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 |
|:---------------------|-----------:|----------:|------------:|---------:|------------:|----------:|---------:|---------:|----------:|------------:|----------:|
| Alabama              |  306169487 |  10990    | 3.94413e+07 | 3588.83  | 2.66728e+08 |   5834.62 |   468.85 |  1318.75 |   7622.22 | 3.00185e+08 |  16824.6  |
| Alaska               |  131654352 |   3210    | 9.25782e+06 | 2884.06  | 1.22397e+08 |   2487.6  |   107.37 |   481.38 |   3076.36 | 1.32749e+08 |   5697.6  |
| Arizona              |  631710296 |  39360    | 5.26222e+06 |  133.695 | 6.26448e+08 |  13922.3  |  1311.92 |  3302.48 |  18536.7  | 7.09232e+08 |  53282.3  |
| Arkansas             |  413992107 |  14600    | 9.8204e+06  |  672.63  | 4.04172e+08 |   9061    |   694.69 |  1584.88 |  11340.6  | 4.01687e+08 |  23661    |
| California           | 7623688302 | 511200    | 5.39253e+08 | 1054.88  | 7.08444e+09 | 152167    | 12120.3  | 30527.8  | 194815    | 7.95863e+09 | 663367    |
| Colorado             |  541142824 |  26650    | 7.22719e+07 | 2711.89  | 4.68871e+08 |   9825.59 |   830.14 |  2711.07 |  13366.8  | 5.74576e+08 |  36475.6  |
| Connecticut          |  683391400 |  22830    | 3.65743e+07 | 1602.03  | 6.46817e+08 |  12112    |   856    |  2569.96 |  15537.9  | 8.89115e+08 |  34942    |
| Delaware             |  130938887 |   5710    | 8.36278e+06 | 1464.59  | 1.22576e+08 |   2616.79 |   177.52 |   475.01 |   3269.31 | 1.3578e+08  |   8326.79 |
| District of Columbia |  313632322 |   8210    | 1.22165e+07 | 1488     | 3.01416e+08 |   5691.09 |   298.48 |   335.37 |   6324.94 | 3.15568e+08 |  13901.1  |
| Florida              | 1123050990 |  40710    | 1.70472e+08 | 4187.48  | 9.52579e+08 |  19777.3  |  2014.38 |  6659.55 |  28451.2  | 1.2101e+09  |  60487.3  |
| Georgia              |  546742146 |  24140    | 7.21762e+07 | 2989.9   | 4.74566e+08 |  10960.1  |  1022.19 |  2823.97 |  14806.3  | 5.69437e+08 |  35100.1  |
| Hawaii               |   96683363 |   2870    | 1.42215e+07 | 4955.22  | 8.24619e+07 |   1700.44 |   115.3  |   391.39 |   2207.13 | 9.27656e+07 |   4570.44 |
| Idaho                |  187955406 |  11030    | 3.20547e+07 | 2906.14  | 7.79504e+07 |   3893.34 |   302.34 |   816.49 |   5012.17 | 1.65205e+08 |  14923.3  |
| Illinois             |  622304180 |  63960    | 1.01943e+08 | 1593.86  | 5.20361e+08 |  11884.7  |   946.15 |  3123.94 |  15954.8  | 6.49626e+08 |  75844.7  |
| Indiana              |  490515239 |  24260    | 4.32908e+07 | 1784.45  | 4.47224e+08 |   9598.93 |   711.92 |  2322.75 |  12633.6  | 5.10182e+08 |  33858.9  |
| Iowa                 |  327167121 |  10230    | 3.66097e+07 | 3578.66  | 2.90557e+08 |   6501.48 |   394.56 |  1351.37 |   8247.41 | 3.15003e+08 |  16731.5  |
| Kansas               |  492242405 |  17860    | 2.41843e+07 | 1354.1   | 4.68058e+08 |  10313.8  |   722.76 |  1824.46 |  12861    | 4.82279e+08 |  28173.8  |
