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 |
|:------|-----------------:|-----------------:|------------------:|
| V4462 |      0           |      2.86271e+07 |       2.86271e+07 |
| V4478 | 249136           |      1.50043e+07 |       1.47552e+07 |
| V4579 |      0           |      1.26501e+07 |       1.26501e+07 |
| V4415 | 657945           |      1.06315e+07 |       9.9735e+06  |
| V4548 |      0           |      7.19848e+06 |       7.19848e+06 |
| V4453 |      1.27979e+07 |      1.80006e+07 |       5.20272e+06 |
| V4468 |      0           |      4.41322e+06 |       4.41322e+06 |
| V4557 |      0           |      4.11657e+06 |       4.11657e+06 |
| V4467 |      0           |      3.76026e+06 |       3.76026e+06 |
| V4502 |      0           |      3.70084e+06 |       3.70084e+06 |
| V4432 |      0           |      3.63316e+06 |       3.63316e+06 |
| V4416 | 789925           |      4.17178e+06 |       3.38186e+06 |
| V4458 |      2.50308e+06 |      5.85059e+06 |       3.34752e+06 |
| V4535 |      0           |      2.63511e+06 |       2.63511e+06 |
| V4506 |      1.05381e+06 |      3.10855e+06 |       2.05474e+06 |
| V4498 |      1.79544e+06 |      3.40374e+06 |       1.60829e+06 |
| V4580 |      0           |      1.60829e+06 |       1.60829e+06 |
| V4480 | 611871           |      2.11021e+06 |       1.49834e+06 |
| V4466 | 553328           |      1.87145e+06 |       1.31812e+06 |
| V4558 | 945969           |      1.96897e+06 |       1.023e+06   |
| V4450 | 167051           |      1.15891e+06 |  991860           |
| V4556 | 290589           |      1.26437e+06 |  973781           |
| V4536 | 251456           |      1.14978e+06 |  898320           |
| V4564 |      4.15889e+06 |      4.88147e+06 |  722586           |
| V4514 |      0           | 672543           |  672543           |
| V4566 |      0           | 596112           |  596112           |
| V4435 |      0           | 593836           |  593836           |
| V4518 |      0           | 526846           |  526846           |
| V4565 |  91535.8         | 599087           |  507551           |
| V4437 | 819591           |      1.32124e+06 |  501651           |
| V4434 | 606311           |      1.09862e+06 |  492312           |
| V4460 | 305842           | 764886           |  459044           |
| V4513 | 596486           | 988304           |  391818           |
| V4540 | 354388           | 719330           |  364942           |
| V4461 |  32957.9         | 397182           |  364224           |
| V4562 | 161624           | 516292           |  354669           |
| V4501 |  38104.5         | 370315           |  332211           |
| V4531 |  71417.2         | 395748           |  324331           |
| V4412 |      0           | 323228           |  323228           |
| V4495 |  64305.5         | 381154           |  316849           |
| V4423 | 969722           |      1.27199e+06 |  302267           |
| V4464 | 273914           | 563735           |  289821           |
| V4430 |      0           | 289260           |  289260           |
| V4419 | 269703           | 545835           |  276132           |
| V4440 |      0           | 269703           |  269703           |
| V4528 |      0           | 250145           |  250145           |
| V4503 |      0           | 247151           |  247151           |
| V4529 | 587390           | 826110           |  238720           |
| V4485 |      0           | 223383           |  223383           |
| V4488 |      0           | 223383           |  223383           |
| V4546 |      0           | 223383           |  223383           |
| V4523 |      0           | 221418           |  221418           |
| V4475 |      1.05171e+06 |      1.27092e+06 |  219210           |
| V4472 |      0           | 202609           |  202609           |
| V4530 |      0           | 193197           |  193197           |
| V4541 | 498049           | 658604           |  160555           |
| V4551 |      0           | 112964           |  112964           |
| V4493 |      0           | 101736           |  101736           |
| V4490 |      0           |  99466.3         |   99466.3         |
| V4491 | 160099           | 259097           |   98998.4         |
