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 |
|------:|--------:|--------:|--------:|---------:|--------:|------------:|
| 42370 | 2938.09 | 1994    | 2938.09 |  944.093 | 2462.19 |  0.19328    |
| 42401 | 2534.29 | 1426.21 | 2534.29 | 1108.08  | 2010.28 |  0.260669   |
| 42430 | 2486.32 | 1184.89 | 2486.32 | 1301.43  | 1830.67 |  0.358148   |
| 42461 | 2645.56 | 1426.8  | 2645.56 | 1218.76  | 2051.1  |  0.289825   |
| 42491 | 2966.26 | 1847.45 | 2966.26 | 1118.81  | 2449.77 |  0.210835   |
| 42522 | 3186.03 | 2195.23 | 3186.03 |  990.806 | 2776.38 |  0.147548   |
| 42552 | 3318.14 | 2381.27 | 3318.14 |  936.87  | 2952.26 |  0.123932   |
| 42583 | 3441.32 | 2616.84 | 3522.22 |  905.375 | 3165.62 |  0.0870943  |
| 42614 | 3705.16 | 2950.37 | 3839.84 |  889.468 | 3495.51 |  0.0599783  |
| 42644 | 4012.72 | 3236.25 | 4012.72 |  776.469 | 3751.2  |  0.0697161  |
| 42675 | 3976.58 | 3030.08 | 3976.58 |  946.502 | 3651.51 |  0.0890226  |
| 42705 | 3296.94 | 2708.32 | 3340.98 |  632.663 | 3113.42 |  0.058947   |
| 42736 | 2622.16 | 1994    | 2938.09 |  944.093 | 2462.19 |  0.0649677  |
| 42767 | 2337.33 | 1426.21 | 2534.29 | 1108.08  | 2010.28 |  0.162692   |
| 42795 | 2062.5  | 1184.89 | 2486.32 | 1301.43  | 1830.67 |  0.126638   |
| 42826 | 2291.25 | 1426.8  | 2645.56 | 1218.76  | 2051.1  |  0.117083   |
| 42856 | 2626.51 | 1847.45 | 2966.26 | 1118.81  | 2449.77 |  0.0721451  |
| 42887 | 2906.81 | 2195.23 | 3186.03 |  990.806 | 2776.38 |  0.046977   |
| 42917 | 3054.15 | 2381.27 | 3318.14 |  936.87  | 2952.26 |  0.0345126  |
| 42948 | 3249.9  | 2616.84 | 3522.22 |  905.375 | 3165.62 |  0.0266231  |
| 42979 | 3567.23 | 2950.37 | 3839.84 |  889.468 | 3495.51 |  0.0205182  |
| 43009 | 3816.5  | 3236.25 | 4012.72 |  776.469 | 3751.2  |  0.0174057  |
| 43040 | 3709.26 | 3030.08 | 3976.58 |  946.502 | 3651.51 |  0.0158152  |
| 43070 | 3032.6  | 2708.32 | 3340.98 |  632.663 | 3113.42 | -0.0259575  |
| 43101 | 2140.56 | 1994    | 2938.09 |  944.093 | 2462.19 | -0.130631   |
| 43132 | 1672.66 | 1426.21 | 2534.29 | 1108.08  | 2010.28 | -0.167944   |
| 43160 | 1390.28 | 1184.89 | 2486.32 | 1301.43  | 1830.67 | -0.240563   |
| 43191 | 1426.8  | 1426.8  | 2645.56 | 1218.76  | 2051.1  | -0.304374   |
| 43221 | 1847.45 | 1847.45 | 2966.26 | 1118.81  | 2449.77 | -0.245866   |
| 43252 | 2195.23 | 2195.23 | 3186.03 |  990.806 | 2776.38 | -0.209321   |
| 43282 | 2381.27 | 2381.27 | 3318.14 |  936.87  | 2952.26 | -0.193408   |
| 43313 | 2616.84 | 2616.84 | 3522.22 |  905.375 | 3165.62 | -0.173355   |
| 43344 | 2950.37 | 2950.37 | 3839.84 |  889.468 | 3495.51 | -0.155954   |
| 43374 | 3236.25 | 3236.25 | 4012.72 |  776.469 | 3751.2  | -0.137276   |
| 43405 | 3030.08 | 3030.08 | 3976.58 |  946.502 | 3651.51 | -0.170185   |
| 43435 | 2708.32 | 2708.32 | 3340.98 |  632.663 | 3113.42 | -0.130114   |
| 43466 | 1994    | 1994    | 2938.09 |  944.093 | 2462.19 | -0.190155   |
| 43497 | 1426.21 | 1426.21 | 2534.29 | 1108.08  | 2010.28 | -0.29054    |
| 43525 | 1184.89 | 1184.89 | 2486.32 | 1301.43  | 1830.67 | -0.352756   |
| 43556 | 1559.4  | 1426.8  | 2645.56 | 1218.76  | 2051.1  | -0.239725   |
| 43586 | 2031.03 | 1847.45 | 2966.26 | 1118.81  | 2449.77 | -0.170929   |
| 43617 | 2460.75 | 2195.23 | 3186.03 |  990.806 | 2776.38 | -0.113685   |
