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 |
|-----:|---------:|---------:|--------:|--------:|---------:|---------:|
|  450 |  94.7933 |  749.879 | 1294.67 | 1.05807 |  2297.85 |  6.10352 |
|  500 |  99.2014 |  754.287 | 1353.49 | 1.06448 |  2543.93 |  6.78168 |
|  550 | 103.588  |  758.674 | 1412.26 | 1.07089 |  2788.27 |  7.45985 |
|  600 | 107.955  |  763.041 | 1471    | 1.07729 |  3030.89 |  8.13802 |
|  650 | 112.306  |  767.392 | 1529.7  | 1.08368 |  3271.8  |  8.81619 |
|  700 | 116.641  |  771.727 | 1588.37 | 1.09007 |  3511.04 |  9.49436 |
|  750 | 120.962  |  776.048 | 1647.01 | 1.09645 |  3748.62 | 10.1725  |
|  800 | 125.271  |  780.357 | 1705.63 | 1.10282 |  3984.57 | 10.8507  |
|  850 | 129.569  |  784.655 | 1764.22 | 1.10919 |  4218.9  | 11.5289  |
|  900 | 133.855  |  788.941 | 1822.8  | 1.11555 |  4451.65 | 12.207   |
|  950 | 138.132  |  793.218 | 1881.35 | 1.1219  |  4682.82 | 12.8852  |
| 1000 | 142.4    |  797.486 | 1939.89 | 1.12825 |  4912.44 | 13.5634  |
| 1050 | 146.659  |  801.745 | 1998.4  | 1.13459 |  5140.53 | 14.2415  |
| 1100 | 150.91   |  805.996 | 2056.91 | 1.14092 |  5367.1  | 14.9197  |
| 1150 | 155.154  |  810.24  | 2115.39 | 1.14724 |  5592.19 | 15.5979  |
| 1200 | 159.39   |  814.476 | 2173.87 | 1.15356 |  5815.79 | 16.276   |
| 1250 | 163.62   |  818.706 | 2232.33 | 1.15987 |  6037.94 | 16.9542  |
| 1300 | 167.844  |  822.929 | 2290.77 | 1.16618 |  6258.66 | 17.6324  |
| 1350 | 172.061  |  827.147 | 2349.21 | 1.17248 |  6477.94 | 18.3105  |
| 1400 | 176.273  |  831.358 | 2407.63 | 1.17877 |  6695.83 | 18.9887  |
| 1450 | 180.479  |  835.565 | 2466.04 | 1.18505 |  6912.33 | 19.6669  |
| 1500 | 184.68   |  839.766 | 2524.45 | 1.19133 |  7127.45 | 20.3451  |
| 1550 | 188.876  |  843.962 | 2582.84 | 1.1976  |  7341.22 | 21.0232  |
| 1600 | 193.067  |  848.153 | 2641.22 | 1.20387 |  7553.65 | 21.7014  |
| 1650 | 197.254  |  852.339 | 2699.59 | 1.21013 |  7764.76 | 22.3796  |
| 1700 | 201.436  |  856.522 | 2757.96 | 1.21638 |  7974.56 | 23.0577  |
| 1750 | 205.614  |  860.7   | 2816.31 | 1.22263 |  8183.07 | 23.7359  |
| 1800 | 209.788  |  864.874 | 2874.66 | 1.22887 |  8390.3  | 24.4141  |
| 1850 | 213.958  |  869.044 | 2933    | 1.2351  |  8596.26 | 25.0922  |
| 1900 | 218.124  |  873.21  | 2991.33 | 1.24132 |  8800.98 | 25.7704  |
| 1950 | 222.287  |  877.373 | 3049.66 | 1.24754 |  9004.46 | 26.4486  |
| 2000 | 226.446  |  881.532 | 3107.98 | 1.25376 |  9206.71 | 27.1267  |
| 2050 | 230.602  |  885.688 | 3166.29 | 1.25996 |  9407.76 | 27.8049  |
| 2100 | 234.754  |  889.84  | 3224.59 | 1.26617 |  9607.62 | 28.4831  |
| 2150 | 238.903  |  893.989 | 3282.89 | 1.27236 |  9806.29 | 29.1612  |
| 2200 | 243.05   |  898.136 | 3341.19 | 1.27855 | 10003.8  | 29.8394  |
| 2250 | 247.193  |  902.279 | 3399.47 | 1.28473 | 10200.1  | 30.5176  |
