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 | P9K10A          | HPE 42U 600mmx1200mm G2 Kitted Advanced Shock Rack with Side Panels and Baying             |   0 |   0 |
|   1 | P9K10A      001 | HPE Factory Express Base Racking Service                                                   |   0 |   0 |
|   2 | R4D36A          | HPE SimpliVity 380 Gen10 SFF H Node                                                        |   0 |   0 |
|   2 | R4D36A      0D1 | Factory Integrated                                                                         |   0 |   0 |
|   2 | R2G97A          | HPE SimpliVity 380 Gen10 Node with VMware Tracking                                         |   0 |   0 |
|   2 | R2G97A      0D1 | Factory Integrated                                                                         |   0 |   0 |
|   2 | P24466-L21      | Intel Xeon-Gold 5218R (2.1GHz/20-core/125W) FIO Processor Kit for HPE ProLiant DL380 Gen10 |   0 |   0 |
|   2 | P24466-B21      | Intel Xeon-Gold 5218R (2.1GHz/20-core/125W) Processor Kit for HPE ProLiant DL380 Gen10     |   0 |   0 |
|   2 | P24466-B21  0D1 | Factory Integrated                                                                         |   0 |   0 |
|   4 | R4C22A          | HPE SimpliVity 256GB (4x64GB) DDR4-2933 Load Reduced Memory Kit                            |   0 |   0 |
|   4 | R4C22A      0D1 | Factory Integrated                                                                         |   0 |   0 |
|   4 | 872475-K21      | HPE 300GB SAS 12G Enterprise 10K SFF (2.5in) SC 3yr Wty Digitally Signed Firmware HDD      |   0 |   0 |
|   4 | 872475-K21  0D1 | Factory Integrated                                                                         |   0 |   0 |
|   2 | R4D37A          | HPE SimpliVity 1.2TB SAS 12G SFF (2.5in) 20-pack HDD                                       |   0 |   0 |
|   2 | R4D37A      0D1 | Factory Integrated                                                                         |   0 |   0 |
|   2 | R4D38A          | HPE SimpliVity 1.92T SATA MU SFF 4pk SSD                                                   |   0 |   0 |
|   2 | R4D38A      0D1 | Factory Integrated                                                                         |   0 |   0 |
|   2 | 870549-B21      | HPE DL38X Gen10 12Gb SAS Expander Card Kit with Cables                                     |   0 |   0 |
|   2 | 870549-B21  0D1 | Factory Integrated                                                                         |   0 |   0 |
|   2 | 647594-B21      | HPE Ethernet 1Gb 4-port BASE-T BCM5719 Adapter                                             |   0 |   0 |
|   2 | 647594-B21  0D1 | Factory Integrated                                                                         |   0 |   0 |
|   2 | P01366-B21      | HPE 96W Smart Storage Lithium-ion Battery with 145mm Cable Kit                             |   0 |   0 |
|   2 | P01366-B21  0D1 | Factory Integrated                                                                         |   0 |   0 |
|   2 | 804331-B21      | HPE Smart Array P408i-a SR Gen10 (8 Internal Lanes/2GB Cache) 12G SAS Modular Controller   |   0 |   0 |
|   2 | 804331-B21  0D1 | Factory Integrated                                                                         |   0 |   0 |
|   2 | 817709-B21      | HPE Ethernet 10/25Gb 2-port FLR-SFP28 BCM57414 Adapter                                     |   0 |   0 |
|   2 | 817709-B21  0D1 | Factory Integrated                                                                         |   0 |   0 |
|   4 | 830272-B21      | HPE 1600W Flex Slot Platinum Hot Plug Low Halogen Power Supply Kit                         |   0 |   0 |
|   4 | 830272-B21  0D1 | Factory Integrated                                                                         |   0 |   0 |
|   2 | BD505A          | HPE iLO Advanced 1-server License with 3yr Support on iLO Licensed Features                |   0 |   0 |
|   2 | BD505A      0D1 | Factory Integrated                                                                         |   0 |   0 |
|   2 | R4D20A          | HPE SimpliVity 380 H 2 Processors 20TB Software                                            |   0 |   0 |
|   6 | 861413-B21      | HPE Synergy Frame Link Module CAT6A 3m Cable                                               |   0 |   0 |
|   6 | 861413-B21  0D1 | Factory Integrated                                                                         |   0 |   0 |
|   2 | 733664-B21      | HPE 2U Cable Management Arm for Easy Install Rail Kit                                      |   0 |   0 |
|   2 | 733664-B21  0D1 | Factory Integrated                                                                         |   0 |   0 |
|   2 | 867809-B21      | HPE Gen10 2U Bezel Kit                                                                     |   0 |   0 |
|   2 | 867809-B21  0D1 | Factory Integrated                                                                         |   0 |   0 |
|   2 | 826703-B21      | HPE DL380 Gen10 SFF Systems Insight Display Kit                                            |   0 |   0 |
|   2 | 826703-B21  0D1 | Factory Integrated                                                                         |   0 |   0 |
|   2 | 733660-B21      | HPE 2U Small Form Factor Easy Install Rail Kit                                             |   0 |   0 |
|   2 | 733660-B21  0D1 | Factory Integrated                                                                         |   0 |   0 |
|   2 | 826706-B21      | HPE DL380 Gen10 High Performance Heat Sink Kit                                             |   0 |   0 |
