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 |       K |       L |       M |       N |       O |       P |       Q |       R |          S |       T |
|:------------------------------|--------:|--------:|--------:|--------:|--------:|--------:|--------:|--------:|--------:|--------:|--------:|--------:|--------:|--------:|--------:|--------:|--------:|-----------:|--------:|
| Alabama                       |  142.24 |  133.63 |  138.49 |  139.36 |  141.66 |  143.33 |  145.78 |  147.43 |  139.63 |  120.1  |  132.77 |  129.93 |  123.2  |  120.91 |  123.16 |  120.14 |  115.09 | -0.197028  |  -28.24 |
| Alaska                        |   44.4  |   43.5  |   43.65 |   43.73 |   46.86 |   48.22 |   45.93 |   44.23 |   39.64 |   38    |   38.92 |   38.79 |   38.24 |   36.18 |   35.34 |   36.23 |   34.91 | -0.276027  |  -13.31 |
| Arizona                       |   86.07 |   88.43 |   87.76 |   89.61 |   96.61 |   96.68 |   99.92 |  101.88 |  102.25 |   93.4  |   95.31 |   93.38 |   91.36 |   95.19 |   93.17 |   90.95 |   87.01 | -0.100021  |   -9.67 |
| Arkansas                      |   63.6  |   62.78 |   61.3  |   61.99 |   62.35 |   60.08 |   61.96 |   63.29 |   64.14 |   61.47 |   65.81 |   67.26 |   66.01 |   68.44 |   69    |   59.25 |   62.41 |  0.0387816 |    2.33 |
| California                    |  377.22 |  381.69 |  380.04 |  368.91 |  386.8  |  383.75 |  392.23 |  397.35 |  381.49 |  368.13 |  362.77 |  348.62 |  353.13 |  355.99 |  352.94 |  360.79 |  361.35 | -0.0583713 |  -22.4  |
| Colorado                      |   84.49 |   92.58 |   90.68 |   90.06 |   93    |   95.21 |   96.21 |   98.82 |   96.88 |   92.72 |   95.29 |   91.63 |   90.5  |   91.14 |   91.73 |   90.42 |   89.04 | -0.0648041 |   -6.17 |
| Connecticut                   |   42.96 |   41.72 |   40.08 |   42.76 |   44.6  |   44.07 |   41.03 |   40.25 |   37.67 |   35.93 |   36.27 |   34.88 |   34.14 |   34.9  |   35.15 |   36.5  |   34.3  | -0.221693  |   -9.77 |
| Delaware                      |   15.96 |   15.49 |   15.24 |   15.79 |   16    |   16.78 |   15.73 |   16.54 |   15.62 |   11.98 |   11.27 |   12.25 |   13.38 |   13.11 |   12.75 |   12.85 |   13.31 | -0.206794  |   -3.47 |
| District of Columbia          |    4.29 |    4.08 |    4.17 |    3.92 |    4    |    3.92 |    3.18 |    3.38 |    3.08 |    3.17 |    3.21 |    3.08 |    2.65 |    2.83 |    3.02 |    2.99 |    2.76 | -0.295918  |   -1.16 |
| Florida                       |  239.76 |  238.58 |  241.79 |  245.93 |  257.28 |  260.66 |  259.14 |  256.84 |  238.56 |  224.27 |  242.3  |  229.22 |  222.88 |  222.02 |  227.71 |  232.19 |  230.06 | -0.117394  |  -30.6  |
| Georgia                       |  168.63 |  160.88 |  165.61 |  168.65 |  173.86 |  184.34 |  181.83 |  184.46 |  171.86 |  162.08 |  171.57 |  156.31 |  136.17 |  134.57 |  139.6  |  137.01 |  136.24 | -0.260931  |  -48.1  |
| Hawaii                        |   18.65 |   19.13 |   20.38 |   21.33 |   22.32 |   22.92 |   23.19 |   24    |   19.26 |   18.85 |   18.99 |   19.44 |   18.89 |   18.42 |   18.36 |   18.52 |   18.44 | -0.195462  |   -4.48 |
