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 |                G |   H |
|:------|:--------------------------|:------|:------------------------------------------------------------------------------------------------|-------:|----------:|-----------------:|----:|
| DCRDN | Daycase and Reg Day/Night | SC21Z | Deliver a Fraction of Treatment on a Superficial or Orthovoltage Machine                        |   3187 |  104.845  | 334140           |   6 |
| DCRDN | Daycase and Reg Day/Night | SC22Z | Deliver a Fraction of Treatment on a Megavoltage Machine                                        |  29411 |  116.342  |      3.42172e+06 |  11 |
| DCRDN | Daycase and Reg Day/Night | SC23Z | Deliver a Fraction of Complex Treatment on a Megavoltage Machine                                | 163612 |  156.332  |      2.55778e+07 |  12 |
| DCRDN | Daycase and Reg Day/Night | SC24Z | Deliver a Fraction of Radiotherapy on a Megavoltage Machine using General Anaesthetic           |    153 |  347.025  |  53094.8         |   2 |
| DCRDN | Daycase and Reg Day/Night | SC25Z | Deliver a Fraction of Total Body Irradiation                                                    |    121 |  517.034  |  62561.1         |   3 |
| DCRDN | Daycase and Reg Day/Night | SC26Z | Deliver a Fraction of Intracavitary Radiotherapy without General Anaesthetic                    |    824 |  492.894  | 406145           |   8 |
| DCRDN | Daycase and Reg Day/Night | SC27Z | Deliver a Fraction of Intracavitary Radiotherapy with General Anaesthetic                       |    282 |  611.79   | 172525           |   5 |
| DCRDN | Daycase and Reg Day/Night | SC28Z | Deliver a Fraction of Interstitial Radiotherapy                                                 |    568 | 2427.87   |      1.37903e+06 |   7 |
| DCRDN | Daycase and Reg Day/Night | SC29Z | Other Radiotherapy Treatment                                                                    |   1700 |  258.49   | 439433           |   8 |
| DCRDN | Daycase and Reg Day/Night | SC30Z | Deliver a Fraction of Intraluminal Brachytherapy                                                |     61 |  853.758  |  52079.3         |   5 |
| DCRDN | Daycase and Reg Day/Night | SC31Z | Deliver a Fraction of Adaptive Radiotherapy on a Megavoltage Machine                            | 140394 |  172.146  |      2.41682e+07 |  14 |
| DCRDN | Daycase and Reg Day/Night | SC40Z | Preparation for Intensity Modulated Radiation Therapy                                           |   7068 | 1355.15   |      9.57823e+06 |  11 |
| DCRDN | Daycase and Reg Day/Night | SC41Z | Preparation for Intensity Modulated Radiation Therapy, with Technical Support                   |   2728 | 1833.87   |      5.00281e+06 |  12 |
| DCRDN | Daycase and Reg Day/Night | SC42Z | Preparation for Total Body Irradiation                                                          |      9 | 1371.35   |  12342.2         |   2 |
| DCRDN | Daycase and Reg Day/Night | SC43Z | Preparation for Total Body Irradiation, with Technical Support                                  |     27 | 1642.53   |  44348.3         |   1 |
| DCRDN | Daycase and Reg Day/Night | SC44Z | Preparation for Hemi-Body Irradiation                                                           |      1 |  556.13   |    556.13        |   1 |
| DCRDN | Daycase and Reg Day/Night | SC45Z | Preparation for Simple Radiotherapy with Imaging and Dosimetry                                  |   2297 |  705.775  |      1.62116e+06 |  12 |
| DCRDN | Daycase and Reg Day/Night | SC46Z | Preparation for Simple Radiotherapy with Imaging and Dosimetry, with Technical Support          |    243 |  483.244  | 117428           |   8 |
| DCRDN | Daycase and Reg Day/Night | SC47Z | Preparation for Simple Radiotherapy with Imaging and Simple Calculation                         |   6180 |  407.587  |      2.51889e+06 |  10 |
| DCRDN | Daycase and Reg Day/Night | SC48Z | Preparation for Simple Radiotherapy with Imaging and Simple Calculation, with Technical Support |   2041 |  647.102  |      1.32074e+06 |   8 |
| DCRDN | Daycase and Reg Day/Night | SC49Z | Preparation for Superficial Radiotherapy with Simple Calculation                                |    341 |  311.188  | 106115           |   9 |
| DCRDN | Daycase and Reg Day/Night | SC50Z | Preparation for Superficial Radiotherapy with Simple Calculation, with Technical Support        |    327 |  684.268  | 223755           |   8 |
| DCRDN | Daycase and Reg Day/Night | SC51Z | Preparation for Complex Conformal Radiotherapy                                                  |   8733 |  807.381  |      7.05086e+06 |  10 |
| DCRDN | Daycase and Reg Day/Night | SC52Z | Preparation for Complex Conformal Radiotherapy, with Technical Support                          |   1015 | 1288.28   |      1.3076e+06  |  11 |
| DCRDN | Daycase and Reg Day/Night | SC53Z | Preparation for Intraluminal Brachytherapy                                                      |     73 | 1091.8    |  79701.3         |   6 |