|   2 | 826706-B21  0D1 | Factory Integrated                                                                         |   0 |   0 |
|   1 | 263474-B22      | HPE 6ft Qty 8 KVM CAT5 Cable                                                               |   0 |   0 |
|   1 | 263474-B22  0D1 | Factory Integrated                                                                         |   0 |   0 |
|   1 | H6J85A          | HPE Rack Hardware Kit                                                                      |   0 |   0 |
|   1 | H6J85A      0D1 | Factory Integrated                                                                         |   0 |   0 |
|   4 | P9Q45A          | HPE G2 Basic 7.3kVA/60309 3-wire 32A/230V Outlets (20) C13/Vertical INTL PDU               |   0 |   0 |
|   4 | P9Q45A      0D1 | Factory Integrated                                                                         |   0 |   0 |
|   1 | AF644A          | HPE LCD8500 1U INTL Rackmount Console Kit                                                  |   0 |   0 |
|   1 | AF644A      0D1 | Factory Integrated                                                                         |   0 |   0 |
|   1 | AF651A          | HPE 0x1x8 G3 KVM Console Switch                                                            |   0 |   0 |
|   1 | AF651A      0D1 | Factory Integrated                                                                         |   0 |   0 |
|   1 | AF655A          | HPE KVM Console USB 8-pack Interface Adapter                                               |   0 |   0 |
|   1 | AF655A      0D1 | Factory Integrated                                                                         |   0 |   0 |
|   1 | BW932A          | HPE 600mm Rack Stabilizer Kit                                                              |   0 |   0 |
|   1 | BW932A      B01 | HPE 600mm Rack include with Complete System Stabilizer Kit                                 |   0 |   0 |
|   1 | P1F64A          | HPE Inside Unpack/Clean Up w/Lift XL SVC                                                   |   0 |   0 |
|   5 | BD711AAE        | VMware vSphere Standard 1 Processor 3yr E-LTU                                              |   0 |   0 |
|   1 | P17081-B21      | HPE ProLiant DL20 Gen10 E-2236 3.40 GHz 6C 1P 16GB-U S100i 4SFF 500W RPS Server            |   0 |   0 |
|   3 | 861413-B21      | HPE Synergy Frame Link Module CAT6A 3m Cable                                               |   0 |   0 |
|   3 | 861413-B21  0D1 | Factory Integrated                                                                         |   0 |   0 |
|   1 | HA113A1         | HPE Installation SVC                                                                       |   0 |   0 |
|   1 | HA113A1     5BY | HPE Rack and Rack Options Install SVC                                                      |   0 |   0 |
|   3 | 879507-B21      | HPE 16GB (1x16GB) Dual Rank x8 DDR4-2666 CAS-19-19-19 Unbuffered Standard Memory Kit       |   0 |   0 |
|   1 | H1K92A3         | HPE 3Y Proactive Care 24x7 SVC                                                             |   0 |   0 |
|   4 | H1K92A3     R5E | HPE VMw vSphere Std 1P 3yr SW Support                                                      |   0 |   0 |
|   2 | H1K92A3     R2M | HPE iLO Advanced Non Blade Support                                                         |   0 |   0 |
|   2 | H1K92A3     Z9X | HPE SVT 380 Gen10 Node (1 Node) Support                                                    |   0 |   0 |
|   2 | H1K92A3     X6M | HPE SimpliVity 380 H 2P 20TB SW Support                                                    |   0 |   0 |
|   2 | P04556-B21      | HPE 240GB SATA 6G Read Intensive SFF SC PM883 SSD                                          |   0 |   0 |
|   1 | P8B24A          | HPE OneView w/o iLO including 3yr 24x7 Support 1-server LTU                                |   0 |   0 |
|   1 | P9U41AAE        | VMware vCenter Server Standard for vSphere (per Instance) 3yr E-LTU                        |   0 |   0 |
|   1 | 647594-B21      | HPE Ethernet 1Gb 4-port BASE-T BCM5719 Adapter                                             |   0 |   0 |
|   1 | HA114A1         | HPE Installation and Startup Service                                                       |   0 |   0 |
|   2 | HA114A1     5LY | HPE Simplivity 380 HW Startup SVC                                                          |   0 |   0 |
|   1 | HA114A1     5T6 | HPE Startup Entry ML DL Svr SVC                                                            |   0 |   0 |
|   1 | HU4A6A3         | HPE 3Y Tech Care Essential Service                                                         |   0 |   0 |
|   1 | HU4A6A3     X7N | HPE ProLiant DL20 Gen10 Support                                                            |   0 |   0 |
|   1 | HA124A1         | HPE Technical Installation Startup SVC                                                     |   0 |   0 |
|   2 | HA124A1     5LZ | HPE SVT for VMware Remote SW St SVC                                                        |   0 |   0 |
|  10 | HF385A1         | HPE Training Credit Servers/HybridIT SVC                                                   |   0 |   0 |
|  10 | HF386A1         | HPE Training Credits for VMware SVC                                                        |   0 |   0 |
|   6 | HF382A1         | HPE Training Credits for Simplivity SVC                                                    |   0 |   0 |



label: E=D*A
labeled_formulas: E=D*A
output: {"Arithmetic-Relationship": ["E=D*A"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_136380___xlsx_4817a709133e8e1111daa0a35aacfa2e127467e1.xlsx___line_211