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 |
|:--------------|--------:|--------:|----------:|--------:|---------:|
| 41641         | 3316    | 311     | 0.0937877 | 643     | 0.193908 |
| 41642         | 3337    | 310     | 0.0928978 | 652     | 0.195385 |
| 41645         | 3435    | 310     | 0.0902475 | 664     | 0.193304 |
| 41646         | 3457    | 321     | 0.0928551 | 698     | 0.201909 |
| 41647         | 3482    | 314     | 0.0901781 | 688     | 0.197588 |
| 41648         | 3437    | 311     | 0.0904859 | 677     | 0.196974 |
| 41649         | 3453    | 325     | 0.0941211 | 667     | 0.193165 |
| 41652         | 3556    | 331     | 0.0930821 | 747     | 0.210067 |
| 41653         | 3583    | 333     | 0.0929389 | 734     | 0.204856 |
| 41654         | 3623    | 333     | 0.0919128 | 731     | 0.201766 |
| 41655         | 3634    | 344     | 0.0946615 | 735     | 0.202256 |
| 41656         | 3657    | 336     | 0.0918786 | 740     | 0.202352 |
| 41660         | 3735    | 351     | 0.0939759 | 755     | 0.202142 |
| 41661         | 3899    | 354     | 0.0907925 | 773     | 0.198256 |
| 41662         | 4002    | 358     | 0.0894553 | 782     | 0.195402 |
| 41663         | 4046    | 348     | 0.0860109 | 783     | 0.193524 |
| 41666         | 4050    | 348     | 0.0859259 | 797     | 0.19679  |
| 41667         | 3976    | 347     | 0.0872736 | 795     | 0.19995  |
| 41668         | 3963    | 348     | 0.0878123 | 781     | 0.197073 |
| 41669         | 3936    | 351     | 0.0891768 | 779     | 0.197917 |
| 41670         | 3832    | 273     | 0.0712422 | 703     | 0.183455 |
| 41673         | 3723    | 273     | 0.073328  | 694     | 0.186409 |
| 41674         | 3740    | 272     | 0.0727273 | 703     | 0.187968 |
| 41675         | 3796    | 268     | 0.0706006 | 702     | 0.184932 |
| 41676         | 3817    | 269     | 0.0704742 | 722     | 0.189154 |
| 41677         | 3907    | 302     | 0.0772972 | 733     | 0.187612 |
| 41681         | 4072    | 333     | 0.081778  | 727     | 0.178536 |
| 41682         | 4232    | 313     | 0.0739603 | 751     | 0.177457 |
| 41683         | 4149    | 323     | 0.0778501 | 763     | 0.1839   |
| 41684         | 4209    | 327     | 0.0776907 | 769     | 0.182704 |
| 41687         | 4259    | 343     | 0.0805353 | 784     | 0.184081 |
| 41688         | 4306    | 331     | 0.0768695 | 789     | 0.183233 |
| 41689         | 4369    | 338     | 0.0773632 | 809     | 0.185168 |
| 41690         | 4631    | 335     | 0.0723386 | 836     | 0.180523 |
| 41691         | 4732    | 333     | 0.0703719 | 835     | 0.176458 |
| 41694         | 4640    | 333     | 0.0717672 | 819     | 0.176509 |
| 41695         | 4748    | 323     | 0.0680286 | 817     | 0.172072 |
| 41696         | 4529    | 343     | 0.0757342 | 804     | 0.177523 |
| 41697         | 4497    | 335     | 0.0744941 | 787     | 0.175006 |
| 41698         | 4416    | 280     | 0.0634058 | 701     | 0.158741 |
| 41701         | 4309    | 280     | 0.0649803 | 702     | 0.162915 |
| 41702         | 4301    | 278     | 0.0646361 | 729     | 0.169495 |
| 41703         | 4217    | 272     | 0.0645008 | 715     | 0.169552 |
| 41704         | 4291    | 273     | 0.0636215 | 739     | 0.172221 |
| 41705         | 4384    | 274     | 0.0625    | 735     | 0.167655 |
| 41708         | 4408    | 290     | 0.0657895 | 759     | 0.172187 |
| 41709         | 4435    | 294     | 0.0662909 | 771     | 0.173844 |
| 41710         | 4485    | 305     | 0.0680045 | 793     | 0.176812 |
| 41711         | 4567    | 315     | 0.0689731 | 779     | 0.170571 |
| 41712         | 4614    | 324     | 0.0702211 | 771     | 0.1671   |
| 41715         | 4604    | 319     | 0.0692876 | 772     | 0.16768  |
| 41716         | 4660    | 319     | 0.0684549 | 794     | 0.170386 |
| 41717         | 4683    | 317     | 0.0676917 | 811     | 0.17318  |
| 41718         | 4717    | 323     | 0.0684757 | 807     | 0.171083 |
