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 |
|----:|--------:|--------:|---------:|--------:|
|   1 | 546.197 | 473.693 |  72.5049 | 84139.5 |
|   2 | 546.197 | 473.285 |  72.9128 | 84066.6 |
|   3 | 546.197 | 472.875 |  73.3229 | 83993.3 |
|   4 | 546.197 | 472.462 |  73.7353 | 83919.5 |
|   5 | 546.197 | 472.047 |  74.1501 | 83845.4 |
|   6 | 546.197 | 471.63  |  74.5672 | 83770.8 |
|   7 | 546.197 | 471.211 |  74.9866 | 83695.8 |
|   8 | 546.197 | 470.789 |  75.4084 | 83620.4 |
|   9 | 546.197 | 470.365 |  75.8326 | 83544.6 |
|  10 | 546.197 | 469.938 |  76.2592 | 83468.3 |
|  11 | 546.197 | 469.509 |  76.6881 | 83391.6 |
|  12 | 546.197 | 469.078 |  77.1195 | 83314.5 |
|  13 | 546.197 | 468.644 |  77.5533 | 83237   |
|  14 | 546.197 | 468.208 |  77.9895 | 83159   |
|  15 | 546.197 | 467.769 |  78.4282 | 83080.5 |
|  16 | 546.197 | 467.328 |  78.8694 | 83001.7 |
|  17 | 546.197 | 466.884 |  79.313  | 82922.4 |
|  18 | 546.197 | 466.438 |  79.7592 | 82842.6 |
|  19 | 546.197 | 465.99  |  80.2078 | 82762.4 |
|  20 | 546.197 | 465.538 |  80.659  | 82681.7 |
|  21 | 546.197 | 465.085 |  81.1127 | 82600.6 |
|  22 | 546.197 | 464.628 |  81.5689 | 82519.1 |
|  23 | 546.197 | 464.17  |  82.0278 | 82437   |
|  24 | 546.197 | 463.708 |  82.4892 | 82354.5 |
|  25 | 546.197 | 463.244 |  82.9532 | 82271.6 |
|  26 | 546.197 | 462.778 |  83.4198 | 82188.2 |
|  27 | 546.197 | 462.308 |  83.889  | 82104.3 |
|  28 | 546.197 | 461.837 |  84.3609 | 82019.9 |
|  29 | 546.197 | 461.362 |  84.8354 | 81935.1 |
|  30 | 546.197 | 460.885 |  85.3126 | 81849.8 |
|  31 | 546.197 | 460.405 |  85.7925 | 81764   |
|  32 | 546.197 | 459.922 |  86.2751 | 81677.7 |
|  33 | 546.197 | 459.437 |  86.7604 | 81590.9 |
|  34 | 546.197 | 458.949 |  87.2484 | 81503.7 |
|  35 | 546.197 | 458.458 |  87.7392 | 81415.9 |
|  36 | 546.197 | 457.965 |  88.2327 | 81327.7 |
|  37 | 546.197 | 457.468 |  88.729  | 81239   |
|  38 | 546.197 | 456.969 |  89.2281 | 81149.8 |
|  39 | 546.197 | 456.467 |  89.73   | 81060   |
|  40 | 546.197 | 455.963 |  90.2348 | 80969.8 |
|  41 | 546.197 | 455.455 |  90.7423 | 80879.1 |
|  42 | 546.197 | 454.945 |  91.2528 | 80787.8 |
|  43 | 546.197 | 454.431 |  91.7661 | 80696   |
|  44 | 546.197 | 453.915 |  92.2822 | 80603.7 |
|  45 | 546.197 | 453.396 |  92.8013 | 80510.9 |
|  46 | 546.197 | 452.874 |  93.3233 | 80417.6 |
|  47 | 546.197 | 452.349 |  93.8483 | 80323.8 |
|  48 | 546.197 | 451.821 |  94.3762 | 80229.4 |
|  49 | 546.197 | 451.29  |  94.9071 | 80134.5 |
