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:
|       AA |       AB |      AC |       AD |      AE |       AF |
|---------:|---------:|--------:|---------:|--------:|---------:|
|  411.898 |  27949   | 16.0887 |  25.6017 | 1737.18 | 1.47375  |
|  359.862 |  28295.8 | 16.261  |  22.1304 | 1740.1  | 1.27179  |
|  355.802 |  27725.6 | 16.4764 |  21.5946 | 1682.75 | 1.2833   |
|  377.946 |  27711.6 | 16.706  |  22.6234 | 1658.79 | 1.36385  |
|  411.662 |  29387.1 | 16.9715 |  24.2561 | 1731.55 | 1.40083  |
|  417.45  |  29283.6 | 17.2317 |  24.2258 | 1699.4  | 1.42554  |
|  445.436 |  31192.8 | 17.4887 |  25.47   | 1783.6  | 1.42801  |
|  435.95  |  29765.1 | 17.7438 |  24.5691 | 1677.49 | 1.46463  |
|  475.102 |  30707   | 17.9941 |  26.4032 | 1706.5  | 1.54721  |
|  521.871 |  32686   | 18.2352 |  28.6189 | 1792.47 | 1.59662  |
|  500.573 |  32364.4 | 18.4907 |  27.0716 | 1750.3  | 1.54668  |
|  509.081 |  31050   | 18.7541 |  27.1451 | 1655.64 | 1.63955  |
|  546.434 |  32728.4 | 19.0479 |  28.6874 | 1718.22 | 1.6696   |
|  523.456 |  32016.3 | 19.3241 |  27.0882 | 1656.81 | 1.63496  |
|  539.784 |  35412.2 | 19.654  |  27.4643 | 1801.78 | 1.52429  |
|  482.496 |  33575.3 | 19.9701 |  24.1609 | 1681.28 | 1.43705  |
|  500.147 |  34141.3 | 20.2923 |  24.6471 | 1682.47 | 1.46493  |
|  519.261 |  34116.3 | 20.5996 |  25.2073 | 1656.16 | 1.52203  |
|  486.826 |  33572.3 | 20.9177 |  23.2734 | 1604.97 | 1.45008  |
|  493.959 |  36285.7 | 21.2209 |  23.277  | 1709.9  | 1.3613   |
|  474.564 |  36893.9 | 21.551  |  22.0206 | 1711.94 | 1.28629  |
|  452.996 |  37569.3 | 21.8498 |  20.7322 | 1719.43 | 1.20576  |
|  472.29  |  38636.8 | 22.1412 |  21.3308 | 1745.02 | 1.22238  |
|  506.08  |  40711.5 | 22.4243 |  22.5683 | 1815.51 | 1.24309  |
|  556.479 |  41601.3 | 22.7212 |  24.4916 | 1830.94 | 1.33765  |
|  490.962 |  39381.3 | 22.9962 |  21.3497 | 1712.51 | 1.24669  |
|  509.784 |  42371.1 | 23.2574 |  21.9192 | 1821.83 | 1.20314  |
|  509.606 |  42477.3 | 23.5685 |  21.6223 | 1802.29 | 1.19971  |
|  493.744 |  42814   | 23.8552 |  20.6975 | 1794.74 | 1.15323  |
|  511.409 |  44697.3 | 24.1389 |  21.1861 | 1851.67 | 1.14416  |
|  503.012 |  45933.7 | 24.4324 |  20.5879 | 1880.03 | 1.09508  |
|  502.584 |  46287   | 24.659  |  20.3813 | 1877.08 | 1.0858   |
|  491.708 |  46755.7 | 24.9162 |  19.7345 | 1876.52 | 1.05165  |
|  518.543 |  48271.3 | 25.1991 |  20.5778 | 1915.59 | 1.07423  |
|  545.407 |  51198.9 | 25.4479 |  21.4323 | 2011.91 | 1.06527  |
|  588.177 |  52555.1 | 25.7152 |  22.8727 | 2043.74 | 1.11916  |
|  572.704 |  52076.9 | 25.9672 |  22.0549 | 2005.48 | 1.09973  |
|  599.5   |  54500.5 | 26.2124 |  22.8709 | 2079.19 | 1.09999  |
|  621.694 |  55475.3 | 26.4825 |  23.4756 | 2094.79 | 1.12067  |
