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 |
|-----:|--------:|--------:|---------:|--------:|--------:|---------:|---------:|---------:|
| 1960 | 180.671 |  363.3  |   22.8   |  386.1  |  10.444 |  375.656 |  2.07923 |  1.91289 |
| 1961 | 183.691 |  398.9  |   13.3   |  412.2  |  11.796 |  400.404 |  2.17977 |  2.00539 |
| 1962 | 186.538 |  371.5  |   17.5   |  389    |  11.896 |  377.104 |  2.02159 |  1.85987 |
| 1963 | 189.242 |  398.5  |   16.6   |  415.1  |  11.507 |  403.593 |  2.13268 |  1.96207 |
| 1964 | 191.889 |  387.4  |   14.8   |  402.2  |  14.61  |  387.59  |  2.01987 |  1.85828 |
| 1965 | 194.303 |  389.1  |   19.1   |  408.2  |  16.103 |  392.097 |  2.01797 |  1.85653 |
| 1966 | 196.56  |  402.4  |   26.4   |  428.8  |  16.829 |  411.971 |  2.0959  |  1.92823 |
| 1967 | 198.712 |  432.8  |   30.1   |  462.9  |  14.089 |  448.811 |  2.2586  |  2.07791 |
| 1968 | 200.706 |  491.6  |   27.1   |  518.7  |  17.542 |  501.158 |  2.49698 |  2.29722 |
| 1969 | 202.677 |  436.1  |   45.4   |  481.5  |  17.622 |  463.878 |  2.28876 |  2.10565 |
| 1970 | 205.052 |  387.2  |   69.9   |  457.1  |  13.6   |  443.5   |  2.16287 |  1.98984 |
| 1971 | 207.661 |  407.2  |   78.4   |  485.6  |  15.3   |  470.3   |  2.26475 |  2.08357 |
| 1972 | 209.896 |  465.1  |   64.9   |  530    |  25.5   |  504.5   |  2.40357 |  2.21129 |
| 1973 | 211.909 |  473.8  |   92.2   |  566    |  29     |  537     |  2.53411 |  2.33138 |
| 1974 | 213.854 |  525.1  |   90.5   |  615.6  |  32.9   |  582.7   |  2.72476 |  2.50678 |
| 1975 | 215.973 |  510.6  |   67.8   |  578.4  |  41.8   |  536.6   |  2.48457 |  2.2858  |
| 1976 | 218.035 |  526.9  |   94.1   |  621    |  39.5   |  581.5   |  2.667   |  2.45364 |
| 1977 | 220.239 |  537    |  121.5   |  658.5  |  42     |  616.5   |  2.79923 |  2.57529 |
| 1978 | 222.585 |  520.1  |  156.1   |  676.2  |  60.5   |  615.7   |  2.76613 |  2.54484 |
| 1979 | 225.055 |  581.9  |  143.7   |  725.6  |  64.5   |  661.1   |  2.9375  |  2.7025  |
| 1980 | 227.726 |  549.4  |  174.2   |  723.6  |  66.5   |  657.1   |  2.88549 |  2.65465 |
| 1981 | 229.966 |  587.5  |  127     |  714.5  |  73.8   |  640.7   |  2.78606 |  2.56318 |
| 1982 | 232.188 |  592.7  |  168.8   |  761.5  |  71.4   |  690.1   |  2.97216 |  2.73439 |
| 1983 | 234.307 |  698.7  |  153.9   |  852.6  |  73.4   |  779.2   |  3.32555 |  3.05951 |
| 1984 | 236.348 |  715    |  217.3   |  932.3  |  75.6   |  856.7   |  3.62474 |  3.33476 |
| 1985 | 238.466 |  765.2  |  214.7   |  979.9  |  73.7   |  906.2   |  3.80012 |  3.49611 |
| 1986 | 240.651 |  859.3  |  180.5   | 1039.8  |  85.5   |  954.3   |  3.96549 |  3.64825 |
| 1987 | 242.804 |  917.6  |  198.9   | 1116.5  |  89.6   | 1026.9   |  4.22934 |  3.89099 |
| 1988 | 245.021 |  990.5  |  200.2   | 1190.7  |  94.1   | 1096.6   |  4.47553 |  4.11749 |
| 1989 | 247.342 | 1014.4  |  243.581 | 1257.98 |  98.3   | 1159.68  |  4.68857 |  4.31349 |
