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:
|      D |      E |      F |
|-------:|-------:|-------:|
| 314    | 306    |   8    |
| 268    | 274.5  |  -6.5  |
| 268.5  | 273.25 |  -4.75 |
| 261    | 264.5  |  -3.5  |
| 267    | 275    |  -8    |
| 281.5  | 292.75 | -11.25 |
| 293.5  | 305.25 | -11.75 |
| 280.5  | 290.75 | -10.25 |
| 263    | 269.5  |  -6.5  |
| 240.5  | 250.25 |  -9.75 |
| 256    | 258    |  -2    |
| 266.5  | 268.5  |  -2    |
| 248.5  | 257.5  |  -9    |
| 269    | 281.25 | -12.25 |
| 266    | 270.25 |  -4.25 |
| 254.5  | 267.25 | -12.75 |
| 265    | 277.5  | -12.5  |
| 256.5  | 263.75 |  -7.25 |
| 251.5  | 262.25 | -10.75 |
| 239.5  | 246.5  |  -7    |
| 228.5  | 237    |  -8.5  |
| 234.5  | 250.5  | -16    |
| 201    | 220    | -19    |
| 173    | 195.5  | -22.5  |
| 182.5  | 212.75 | -30.25 |
| 195.5  | 219    | -23.5  |
| 210.5  | 216.75 |  -6.25 |
| 206    | 218.75 | -12.75 |
| 208    | 215.5  |  -7.5  |
| 198.5  | 208.75 | -10.25 |
| 217.5  | 232    | -14.5  |
| 202.5  | 214.75 | -12.25 |
| 197.5  | 214.75 | -17.25 |
| 192    | 211    | -19    |
| 164.5  | 196    | -31.5  |
| 174.5  | 201.75 | -27.25 |
| 182.5  | 213.75 | -31.25 |
| 176    | 200.5  | -24.5  |
| 183.5  | 191.25 |  -7.75 |
| 188.5  | 204.75 | -16.25 |
| 201    | 225.75 | -24.75 |
| 197.5  | 213.25 | -15.75 |
| 204    | 227    | -23    |
| 212    | 227.5  | -15.5  |
| 209.5  | 233.5  | -24    |
| 168    | 192.75 | -24.75 |
| 147    | 181    | -34    |
| 159    | 184.25 | -25.25 |
| 160    | 190.5  | -30.5  |
| 184    | 196.25 | -12.25 |
| 196    | 207.75 | -11.75 |
| 209.5  | 220.25 | -10.75 |
| 187.5  | 208.25 | -20.75 |
| 196    | 209.25 | -13.25 |
| 188.5  | 209.25 | -20.75 |
| 183.5  | 199.75 | -16.25 |
| 171    | 189.25 | -18.25 |
| 173.5  | 188    | -14.5  |
| 198.5  | 220.5  | -22    |
| 201.5  | 218    | -16.5  |
| 189.5  | 212.5  | -23    |
| 181    | 198.5  | -17.5  |
| 191    | 198.75 |  -7.75 |
| 192.5  | 200.5  |  -8    |
| 191    | 200.25 |  -9.25 |
| 189    | 198.75 |  -9.75 |
| 191.5  | 204.5  | -13    |
| 186.5  | 196.25 |  -9.75 |
| 200.5  | 211.5  | -11    |
| 213.5  | 221.5  |  -8    |
| 219.5  | 231    | -11.5  |
| 253    | 259.5  |  -6.5  |
| 246    | 260.5  | -14.5  |
| 240    | 249    |  -9    |
| 235    | 242.25 |  -7.25 |
| 232    | 239.75 |  -7.75 |
| 229.5  | 235.5  |  -6    |
| 229.5  | 231.75 |  -2.25 |
| 226.5  | 228.75 |  -2.25 |
| 229.5  | 231.75 |  -2.25 |
| 234.5  | 241.25 |  -6.75 |
| 232    | 233    |  -1    |
| 207    | 210    |  -3    |
| 226.5  | 229    |  -2.5  |