|  599.113 |  55929.2 | 26.7504 |  22.3964 | 2090.78 | 1.0712   |
|  584.125 |  54445.9 | 27.0048 |  21.6304 | 2016.16 | 1.07285  |
|  554.757 |  53920.2 | 27.2053 |  20.3915 | 1981.97 | 1.02885  |
|  558.525 |  56348   | 27.4572 |  20.3416 | 2052.21 | 0.991206 |
|  599.251 |  59839.2 | 27.7272 |  21.6124 | 2158.14 | 1.00144  |
|  638.941 |  62923.5 | 27.9781 |  22.8372 | 2249.03 | 1.01542  |
|  648.999 |  63809.4 | 28.2041 |  23.0108 | 2262.42 | 1.01709  |
|  677.973 |  62202.5 | 28.152  |  24.0826 | 2209.52 | 1.08994  |
|  647.714 |  65146.8 | 27.8199 |  23.2824 | 2341.73 | 0.994238 |
|  660.329 |  67186.7 | 27.6697 |  23.8647 | 2428.17 | 0.982826 |
|  610.531 |  66289.6 | 27.5243 |  22.1815 | 2408.4  | 0.921005 |
|  627.832 |  69268.1 | 27.3928 |  22.9196 | 2528.69 | 0.90638  |
|  650.237 |  71456.8 | 27.4482 |  23.6896 | 2603.33 | 0.909973 |
|  727.008 |  73415.3 | 27.5424 |  26.396  | 2665.54 | 0.990267 |
|  782.399 |  74943.3 | 27.6583 |  28.288  | 2709.61 | 1.04399  |
|  788.574 |  75168   | 27.822  |  28.3435 | 2701.75 | 1.04908  |
|  829.609 |  79250.4 | 28.0124 |  29.6158 | 2829.12 | 1.04682  |
|  820.809 |  79114.4 | 28.1885 |  29.1186 | 2806.62 | 1.0375   |
|  784.501 |  78891.8 | 28.3903 |  27.6327 | 2778.83 | 0.994401 |
|  839.254 |  82451   | 28.5907 |  29.3541 | 2883.84 | 1.01788  |
|  856.538 |  83536.4 | 28.7787 |  29.7629 | 2902.71 | 1.02535  |
|  888.268 |  85015.5 | 28.9763 |  30.655  | 2933.97 | 1.04483  |
|  891.024 |  84856.6 | 29.245  |  30.4676 | 2901.58 | 1.05004  |
|  964.199 |  89202.6 | 29.4709 |  32.717  | 3026.81 | 1.08091  |
| 1012.23  |  90368.2 | 29.6809 |  34.1037 | 3044.66 | 1.12011  |
| 1028.31  |  93800.7 | 29.9252 |  34.3628 | 3134.51 | 1.09627  |
| 1061.23  |  94692.8 | 30.0577 |  35.3063 | 3150.37 | 1.1207   |
| 1053.75  |  94625.4 | 30.4095 |  34.6519 | 3111.7  | 1.1136   |
| 1063.86  |  98235.1 | 30.6897 |  34.665  | 3200.91 | 1.08297  |
| 1088.02  | 101018   | 30.9783 |  35.1222 | 3260.93 | 1.07706  |
| 1159.9   | 108404   | 31.2573 |  37.1081 | 3468.11 | 1.06998  |
| 1242.9   | 114191   | 31.5555 |  39.3877 | 3618.74 | 1.08844  |
| 1311.9   | 114673   | 31.8743 |  41.1585 | 3597.66 | 1.14403  |
| 1370.9   | 115740   | 32.1777 |  42.6041 | 3596.9  | 1.18447  |
| 1366.9   | 120309   | 32.5015 |  42.0565 | 3701.64 | 1.13616  |
| 1337.9   | 121670   | 32.8391 |  40.741  | 3705.02 | 1.09962  |
| 1320.9   | 122544   | 33.2005 |  39.7855 | 3691.03 | 1.0779   |
| 1305.9   | 123312   | 33.5755 |  38.8944 | 3672.66 | 1.05902  |
| 1280.9   | 123719   | 33.9436 |  37.7361 | 3644.83 | 1.03533  |
| 1232.9   | 121365   | 34.3044 |  35.9399 | 3537.88 | 1.01586  |
| 1315.9   | 129951   | 34.6233 |  38.0062 | 3753.28 | 1.01261  |
| 1334.9   | 132786   | 34.9347 |  38.2113 | 3800.99 | 1.0053   |
| 1373.9   | 134984   | 35.2066 |  39.0239 | 3834.05 | 1.01783  |