| 1990 | 250.132 | 1050.5  |  571.743 | 1622.24 | 151.2   | 1471.04  |  5.88107 |  5.41058 |
| 1991 | 253.493 | 1236.1  |  528.811 | 1764.91 | 167.6   | 1597.31  |  6.3012  |  5.79711 |
| 1992 | 256.894 | 1442.8  |  571.029 | 2013.83 | 189.4   | 1824.43  |  7.10187 |  6.53372 |
| 1993 | 260.255 | 1449.8  |  658.803 | 2108.6  | 122.6   | 1986     |  7.63099 |  7.02051 |
| 1994 | 263.436 | 1542.2  |  435.158 | 1977.36 | 117.7   | 1859.66  |  7.05924 |  6.4945  |
| 1995 | 266.557 | 1443.1  |  533.564 | 1976.66 | 107.96  | 1868.7   |  7.01052 |  6.44968 |
| 1996 | 269.667 | 1663.9  |  645.343 | 2309.24 | 133.321 | 2175.92  |  8.06892 |  7.42341 |
| 1997 | 272.912 | 1495.9  |  639.42  | 2135.32 | 133.795 | 2001.53  |  7.33396 |  6.74724 |
| 1998 | 276.115 | 1455.6  |  815.59  | 2271.19 | 127.767 | 2143.42  |  7.76279 |  7.14177 |
| 1999 | 279.295 | 1556.2  |  745.922 | 2302.12 | 146.201 | 2155.92  |  7.71916 |  7.10162 |
| 2000 | 282.385 | 1687.9  |  781.236 | 2469.14 | 157.633 | 2311.5   |  8.18565 |  7.53079 |
| 2001 | 285.309 | 1649.4  |  828.891 | 2478.29 | 161.737 | 2316.55  |  8.11946 |  7.4699  |
| 2002 | 288.105 | 1566.8  |  975.562 | 2542.36 | 161.299 | 2381.06  |  8.26457 |  7.6034  |
| 2003 | 290.82  | 1611.8  |  994.452 | 2606.25 | 159.233 | 2447.02  |  8.41422 |  7.74108 |
| 2004 | 293.463 | 1640    | 1057.37  | 2697.37 | 162.79  | 2534.58  |  8.63679 |  7.94584 |
| 2005 | 296.186 | 1603.6  | 1279.36  | 2882.96 | 156.374 | 2726.58  |  9.20563 |  8.46918 |
| 2006 | 298.996 | 1571    | 1396.49  | 2967.49 | 139.76  | 2827.73  |  9.45744 |  8.70084 |
| 2007 | 302.004 | 1610    | 1370.86  | 2980.86 | 152.793 | 2828.06  |  9.36432 |  8.61518 |
| 2008 | 304.798 | 1588.8  | 1447.42  | 3036.22 | 147.022 | 2889.19  |  9.47905 |  8.72073 |
| 2009 | 307.439 | 1699.7  | 1453.28  | 3152.98 | 139.909 | 3013.07  |  9.80055 |  9.0165  |
| 2010 | 309.741 | 1615.6  | 1700.28  | 3315.88 | 115.891 | 3199.99  | 10.3312  |  9.50467 |
| 2011 | 311.974 | 1761.8  | 1666.05  | 3427.85 | 131.13  | 3296.72  | 10.5673  |  9.7219  |
| 2012 | 314.168 | 1568.7  | 1931.38  | 3500.08 | 122.717 | 3377.36  | 10.7502  |  9.89019 |
| 2013 | 316.295 | 1443.3  | 1856.15  | 3299.45 | 126.735 | 3172.72  | 10.0309  |  9.22841 |
| 2014 | 318.577 | 1553.6  | 1972.7   | 3526.3  | 112.305 | 3413.99  | 10.7164  |  9.85907 |
| 2015 | 320.871 | 1515.5  | 2041.64  | 3557.14 | 113.063 | 3444.07  | 10.7335  |  9.87484 |
| 2016 | 323.161 | 1469.85 | 2211.4   | 3681.25 | 101.7   | 3579.55  | 11.0767  | 10.1905  |
| 2017 | 325.206 | 1439    | 2344.13  | 3783.13 | 106.83  | 3676.3   | 11.3045  | 10.4002  |
| 2018 | 326.924 | 1289.5  | 2465.17  | 3754.67 | 103.812 | 3650.86  | 11.1673  | 10.2739  |
| 2019 | 328.476 | 1306.71 | 2518.34  | 3825.04 | 103.255 | 3721.79  | 11.3305  | 10.424   |



label: G=E-F
labeled_formulas: G=E-F
output: {"Arithmetic-Relationship": ["G=E-F"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_11049___xlsx_07183542e1125e6d4835ba3dc9c6c90151f24b15.xlsx___line_76