| 41719         | 4802    | 328     | 0.0683049 | 804     | 0.16743  |
| 41722         | 4852    | 335     | 0.0690437 | 820     | 0.169002 |
| 41723         | 4858    | 339     | 0.0697818 | 838     | 0.172499 |
| 41724         | 4855    | 332     | 0.0683831 | 816     | 0.168074 |
| 41725         | 4832    | 337     | 0.0697434 | 813     | 0.168253 |
| 41726         | 4639    | 272     | 0.0586333 | 707     | 0.152404 |
| 41729         | 4550    | 288     | 0.0632967 | 718     | 0.157802 |
| 41730         | 4441    | 294     | 0.0662013 | 731     | 0.164603 |
| 41731         | 4407    | 295     | 0.066939  | 717     | 0.162696 |
| 41732         | 4498    | 308     | 0.0684749 | 719     | 0.159849 |
| 41733         | 4506    | 313     | 0.0694629 | 724     | 0.160675 |
| 41736         | 4571    | 316     | 0.0691315 | 721     | 0.157734 |
| 41737         | 4605    | 317     | 0.0688382 | 726     | 0.157655 |
| 41738         | 4658    | 319     | 0.0684843 | 729     | 0.156505 |
| 41739         | 4690    | 311     | 0.0663113 | 737     | 0.157143 |
| 41740         | 4705    | 314     | 0.0667375 | 741     | 0.157492 |
| 41743         | 4630    | 318     | 0.0686825 | 743     | 0.160475 |
| 41744         | 4528    | 317     | 0.0700088 | 717     | 0.158348 |
| 41745         | 4579    | 304     | 0.06639   | 731     | 0.159642 |
| 41747         | 4832    | 303     | 0.062707  | 767     | 0.158733 |
| 41750         | 4694    | 296     | 0.0630592 | 794     | 0.169152 |
| 41751         | 4574    | 291     | 0.0636205 | 790     | 0.172715 |
| 41752         | 4751    | 298     | 0.0627236 | 776     | 0.163334 |
| 41753         | 4748    | 236     | 0.0497051 | 707     | 0.148905 |
| 41754         | 4763    | 254     | 0.0533277 | 709     | 0.148856 |
| 41757         | 4631    | 248     | 0.0535521 | 559     | 0.120708 |
| 41758         | 4473    | 241     | 0.0538788 | 514     | 0.114912 |
| 41759         | 4376    | 236     | 0.0539305 | 523     | 0.119516 |
| 41760         | 4317    | 233     | 0.0539727 | 534     | 0.123697 |
| 41761         | 4242    | 236     | 0.0556341 | 542     | 0.12777  |
| 41764         | 4339    | 239     | 0.0550818 | 561     | 0.129292 |
| 41765         | 4407    | 251     | 0.0569548 | 546     | 0.123894 |
| 41766         | 4367    | 253     | 0.0579345 | 545     | 0.1248   |
| 41767         | 4369    | 258     | 0.0590524 | 530     | 0.121309 |
| 41768         | 4437    | 259     | 0.0583728 | 530     | 0.11945  |
| 41771         | 4473    | 266     | 0.0594679 | 536     | 0.11983  |
| 41772         | 4487    | 267     | 0.0595052 | 533     | 0.118788 |
| 41773         | 4476    | 263     | 0.0587578 | 548     | 0.122431 |
| 41774         | 4478    | 266     | 0.0594015 | 548     | 0.122376 |
| 41775         | 4502    | 278     | 0.0617503 | 540     | 0.119947 |
| 41778         | 4520    | 278     | 0.0615044 | 541     | 0.11969  |
| 41779         | 4484    | 271     | 0.0604371 | 548     | 0.122212 |
| 41780         | 4486    | 272     | 0.0606331 | 543     | 0.121043 |
| 41781         | 4497    | 271     | 0.0602624 | 546     | 0.121414 |
| 41782         | 4695    | 282     | 0.0600639 | 566     | 0.120554 |
| 41786         | 4677    | 280     | 0.0598674 | 585     | 0.12508  |
| 41787         | 4625    | 281     | 0.0607568 | 576     | 0.124541 |
| 41788         | 4526    | 245     | 0.0541317 | 531     | 0.117322 |
| 41789         | 4439    | 247     | 0.0556432 | 521     | 0.117369 |
| 41792         | 4238    | 249     | 0.0587541 | 514     | 0.121284 |
| 41793         | 4028    | 236     | 0.0585899 | 497     | 0.123386 |
| 41794         | 4047    | 247     | 0.0610329 | 500     | 0.123548 |
| 41795         | 4109    | 253     | 0.0615722 | 508     | 0.123631 |
| 41796         | 4182    | 248     | 0.0593018 | 497     | 0.118843 |
| 41799         | 4242    | 261     | 0.0615276 | 491     | 0.115747 |