| DCRDN | Daycase and Reg Day/Night | SC54Z | Preparation for Intracavitary Brachytherapy                                                     |    735 |  922.398  | 677963           |  11 |
| DCRDN | Daycase and Reg Day/Night | SC55Z | Preparation for Interstitial Brachytherapy                                                      |    471 | 1224.92   | 576935           |   8 |
| DCRDN | Daycase and Reg Day/Night | SC56Z | Other External Beam Radiotherapy Preparation                                                    |    247 | 1439.21   | 355485           |   7 |
| DCRDN | Daycase and Reg Day/Night | SC57Z | Other Brachytherapy Preparation                                                                 |      1 |  503.96   |    503.96        |   1 |
| DCRDN | Daycase and Reg Day/Night | SC97Z | Same Day Radiotherapy Admission or Attendance (excluding Brachytherapy)                         | 236987 |    0      |      0           |  21 |
| IP    | Inpatient                 | SC21Z | Deliver a Fraction of Treatment on a Superficial or Orthovoltage Machine                        |      7 |  108.579  |    760.05        |   2 |
| IP    | Inpatient                 | SC22Z | Deliver a Fraction of Treatment on a Megavoltage Machine                                        |   3325 |   75.1019 | 249714           |  11 |
| IP    | Inpatient                 | SC23Z | Deliver a Fraction of Complex Treatment on a Megavoltage Machine                                |   9672 |   82.6398 | 799292           |  11 |
| IP    | Inpatient                 | SC24Z | Deliver a Fraction of Radiotherapy on a Megavoltage Machine using General Anaesthetic           |     17 |  272.275  |   4628.68        |   2 |
| IP    | Inpatient                 | SC25Z | Deliver a Fraction of Total Body Irradiation                                                    |     73 |  433.827  |  31669.4         |   5 |
| IP    | Inpatient                 | SC26Z | Deliver a Fraction of Intracavitary Radiotherapy without General Anaesthetic                    |    803 | 1399.75   |      1.124e+06   |  13 |
| IP    | Inpatient                 | SC27Z | Deliver a Fraction of Intracavitary Radiotherapy with General Anaesthetic                       |    351 |  969.565  | 340317           |   7 |
| IP    | Inpatient                 | SC28Z | Deliver a Fraction of Interstitial Radiotherapy                                                 |   1115 | 2082.15   |      2.3216e+06  |  14 |
| IP    | Inpatient                 | SC29Z | Other Radiotherapy Treatment                                                                    |    782 |  934.307  | 730628           |   9 |
| IP    | Inpatient                 | SC30Z | Deliver a Fraction of Intraluminal Brachytherapy                                                |     18 |  752.502  |  13545           |   7 |
| IP    | Inpatient                 | SC31Z | Deliver a Fraction of Adaptive Radiotherapy on a Megavoltage Machine                            |  18911 |  111.271  |      2.10425e+06 |  10 |
| IP    | Inpatient                 | SC40Z | Preparation for Intensity Modulated Radiation Therapy                                           |    186 | 1665.18   | 309724           |   7 |
| IP    | Inpatient                 | SC41Z | Preparation for Intensity Modulated Radiation Therapy, with Technical Support                   |     63 | 1566.35   |  98680.2         |   8 |
| IP    | Inpatient                 | SC42Z | Preparation for Total Body Irradiation                                                          |     19 | 2206.1    |  41915.9         |   2 |
| IP    | Inpatient                 | SC43Z | Preparation for Total Body Irradiation, with Technical Support                                  |      2 | 1168.62   |   2337.24        |   1 |
| IP    | Inpatient                 | SC45Z | Preparation for Simple Radiotherapy with Imaging and Dosimetry                                  |    683 |  490.619  | 335093           |   8 |
| IP    | Inpatient                 | SC46Z | Preparation for Simple Radiotherapy with Imaging and Dosimetry, with Technical Support          |     24 |  629.803  |  15115.3         |   8 |
| IP    | Inpatient                 | SC47Z | Preparation for Simple Radiotherapy with Imaging and Simple Calculation                         |    438 |  568.124  | 248839           |   8 |
| IP    | Inpatient                 | SC48Z | Preparation for Simple Radiotherapy with Imaging and Simple Calculation, with Technical Support |     43 | 1191.61   |  51239.2         |   6 |
| IP    | Inpatient                 | SC49Z | Preparation for Superficial Radiotherapy with Simple Calculation                                |     12 |  458.689  |   5504.27        |   5 |
| IP    | Inpatient                 | SC50Z | Preparation for Superficial Radiotherapy with Simple Calculation, with Technical Support        |      2 | 2312.13   |   4624.26        |   1 |
| IP    | Inpatient                 | SC51Z | Preparation for Complex Conformal Radiotherapy                                                  |    149 |  721.464  | 107498           |   9 |
