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 |
|----:|---------:|--------:|--------:|----:|----:|----:|
|   1 |  47.3507 | 1.47694 | 1.54347 |   0 |   0 |   0 |
|   2 |  48.8277 | 1.49779 | 1.56466 |   0 |   0 |   0 |
|   3 |  50.3255 | 1.51835 | 1.58577 |   0 |   0 |   0 |
|   4 |  51.8438 | 1.53862 | 1.60678 |   0 |   0 |   0 |
|   5 |  53.3824 | 1.55859 | 1.62771 |   0 |   0 |   0 |
|   6 |  54.941  | 1.57826 | 1.64852 |   0 |   0 |   0 |
|   7 |  56.5193 | 1.59763 | 1.66923 |   0 |   0 |   0 |
|   8 |  58.1169 | 1.61668 | 1.68982 |   0 |   0 |   0 |
|   9 |  59.7336 | 1.63543 | 1.71028 |   0 |   0 |   0 |
|  10 |  61.369  | 1.65387 | 1.73062 |   0 |   0 |   0 |
|  11 |  63.0229 | 1.67198 | 1.75082 |   0 |   0 |   0 |
|  12 |  64.6949 | 1.68978 | 1.77087 |   0 |   0 |   0 |
|  13 |  66.3846 | 1.70725 | 1.79078 |   0 |   0 |   0 |
|  14 |  68.0919 | 1.7244  | 1.81054 |   0 |   0 |   0 |
|  15 |  69.8163 | 1.74122 | 1.83014 |   0 |   0 |   0 |
|  16 |  71.5575 | 1.75771 | 1.84958 |   0 |   0 |   0 |
|  17 |  73.3152 | 1.77387 | 1.86887 |   0 |   0 |   0 |
|  18 |  75.0891 | 1.78969 | 1.88798 |   0 |   0 |   0 |
|  19 |  76.8788 | 1.80518 | 1.90693 |   0 |   0 |   0 |
|  20 |  78.684  | 1.82034 | 1.92571 |   0 |   0 |   0 |
|  21 |  80.5043 | 1.83515 | 1.94432 |   0 |   0 |   0 |
|  22 |  82.3394 | 1.84963 | 1.96275 |   0 |   0 |   0 |
|  23 |  84.1891 | 1.86377 | 1.98101 |   0 |   0 |   0 |
|  24 |  86.0528 | 1.87757 | 1.9991  |   0 |   0 |   0 |
|  25 |  87.9304 | 1.89103 | 2.01701 |   0 |   0 |   0 |
|  26 |  89.8214 | 1.90414 | 2.03474 |   0 |   0 |   0 |
|  27 |  91.7256 | 1.91692 | 2.0523  |   0 |   0 |   0 |
|  28 |  93.6425 | 1.92936 | 2.06969 |   0 |   0 |   0 |
|  29 |  95.5719 | 1.94145 | 2.0869  |   0 |   0 |   0 |
|  30 |  97.5133 | 1.95321 | 2.10394 |   0 |   0 |   0 |
|  31 |  99.4665 | 1.96462 | 2.12081 |   0 |   0 |   0 |
|  32 | 101.431  | 1.9757  | 2.1375  |   0 |   0 |   0 |
|  33 | 103.407  | 1.98644 | 2.15403 |   0 |   0 |   0 |
|  34 | 105.393  | 1.99684 | 2.1704  |   0 |   0 |   0 |
|  35 | 107.39   | 2.00691 | 2.1866  |   0 |   0 |   0 |
|  36 | 109.397  | 2.01664 | 2.20265 |   0 |   0 |   0 |
|  37 | 111.414  | 2.02603 | 2.21853 |   0 |   0 |   0 |
|  38 | 113.44   | 2.0351  | 2.23427 |   0 |   0 |   0 |
|  39 | 115.475  | 2.04383 | 2.24985 |   0 |   0 |   0 |
|  40 | 117.519  | 2.05224 | 2.26529 |   0 |   0 |   0 |
|  41 | 119.571  | 2.06032 | 2.28058 |   0 |   0 |   0 |
|  42 | 121.631  | 2.06807 | 2.29574 |   0 |   0 |   0 |
|  43 | 123.699  | 2.0755  | 2.31076 |   0 |   0 |   0 |
