | Individual |  3.7 |  370   |  340.4   |    29.6   |
| Jesseca  | March    | 1040               | Coleman | Robert Kennedy     | Individual |  8.4 |  840   |  940.8   |  -100.8   |
| Jesseca  | March    | 1040               | Coleman | Tommy Pruitt       | Individual |  8   |  800   |  896     |   -96     |
| Jesseca  | January  | 1040               | Coleman | Tommy Pruitt       | Individual |  6   |  600   |  552     |    48     |
| John     | March    | 1120               | Coleman | Camera Shot        | Corporate  |  2   |  150   |  168     |   -18     |
| Kathleen | April    | 1040               | Coleman | Robert Kennedy     | Individual |  2   |  200   |  270     |   -70     |
| Keith    | February | 1040               | Coleman | Mindy Simmon       | Individual | 32   | 3200   | 3168     |    32     |
| Martha   | February | 1120               | Coleman | Course Concrete    | Corporate  |  8   |  800   |  792     |     8     |
| Martha   | April    | Fidiciary          | Coleman | Molly Francis      | Individual |  6   |  600   |  810     |  -210     |
| Martin   | April    | Fidiciary          | Coleman | Boris Tellman      | Individual |  6   |  750   | 1012.5   |  -262.5   |
| Martin   | February | 1040               | Coleman | Boris Tellman      | Individual |  3.5 |  437.5 |  433.125 |     4.375 |
| Martin   | February | 1040               | Coleman | Charlie Sullivan   | Individual |  2   |  250   |  247.5   |     2.5   |
| Martin   | April    | 1040               | Coleman | Charlie Sullivan   | Individual | 10.2 | 1275   | 1721.25  |  -446.25  |
| Martin   | April    | 1120               | Coleman | Door to Door, Inc. | Corporate  | 12   | 1500   | 2025     |  -525     |
| Martin   | February | 1040               | Coleman | Doug Thomas        | Individual |  4.5 |  562.5 |  556.875 |     5.625 |
| Martin   | April    | 1065               | Coleman | Granite Right      | Corporate  |  8   | 1000   | 1350     |  -350     |
| Martin   | April    | 1040               | Coleman | Joey Rayhoney      | Individual |  4   |  500   |  675     |  -175     |
| Martin   | February | Fidiciary          | Coleman | Joey Rayhoney      | Individual |  2.4 |  300   |  297     |     3     |
| Martin   | February | Fidiciary          | Coleman | Mars, Inc.         | Corporate  |  8.4 | 1050   | 1039.5   |    10.5   |
| Martin   | April    | 1120               | Coleman | Mars, Inc.         | Corporate  | 19   | 2375   | 3206.25  |  -831.25  |
| Martin   | February | 1120               | Coleman | Plasma Medical     | Corporate  |  3.7 |  462.5 |  457.875 |     4.625 |
| nancy    | February | 1040               | Coleman | Betty Harrington   | Individual | 17   | 1700   | 1683     |    17     |
| nancy    | April    | 1065               | Coleman | Course Concrete    | Corporate  | 19   | 1900   | 2565     |  -665     |
| nancy    | February | 1040               | Coleman | Molly Francis      | Individual |  5.5 |  550   |  544.5   |     5.5   |
| Phil     | April    | Property Taxes     | Coleman | Camera Shot        | Corporate  |  3.7 |  277.5 |  374.625 |   -97.125 |
| Phil     | February | 1120               | Coleman | Camera Shot        | Corporate  |  8.4 |  630   |  623.7   |     6.3   |
| Phil     | April    | 1120               | Coleman | Clothes Barn       | Corporate  |  2.6 |  195   |  263.25  |   -68.25  |
| Phil     | February | Fidiciary          | Coleman | Clothes Barn       | Corporate  | 12.9 |  967.5 |  957.825 |     9.675 |
| Phil     | February | 1040               | Coleman | Lisa Sullivan      | Individual | 10.2 |  765   |  757.35  |     7.65  |