|  50 | 546.197 | 450.757 |  95.4409 | 80039.1 |
|  51 | 546.197 | 450.22  |  95.9778 | 79943.1 |
|  52 | 546.197 | 449.68  |  96.5176 | 79846.6 |
|  53 | 546.197 | 449.137 |  97.0605 | 79749.5 |
|  54 | 546.197 | 448.591 |  97.6065 | 79651.9 |
|  55 | 546.197 | 448.042 |  98.1555 | 79553.7 |
|  56 | 546.197 | 447.49  |  98.7077 | 79455   |
|  57 | 546.197 | 446.935 |  99.2629 | 79355.8 |
|  58 | 546.197 | 446.376 |  99.8213 | 79255.9 |
|  59 | 546.197 | 445.815 | 100.383  | 79155.6 |
|  60 | 546.197 | 445.25  | 100.947  | 79054.6 |
|  61 | 546.197 | 444.682 | 101.515  | 78953.1 |
|  62 | 546.197 | 444.111 | 102.086  | 78851   |
|  63 | 546.197 | 443.537 | 102.66   | 78748.4 |
|  64 | 546.197 | 442.959 | 103.238  | 78645.1 |
|  65 | 546.197 | 442.379 | 103.819  | 78541.3 |
|  66 | 546.197 | 441.795 | 104.403  | 78436.9 |
|  67 | 546.197 | 441.208 | 104.99   | 78331.9 |
|  68 | 546.197 | 440.617 | 105.58   | 78226.3 |
|  69 | 546.197 | 440.023 | 106.174  | 78120.1 |
|  70 | 546.197 | 439.426 | 106.772  | 78013.4 |
|  71 | 546.197 | 438.825 | 107.372  | 77906   |
|  72 | 546.197 | 438.221 | 107.976  | 77798   |
|  73 | 546.197 | 437.614 | 108.584  | 77689.4 |
|  74 | 546.197 | 437.003 | 109.194  | 77580.2 |
|  75 | 546.197 | 436.389 | 109.809  | 77470.4 |
|  76 | 546.197 | 435.771 | 110.426  | 77360   |
|  77 | 546.197 | 435.15  | 111.047  | 77249   |
|  78 | 546.197 | 434.525 | 111.672  | 77137.3 |
|  79 | 546.197 | 433.897 | 112.3    | 77025   |
|  80 | 546.197 | 433.266 | 112.932  | 76912.1 |
|  81 | 546.197 | 432.63  | 113.567  | 76798.5 |
|  82 | 546.197 | 431.992 | 114.206  | 76684.3 |
|  83 | 546.197 | 431.349 | 114.848  | 76569.4 |
|  84 | 546.197 | 430.703 | 115.494  | 76453.9 |
|  85 | 546.197 | 430.053 | 116.144  | 76337.8 |
|  86 | 546.197 | 429.4   | 116.797  | 76221   |
|  87 | 546.197 | 428.743 | 117.454  | 76103.6 |
|  88 | 546.197 | 428.082 | 118.115  | 75985.4 |
|  89 | 546.197 | 427.418 | 118.779  | 75866.7 |
|  90 | 546.197 | 426.75  | 119.447  | 75747.2 |
|  91 | 546.197 | 426.078 | 120.119  | 75627.1 |
|  92 | 546.197 | 425.402 | 120.795  | 75506.3 |
|  93 | 546.197 | 424.723 | 121.475  | 75384.8 |
|  94 | 546.197 | 424.04  | 122.158  | 75262.7 |
|  95 | 546.197 | 423.352 | 122.845  | 75139.8 |
|  96 | 546.197 | 422.661 | 123.536  | 75016.3 |
|  97 | 546.197 | 421.967 | 124.231  | 74892.1 |
|  98 | 546.197 | 421.268 | 124.93   | 74767.1 |
|  99 | 546.197 | 420.565 | 125.632  | 74641.5 |