| 206.5  | 226.25 | -19.75 |
| 233    | 248.25 | -15.25 |
| 232    | 239.5  |  -7.5  |
| 233.5  | 242.75 |  -9.25 |
| 256    | 270.75 | -14.75 |
| 282.5  | 291.75 |  -9.25 |
| 288    | 305    | -17    |
| 298.5  | 308.25 |  -9.75 |
| 290.5  | 300.75 | -10.25 |
| 260.5  | 271.25 | -10.75 |
| 206.5  | 218.5  | -12    |
| 217    | 220.25 |  -3.25 |
| 180.5  | 208.5  | -28    |
| 180    | 206.25 | -26.25 |
| 184.25 | 197    | -12.75 |
| 191    | 207    | -16    |
| 182    | 197    | -15    |
| 191    | 205.75 | -14.75 |
| 199    | 213    | -14    |
| 195.5  | 208.25 | -12.75 |
| 203    | 225    | -22    |
| 201    | 218.5  | -17.5  |
| 218    | 236.5  | -18.5  |
| 189    | 204.75 | -15.75 |
| 167    | 203.25 | -36.25 |
| 167.5  | 197.75 | -30.25 |
| 175.5  | 187.75 | -12.25 |
| 200    | 216.25 | -16.25 |
| 203    | 218.75 | -15.75 |
| 212.5  | 227.75 | -15.25 |
| 203.5  | 224.25 | -20.75 |
| 216    | 231.5  | -15.5  |
| 224    | 254    | -30    |
| 207.5  | 226    | -18.5  |
| 211.5  | 237.75 | -26.25 |
| 205    | 222.75 | -17.75 |
| 229    | 253.75 | -24.75 |
| 314.5  | 332.5  | -18    |
| 358    | 368.75 | -10.75 |
| 362.5  | 386.75 | -24.25 |
| 375.5  | 400    | -24.5  |
| 403.5  | 425.5  | -22    |
| 357    | 388.5  | -31.5  |
| 344.5  | 364.75 | -20.25 |
| 347.5  | 364.75 | -17.25 |
| 329.5  | 343.75 | -14.25 |
| 288.5  | 321    | -32.5  |
| 301    | 322.75 | -21.75 |
| 334    | 375    | -41    |
| 356.5  | 376    | -19.5  |
| 373.5  | 387.25 | -13.75 |
| 425    | 454.75 | -29.75 |
| 469.5  | 501    | -31.5  |
| 499.5  | 525    | -25.5  |
| 520.5  | 555.5  | -35    |
| 566    | 600    | -34    |
| 549    | 592.5  | -43.5  |
| 710    | 753.75 | -43.75 |
| 544    | 594    | -50    |
| 537.5  | 577.5  | -40    |
| 495.5  | 543    | -47.5  |
| 382.5  | 390.75 |  -8.25 |
| 321.5  | 353.5  | -32    |
| 363.5  | 393.5  | -30    |
| 357    | 384.5  | -27.5  |
| 353    | 363.75 | -10.75 |
| 367.5  | 387    | -19.5  |
| 360    | 375    | -15    |
| 402.5  | 426    | -23.5  |
| 373.5  | 384.25 | -10.75 |
| 316.5  | 320.75 |  -4.25 |
| 316.5  | 323    |  -6.5  |
| 323.5  | 338.75 | -15.25 |
| 346    | 369    | -23    |
| 364    | 392    | -28    |
| 376.5  | 417    | -40.5  |
| 328    | 358.25 | -30.25 |
| 354.5  | 375.25 | -20.75 |
| 333.5  | 357    | -23.5  |
| 341    | 357    | -16    |
| 345.5  | 371.5  | -26    |
| 312    | 333.75 | -21.75 |
| 347.5  | 376.25 | -28.75 |
| 392.5  | 421    | -28.5  |
| 468    | 500    | -32    |
| 554    | 577.25 | -23.25 |
| 521    | 538.25 | -17.25 |
| 598.5  | 624    | -25.5  |
| 625    | 650.75 | -25.75 |