| Phil     | February | 1120               | Coleman | Sam's Services     | Corporate  | 16   | 1200   | 1188     |    12     |
| Phil     | April    | 1040               | Coleman | Tony Davis         | Individual |  9   |  675   |  911.25  |  -236.25  |
| Phil     | February | 1040               | Coleman | Tony Davis         | Individual |  2.9 |  217.5 |  215.325 |     2.175 |
| Sam      | March    | 1065               | Coleman | Clothes Barn       | Corporate  |  2.9 |  217.5 |  243.6   |   -26.1   |
| Sandra   | March    | 1040               | Coleman | Boris Tellman      | Individual |  5.5 |  687.5 |  770     |   -82.5   |
| Sandra   | January  | 1040               | Coleman | Charlie Sullivan   | Individual |  8.4 | 1050   |  966     |    84     |
| Sandra   | January  | 1120               | Coleman | Door to Door, Inc. | Corporate  | 32   | 4000   | 3680     |   320     |
| Sandra   | March    | 1120               | Coleman | Door to Door, Inc. | Corporate  | 14   | 1750   | 1960     |  -210     |
| Sandra   | March    | 1040               | Coleman | Doug Thomas        | Individual |  6   |  750   |  840     |   -90     |
| Sandra   | January  | 1040               | Coleman | Doug Thomas        | Individual |  3.7 |  462.5 |  425.5   |    37     |
| Sandra   | January  | 1120               | Coleman | Granite Right      | Corporate  | 17   | 2125   | 1955     |   170     |
| Sandra   | March    | 1120               | Coleman | Granite Right      | Corporate  |  4   |  500   |  560     |   -60     |
| Sandra   | March    | 1040               | Coleman | Joey Rayhoney      | Individual |  6   |  750   |  840     |   -90     |
| Sandra   | January  | 1120               | Coleman | Mars, Inc.         | Corporate  | 10.2 | 1275   | 1173     |   102     |
| Sandra   | March    | Financial Planning | Coleman | Plasma Medical     | Corporate  |  4.5 |  562.5 |  630     |   -67.5   |
| Sandra   | January  | 1120               | Coleman | Plasma Medical     | Corporate  |  2   |  250   |  230     |    20     |
| Steve    | April    | 1040               | Coleman | Mindy Simmon       | Individual | 22   | 2200   | 2970     |  -770     |
| Steve    | February | 1040               | Coleman | Tommy Pruitt       | Individual |  4   |  400   |  396     |     4     |
| Bill     | January  | 1040               | Johnson | Pam Duncan         | Individual |  6   |  450   |  414     |    36     |
| Bill     | March    | 1040               | Johnson | Peter Hanson       | Individual |  5   |  375   |  420     |   -45     |
| Bill     | January  | 1120               | Johnson | Simpson            | Corporate  | 17   | 1275   | 1173     |   102     |
| Brenda   | April    | 1120               | Johnson | Catcher's Creamery | Corporate  |  2.6 |  260   |  351     |   -91     |
| Brenda   | February | 1120               | Johnson | Fancy Daze         | Corporate  |  6   |  600   |  594     |     6     |
| Jennifer | March    | 1040               | Johnson | Pam Duncan         | Individual |  3.5 |  262.5 |  294     |   -31.5   |
| Jesseca  | January  | Financial Planning | Johnson | Beverly Crusher    | Individual |  5   |  500   |  460     |    40     |
| Jesseca  | March    | Fidiciary          | Johnson | Books O'Toole      | Corporate  |  4   |  400   |  448     |   -48     |
| Jesseca  | January  | 1120               | Johnson | Books O'Toole      | Corporate  |  2.4 |  240   |  220.8   |    19.2   |
| Jesseca  | January  | 1065               | Johnson | Cascade, Inc.      | Corporate  |  4.5 |  450   |  414     |    36     |
| Jesseca  | January  | 1120               | Johnson | Catcher's Creamery | Corporate  |  9   |  900   |  828     |    72     |
