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 |         H |        I |         J |
|-----:|--------:|----------:|---------:|----------:|---------:|----------:|----------:|---------:|----------:|
| 1970 | 205.052 | 129.8     |  3.1     |  54.9     | 187.8    |  8.90834  |  56.9061  | 121.986  | 0.5949    |
| 1971 | 207.661 | 134.4     |  6.6     |  56.9061  | 197.906  |  8.90834  |  58.3726  | 130.625  | 0.629031  |
| 1972 | 209.896 | 123.4     | 12       |  58.3726  | 193.773  |  5.33596  |  59.8709  | 128.566  | 0.612521  |
| 1973 | 211.909 | 123.6     | 15.3     |  59.8709  | 198.771  |  4.54818  |  57.5546  | 136.668  | 0.644938  |
| 1974 | 213.854 | 149.4     | 10.8     |  57.5546  | 217.755  |  4.82307  | 100.284   | 112.647  | 0.526749  |
| 1975 | 215.973 |  86.4     |  9.8     | 100.284   | 196.484  |  6.08923  |  64.2753  | 126.12   | 0.58396   |
| 1976 | 218.035 |  82.5     |  7.4     |  64.2753  | 154.175  |  3.42839  |  34.5153  | 116.232  | 0.533087  |
| 1977 | 220.239 |  96.9     | 12.9     |  34.5153  | 144.315  |  3.22371  |  41.6846  |  99.407  | 0.45136   |
| 1978 | 222.585 |  86.46    |  7       |  41.6846  | 135.145  |  4.12335  |  46.6351  |  84.3861 | 0.379119  |
| 1979 | 225.055 |  78.86    |  6.3     |  46.6351  | 131.795  |  5.0203   |  54.3759  |  72.3989 | 0.321694  |
| 1980 | 227.726 |  69.08    |  9.8     |  54.3759  | 133.256  |  5.50708  |  44.7794  |  82.9694 | 0.364339  |
| 1981 | 229.966 |  69.9     |  5       |  44.7794  | 119.679  |  6.01094  |  26.8424  |  86.8261 | 0.37756   |
| 1982 | 232.188 |  68.9     |  5.6     |  26.8424  | 101.342  |  3.2879   |  31.9108  |  66.1437 | 0.284871  |
| 1983 | 234.307 |  67.9     |  3.6     |  31.9108  | 103.411  |  2.873    |  31.2196  |  69.3182 | 0.295843  |
| 1984 | 236.348 |  66.94    |  8.029   |  31.2196  | 106.189  |  2.593    |  28.4404  |  75.1553 | 0.317986  |
| 1985 | 238.466 |  67.66    |  6.404   |  28.4404  | 102.504  |  1.915    |  31.3504  |  69.239  | 0.290352  |
| 1986 | 240.651 |  58.66    |  6.2     |  31.3504  |  96.2104 |  1.708    |  24.1679  |  70.3345 | 0.292267  |
| 1987 | 242.804 |  66.3     |  7.226   |  24.1679  |  97.6939 |  3.238    |  30.2991  |  64.1568 | 0.264233  |
| 1988 | 245.021 |  65.86    |  6.709   |  30.2991  | 102.868  |  4.387    |  17.3212  |  81.1599 | 0.331237  |
| 1989 | 247.342 |  77.66    |  4.09216 |  17.3212  |  99.0733 |  3.765    |  20.4246  |  74.8838 | 0.302754  |
| 1990 | 250.132 |  76.74    |  2.35814 |  20.4246  |  99.5227 |  4.65227  |  20.1826  |  74.6878 | 0.298594  |
| 1991 | 253.493 |  70.8     |  2.16033 |  20.1826  |  93.143  |  3.80939  |  18.6204  |  70.7132 | 0.278955  |
| 1992 | 256.894 |  77.34    |  1.96005 |  18.6204  |  97.9205 |  3.904    |  20.3404  |  73.676  | 0.286795  |
| 1993 | 260.255 |  70.8     |  4.08732 |  20.3404  |  95.2277 |  3.97835  |  18.6204  |  72.629  | 0.279069  |
| 1994 | 263.436 |  67.72    |  2.24121 |  18.6204  |  88.5816 |  5.65719  |  17.8104  |  65.1141 | 0.247172  |