| 41800         | 4258    | 263     | 0.0617661 | 502     | 0.117896 |
| 41801         | 4245    | 260     | 0.0612485 | 486     | 0.114488 |
| 41802         | 4468    | 271     | 0.0606535 | 485     | 0.10855  |
| 41803         | 4294    | 263     | 0.0612483 | 460     | 0.107126 |
| 41806         | 4261    | 274     | 0.0643042 | 469     | 0.110068 |
| 41807         | 4258    | 283     | 0.0664631 | 470     | 0.11038  |
| 41808         | 4247    | 289     | 0.068048  | 462     | 0.108783 |
| 41809         | 4213    | 299     | 0.0709708 | 456     | 0.108236 |
| 41810         | 4378    | 298     | 0.0680676 | 467     | 0.10667  |
| 41813         | 4308    | 293     | 0.068013  | 451     | 0.104689 |
| 41814         | 4267    | 287     | 0.0672604 | 450     | 0.105461 |
| 41815         | 4243    | 297     | 0.0699976 | 468     | 0.110299 |
| 41816         | 4157    | 241     | 0.0579745 | 439     | 0.105605 |
| 41817         | 4101    | 241     | 0.0587662 | 430     | 0.104852 |
| 41820         | 3897    | 240     | 0.0615858 | 425     | 0.109058 |
| 41821         | 3712    | 245     | 0.0660022 | 422     | 0.113685 |
| 41822         | 3559    | 245     | 0.0688396 | 414     | 0.116325 |
| 41823         | 3626    | 251     | 0.0692223 | 422     | 0.116382 |
| 41827         | 3671    | 260     | 0.0708254 | 435     | 0.118496 |
| 41828         | 3683    | 266     | 0.0722237 | 430     | 0.116753 |
| 41829         | 3734    | 269     | 0.0720407 | 435     | 0.116497 |
| 41830         | 3745    | 272     | 0.0726302 | 438     | 0.116956 |
| 41831         | 3744    | 272     | 0.0726496 | 460     | 0.122863 |
| 41834         | 3697    | 274     | 0.0741141 | 463     | 0.125237 |
| 41835         | 3683    | 271     | 0.0735813 | 447     | 0.121368 |
| 41836         | 3670    | 276     | 0.0752044 | 441     | 0.120163 |
| 41837         | 3676    | 276     | 0.0750816 | 451     | 0.122688 |
| 41838         | 3681    | 279     | 0.0757946 | 446     | 0.121163 |
| 41841         | 3694    | 283     | 0.0766107 | 452     | 0.122361 |
| 41842         | 3803    | 279     | 0.0733631 | 449     | 0.118065 |
| 41843         | 3862    | 280     | 0.0725013 | 445     | 0.115225 |
| 41844         | 3772    | 209     | 0.0554083 | 425     | 0.112672 |
| 41845         | 3723    | 209     | 0.0561375 | 423     | 0.113618 |
| 41848         | 3746    | 219     | 0.0584624 | 428     | 0.114255 |
| 41849         | 3651    | 215     | 0.058888  | 419     | 0.114763 |
| 41850         | 3609    | 227     | 0.0628983 | 412     | 0.114159 |
| 41851         | 3524    | 223     | 0.0632804 | 406     | 0.11521  |
| 41852         | 3469    | 225     | 0.0648602 | 396     | 0.114154 |
| 41855         | 3442    | 231     | 0.0671121 | 391     | 0.113597 |
| 41856         | 3496    | 239     | 0.0683638 | 406     | 0.116133 |
| 41857         | 3516    | 243     | 0.0691126 | 414     | 0.117747 |
| 41858         | 3561    | 243     | 0.0682393 | 404     | 0.113451 |
| 41859         | 3561    | 241     | 0.0676776 | 393     | 0.110362 |
| 41862         | 3654    | 259     | 0.0708812 | 407     | 0.111385 |
| 41863         | 3700    | 258     | 0.0697297 | 422     | 0.114054 |
| 41864         | 3820    | 267     | 0.0698953 | 417     | 0.109162 |
| 41865         | 3838    | 274     | 0.0713913 | 414     | 0.107869 |
| 41866         | 3903    | 277     | 0.070971  | 418     | 0.107097 |
| 41869         | 3950    | 280     | 0.0708861 | 434     | 0.109873 |
| 41870         | 4003    | 284     | 0.0709468 | 441     | 0.110167 |
| 41871         | 4316    | 285     | 0.0660334 | 480     | 0.111214 |
| Daily Average | 4166.76 | 286.056 | 0.0686519 | 610.712 | 0.146568 |



label: D=C/B
F=E/B
labeled_formulas: D=C/B
F=E/B
output: {"Arithmetic-Relationship": ["D=C/B", "F=E/B"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_739807___xlsx_db5d7fea6887db7943e4ca75c6083143f55feda8.xlsx___line_596