| 662.5  | 685.75 | -23.25 |
| 650.5  | 671.75 | -21.25 |
| 733    | 752.25 | -19.25 |
| 738    | 745.5  |  -7.5  |
| 681    | 683    |  -2    |
| 722    | 691.5  |  30.5  |
| 763    | 756.25 |   6.75 |
| 613.5  | 630.75 | -17.25 |
| 645    | 651.5  |  -6.5  |
| 586.5  | 591.75 |  -5.25 |
| 636.25 | 642.5  |  -6.25 |
| 649.5  | 641.75 |   7.75 |
| 648    | 644.5  |   3.5  |
| 617.5  | 620.25 |  -2.75 |
| 622    | 624    |  -2    |
| 588    | 562.5  |  25.5  |
| 669    | 649.5  |  19.5  |
| 812    | 798.5  |  13.5  |
| 827    | 810.25 |  16.75 |
| 727    | 724.75 |   2.25 |
| 737.5  | 737    |   0.5  |
| 761.5  | 760.25 |   1.25 |
| 692.5  | 691.5  |   1    |
| 735.5  | 729.5  |   6    |
| 712.5  | 705    |   7.5  |
| 745.5  | 730.25 |  15.25 |
| 647.5  | 644    |   3.5  |
| 699    | 665    |  34    |
| 700.5  | 664.5  |  36    |
| 591    | 489.25 | 101.75 |
| 609    | 504.25 | 104.75 |
| 437    | 456.75 | -19.75 |
| 419    | 432    | -13    |
| 409    | 418.5  |  -9.5  |
| 410.5  | 427.5  | -17    |
| 412.5  | 427.5  | -15    |
| 440.5  | 455.5  | -15    |
| 472.5  | 492    | -19.5  |
| 491.5  | 507.75 | -16.25 |
| 457    | 472.5  | -15.5  |
| 435.5  | 442.75 |  -7.25 |
| 358    | 361.5  |  -3.5  |
| 359.5  | 356    |   3.5  |
| 285    | 323    | -38    |
| 333    | 375.25 | -42.25 |
| 350    | 374.25 | -24.25 |
| 388    | 412.75 | -24.75 |
| 354.5  | 373.25 | -18.75 |
| 358.5  | 375.75 | -17.25 |
| 375.5  | 391    | -15.5  |
| 348    | 361    | -13    |
| 337.5  | 349.5  | -12    |
| 370    | 385    | -15    |
| 344.5  | 367.75 | -23.25 |
| 347.5  | 363.75 | -16.25 |
| 365.5  | 386.75 | -21.25 |
| 363    | 376    | -13    |
| 363    | 366    |  -3    |
| 351.5  | 362.5  | -11    |
| 364    | 369.25 |  -5.25 |
| 348.5  | 355.5  |  -7    |
| 363    | 373    | -10    |
| 366.5  | 380.75 | -14.25 |
| 390    | 408.25 | -18.25 |
| 367.5  | 385.25 | -17.75 |
| 323.5  | 335.75 | -12.25 |
| 296    | 311.75 | -15.75 |
| 301.5  | 329.25 | -27.75 |
| 337.5  | 357.5  | -20    |
| 333    | 348.5  | -15.5  |
| 332    | 348.25 | -16.25 |
| 345.5  | 362.5  | -17    |
| 345.5  | 364    | -18.5  |
| 332.5  | 358.5  | -26    |
| 338    | 359    | -21    |
| 352    | 374.25 | -22.25 |
| 335    | 358.75 | -23.75 |
| 344    | 374.25 | -30.25 |
| 311    | 333.5  | -22.5  |
| 318    | 354    | -36    |
| 315.5  | 348.75 | -33.25 |



label: F=D-E
labeled_formulas: F=D-E
output: {"Arithmetic-Relationship": ["F=D-E"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_560914___xlsx_3df75db5214ebd4ffbeb12c57da03042ac55531e.xlsx___line_144