| Kentucky             |  340308344 |  16290    | 6.78194e+07 | 4163.25  | 2.72489e+08 |   5516.89 |   423.99 |  1514.16 |   7455.04 | 3.20784e+08 |  21806.9  |
| Louisiana            |  318442383 |  26780    | 2.33432e+07 |  871.666 | 2.95099e+08 |   6963.37 |   539.5  |  1382.34 |   8885.21 | 3.0648e+08  |  33743.4  |
| Maine                |  211535531 |   9300    | 1.00568e+07 | 1081.38  | 2.01479e+08 |   4010.1  |   298.74 |  1098.43 |   5407.28 | 2.25746e+08 |  13310.1  |
| Maryland             |  823759947 |  17440    | 4.08138e+07 | 2340.24  | 7.82946e+08 |  16167.7  |  1149.77 |  3180.42 |  20497.9  | 8.96115e+08 |  33607.7  |
| Massachusetts        | 1438110025 |  83260    | 1.39703e+08 | 1677.91  | 1.29841e+09 |  25107    |  1680.89 |  6427.51 |  33215.4  | 1.64014e+09 | 108367    |
| Michigan             |  488949720 |  30690    | 9.63475e+07 | 3139.38  | 3.92602e+08 |   8481.53 |   722.26 |  2697.67 |  11901.5  | 4.98458e+08 |  39171.5  |
| Minnesota            | 1717006449 |  60390    | 9.93864e+07 | 1645.74  | 1.61762e+09 |  36187.8  |  2770.56 |  8945.17 |  47903.5  | 1.93689e+09 |  96577.8  |
| Mississippi          |  189249287 |   9640    | 2.0727e+07  | 2150.1   | 1.68522e+08 |   3825.46 |   277.65 |   760.36 |   4863.47 | 1.73216e+08 |  13465.5  |
| Missouri             |  803441935 |  52920    | 4.98276e+07 |  941.564 | 7.53614e+08 |  17810.9  |  1377.3  |  3552.32 |  22740.5  | 7.84324e+08 |  70730.9  |
| Montana              |  113795136 |   1480    | 6.80814e+06 | 4600.1   | 1.06987e+08 |   2549.16 |   191.44 |   533.95 |   3274.55 | 1.14815e+08 |   4029.16 |
| Nebraska             |  170329876 |   6260    | 2.04152e+07 | 3261.22  | 1.49915e+08 |   3358.4  |   228.68 |   739.83 |   4326.9  | 1.648e+08   |   9618.4  |
| Nevada               |  212904614 |  11300    | 1.61205e+07 | 1426.59  | 1.96784e+08 |   4344.86 |   340.85 |   800.23 |   5485.94 | 2.06461e+08 |  15644.9  |
| New Hampshire        |  152229594 |   4310    | 1.99458e+07 | 4627.79  | 1.32284e+08 |   2680.45 |   190.97 |   663.16 |   3534.59 | 1.62324e+08 |   6990.45 |
| New Jersey           |  606856320 |  46350    | 1.27167e+08 | 2743.62  | 4.7969e+08  |   9587.66 |   759.66 |  2493.4  |  12840.7  | 6.05925e+08 |  55937.7  |
| New Mexico           |  293994985 |  26820    | 2.52279e+07 |  940.637 | 2.68767e+08 |   7037.35 |   415.59 |  1092.59 |   8545.53 | 2.4878e+08  |  33857.3  |
| New York             | 4431094602 | 371260    | 6.50493e+08 | 1752.12  | 3.7806e+09  |  76067.8  |  4978.8  | 16667.5  |  97714.1  | 4.6469e+09  | 447328    |
| North Carolina       |  640713700 |  34270    | 9.07182e+07 | 2647.16  | 5.49996e+08 |  12580.2  |  1130.36 |  2948.22 |  16658.8  | 6.25381e+08 |  46850.2  |