| Idaho                         |   15.69 |   15.61 |   15.04 |   14.42 |   15.65 |   15.81 |   15.84 |   16.35 |   15.57 |   15.19 |   15.99 |   15.81 |   15.68 |   17.16 |   16.69 |   17.96 |   18.38 |  0.162555  |    2.57 |
| Illinois                      |  231.63 |  222.95 |  225.29 |  228.69 |  235.91 |  242.01 |  233.9  |  241.58 |  240.01 |  224.82 |  229.93 |  228.79 |  216.02 |  229.53 |  232.41 |  215.03 |  204.07 | -0.15677   |  -37.94 |
| Indiana                       |  236.27 |  225.95 |  229.23 |  235.13 |  234.52 |  233.5  |  231.34 |  231.19 |  226.77 |  203.89 |  216.29 |  209.01 |  194.34 |  199.94 |  205.3  |  186.02 |  181.85 | -0.221199  |  -51.65 |
| Iowa                          |   77.76 |   76.57 |   77.18 |   76.72 |   79.01 |   78.66 |   79.98 |   85.23 |   89.05 |   83.98 |   88.38 |   85.48 |   79.38 |   80.95 |   81.8  |   75.85 |   73.13 | -0.0703026 |   -5.53 |
| Kansas                        |   75.74 |   71.47 |   76.43 |   78.28 |   75.32 |   71.58 |   71.86 |   79.65 |   74.23 |   72.44 |   72.2  |   70.4  |   65.62 |   69.37 |   69.59 |   63.93 |   62.06 | -0.132998  |   -9.52 |
| Kentucky                      |  143.77 |  145.31 |  145.95 |  142.05 |  147.39 |  149.58 |  152    |  152.48 |  150.11 |  139.75 |  149.11 |  148.04 |  136.66 |  136.17 |  137.55 |  128.19 |  123.92 | -0.171547  |  -25.66 |
| Louisiana                     |  225.68 |  198.38 |  207.01 |  203.72 |  214.01 |  205.4  |  217.52 |  222.4  |  225.57 |  208.82 |  221.41 |  224.16 |  211.83 |  203.53 |  201.18 |  203.86 |  209.13 |  0.0181597 |    3.73 |
| Maine                         |   22.36 |   22.48 |   24    |   23.65 |   24.01 |   23.13 |   21.26 |   20.96 |   19.09 |   18.4  |   18.09 |   17.55 |   15.83 |   16.6  |   16.65 |   16.86 |   16.46 | -0.28837   |   -6.67 |
| Maryland                      |   76.78 |   76.53 |   76.49 |   79.3  |   79.85 |   82.01 |   77.17 |   77.53 |   73.77 |   70.48 |   69.12 |   64.43 |   59.86 |   59.15 |   61.39 |   59.47 |   57.56 | -0.298134  |  -24.45 |
| Massachusetts                 |   82.5  |   82.36 |   83.21 |   84.53 |   82.88 |   84.46 |   76.5  |   79.88 |   76.71 |   70.27 |   71.81 |   68.05 |   61.73 |   65.62 |   63.77 |   65.62 |   64.19 | -0.239995  |  -20.27 |
| Michigan                      |  193.36 |  189.62 |  189.13 |  185.89 |  188.24 |  190.45 |  179.27 |  181.4  |  175.04 |  164    |  164.75 |  159.55 |  152.76 |  161.59 |  161.48 |  161.68 |  151.77 | -0.203098  |  -38.68 |
| Minnesota                     |   97.43 |   94.45 |   97.01 |  101.01 |  100.31 |  101.37 |   98.73 |  100.34 |   99.85 |   92.09 |   91.89 |   91.59 |   86.64 |   89.58 |   94.78 |   87.77 |   89.25 | -0.119562  |  -12.12 |
| Mississippi                   |   61.21 |   69.92 |   62.5  |   64.1  |   65.59 |   63.88 |   65.91 |   68.01 |   64.55 |   60.49 |   65.32 |   60.49 |   62.33 |   60.61 |   63.89 |   65.18 |   68.92 |  0.0788979 |    5.04 |
| Missouri                      |  125.04 |  129.76 |  130.8  |  137.55 |  138.09 |  141.16 |  139.37 |  138.5  |  135.18 |  129.54 |  133.57 |  134.2  |  126.43 |  132.02 |  131.63 |  122.36 |  117.68 | -0.166336  |  -23.48 |