| 1995 | 266.557 |  75.1     |  1.82603 |  17.8104  |  94.7364 |  5.59505  |  19.7513  |  69.39   | 0.26032   |
| 1996 | 269.667 |  70.06    |  3.04757 |  19.7513  |  92.8589 |  8.73703  |  18.4258  |  65.6961 | 0.243619  |
| 1997 | 272.912 |  56.82    |  2.56873 |  18.4258  |  77.8145 | 10.9135   |  14.9437  |  51.9574 | 0.190381  |
| 1998 | 276.115 |  57.98    |  3.23677 |  14.9437  |  76.1604 |  8.45854  |  15.2487  |  52.4531 | 0.189968  |
| 1999 | 279.295 |  61.14    |  2.59902 |  15.2487  |  78.9878 |  3.93208  |  16.0798  |  58.9759 | 0.21116   |
| 2000 | 282.385 |  63       |  4.45581 |  16.0798  |  83.5356 |  4.70079  |  16.569   |  62.2658 | 0.2205    |
| 2001 | 285.309 |  59.4     |  3.44809 |  16.569   |  79.4171 |  1.64474  |  15.6222  |  62.1501 | 0.217834  |
| 2002 | 288.105 |  52.3     |  4.67719 |  15.6222  |  72.5994 |  1.60828  |  13.7549  |  57.2362 | 0.198665  |
| 2003 | 290.82  |  57.3     | 12.6393  |  13.7549  |  83.6942 |  1.72818  |  15.0699  |  66.8961 | 0.230026  |
| 2004 | 293.463 |  42.6     | 14.8123  |  15.0699  |  72.4822 |  1.35948  |  11.2038  |  59.9189 | 0.204179  |
| 2005 | 296.186 |  32.2     | 22.6123  |  11.2038  |  66.0161 |  1.04456  |   8.4686  |  56.5029 | 0.190768  |
| 2006 | 298.996 |  16       | 32.8661  |   8.4686  |  57.3347 |  0.943204 |   4.208   |  52.1835 | 0.174529  |
| 2007 | 302.004 |  11.8     | 31.1007  |   4.208   |  47.1087 |  0.698972 |   3.1034  |  43.3063 | 0.143397  |
| 2008 | 304.798 |  14.2     | 49.7492  |   3.1034  |  67.0526 |  0.433806 |   3.7346  |  62.8841 | 0.206314  |
| 2009 | 307.439 |  10.2     | 38.3338  |   3.7346  |  52.2684 |  0.699028 |   2.6826  |  48.8867 | 0.159013  |
| 2010 | 309.741 |   4.2     | 28.0692  |   2.6826  |  34.9518 |  0.641268 |   1.1046  |  33.206  | 0.107206  |
| 2011 | 311.974 |   6.2     | 36.247   |   1.1046  |  43.5516 |  0.233111 |   1.6306  |  41.6879 | 0.133626  |
| 2012 | 314.168 |   4.4     | 37.555   |   1.6306  |  43.5856 |  0.71823  |   1.1572  |  41.7102 | 0.132764  |
| 2013 | 316.295 |   4.4     | 30.6999  |   1.1572  |  36.2571 |  0.264765 |   1.1572  |  34.8351 | 0.110135  |
| 2014 | 318.577 |   4       | 18.4053  |   1.1572  |  23.5625 |  0.230338 |   1.052   |  22.2802 | 0.0699367 |
| 2015 | 320.871 |   4.6     | 16.5548  |   1.052   |  22.2068 |  0.314634 |   1.2098  |  20.6824 | 0.064457  |
| 2016 | 323.161 |   5.43809 | 20.3212  |   1.2098  |  26.9691 |  0.19076  |   1.43022 |  25.3481 | 0.0784381 |
| 2017 | 325.206 |   5.52415 | 16.7302  |   1.43022 |  23.6846 |  0.411662 |   1.45285 |  21.8201 | 0.0670961 |
| 2018 | 326.924 |   4.66054 | 14.3045  |   1.45285 |  20.4179 |  0.192365 |   1.22572 |  18.9998 | 0.0581169 |
| 2019 | 328.476 |   4.62196 | 15.0648  |   1.22572 |  20.9125 |  0.127236 |   1.21558 |  19.5696 | 0.0595771 |



label: I=F-G-H
labeled_formulas: I=F-G-H
output: {"Arithmetic-Relationship": ["I=F-G-H"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_111942___xlsx_c3b9843bbc5d75dd5b0939ac3c9cc0d6151915a6.xlsx___line_465