|  44 | 125.775  | 2.08261 | 2.32565 |   0 |   0 |   0 |
|  45 | 127.857  | 2.0894  | 2.34041 |   0 |   0 |   0 |
|  46 | 129.947  | 2.09587 | 2.35505 |   0 |   0 |   0 |
|  47 | 132.043  | 2.10203 | 2.36958 |   0 |   0 |   0 |
|  48 | 134.145  | 2.10788 | 2.38399 |   0 |   0 |   0 |
|  49 | 136.253  | 2.11342 | 2.39829 |   0 |   0 |   0 |
|  50 | 138.366  | 2.11866 | 2.41249 |   0 |   0 |   0 |
|  51 | 140.485  | 2.12359 | 2.4266  |   0 |   0 |   0 |
|  52 | 142.608  | 2.12823 | 2.44061 |   0 |   0 |   0 |
|  53 | 144.736  | 2.13256 | 2.45453 |   0 |   0 |   0 |
|  54 | 146.869  | 2.1366  | 2.46837 |   0 |   0 |   0 |
|  55 | 149.006  | 2.14036 | 2.48213 |   0 |   0 |   0 |
|  56 | 151.146  | 2.14382 | 2.49582 |   0 |   0 |   0 |
|  57 | 153.29   | 2.147   | 2.50944 |   0 |   0 |   0 |
|  58 | 155.437  | 2.1499  | 2.523   |   0 |   0 |   0 |
|  59 | 157.587  | 2.15252 | 2.53651 |   0 |   0 |   0 |
|  60 | 159.739  | 2.15486 | 2.54996 |   0 |   0 |   0 |
|  61 | 161.894  | 2.15694 | 2.56336 |   0 |   0 |   0 |
|  62 | 164.051  | 2.15875 | 2.57673 |   0 |   0 |   0 |
|  63 | 166.21   | 2.16029 | 2.59005 |   0 |   0 |   0 |
|  64 | 168.37   | 2.16158 | 2.60335 |   0 |   0 |   0 |
|  65 | 170.532  | 2.1626  | 2.61662 |   0 |   0 |   0 |
|  66 | 172.694  | 2.16338 | 2.62987 |   0 |   0 |   0 |
|  67 | 174.858  | 2.16391 | 2.6431  |   0 |   0 |   0 |
|  68 | 177.022  | 2.16419 | 2.65632 |   0 |   0 |   0 |
|  69 | 179.186  | 2.16422 | 2.66953 |   0 |   0 |   0 |
|  70 | 181.35   | 2.16402 | 2.68275 |   0 |   0 |   0 |
|  71 | 183.514  | 2.16359 | 2.69596 |   0 |   0 |   0 |
|  72 | 185.678  | 2.16293 | 2.70918 |   0 |   0 |   0 |
|  73 | 187.84   | 2.16203 | 2.72242 |   0 |   0 |   0 |
|  74 | 190.003  | 2.16092 | 2.73567 |   0 |   0 |   0 |
|  75 | 192.163  | 2.15959 | 2.74895 |   0 |   0 |   0 |
|  76 | 194.323  | 2.15804 | 2.76225 |   0 |   0 |   0 |
|  77 | 196.481  | 2.15628 | 2.77558 |   0 |   0 |   0 |
|  78 | 198.637  | 2.15431 | 2.78894 |   0 |   0 |   0 |
|  79 | 200.792  | 2.15214 | 2.80234 |   0 |   0 |   0 |
|  80 | 202.944  | 2.14977 | 2.81579 |   0 |   0 |   0 |
|  81 | 205.094  | 2.1472  | 2.82928 |   0 |   0 |   0 |
|  82 | 207.241  | 2.14444 | 2.84283 |   0 |   0 |   0 |
|  83 | 209.385  | 2.14149 | 2.85643 |   0 |   0 |   0 |
|  84 | 211.527  | 2.13836 | 2.87009 |   0 |   0 |   0 |
|  85 | 213.665  | 2.13504 | 2.88381 |   0 |   0 |   0 |
|  86 | 215.8    | 2.13155 | 2.89759 |   0 |   0 |   0 |
|  87 | 217.932  | 2.12788 | 2.91145 |   0 |   0 |   0 |
|  88 | 220.059  | 2.12405 | 2.92538 |   0 |   0 |   0 |