| Montana                       |   30.44 |   31.61 |   29.96 |   32.19 |   33.8  |   34.9  |   35.06 |   36.52 |   35.79 |   32.35 |   34.27 |   31.41 |   30.14 |   31.52 |   31.97 |   31.92 |   30.46 | -0.127221  |   -4.44 |
| Nebraska                      |   41.59 |   42.9  |   42.39 |   43.46 |   43.29 |   43.68 |   44.28 |   44.61 |   46.63 |   47.31 |   49.82 |   52.25 |   50.52 |   53.49 |   52.17 |   50.69 |   48.55 |  0.111493  |    4.87 |
| Nevada                        |   45.37 |   44.68 |   41.45 |   43.58 |   47.74 |   49.86 |   41.48 |   41.68 |   40.88 |   39.39 |   37.56 |   33.85 |   34.52 |   36.4  |   37.21 |   35.26 |   36.65 | -0.264942  |  -13.21 |
| New Hampshire                 |   17.48 |   16.93 |   17.63 |   20.94 |   21.93 |   21.26 |   19.38 |   19.18 |   18.74 |   17.06 |   16.59 |   16.23 |   14.56 |   14.31 |   15.01 |   15.2  |   13.75 | -0.353246  |   -7.51 |
| New Jersey                    |  121.93 |  119.07 |  119.61 |  121.06 |  123.61 |  128.39 |  121.28 |  128.89 |  126.65 |  109.6  |  113.87 |  114.18 |  103.59 |  107.34 |  113.27 |  111.58 |  110.83 | -0.136771  |  -17.56 |
| New Mexico                    |   57.96 |   58.13 |   55.15 |   57.33 |   58.43 |   59.03 |   59.59 |   58.79 |   56.2  |   57.07 |   53.04 |   55.46 |   53.43 |   53.03 |   49.98 |   50.09 |   48.39 | -0.180247  |  -10.64 |
| New York                      |  211.59 |  205.8  |  200.18 |  210.82 |  213.1  |  209.39 |  190.91 |  197.6  |  187.77 |  172.04 |  173.84 |  164.05 |  160.37 |  162.09 |  169.78 |  167.72 |  163.66 | -0.218396  |  -45.73 |
| North Carolina                |  148.85 |  143.81 |  145.33 |  146.5  |  149.71 |  154.03 |  148.63 |  154.46 |  149.2  |  132.99 |  143.01 |  128.62 |  121.31 |  125.06 |  127.38 |  121.05 |  120.55 | -0.21736   |  -33.48 |
| North Dakota                  |   50.67 |   51.56 |   51.2  |   50.82 |   49.36 |   52.25 |   50.57 |   52.37 |   52.73 |   51.22 |   52.05 |   53.56 |   55.93 |   56.64 |   58.6  |   57.22 |   54.28 |  0.0388517 |    2.03 |
| Ohio                          |  264.27 |  253.51 |  259.73 |  267.55 |  262.67 |  270.74 |  263.55 |  267.33 |  259.92 |  235.06 |  246.76 |  235.1  |  215.16 |  229.45 |  231.37 |  212.66 |  206.27 | -0.238125  |  -64.47 |
| Oklahoma                      |   99.53 |  100.9  |  101.14 |  103.32 |   99.29 |  106.31 |  109.63 |  108.87 |  111.56 |  105.84 |  105.52 |  107.24 |  104.43 |  103.26 |  104.52 |  100.67 |   96.91 | -0.0884207 |   -9.4  |
| Oregon                        |   40.96 |   40.72 |   39.19 |   39.64 |   40.72 |   41.11 |   40.32 |   43.75 |   42.77 |   40.86 |   40.71 |   37.24 |   36.92 |   39.15 |   38.04 |   38.13 |   37.97 | -0.0763804 |   -3.14 |
| Pennsylvania                  |  275.35 |  262.35 |  269.08 |  272.75 |  275.46 |  278.69 |  272.91 |  275.72 |  267.55 |  242.49 |  254.38 |  247.2  |  236.42 |  246.27 |  245.94 |  229.77 |  217.41 | -0.219886  |  -61.28 |
