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 |
|:------------|-----:|----:|---------:|
| FA2103      |    1 |   1 | 1        |
| FA2486      |    1 |   0 | 0        |
| FA2487      |    6 |   5 | 0.833333 |
| FA2517      |    4 |   4 | 1        |
| FA2860      |    1 |   0 | 0        |
| FA4654      |    3 |   0 | 0        |
| FA4877      |    1 |   0 | 0        |
| FA5587      |    1 |   1 | 1        |
| FA6606      |    2 |   0 | 0        |
| FA6643      |    5 |   0 | 0        |
| FA6670      |    9 |   0 | 0        |
| FA7014      |    8 |   8 | 1        |
| FA7022      |    3 |   3 | 1        |
| FA7037      |    1 |   1 | 1        |
| FA8075      |   18 |  18 | 1        |
| FA8101      |   12 |   0 | 0        |
| FA8102      |    1 |   0 | 0        |
| FA8207      |    1 |   1 | 1        |
| FA8210      |    1 |   1 | 1        |
| FA8213      |    1 |   1 | 1        |
| FA8220      |    2 |   2 | 1        |
| FA8224      |    1 |   1 | 1        |
| FA8232      |    3 |   3 | 1        |
| FA8501      |    2 |   1 | 0.5      |
| FA8504      |    3 |   3 | 1        |
| FA8505      |    2 |   2 | 1        |
| FA8509      |    2 |   2 | 1        |
| FA8520      |    2 |   2 | 1        |
| FA8527      |    2 |   2 | 1        |
| FA8528      |    1 |   1 | 1        |
| FA8533      |    5 |   5 | 1        |
| FA8538      |    2 |   2 | 1        |
| FA8539      |    1 |   1 | 1        |
| FA8540      |    2 |   2 | 1        |
| FA8553      |    1 |   1 | 1        |
| FA8604      |   10 |  10 | 1        |
| FA8606      |    4 |   4 | 1        |
| FA8616      |    1 |   1 | 1        |
| FA8617      |    1 |   1 | 1        |
| FA8620      |   11 |  10 | 0.909091 |
| FA8625      |    1 |   1 | 1        |
| FA8634      |    2 |   2 | 1        |
| FA8637      |    2 |   1 | 0.5      |
| FA8650      |   46 |  44 | 0.956522 |
| FA8651      |    5 |   5 | 1        |
| FA8675      |    2 |   2 | 1        |
| FA8678      |    1 |   1 | 1        |
| FA8681      |    3 |   3 | 1        |
| FA8682      |    1 |   1 | 1        |
| FA8702      |    1 |   1 | 1        |
| FA8721      |    9 |   4 | 0.444444 |
| FA8723      |    1 |   1 | 1        |
| FA8726      |    3 |   3 | 1        |
| FA8730      |    5 |   5 | 1        |
| FA8735      |    1 |   1 | 1        |
| FA8750      |   57 |  56 | 0.982456 |
| FA8751      |    2 |   0 | 0        |
| FA8770      |    1 |   0 | 0        |
| FA8773      |    3 |   2 | 0.666667 |
| FA8802      |    1 |   1 | 1        |
| FA8807      |    1 |   1 | 1        |
| FA8810      |    4 |   4 | 1        |
| FA8811      |    2 |   2 | 1        |
| FA8814      |    1 |   0 | 0        |
| FA8818      |    2 |   1 | 0.5      |
| FA8819      |    3 |   2 | 0.666667 |
| FA8823      |    4 |   3 | 0.75     |
| FA9101      |    1 |   1 | 1        |
| FA9300      |    1 |   1 | 1        |
| FA9302      |    1 |   1 | 1        |
| FA9401      |    2 |   0 | 0        |
| FA9451      |    1 |   1 | 1        |
| FA9453      |    9 |   9 | 1        |
| H92241      |    3 |   3 | 1        |
| H92400      |    1 |   0 | 0        |
| H92401      |   12 |  12 | 1        |
| H92402      |    2 |   2 | 1        |
| H92403      |    3 |   3 | 1        |
| H92404      |    8 |   8 | 1        |
| H92405      |    5 |   5 | 1        |
| HC1028      |   21 |  21 | 1        |
| HDTRA1      |    4 |   4 | 1        |
| HQ0034      |   15 |   5 | 0.333333 |
| HQ0147      |   42 |  42 | 1        |
| HQ0276      |    1 |   1 | 1        |
| HQ0277      |    1 |   1 | 1        |
| HQ0727      |    1 |   0 | 0        |
| HQ0796      |    1 |   1 | 1        |