| 2300 | 251.333  |  906.419 | 3457.75 | 1.2909  | 10395.4  | 31.1957  |
| 2350 | 255.471  |  910.557 | 3516.03 | 1.29707 | 10589.4  | 31.8739  |
| 2400 | 259.605  |  914.691 | 3574.3  | 1.30323 | 10782.4  | 32.5521  |
| 2450 | 263.738  |  918.823 | 3632.56 | 1.30939 | 10974.2  | 33.2303  |
| 2500 | 267.867  |  922.953 | 3690.82 | 1.31554 | 11165    | 33.9084  |
| 2550 | 271.994  |  927.08  | 3749.07 | 1.32168 | 11354.7  | 34.5866  |
| 2600 | 276.119  |  931.204 | 3807.32 | 1.32782 | 11543.2  | 35.2648  |
| 2650 | 280.241  |  935.327 | 3865.57 | 1.33395 | 11730.8  | 35.9429  |
| 2700 | 284.36   |  939.446 | 3923.81 | 1.34007 | 11917.3  | 36.6211  |
| 2750 | 288.478  |  943.564 | 3982.04 | 1.34619 | 12102.7  | 37.2993  |
| 2800 | 292.593  |  947.679 | 4040.27 | 1.3523  | 12287.1  | 37.9774  |
| 2850 | 296.706  |  951.792 | 4098.5  | 1.35841 | 12470.5  | 38.6556  |
| 2900 | 300.817  |  955.903 | 4156.72 | 1.36451 | 12652.9  | 39.3338  |
| 2950 | 304.926  |  960.012 | 4214.94 | 1.3706  | 12834.3  | 40.0119  |
| 3000 | 309.033  |  964.119 | 4273.15 | 1.37669 | 13014.7  | 40.6901  |
| 3050 | 313.138  |  968.224 | 4331.36 | 1.38277 | 13194.1  | 41.3683  |
| 3100 | 317.241  |  972.327 | 4389.57 | 1.38885 | 13372.6  | 42.0464  |
| 3150 | 321.342  |  976.428 | 4447.77 | 1.39491 | 13550.1  | 42.7246  |
| 3200 | 325.442  |  980.528 | 4505.97 | 1.40098 | 13726.7  | 43.4028  |
| 3250 | 329.539  |  984.625 | 4564.16 | 1.40703 | 13902.3  | 44.0809  |
| 3300 | 333.635  |  988.721 | 4622.36 | 1.41308 | 14077    | 44.7591  |
| 3350 | 337.729  |  992.815 | 4680.54 | 1.41913 | 14250.7  | 45.4373  |
| 3400 | 341.821  |  996.907 | 4738.73 | 1.42516 | 14423.6  | 46.1155  |
| 3450 | 345.911  | 1001     | 4796.91 | 1.4312  | 14595.5  | 46.7936  |
| 3500 | 350      | 1005.09  | 4855.09 | 1.43722 | 14766.6  | 47.4718  |
| 3550 | 354.088  | 1009.17  | 4913.26 | 1.44324 | 14936.7  | 48.15    |
| 3600 | 358.173  | 1013.26  | 4971.43 | 1.44926 | 15106    | 48.8281  |
| 3650 | 362.258  | 1017.34  | 5029.6  | 1.45526 | 15274.4  | 49.5063  |
| 3700 | 366.34   | 1021.43  | 5087.77 | 1.46126 | 15442    | 50.1845  |
| 3750 | 370.421  | 1025.51  | 5145.93 | 1.46726 | 15608.7  | 50.8626  |
| 3800 | 374.501  | 1029.59  | 5204.09 | 1.47325 | 15774.5  | 51.5408  |
| 3850 | 378.579  | 1033.67  | 5262.24 | 1.47923 | 15939.5  | 52.219   |
| 3900 | 382.656  | 1037.74  | 5320.4  | 1.48521 | 16103.7  | 52.8971  |
| 3950 | 386.732  | 1041.82  | 5378.55 | 1.49118 | 16267.1  | 53.5753  |
| 4000 | 390.806  | 1045.89  | 5436.7  | 1.49715 | 16429.6  | 54.2535  |



label: D=(A+B+C)
labeled_formulas: D=(A+B+C)
output: {"Arithmetic-Relationship": ["D=(A+B+C)"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_765748___xlsx_3a013d31acd4886a6bd02fca55ba5d62ced3770d.xlsx___line_227