| V4497 |      0           |  97056.8         |   97056.8         |
| V4429 |      0           |  94662.8         |   94662.8         |
| V4459 |  42858.1         | 137294           |   94435.9         |
| V4486 |      0           |  87699.2         |   87699.2         |
| V4500 |      0           |  85827.8         |   85827.8         |
| V4559 |      1.60986e+06 |      1.6921e+06  |   82239.7         |
| V4574 | 762921           | 844144           |   81223.1         |
| V4555 |      0           |  76002.4         |   76002.4         |
| V4404 |      0           |  74352.6         |   74352.6         |
| V4549 |      0           |  73663           |   73663           |
| V4505 |      0           |  71604.4         |   71604.4         |
| V4484 |      0           |  69265           |   69265           |
| V4561 | 472480           | 526679           |   54199.4         |
| V4517 | 216132           | 263679           |   47547           |
| V4409 |  21392           |  68048.5         |   46656.5         |
| V4538 |      0           |  28747           |   28747           |
| V4527 | 376998           | 405070           |   28072.5         |
| V4568 | 122622           | 134132           |   11509.7         |
| V4421 |      1.52136e+06 |      1.52136e+06 |       0           |
| V4520 |      2.34072e+06 |      2.34072e+06 |       0           |
| V4507 | 321637           | 318100           |   -3536.38        |
| V4545 |  72820.8         |  68984.2         |   -3836.58        |
| V4424 | 268545           | 264650           |   -3895           |
| V4476 |  41941.1         |  24910.4         |  -17030.6         |
| V4508 | 142721           | 113994           |  -28727.5         |
| V4576 |  79090.4         |  48959.2         |  -30131.2         |
| V4552 | 404154           | 358696           |  -45458           |
| V4438 | 494696           | 446037           |  -48659           |
| V4515 |  49239.9         |      0           |  -49239.9         |
| V4560 |  54948           |      0           |  -54948           |
| V4433 |  57380.9         |      0           |  -57380.9         |
| V4526 | 423827           | 356092           |  -67735.8         |
| V4509 |  73663           |      0           |  -73663           |
| V4422 |  88575.1         |      0           |  -88575.1         |
| V4519 |  97948.5         |      0           |  -97948.5         |
| V4465 | 282299           | 181425           | -100874           |
| V4470 | 105478           |      0           | -105478           |
| V4402 | 291973           | 178467           | -113506           |
| V4542 | 300676           | 185953           | -114723           |
| V4473 | 516780           | 398181           | -118598           |
| V4477 | 120450           |      0           | -120450           |
| V4573 | 137294           |      0           | -137294           |
| V4448 | 157880           |      0           | -157880           |
| V4572 | 254676           |  84892           | -169784           |
| V4496 | 170720           |      0           | -170720           |
| V4532 |      1.87139e+06 |      1.69947e+06 | -171917           |
| V4577 | 191493           |      0           | -191493           |
| V4578 | 203732           |      0           | -203732           |
| V4420 | 207850           |      0           | -207850           |
| V4426 | 256140           |  46994.1         | -209146           |
| V4539 | 223383           |      0           | -223383           |
| V4482 | 233676           |      0           | -233676           |
| V4401 | 237419           |      0           | -237419           |
| V4431 | 238355           |      0           | -238355           |
| V4567 |      1.76586e+06 |      1.52582e+06 | -240039           |
| V4516 | 975827           | 720044           | -255783           |
| V4569 |      1.27382e+06 |      1.00153e+06 | -272295           |
| V4479 | 292628           |      0           | -292628           |
| V4456 | 298243           |      0           | -298243           |
| V4449 | 315086           |      0           | -315086           |
| V4547 |      2.74273e+06 |      2.40705e+06 | -335673           |
| V4554 | 750124           | 406088           | -344036           |