| Rhode Island                  |   11.74 |   12.3  |   11.72 |   11.51 |   10.94 |   11.2  |   10.52 |   11.07 |   10.67 |   11.25 |   11.02 |   11.05 |   10.54 |   10.15 |   10.65 |   10.9  |    9.75 | -0.129464  |   -1.45 |
| South Carolina                |   80.73 |   78.36 |   79.93 |   80.48 |   87.38 |   86.01 |   86.34 |   86.84 |   84.58 |   79.12 |   83.37 |   79.51 |   72.96 |   69.99 |   74.23 |   72.62 |   71.71 | -0.16626   |  -14.3  |
| South Dakota                  |   14.19 |   13.48 |   13.82 |   13.72 |   13.8  |   13.3  |   13.39 |   13.91 |   15    |   14.76 |   15.1  |   14.64 |   15.01 |   15.46 |   15.49 |   14.25 |   15    |  0.12782   |    1.7  |
| Tennessee                     |  126.94 |  124.72 |  124.05 |  122.32 |  123.72 |  125.14 |  127.18 |  126.91 |  120.42 |  101.97 |  109.57 |  106.07 |   99.65 |   98.27 |  103.65 |   99.95 |  103.07 | -0.176362  |  -22.07 |
| Texas                         |  647.33 |  640.64 |  651.13 |  644.93 |  637.84 |  601.57 |  611.27 |  608.59 |  574.87 |  541.13 |  576.23 |  595.18 |  590.12 |  620    |  618.03 |  618.55 |  653.82 |  0.0868561 |   52.25 |
| Utah                          |   64.88 |   62.72 |   61.96 |   62.71 |   65.14 |   66.76 |   68.05 |   70    |   69.15 |   64.38 |   63.63 |   64.11 |   61.41 |   66.78 |   65.11 |   63.47 |   58.76 | -0.119832  |   -8    |
| Vermont                       |    6.75 |    6.61 |    6.36 |    6.6  |    7.03 |    6.81 |    6.68 |    6.51 |    5.94 |    6.18 |    5.9  |    5.82 |    5.47 |    5.76 |    5.9  |    6.16 |    5.95 | -0.126285  |   -0.86 |
| Virginia                      |  122.89 |  120.59 |  119.13 |  123.26 |  127.09 |  128.94 |  122.46 |  127.72 |  116.53 |  105.46 |  108.65 |   99.82 |   97.8  |  105.04 |  104.08 |  103.2  |  104.24 | -0.191562  |  -24.7  |
| Washington                    |   78.09 |   77.94 |   71.52 |   73.52 |   74.77 |   75.75 |   73.37 |   78.86 |   75.54 |   73.37 |   73.42 |   68.54 |   68.29 |   73.08 |   71.54 |   73.42 |   78.86 |  0.0410561 |    3.11 |
| West Virginia                 |  114.19 |  103.53 |  116.48 |  113.06 |  109.79 |  111.98 |  112.15 |  114.37 |  110.2  |   89.37 |  100.39 |   97.73 |   92.06 |   94.33 |   99.96 |   92.08 |   94.55 | -0.155653  |  -17.43 |
| Wisconsin                     |  107.76 |  105.57 |  106.74 |  104.75 |  107.21 |  110.48 |  102.65 |  104.38 |  104.78 |   95.85 |   98.23 |   97.38 |   90.19 |  100.81 |  101.06 |   99.83 |   95.61 | -0.134594  |  -14.87 |
| Wyoming                       |   62.9  |   63.17 |   61.89 |   63.78 |   63.64 |   62.98 |   63.86 |   66.22 |   66.66 |   63.45 |   65    |   63.84 |   66.11 |   68.23 |   65.32 |   63.37 |   60.67 | -0.0366783 |   -2.31 |
| Total of states (unadjusted)¹ | 5797.9  | 5685.47 | 5725.25 | 5777.69 | 5873.57 | 5893.55 | 5822.3  | 5919.12 | 5726.29 | 5313.84 | 5514.3  | 5382.45 | 5162.56 | 5301.45 | 5350.27 | 5207.39 | 5160.99 | -0.124299  | -732.56 |



label: T=R-G
labeled_formulas: T=R-G
output: {"Arithmetic-Relationship": ["T=R-G"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_250092___xlsx_38ace9b818b94965e694cf4e06da8cb2cff9a6a1.xlsx___line_280