| 100 | 546.197 | 419.858 | 126.339  | 74515.2 |
| 101 | 546.197 | 419.148 | 127.05   | 74388.1 |
| 102 | 546.197 | 418.433 | 127.764  | 74260.3 |
| 103 | 546.197 | 417.714 | 128.483  | 74131.9 |
| 104 | 546.197 | 416.992 | 129.206  | 74002.6 |
| 105 | 546.197 | 416.265 | 129.933  | 73872.7 |
| 106 | 546.197 | 415.534 | 130.663  | 73742.1 |
| 107 | 546.197 | 414.799 | 131.398  | 73610.7 |
| 108 | 546.197 | 414.06  | 132.138  | 73478.5 |
| 109 | 546.197 | 413.317 | 132.881  | 73345.6 |
| 110 | 546.197 | 412.569 | 133.628  | 73212   |
| 111 | 546.197 | 411.818 | 134.38   | 73077.6 |
| 112 | 546.197 | 411.062 | 135.136  | 72942.5 |
| 113 | 546.197 | 410.302 | 135.896  | 72806.6 |
| 114 | 546.197 | 409.537 | 136.66   | 72669.9 |
| 115 | 546.197 | 408.768 | 137.429  | 72532.5 |
| 116 | 546.197 | 407.995 | 138.202  | 72394.3 |
| 117 | 546.197 | 407.218 | 138.979  | 72255.3 |
| 118 | 546.197 | 406.436 | 139.761  | 72115.6 |
| 119 | 546.197 | 405.65  | 140.547  | 71975   |
| 120 | 546.197 | 404.859 | 141.338  | 71833.7 |
| 121 | 546.197 | 404.064 | 142.133  | 71691.5 |
| 122 | 546.197 | 403.265 | 142.932  | 71548.6 |
| 123 | 546.197 | 402.461 | 143.736  | 71404.9 |
| 124 | 546.197 | 401.652 | 144.545  | 71260.3 |
| 125 | 546.197 | 400.839 | 145.358  | 71115   |
| 126 | 546.197 | 400.022 | 146.176  | 70968.8 |
| 127 | 546.197 | 399.199 | 146.998  | 70821.8 |
| 128 | 546.197 | 398.373 | 147.825  | 70674   |
| 129 | 546.197 | 397.541 | 148.656  | 70525.3 |
| 130 | 546.197 | 396.705 | 149.493  | 70375.8 |
| 131 | 546.197 | 395.864 | 150.333  | 70225.5 |
| 132 | 546.197 | 395.018 | 151.179  | 70074.3 |
| 133 | 546.197 | 394.168 | 152.029  | 69922.3 |
| 134 | 546.197 | 393.313 | 152.885  | 69769.4 |
| 135 | 546.197 | 392.453 | 153.745  | 69615.7 |
| 136 | 546.197 | 391.588 | 154.609  | 69461   |
| 137 | 546.197 | 390.718 | 155.479  | 69305.6 |
| 138 | 546.197 | 389.844 | 156.354  | 69149.2 |
| 139 | 546.197 | 388.964 | 157.233  | 68992   |
| 140 | 546.197 | 388.08  | 158.118  | 68833.9 |
| 141 | 546.197 | 387.19  | 159.007  | 68674.9 |
| 142 | 546.197 | 386.296 | 159.901  | 68515   |
| 143 | 546.197 | 385.397 | 160.801  | 68354.2 |
| 144 | 546.197 | 384.492 | 161.705  | 68192.4 |
| 145 | 546.197 | 383.583 | 162.615  | 68029.8 |
| 146 | 546.197 | 382.668 | 163.53   | 67866.3 |
| 147 | 546.197 | 381.748 | 164.449  | 67701.9 |
| 148 | 546.197 | 380.823 | 165.375  | 67536.5 |
| 149 | 546.197 | 379.893 | 166.305  | 67370.2 |
| 150 | 546.197 | 378.957 | 167.24   | 67202.9 |