| 1379.9   | 138987   | 35.4499 |  38.9254 | 3920.67 | 0.992825 |
| 1340.9   | 137749   | 35.7247 |  37.5342 | 3855.86 | 0.973434 |
| 1311.9   | 136717   | 36.0159 |  36.4255 | 3796.03 | 0.95957  |
| 1319.9   | 137574   | 36.3137 |  36.3472 | 3788.5  | 0.959407 |
| 1370.9   | 143119   | 36.599  |  37.4573 | 3910.47 | 0.957871 |
| 1421.9   | 147572   | 36.881  |  38.5537 | 4001.3  | 0.96353  |
| 1494.9   | 152337   | 37.1785 |  40.2087 | 4097.44 | 0.981312 |
| 1529.9   | 153687   | 37.4848 |  40.8138 | 4099.98 | 0.995464 |
| 1532.9   | 157279   | 37.802  |  40.5507 | 4160.58 | 0.97464  |
| 1496.9   | 154175   | 38.1343 |  39.2533 | 4042.94 | 0.970911 |
| 1495.9   | 153201   | 38.4898 |  38.8648 | 3980.3  | 0.976428 |
| 1572.9   | 160271   | 38.8588 |  40.4773 | 4124.44 | 0.981402 |
| 1607.9   | 165566   | 39.2211 |  40.9957 | 4221.36 | 0.97115  |
| 1658.9   | 172617   | 39.5991 |  41.8924 | 4359.13 | 0.961027 |
| 1699.9   | 174575   | 39.9873 |  42.5109 | 4365.75 | 0.973738 |
| 1789.9   | 182422   | 40.3803 |  44.326  | 4517.6  | 0.981185 |
| 1894.9   | 188921   | 40.7739 |  46.4733 | 4633.37 | 1.00301  |
| 1968.9   | 188307   | 41.1552 |  47.8409 | 4575.53 | 1.04558  |
| 1983.9   | 192272   | 41.5381 |  47.7609 | 4628.8  | 1.03182  |
| 1993.9   | 195163   | 41.8931 |  47.5949 | 4658.6  | 1.02166  |
| 1969.9   | 193354   | 42.2468 |  46.6283 | 4576.77 | 1.0188   |
| 1972.9   | 195578   | 42.6113 |  46.2999 | 4589.82 | 1.00875  |
| 2039.9   | 201306   | 42.9804 |  47.4611 | 4683.66 | 1.01333  |
| 2117.9   | 206356   | 43.3615 |  48.8429 | 4758.96 | 1.02633  |
| 2194.9   | 210281   | 43.7374 |  50.1836 | 4807.8  | 1.0438   |
| 2098.9   | 202461   | 44.1242 |  47.568  | 4588.43 | 1.03669  |
| 2138.9   | 207249   | 44.5198 |  48.0437 | 4655.2  | 1.03204  |
| 2223.9   | 212706   | 44.9041 |  49.5255 | 4736.89 | 1.04553  |
| 2311.9   | 219724   | 45.2625 |  51.0776 | 4854.43 | 1.05218  |
| 2406.9   | 222970   | 45.4588 |  52.9468 | 4904.89 | 1.07947  |
| 2502.9   | 232155   | 45.7022 |  54.7654 | 5079.74 | 1.07811  |
| 2532.63  | 236810   | 46.1017 |  54.9356 | 5136.7  | 1.06947  |
| 3033.87  | 249756   | 46.34   |  65.4698 | 5389.64 | 1.21474  |
| 3516.09  | 252516   | 46.514  |  75.592  | 5428.82 | 1.39242  |
| 4350.16  | 251010   | 46.614  |  93.3229 | 5384.87 | 1.73306  |
| 5163.43  | 255752   | 46.575  | 110.863  | 5491.18 | 2.01892  |
| 5545.17  | 235683   | 46.534  | 119.164  | 5064.75 | 2.35281  |
| 6073.02  | 221820   | 46.821  | 129.707  | 4737.61 | 2.73782  |



label: AD=AA/AC
AE=AB/AC
labeled_formulas: AD=AA/AC
AE=AB/AC
output: {"Arithmetic-Relationship": ["AD=AA/AC", "AE=AB/AC"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_565415___xlsx_1601a7f2aad17d4e02620ba5a76c60aaa0e2cc9d.xlsx___line_124