|  89 | 222.184  | 2.12005 | 2.93938 |   0 |   0 |   0 |
|  90 | 224.304  | 2.11588 | 2.95347 |   0 |   0 |   0 |
|  91 | 226.419  | 2.11156 | 2.96764 |   0 |   0 |   0 |
|  92 | 228.531  | 2.10708 | 2.98189 |   0 |   0 |   0 |
|  93 | 230.638  | 2.10245 | 2.99624 |   0 |   0 |   0 |
|  94 | 232.741  | 2.09768 | 3.01068 |   0 |   0 |   0 |
|  95 | 234.838  | 2.09275 | 3.02521 |   0 |   0 |   0 |
|  96 | 236.931  | 2.08769 | 3.03984 |   0 |   0 |   0 |
|  97 | 239.019  | 2.08249 | 3.05458 |   0 |   0 |   0 |
|  98 | 241.101  | 2.07716 | 3.06942 |   0 |   0 |   0 |
|  99 | 243.178  | 2.07169 | 3.08436 |   0 |   0 |   0 |
| 100 | 245.25   | 2.0661  | 3.09942 |   0 |   0 |   0 |
| 101 | 247.316  | 2.06038 | 3.11458 |   0 |   0 |   0 |
| 102 | 249.377  | 2.05455 | 3.12987 |   0 |   0 |   0 |
| 103 | 251.431  | 2.0486  | 3.14527 |   0 |   0 |   0 |
| 104 | 253.48   | 2.04253 | 3.16079 |   0 |   0 |   0 |
| 105 | 255.522  | 2.03635 | 3.17643 |   0 |   0 |   0 |
| 106 | 257.559  | 2.03007 | 3.1922  |   0 |   0 |   0 |
| 107 | 259.589  | 2.02368 | 3.20809 |   0 |   0 |   0 |
| 108 | 261.612  | 2.01718 | 3.22411 |   0 |   0 |   0 |
| 109 | 263.629  | 2.0106  | 3.24027 |   0 |   0 |   0 |
| 110 | 265.64   | 2.00391 | 3.25656 |   0 |   0 |   0 |
| 111 | 267.644  | 1.99714 | 3.27298 |   0 |   0 |   0 |
| 112 | 269.641  | 1.99027 | 3.28954 |   0 |   0 |   0 |
| 113 | 271.631  | 1.98332 | 3.30624 |   0 |   0 |   0 |
| 114 | 273.615  | 1.97628 | 3.32308 |   0 |   0 |   0 |
| 115 | 275.591  | 1.96917 | 3.34006 |   0 |   0 |   0 |
| 116 | 277.56   | 1.96198 | 3.35719 |   0 |   0 |   0 |
| 117 | 279.522  | 1.95471 | 3.37447 |   0 |   0 |   0 |
| 118 | 281.477  | 1.94737 | 3.39189 |   0 |   0 |   0 |
| 119 | 283.424  | 1.93996 | 3.40947 |   0 |   0 |   0 |
| 120 | 285.364  | 1.93248 | 3.42719 |   0 |   0 |   0 |
| 121 | 287.297  | 1.92494 | 3.44507 |   0 |   0 |   0 |
| 122 | 289.222  | 1.91734 | 3.46311 |   0 |   0 |   0 |
| 123 | 291.139  | 1.90967 | 3.4813  |   0 |   0 |   0 |
| 124 | 293.049  | 1.90195 | 3.49965 |   0 |   0 |   0 |
| 125 | 294.951  | 1.89418 | 3.51816 |   0 |   0 |   0 |
| 126 | 296.845  | 1.88635 | 3.53683 |   0 |   0 |   0 |
| 127 | 298.731  | 1.87848 | 3.55566 |   0 |   0 |   0 |
| 128 | 300.61   | 1.87056 | 3.57466 |   0 |   0 |   0 |
| 129 | 302.48   | 1.86259 | 3.59382 |   0 |   0 |   0 |
| 130 | 304.343  | 1.85458 | 3.61316 |   0 |   0 |   0 |



label: G=E*F
labeled_formulas: G=E*F
output: {"Arithmetic-Relationship": ["G=E*F"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_356612___xlsx_17c93e6403bdda4f27936b54cd145b5244aa812e.xlsx___line_259