| North Dakota         |  111045023 |   1850    | 6.30025e+06 | 3405.54  | 1.04745e+08 |   2163.88 |   111.96 |   419.62 |   2695.47 | 1.14239e+08 |   4013.88 |
| Ohio                 | 1526689587 |  56450    | 9.44114e+07 | 1672.48  | 1.43228e+09 |  31541.4  |  2592.96 |  7999.2  |  42133.5  | 1.6625e+09  |  87991.4  |
| Oklahoma             |  232154700 |  10360    | 4.86453e+07 | 4695.5   | 1.83509e+08 |   4002.67 |   327.08 |  1006.43 |   5336.18 | 2.04873e+08 |  14362.7  |
| Oregon               |  435897776 |  10950    | 3.25792e+07 | 2975.27  | 4.03319e+08 |   8304.47 |   667.61 |  1995.28 |  10967.4  | 4.57192e+08 |  19254.5  |
| Pennsylvania         | 2562234565 | 140500    | 3.1736e+08  | 2258.79  | 2.24487e+09 |  42677.6  |  3041.79 | 13063.1  |  58782.5  | 2.80135e+09 | 183178    |
| Rhode Island         |  119027940 |   3500    | 1.2617e+07  | 3604.87  | 1.06411e+08 |   2210.5  |   171.43 |   500.65 |   2882.57 | 1.21249e+08 |   5710.5  |
| South Carolina       |  297869952 |  17750    | 4.42461e+07 | 2492.74  | 2.53624e+08 |   6154.72 |   549.05 |  1290.33 |   7994.09 | 2.72725e+08 |  23904.7  |
| South Dakota         |   71270649 |   1610    | 5.38703e+06 | 3345.98  | 6.58836e+07 |   1487.2  |    81.8  |   315.98 |   1884.97 | 7.4818e+07  |   3097.2  |
| Tennessee            |  551637600 |  15090    | 7.31327e+07 | 4846.44  | 4.78505e+08 |   9755.74 |   824.89 |  2678.29 |  13258.9  | 5.93352e+08 |  24845.7  |
| Texas                | 3029524951 | 270230    | 2.95095e+08 | 1092.01  | 2.73443e+09 |  73507.8  |  6539.73 | 15482.4  |  95530    | 3.23851e+09 | 343738    |
| Utah                 |  164579097 |   8780    | 4.92121e+07 | 5605.03  | 1.15367e+08 |   2603.12 |   223.16 |   850.44 |   3676.72 | 1.43558e+08 |  11383.1  |
| Vermont              |  169659391 |   6185.59 | 1.60537e+07 | 2595.34  | 1.53606e+08 |   3355.11 |   213    |   777.66 |   4345.81 | 1.69673e+08 |   9540.7  |
| Virginia             |  749771866 |  41510    | 1.0878e+08  | 2620.58  | 6.40992e+08 |  14702.3  |  1102.12 |  2961.48 |  18765.9  | 7.21538e+08 |  56212.3  |
| Washington           |  889143120 |  44790    | 1.26893e+08 | 2833.06  | 7.62251e+08 |  14079.3  |   943.64 |  3458.98 |  18482    | 9.25791e+08 |  58869.3  |
| West Virginia        |  220314386 |  10640    | 3.32769e+06 |  312.753 | 2.16987e+08 |   4940.85 |   283.61 |   794.24 |   6018.7  | 2.16581e+08 |  15580.9  |
| Wisconsin            | 1184043682 |  43090    | 6.51844e+07 | 1512.75  | 1.11886e+09 |  24400.8  |  1784.67 |  5632.22 |  31817.6  | 1.21961e+09 |  67490.8  |
| Wyoming              |   69432438 |   2420    | 6.97319e+06 | 2881.49  | 6.24592e+07 |   1427.63 |    87.62 |   185.47 |   1700.72 | 6.07583e+07 |   3847.63 |



label: E=D/C
L=G+C
labeled_formulas: E=D/C
L=G+C
output: {"Arithmetic-Relationship": ["E=D/C", "L=G+C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_741360___xlsx_8dac080a5046392abd410a2ed3c7de923062af3c.xlsx___line_401