| 151 | 546.197 | 378.016 | 168.181  | 67034.8 |
| 152 | 546.197 | 377.07  | 169.127  | 66865.6 |
| 153 | 546.197 | 376.119 | 170.078  | 66695.5 |
| 154 | 546.197 | 375.162 | 171.035  | 66524.5 |
| 155 | 546.197 | 374.2   | 171.997  | 66352.5 |
| 156 | 546.197 | 373.233 | 172.965  | 66179.6 |
| 157 | 546.197 | 372.26  | 173.937  | 66005.6 |
| 158 | 546.197 | 371.282 | 174.916  | 65830.7 |
| 159 | 546.197 | 370.298 | 175.9    | 65654.8 |
| 160 | 546.197 | 369.308 | 176.889  | 65477.9 |
| 161 | 546.197 | 368.313 | 177.884  | 65300   |
| 162 | 546.197 | 367.313 | 178.885  | 65121.1 |
| 163 | 546.197 | 366.306 | 179.891  | 64941.2 |
| 164 | 546.197 | 365.295 | 180.903  | 64760.3 |
| 165 | 546.197 | 364.277 | 181.92   | 64578.4 |
| 166 | 546.197 | 363.254 | 182.944  | 64395.5 |
| 167 | 546.197 | 362.225 | 183.973  | 64211.5 |
| 168 | 546.197 | 361.19  | 185.008  | 64026.5 |
| 169 | 546.197 | 360.149 | 186.048  | 63840.5 |
| 170 | 546.197 | 359.103 | 187.095  | 63653.4 |
| 171 | 546.197 | 358.05  | 188.147  | 63465.2 |
| 172 | 546.197 | 356.992 | 189.206  | 63276   |
| 173 | 546.197 | 355.928 | 190.27   | 63085.7 |
| 174 | 546.197 | 354.857 | 191.34   | 62894.4 |
| 175 | 546.197 | 353.781 | 192.416  | 62702   |
| 176 | 546.197 | 352.699 | 193.499  | 62508.5 |
| 177 | 546.197 | 351.61  | 194.587  | 62313.9 |
| 178 | 546.197 | 350.516 | 195.682  | 62118.2 |
| 179 | 546.197 | 349.415 | 196.782  | 61921.4 |
| 180 | 546.197 | 348.308 | 197.889  | 61723.5 |
| 181 | 546.197 | 347.195 | 199.003  | 61524.5 |
| 182 | 546.197 | 346.076 | 200.122  | 61324.4 |
| 183 | 546.197 | 344.95  | 201.248  | 61123.2 |
| 184 | 546.197 | 343.818 | 202.38   | 60920.8 |
| 185 | 546.197 | 342.679 | 203.518  | 60717.3 |
| 186 | 546.197 | 341.535 | 204.663  | 60512.6 |
| 187 | 546.197 | 340.383 | 205.814  | 60306.8 |
| 188 | 546.197 | 339.226 | 206.972  | 60099.8 |
| 189 | 546.197 | 338.061 | 208.136  | 59891.7 |
| 190 | 546.197 | 336.891 | 209.307  | 59682.4 |
| 191 | 546.197 | 335.713 | 210.484  | 59471.9 |
| 192 | 546.197 | 334.529 | 211.668  | 59260.2 |
| 193 | 546.197 | 333.339 | 212.859  | 59047.4 |
| 194 | 546.197 | 332.141 | 214.056  | 58833.3 |
| 195 | 546.197 | 330.937 | 215.26   | 58618.1 |
| 196 | 546.197 | 329.727 | 216.471  | 58401.6 |
| 197 | 546.197 | 328.509 | 217.689  | 58183.9 |
| 198 | 546.197 | 327.284 | 218.913  | 57965   |
| 199 | 546.197 | 326.053 | 220.144  | 57744.8 |
| 200 | 546.197 | 324.815 | 221.383  | 57523.5 |
| 201 | 546.197 | 323.569 | 222.628  | 57300.8 |