| 43647 | 2714.2  | 2381.27 | 3318.14 |  936.87  | 2952.26 | -0.0806381  |
| 43678 | 2997.81 | 2616.84 | 3522.22 |  905.375 | 3165.62 | -0.0530094  |
| 43709 | 3414.94 | 2950.37 | 3839.84 |  889.468 | 3495.51 | -0.0230488  |
| 43739 | 3762.04 | 3236.25 | 4012.72 |  776.469 | 3751.2  |  0.00288953 |
| 43770 | 3610.03 | 3030.08 | 3976.58 |  946.502 | 3651.51 | -0.0113609  |
| 43800 | 3188.24 | 2708.32 | 3340.98 |  632.663 | 3113.42 |  0.0240333  |
| 43831 | 2616.18 | 1994    | 2938.09 |  944.093 | 2462.19 |  0.0625378  |
| 43862 | 2080.88 | 1426.21 | 2534.29 | 1108.08  | 2010.28 |  0.0351232  |
| 43891 | 2029.36 | 1184.89 | 2486.32 | 1301.43  | 1830.67 |  0.108533   |
| 43922 | 2332.49 | 1426.8  | 2645.56 | 1218.76  | 2051.1  |  0.137191   |
| 43952 | 2777.58 | 1847.45 | 2966.26 | 1118.81  | 2449.77 |  0.133815   |
| 43983 | 3133.09 | 2195.23 | 3186.03 |  990.806 | 2776.38 |  0.128481   |
| 44013 | 3293.55 | 2381.27 | 3318.14 |  936.87  | 2952.26 |  0.115602   |
| 44044 | 3522.22 | 2616.84 | 3522.22 |  905.375 | 3165.62 |  0.112647   |
| 44075 | 3839.84 | 2950.37 | 3839.84 |  889.468 | 3495.51 |  0.0985064  |
| 44105 | 3928.5  | 3236.25 | 4012.72 |  776.469 | 3751.2  |  0.0472646  |
| 44136 | 3931.62 | 3030.08 | 3976.58 |  946.502 | 3651.51 |  0.0767086  |
| 44166 | 3340.98 | 2708.32 | 3340.98 |  632.663 | 3113.42 |  0.0730913  |
| 44197 | 2634.96 | 1994    | 2938.09 |  944.093 | 2462.19 |  0.0701688  |
| 44228 | 1858.22 | 1426.21 | 2534.29 | 1108.08  | 2010.28 | -0.0756382  |
| 44256 | 1800.64 | 1184.89 | 2486.32 | 1301.43  | 1830.67 | -0.0164015  |
| 44287 | 1974.33 | 1426.8  | 2645.56 | 1218.76  | 2051.1  | -0.0374285  |
| 44317 | 2388.06 | 1847.45 | 2966.26 | 1118.81  | 2449.77 | -0.0251894  |
| 44348 | 2582.86 | 2195.23 | 3186.03 |  990.806 | 2776.38 | -0.069704   |
| 44378 | 2752.44 | 2381.27 | 3318.14 |  936.87  | 2952.26 | -0.067684   |
| 44409 | 2915.6  | 2616.84 | 3522.22 |  905.375 | 3165.62 | -0.0789797  |
| 44440 | 3304.68 | 2950.37 | 3839.84 |  889.468 | 3495.51 | -0.0545913  |
| 44470 | 3643.56 | 3236.25 | 4012.72 |  776.469 | 3751.2  | -0.0286966  |
| 44501 | 3540.38 | 3030.08 | 3976.58 |  946.502 | 3651.51 | -0.0304357  |
| 44531 | 2961.82 | 2708.32 | 3340.98 |  632.663 | 3113.42 | -0.0486923  |
| 44562 | 2258.44 | 1994    | 2938.09 |  944.093 | 2462.19 | -0.0827533  |
| 44593 | 1756.19 | 1426.21 | 2534.29 | 1108.08  | 2010.28 | -0.126391   |
| 44621 | 1659.46 | 1184.89 | 2486.32 | 1301.43  | 1830.67 | -0.0935219  |
| 44652 | 1887.6  | 1426.8  | 2645.56 | 1218.76  | 2051.1  | -0.0797136  |
| 44682 | 2309.53 | 1847.45 | 2966.26 | 1118.81  | 2449.77 | -0.0572463  |
| 44713 | 2588.19 | 2195.23 | 3186.03 |  990.806 | 2776.38 | -0.0677824  |
| 44743 | 2739.7  | 2381.27 | 3318.14 |  936.87  | 2952.26 | -0.072      |
| 44774 | 2955.06 | 2616.84 | 3522.22 |  905.375 | 3165.62 | -0.0665149  |
| 44805 | 3311.49 | 2950.37 | 3839.84 |  889.468 | 3495.51 | -0.0526446  |
| 44835 | 3588.49 | 3236.25 | 4012.72 |  776.469 | 3751.2  | -0.0433759  |
| 44866 | 3496.68 | 3030.08 | 3976.58 |  946.502 | 3651.51 | -0.0424039  |
| 44896 | 2861.89 | 2708.32 | 3340.98 |  632.663 | 3113.42 | -0.0807888  |



label: E=D-C
labeled_formulas: E=D-C
output: {"Arithmetic-Relationship": ["E=D-C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_35984___xlsx_c31dcfd1f13016a4b20598df6b868a9ca7600765.xlsx___line_570