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:
| C                                                  |                D |                E |                 F | G                      |
|:---------------------------------------------------|-----------------:|-----------------:|------------------:|:-----------------------|
| 10701 Realty Transfer                              |      1.54131e+07 |      1.58365e+07 |  423436           | 2.7472516104285839E-2  |
| 10706 Criminal Injuries Comp                       | 229467           |  97049.6         | -132417           | -0.5770650464705428    |
| 10707 Penalties                                    |  16691.3         | -15832.4         |  -32523.8         | -1.9485409799333069    |
| 10709 Marriage License                             |  66861.4         |  33469.3         |  -33392.2         | -0.49942350918907946   |
| 10710 Tire Tax                                     | 669067           | 185401           | -483666           | -0.72289558768905504   |
| 10713 Professional Tax                             |      4.22198e+07 |      1.53359e+07 |      -2.68839e+07 | -0.63676137968930868   |
| 10714 Used Oil                                     |  70082.3         |  46757.8         |  -23324.5         | -0.33281541844374402   |
| 10715 Auto Rental Surcharge                        |    764.23        | 286881           |  286117           | 374.38594402208764     |
| 10716 Realty Mortgage                              |      6.26909e+06 |      1.06182e+07 |       4.34911e+06 | 0.69373892758285083    |
| 10717 UCC                                          |      1.42932e+06 | 725848           | -703471           | -0.49217191756562351   |
| 10718 Attorneys Administrative Fee                 | 135233           |  68617.2         |  -66616.2         | -0.49260153515261679   |
| 10719 Forfeiture of Bonds                          |  61822.3         |  55346.1         |   -6476.28        | -0.1047562895942972    |
| 10720 Sex Offenders                                |   8462.81        |  17388.5         |    8925.65        | 1.0546910541534078     |
| 10721 Domestic Violence                            |    283.84        |   1574.3         |    1290.46        | 4.5464346110484781     |
| 10726 Bail Bond Fee                                |  86745.6         | 283579           |  196833           | 2.2690879155931736     |
| 10727 Aggravated Assault                           |   2000.73        |   1548.71        |    -452.02        | -0.22592753644919603   |
| 10728 Marriage License Increase 2002               | 187920           | 107287           |  -80633.1         | -0.42908236076428763   |
| 10729 Drug Violation Cases                         |  11349.3         |   4888.83        |   -6460.47        | -0.56923951256905714   |
| 10730 Sexual Assault                               |   7673.83        |   2290.69        |   -5383.14        | -0.70149325695252562   |
| 10731 Drug Violation -No Treatment                 |  98014.9         |  54073.8         |  -43941.2         | -0.44831103264686639   |
| 10733 Municipal Training Education                 |  32064.2         |   9954.72        |  -22109.4         | -0.68953738053246383   |
| 10734 Blood Alcohol                                | 226133           | 129491           |  -96642.6         | -0.42737041708161388   |
| 10735 Litigation                                   |      1.64006e+06 | 654081           | -985981           | -0.60118532104274103   |
| 10736 Alcohol Drug Treatment Fee                   | 128161           |  78135.2         |  -50025.5         | -0.39033426531379301   |
| 10737 Drag Racing Fine                             |   -954.53        |    894.68        |    1849.21        | 1.937298984840707      |
| 10738 Drug Testing Fee                             | 330014           | 186200           | -143814           | -0.43578151841687063   |
| 10739 Victim Notification Fund                     |  59800.1         |  23587.9         |  -36212.2         | -0.60555373560349635   |
| 10741 Ignition Interlock Device                    |  37590           |  23039.1         |  -14550.9         | -0.38709587313005395   |
| 10742 Cash Bond Forfeiture                         | 118009           |  62715.8         |  -55293.4         | -0.46855177392949027   |
| 10743 Criminal Judical Education                   |  21311.5         |   9692.55        |  -11619           | -0.54519668235771079   |
| 10744 P. Defender/D. Attorney Expungement          |  11727.2         |   -314.13        |  -12041.3         | -1.0267864908699278    |
| 10745 Enviromental Fees                            |  63433.2         |  20351.3         |  -43081.9         | -0.67916983600871783   |
| 10746 Human Trafficking GenFd                      |      0           |      2.99        |       2.99        | 1                      |
| 10747 Motor Vehicle Recycler                       |      0           |      2.98        |       2.98        | 1                      |
| 10748 Human Trafficking LawEnf                     |      0           |      2.99        |       2.99        | 1                      |
| 10749 Human Trafficking D.A.Gen                    |      0           |      2.99        |       2.99        | 1                      |
| 10750 Fantasy Sports                               |      8           |  65509.6         |   65501.6         | 8187.7037499999997     |
| 10751 Vet Drug Violation                           |   1385.98        |   1377.48        |      -8.5         | -6.1328446297926375E-3 |
| 10752 Advanced Age Adult Abuse Violations          |      0           |      0           |       0           | 0.00%                  |
| 10753 Telecom                                      |  96862.5         |      0           |  -96862.5         | -1                     |
| 10754 Adult Performance Business Tax               |  21142           |      0           |  -21142           | -1                     |
| 10755 Pharmacy Board Fine                          |      0           |     17.14        |      17.14        | 1                      |
| 10756 Medical Board Fine                           |      0           |      2.98        |       2.98        | 1                      |
| 10757 Forfeiture of Property                       |      0           |      2.99        |       2.99        | 1                      |
| 10758 Crime Impersonation First Response or Police |      0           |      2.98        |       2.98        | 1                      |
| 10759 Crime Exposure HBV/HCV & Suicide             |      0           |      2.99        |       2.99        | 1                      |
| 10760 Misrepresentation to TennCare                |      0           |      2.98        |       2.98        | 1                      |
| 10761 Confinement Cost of Juveniles                |      0           |      2.99        |       2.99        | 1                      |
| 10762 OCJP Child Like Doll Fine                    |      0           |      2.98        |       2.98        | 1                      |
| TOTAL                                              |      6.97705e+07 |      4.50115e+07 |      -2.4759e+07  | -0.35486296909283882   |



label: F=E-D
labeled_formulas: F=E-D
output: {"Arithmetic-Relationship": ["F=E-D"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_90904___xlsx_79ecfb889a02084cec4aaa4763970a8f203c3e97.xlsx___line_310