| V4487 | 345030           |      0           | -345030           |
| V4550 |      2.5056e+06  |      2.14511e+06 | -360482           |
| V4445 | 370109           |      0           | -370109           |
| V4439 |      1.248e+06   | 876088           | -371914           |
| V4455 |      1.73848e+06 |      1.36243e+06 | -376052           |
| V4481 | 638973           | 260696           | -378277           |
| V4441 | 416261           |      0           | -416261           |
| V4471 | 438606           |      0           | -438606           |
| V4499 |      1.22065e+06 | 776154           | -444501           |
| V4454 |      2.13637e+06 |      1.68135e+06 | -455017           |
| V4405 | 778209           | 315593           | -462615           |
| V4411 |      1.47049e+06 |      1.00773e+06 | -462757           |
| V4469 |      1.90654e+06 |      1.42114e+06 | -485393           |
| V4544 | 583520           |  79558.2         | -503962           |
| V4553 | 801041           | 177063           | -623978           |
| V4417 | 783636           | 111093           | -672543           |
| V4512 | 672543           |      0           | -672543           |
| V4492 |      1.61967e+06 | 859170           | -760504           |
| V4418 | 896565           | 109167           | -787398           |
| V4494 | 792600           |      0           | -792600           |
| V4447 | 857299           |      0           | -857299           |
| V4533 |      1.7999e+06  | 919678           | -880225           |
| V4525 |      3.30532e+06 |      2.40638e+06 | -898940           |
| V4406 |      1.26024e+06 | 335600           | -924637           |
| V4571 | 953268           |      0           | -953268           |
| V4436 |      5.33496e+06 |      4.34155e+06 | -993408           |
| V4524 |      1.10195e+06 | 104753           | -997197           |
| V4452 |      1.06855e+06 |      0           |      -1.06855e+06 |
| V4444 |      1.10389e+06 |      0           |      -1.10389e+06 |
| V4442 |      1.18339e+06 |      0           |      -1.18339e+06 |
| V4489 |      5.87799e+06 |      4.6877e+06  |      -1.19029e+06 |
| V4504 |      1.19303e+06 |      0           |      -1.19303e+06 |
| V4403 |      1.21118e+06 |      0           |      -1.21118e+06 |
| V4537 |      1.48758e+06 | 229481           |      -1.2581e+06  |
| V4446 |      1.39307e+06 |      0           |      -1.39307e+06 |
| V4543 |      2.70314e+06 |      1.2325e+06  |      -1.47064e+06 |
| V4575 |      2.98415e+06 |      1.04104e+06 |      -1.9431e+06  |
| V4408 |      2.33953e+06 | 350384           |      -1.98914e+06 |
| V4425 |      2.16974e+06 |      0           |      -2.16974e+06 |
| V4451 |      2.19364e+06 |      0           |      -2.19364e+06 |
| V4457 |      2.2446e+06  |      0           |      -2.2446e+06  |
| V4570 |      2.35689e+06 |      0           |      -2.35689e+06 |
| V4407 |      4.33766e+06 |      1.70154e+06 |      -2.63612e+06 |
| V4427 |      2.97677e+06 |      0           |      -2.97677e+06 |
| V4410 |      6.50148e+06 |      2.06582e+06 |      -4.43566e+06 |
| V4522 |      6.40466e+06 |      1.95889e+06 |      -4.44577e+06 |
| V4534 |      5.84406e+06 |      1.08633e+06 |      -4.75773e+06 |
| V4483 |      5.93894e+06 | 994553           |      -4.94439e+06 |
| V4463 |      5.2184e+06  |      0           |      -5.2184e+06  |
| V4511 |      6.1642e+06  |      0           |      -6.1642e+06  |
| V4414 |      6.38885e+06 |      0           |      -6.38885e+06 |
| V4521 |      6.56777e+06 |      0           |      -6.56777e+06 |
| V4428 |      1.26219e+07 |      4.9088e+06  |      -7.71307e+06 |
| V4563 |      7.88953e+06 |      0           |      -7.88953e+06 |
| V4510 |      2.30744e+07 |      1.45404e+07 |      -8.53404e+06 |
| V4474 |      1.09399e+07 |      0           |      -1.09399e+07 |
| V4443 |      1.31262e+07 |      0           |      -1.31262e+07 |
| V4581 |      3.18707e+07 |      1.14876e+07 |      -2.0383e+07  |
| V4413 |      3.28681e+07 |      5.96769e+06 |      -2.69004e+07 |



label: D=C-B
labeled_formulas: D=C-B
output: {"Arithmetic-Relationship": ["D=C-B"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_404585___xlsx_08b495898452a52897277a1c8fc9bc9569133f77.xlsx___line_55