| HR0011      |   36 |  36 | 1        |
| HT0011      |    3 |   1 | 0.333333 |
| HTC711      |    2 |   2 | 1        |
| M67854      |   11 |  10 | 0.909091 |
| M95494      |    1 |   1 | 1        |
| N00014      |   26 |  26 | 1        |
| N00019      |   18 |  10 | 0.555556 |
| N00024      |   27 |  24 | 0.888889 |
| N00039      |   10 |   8 | 0.8      |
| N00164      |    6 |   6 | 1        |
| N00167      |    3 |   3 | 1        |
| N00174      |    3 |   2 | 0.666667 |
| N00178      |    5 |   5 | 1        |
| N00189      |   17 |  16 | 0.941176 |
| N00253      |    1 |   1 | 1        |
| N00421      |   34 |  21 | 0.617647 |
| N32253      |    1 |   1 | 1        |
| N39040      |    4 |   4 | 1        |
| N40080      |    3 |   3 | 1        |
| N40085      |    1 |   0 | 0        |
| N50054      |   18 |   0 | 0        |
| N61331      |    1 |   1 | 1        |
| N61340      |   11 |  10 | 0.909091 |
| N62645      |    5 |   5 | 1        |
| N63394      |    1 |   1 | 1        |
| N64267      |    4 |   4 | 1        |
| N64498      |   19 |  18 | 0.947368 |
| N65236      |    7 |   7 | 1        |
| N66001      |   31 |  31 | 1        |
| N66604      |   26 |  26 | 1        |
| N68335      |   82 |  80 | 0.97561  |
| N68936      |    6 |   6 | 1        |
| N69450      |    2 |   0 | 0        |
| SPRDL1      |    1 |   1 | 1        |
| W15P7T      |   14 |  12 | 0.857143 |
| W15QKN      |   30 |  28 | 0.933333 |
| W31P4Q      |   22 |  22 | 1        |
| W56HZV      |   23 |  20 | 0.869565 |
| W56JSR      |    5 |   5 | 1        |
| W56KGU      |    6 |   3 | 0.5      |
| W56KGY      |    1 |   1 | 1        |
| W56KGZ      |    4 |   2 | 0.5      |
| W58RGZ      |    4 |   3 | 0.75     |
| W81XWH      |   37 |  34 | 0.918919 |
| W900KK      |   12 |   7 | 0.583333 |
| W909MY      |   20 |  18 | 0.9      |
| W9113M      |    7 |   4 | 0.571429 |
| W91151      |    1 |   1 | 1        |
| W911NF      |   22 |  16 | 0.727273 |
| W911QX      |    9 |   9 | 1        |
| W911QY      |   15 |   8 | 0.533333 |
| W911RP      |    1 |   1 | 1        |
| W911S0      |    1 |   1 | 1        |
| W911S8      |    1 |   1 | 1        |
| W911SD      |    2 |   2 | 1        |
| W911SR      |    3 |   3 | 1        |
| W911W4      |    1 |   1 | 1        |
| W911W5      |    1 |   1 | 1        |
| W911W6      |   11 |   7 | 0.636364 |
| W9124J      |    1 |   1 | 1        |
| W9124R      |    3 |   0 | 0        |
| W9124V      |    2 |   0 | 0        |
| W91278      |    1 |   1 | 1        |
| W9128Z      |    1 |   0 | 0        |
| W912BV      |    4 |   0 | 0        |
| W912GB      |    2 |   1 | 0.5      |
| W912HN      |    1 |   1 | 1        |
| W912HQ      |   29 |  28 | 0.965517 |
| W912HZ      |    2 |   1 | 0.5      |
| W912JD      |    1 |   1 | 1        |
| W912JM      |    6 |   0 | 0        |
| W912L7      |    1 |   1 | 1        |
| W912L8      |    1 |   0 | 0        |
| W912LA      |    1 |   0 | 0        |
| W912NR      |    6 |   0 | 0        |
| W912P9      |    1 |   1 | 1        |
| W912PP      |    5 |   0 | 0        |
| W912QG      |    1 |   0 | 0        |
| W9132T      |    1 |   0 | 0        |
| W9133L      |    1 |   1 | 1        |
| W91364      |    1 |   0 | 0        |
| W91CRB      |   11 |   4 | 0.363636 |
| W91RUS      |    5 |   3 | 0.6      |
| W91ZRU      |    1 |   1 | 1        |
| Grand Total | 1205 | 993 | 0.824066 |



label: D=C/B
labeled_formulas: D=C/B
output: {"Arithmetic-Relationship": ["D=C/B"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_458851___xlsx_07a06842fb1da13a5016b109d3f5c1396429ee96.xlsx___line_16