| 202 | 546.197 | 322.317 | 223.88   | 57076.9 |
| 203 | 546.197 | 321.058 | 225.14   | 56851.8 |
| 204 | 546.197 | 319.791 | 226.406  | 56625.4 |
| 205 | 546.197 | 318.518 | 227.68   | 56397.7 |
| 206 | 546.197 | 317.237 | 228.96   | 56168.8 |
| 207 | 546.197 | 315.949 | 230.248  | 55938.5 |
| 208 | 546.197 | 314.654 | 231.543  | 55707   |
| 209 | 546.197 | 313.352 | 232.846  | 55474.1 |
| 210 | 546.197 | 312.042 | 234.156  | 55240   |
| 211 | 546.197 | 310.725 | 235.473  | 55004.5 |
| 212 | 546.197 | 309.4   | 236.797  | 54767.7 |
| 213 | 546.197 | 308.068 | 238.129  | 54529.6 |
| 214 | 546.197 | 306.729 | 239.469  | 54290.1 |
| 215 | 546.197 | 305.382 | 240.816  | 54049.3 |
| 216 | 546.197 | 304.027 | 242.17   | 53807.1 |
| 217 | 546.197 | 302.665 | 243.532  | 53563.6 |
| 218 | 546.197 | 301.295 | 244.902  | 53318.7 |
| 219 | 546.197 | 299.918 | 246.28   | 53072.4 |
| 220 | 546.197 | 298.532 | 247.665  | 52824.7 |
| 221 | 546.197 | 297.139 | 249.058  | 52575.7 |
| 222 | 546.197 | 295.738 | 250.459  | 52325.2 |
| 223 | 546.197 | 294.329 | 251.868  | 52073.3 |
| 224 | 546.197 | 292.913 | 253.285  | 51820.1 |
| 225 | 546.197 | 291.488 | 254.71   | 51565.4 |
| 226 | 546.197 | 290.055 | 256.142  | 51309.2 |
| 227 | 546.197 | 288.614 | 257.583  | 51051.6 |
| 228 | 546.197 | 287.165 | 259.032  | 50792.6 |
| 229 | 546.197 | 285.708 | 260.489  | 50532.1 |
| 230 | 546.197 | 284.243 | 261.954  | 50270.1 |
| 231 | 546.197 | 282.77  | 263.428  | 50006.7 |
| 232 | 546.197 | 281.288 | 264.91   | 49741.8 |
| 233 | 546.197 | 279.798 | 266.4    | 49475.4 |
| 234 | 546.197 | 278.299 | 267.898  | 49207.5 |
| 235 | 546.197 | 276.792 | 269.405  | 48938.1 |
| 236 | 546.197 | 275.277 | 270.921  | 48667.2 |
| 237 | 546.197 | 273.753 | 272.444  | 48394.7 |
| 238 | 546.197 | 272.22  | 273.977  | 48120.8 |
| 239 | 546.197 | 270.679 | 275.518  | 47845.2 |
| 240 | 546.197 | 269.13  | 277.068  | 47568.2 |
| 241 | 546.197 | 267.571 | 278.626  | 47289.6 |
| 242 | 546.197 | 266.004 | 280.194  | 47009.4 |
| 243 | 546.197 | 264.428 | 281.77   | 46727.6 |
| 244 | 546.197 | 262.843 | 283.355  | 46444.2 |
| 245 | 546.197 | 261.249 | 284.949  | 46159.3 |
| 246 | 546.197 | 259.646 | 286.551  | 45872.7 |
| 247 | 546.197 | 258.034 | 288.163  | 45584.6 |



label: D=B-C
labeled_formulas: D=B-C
output: {"Arithmetic-Relationship": ["D=B-C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_4827___xlsx_05efed79029e658435567edd3f87c0640e38a1e0.xlsx___line_49