| Jesseca  | January  | 1040               | Johnson | David Pollack      | Individual |  2.6 |  260   |  239.2   |    20.8   |
| Jesseca  | March    | Financial Planning | Johnson | David Pollack      | Individual | 12.9 | 1290   | 1444.8   |  -154.8   |
| Jesseca  | March    | 1120               | Johnson | Fancy Daze         | Corporate  | 14   | 1400   | 1568     |  -168     |
| Jesseca  | January  | 1120               | Johnson | Fancy Daze         | Corporate  |  5.5 |  550   |  506     |    44     |
| Jesseca  | March    | 1120               | Johnson | Superior Pans      | Corporate  | 32   | 3200   | 3584     |  -384     |
| Kathleen | February | 1040               | Johnson | Beverly Crusher    | Individual |  2.4 |  240   |  237.6   |     2.4   |
| Kathleen | February | 1120               | Johnson | Superior Pans      | Corporate  | 12   | 1200   | 1188     |    12     |
| Keith    | February | Financial Planning | Johnson | Books O'Toole      | Corporate  |  6   |  600   |  594     |     6     |
| Keith    | April    | 1120               | Johnson | Cascade, Inc.      | Corporate  |  3.7 |  370   |  499.5   |  -129.5   |
| Keith    | April    | 1065               | Johnson | Superior Pans      | Corporate  | 16   | 1600   | 2160     |  -560     |
| Kevin    | April    | 1040               | Johnson | Beverly Crusher    | Individual |  9   |  900   | 1215     |  -315     |
| Kevin    | February | 1120               | Johnson | Catcher's Creamery | Corporate  |  5   |  500   |  495     |     5     |
| Martin   | April    | 1120               | Johnson | Bessy Boats        | Corporate  |  6   |  750   | 1012.5   |  -262.5   |
| Martin   | February | Financial Planning | Johnson | Bessy Boats        | Corporate  |  5   |  625   |  618.75  |     6.25  |
| Martin   | April    | 1040               | Johnson | Debbie Mavormat    | Individual | 17   | 2125   | 2868.75  |  -743.75  |
| Martin   | February | 1120               | Johnson | Harold Mason, Inc. | Corporate  | 12.9 | 1612.5 | 1596.38  |    16.125 |
| Martin   | April    | 1120               | Johnson | Harold Mason, Inc. | Corporate  | 16   | 2000   | 2700     |  -700     |
| Martin   | April    | 1040               | Johnson | Janet Miller       | Individual | 14   | 1750   | 2362.5   |  -612.5   |
| Martin   | February | 1040               | Johnson | Janet Miller       | Individual |  5.5 |  687.5 |  680.625 |     6.875 |
| nancy    | April    | 1040               | Johnson | David Pollack      | Individual |  2.9 |  290   |  391.5   |  -101.5   |
| Phil     | April    | Financial Planning | Johnson | Pam Duncan         | Individual |  5.5 |  412.5 |  556.875 |  -144.375 |
| Phil     | April    | 1040               | Johnson | Peter Hanson       | Individual |  2.4 |  180   |  243     |   -63     |
| Phil     | February | 1120               | Johnson | Simpson            | Corporate  | 19   | 1425   | 1410.75  |    14.25  |
| Sam      | January  | 1040               | Johnson | Peter Hanson       | Individual |  6   |  450   |  414     |    36     |
| Sam      | March    | 1120               | Johnson | Simpson            | Corporate  | 10.2 |  765   |  856.8   |   -91.8   |
| Sandra   | April    | 1120               | Johnson | Bessy Boats        | Corporate  |  2.4 |  300   |  336     |   -36     |
| Sandra   | January  | 1040               | Johnson | Debbie Mavormat    | Individual | 19   | 2375   | 2185     |   190     |
| Sandra   | March    | 1040               | Johnson | Debbie Mavormat    | Individual |  8   | 1000   | 1120     |  -120     |
| Sandra   | January  | 1065               | Johnson | Harold Mason, Inc. | Corporate  | 22   | 2750   | 2530     |   220     |
| Sandra   | March    | 1040               | Johnson | Janet Miller       | Individual |  6   |  750   |  840     |   -90     |
| Steve    | February | 1120               | Johnson | Cascade, Inc.      | Corporate  |  6   |  600   |  594     |     6     |
| Abby     | January  | 1065               | Smith   | Biss Foods         | Corporate  |  2.4 |  180   |  165.6   |    14.4   |
| Abby     | March    | 1040               | Smith   | Lars Tate          | Individual | 12.9 |  967.5 | 1083.6   |  -116.1   |
| Abby     | January  | Fidiciary          | Smith   | The News Place     | Corporate  | 14   | 1050   |  966     |    84     |
| Abby     | March    | 1120               | Smith   | Tulip Bowls, Ltd   | Corporate  |  4.5 |  337.5 |  378     |   -40.5   |
| Bill     | March    | 1040               | Smith   | Mike Thomas        | Individual |  3.7 |  277.5 |  310.8   |   -33.3   |
| Jennifer | January  | 1120               | Smith   | Granola Bob        | Corporate  |  4   |  300   |  276     |    24     |
| Jennifer | January  | 1040               | Smith   | Tulip Bowls, Ltd   | Corporate  |  3.5 |  262.5 |  241.5   |    21     |
| Jesseca  | January  | 1040               | Smith   | Gay Gray           | Individual |  6   |  600   |  552     |    48     |
| Jesseca  | January  | 1065               | Smith   | Hayes Automotive   | Corporate  |  2   |  200   |  184     |    16     |
| Jesseca  | March    | 1120               | Smith   | Hayes Automotive   | Corporate  | 10.2 | 1020   | 1142.4   |  -122.4   |
| Jesseca  | January  | Financial Planning | Smith   | Kim's Couches      | Corporate  |  2.9 |  290   |  266.8   |    23.2   |
| Jesseca  | March    | 1120               | Smith   | Kim's Couches      | Corporate  | 22   | 2200   | 2464     |  -264     |
| Jesseca  | March    | Financial Planning | Smith   | Terry Parker       | Individual | 12   | 1200   | 1344     |  -144     |
| Jesseca  | January  | Fidiciary          | Smith   | Terry Parker       | Individual |  6   |  600   |  552     |    48     |
| John     | March    | 1065               | Smith   | Biss Foods         | Corporate  |  9   |  675   |  756     |   -81     |
| John     | January  | 1040               | Smith   | Lars Tate          | Individual | 16   | 1200   | 1104     |    96     |
| John     | January  | 1040               | Smith   | Nancy Young        | Individual |  5.5 |  412.5 |  379.5   |    33     |
| John     | January  | 1040               | Smith   | Scott Slade        | Individual |  8   |  600   |  552     |    48     |
| Kevin    | April    | 1120               | Smith   | Hayes Automotive   | Corporate  |  8.4 |  840   | 1134     |  -294     |
| Kevin    | February | Fidiciary          | Smith   | Terry Parker       | Individual | 14   | 1400   | 1386     |    14     |
| Martha   | February | 1065               | Smith   | Gay Gray           | Individual |  3.5 |  350   |  346.5   |     3.5   |
| Martha   | April    | 1120               | Smith   | Kim's Couches      | Corporate  | 12.9 | 1290   | 1741.5   |  -451.5   |
| Martin   | April    | 1065               | Smith   | Cindy Schrieber    | Individual | 32   | 4000   | 5400     | -1400     |
| Martin   | February | 1040               | Smith   | Corneilia Ham      | Individual |  6   |  750   |  742.5   |     7.5   |
| Martin   | February | 1040               | Smith   | David Greene       | Individual |  2.9 |  362.5 |  358.875 |     3.625 |
| Martin   | April    | 1040               | Smith   | David Greene       | Individual | 22   | 2750   | 3712.5   |  -962.5   |
| Martin   | February | 1120               | Smith   | Hanson Fish Sales  | Corporate  |  2.6 |  325   |  321.75  |     3.25  |
| Martin   | February | 1040               | Smith   | Willie McClendon   | Individual |  9   | 1125   | 1113.75  |    11.25  |
| Phil     | April    | 1065               | Smith   | Biss Foods         | Corporate  |  5   |  375   |  506.25  |  -131.25  |
| Phil     | February | 1120               | Smith   | Granola Bob        | Corporate  |  8   |  600   |  594     |     6     |
| Phil     | April    | 1120               | Smith   | Granola Bob        | Corporate  |  6   |  450   |  607.5   |  -157.5   |
| Phil     | February | 1040               | Smith   | Kathy Hankins      | Individual | 32   | 2400   | 2376     |    24     |
| Phil     | April    | Financial Planning | Smith   | Kathy Hankins      | Individual | 14   | 1050   | 1417.5   |  -367.5   |
| Phil     | February | 1040               | Smith   | Lars Tate          | Individual | 22   | 1650   | 1633.5   |    16.5   |
| Phil     | April    | 1040               | Smith   | Mike Thomas        | Individual |  4.5 |  337.5 |  455.625 |  -118.125 |
| Phil     | February | 1040               | Smith   | Mike Thomas        | Individual |  2   |  150   |  148.5   |     1.5   |
| Phil     | April    | Financial Planning | Smith   | Nancy Young        | Individual |  3.5 |  262.5 |  354.375 |   -91.875 |
| Phil     | February | 1040               | Smith   | Scott Slade        | Individual | 17   | 1275   | 1262.25  |    12.75  |
| Phil     | April    | 1040               | Smith   | Scott Slade        | Individual |  4   |  300   |  405     |  -105     |
| Phil     | February | 1065               | Smith   | The News Place     | Corporate  | 12   |  900   |  891     |     9     |
| Phil     | April    | 1120               | Smith   | The News Place     | Corporate  |  6   |  450   |  607.5   |  -157.5   |
| Phil     | April    | 1120               | Smith   | Tulip Bowls, Ltd   | Corporate  |  6   |  450   |  607.5   |  -157.5   |
| Sam      | January  | 1040               | Smith   | Kathy Hankins      | Individual | 12   |  900   |  828     |    72     |
| Sam      | March    | Financial Planning | Smith   | Nancy Young        | Individual |  6   |  450   |  504     |   -54     |
| Sandra   | January  | 1040               | Smith   | Cindy Schrieber    | Individual | 16   | 2000   | 1840     |   160     |
| Sandra   | March    | 1040               | Smith   | Cindy Schrieber    | Individual | 12   | 1500   | 1680     |  -180     |
| Sandra   | March    | Fidiciary          | Smith   | Corneilia Ham      | Individual |  3.5 |  437.5 |  490     |   -52.5   |
| Sandra   | January  | 1040               | Smith   | Corneilia Ham      | Individual |  4.5 |  562.5 |  517.5   |    45     |
| Sandra   | January  | 1040               | Smith   | David Greene       | Individual | 12.9 | 1612.5 | 1483.5   |   129     |
| Sandra   | March    | 1120               | Smith   | Hanson Fish Sales  | Corporate  |  9   | 1125   | 1260     |  -135     |
| Sandra   | January  | 1120               | Smith   | Hanson Fish Sales  | Corporate  |  2.9 |  362.5 |  333.5   |    29     |
| Sandra   | March    | 1040               | Smith   | Willie McClendon   | Individual |  5   |  625   |  700     |   -75     |
| Sandra   | January  | 1040               | Smith   | Willie McClendon   | Individual |  2.6 |  325   |  299     |    26     |
| Steve    | April    | 1040               | Smith   | Gay Gray           | Individual |  4.5 |  450   |  607.5   |  -157.5   |



label: J=H-I
labeled_formulas: J=H-I
output: {"Arithmetic-Relationship": ["J=H-I"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_540043___xlsx_373d548b712f7644efb5427d6f6466369f14f52d.xlsx___line_277