| IP    | Inpatient                 | SC52Z | Preparation for Complex Conformal Radiotherapy, with Technical Support                          |     33 | 1173.02   |  38709.6         |   8 |
| IP    | Inpatient                 | SC53Z | Preparation for Intraluminal Brachytherapy                                                      |     11 |  883.823  |   9722.05        |   4 |
| IP    | Inpatient                 | SC54Z | Preparation for Intracavitary Brachytherapy                                                     |    676 |  762.851  | 515687           |  10 |
| IP    | Inpatient                 | SC55Z | Preparation for Interstitial Brachytherapy                                                      |    673 | 1167.45   | 785691           |  10 |
| IP    | Inpatient                 | SC56Z | Other External Beam Radiotherapy Preparation                                                    |     26 | 1076.63   |  27992.4         |   7 |
| OP    | Outpatient                | SC21Z | Deliver a Fraction of Treatment on a Superficial or Orthovoltage Machine                        |  20095 |   92.5689 |      1.86017e+06 |  35 |
| OP    | Outpatient                | SC22Z | Deliver a Fraction of Treatment on a Megavoltage Machine                                        | 106408 |  108.59   |      1.15548e+07 |  39 |
| OP    | Outpatient                | SC23Z | Deliver a Fraction of Complex Treatment on a Megavoltage Machine                                | 541556 |  127.308  |      6.89446e+07 |  39 |
| OP    | Outpatient                | SC24Z | Deliver a Fraction of Radiotherapy on a Megavoltage Machine using General Anaesthetic           |    824 |  367.661  | 302953           |   9 |
| OP    | Outpatient                | SC25Z | Deliver a Fraction of Total Body Irradiation                                                    |   2497 |  268.913  | 671475           |  19 |
| OP    | Outpatient                | SC26Z | Deliver a Fraction of Intracavitary Radiotherapy without General Anaesthetic                    |   3958 |  396.195  |      1.56814e+06 |  24 |
| OP    | Outpatient                | SC27Z | Deliver a Fraction of Intracavitary Radiotherapy with General Anaesthetic                       |    310 |  976.468  | 302705           |  10 |
| OP    | Outpatient                | SC28Z | Deliver a Fraction of Interstitial Radiotherapy                                                 |   1330 |  847.204  |      1.12678e+06 |  18 |
| OP    | Outpatient                | SC29Z | Other Radiotherapy Treatment                                                                    |  10024 |  437.254  |      4.38303e+06 |  24 |
| OP    | Outpatient                | SC30Z | Deliver a Fraction of Intraluminal Brachytherapy                                                |    750 | 2822.36   |      2.11677e+06 |   8 |
| OP    | Outpatient                | SC31Z | Deliver a Fraction of Adaptive Radiotherapy on a Megavoltage Machine                            | 610097 |  187.495  |      1.1439e+08  |  38 |
| OP    | Outpatient                | SC40Z | Preparation for Intensity Modulated Radiation Therapy                                           |  26969 |  957.281  |      2.58169e+07 |  37 |
| OP    | Outpatient                | SC41Z | Preparation for Intensity Modulated Radiation Therapy, with Technical Support                   |  12952 | 1287.18   |      1.66716e+07 |  36 |
| OP    | Outpatient                | SC42Z | Preparation for Total Body Irradiation                                                          |    213 | 1167.14   | 248602           |  12 |
| OP    | Outpatient                | SC43Z | Preparation for Total Body Irradiation, with Technical Support                                  |     42 | 1354.77   |  56900.5         |  10 |
| OP    | Outpatient                | SC44Z | Preparation for Hemi-Body Irradiation                                                           |      3 |  438.45   |   1315.35        |   3 |
| OP    | Outpatient                | SC45Z | Preparation for Simple Radiotherapy with Imaging and Dosimetry                                  |   7414 |  380.121  |      2.81821e+06 |  33 |
| OP    | Outpatient                | SC46Z | Preparation for Simple Radiotherapy with Imaging and Dosimetry, with Technical Support          |   1187 |  441.164  | 523662           |  31 |
| OP    | Outpatient                | SC47Z | Preparation for Simple Radiotherapy with Imaging and Simple Calculation                         |  18558 |  265.64   |      4.92974e+06 |  36 |
| OP    | Outpatient                | SC48Z | Preparation for Simple Radiotherapy with Imaging and Simple Calculation, with Technical Support |   2925 |  410.473  |      1.20063e+06 |  34 |
| OP    | Outpatient                | SC49Z | Preparation for Superficial Radiotherapy with Simple Calculation                                |   2741 |  391.597  |      1.07337e+06 |  34 |
| OP    | Outpatient                | SC50Z | Preparation for Superficial Radiotherapy with Simple Calculation, with Technical Support        |   1253 |  625.299  | 783499           |  32 |
| OP    | Outpatient                | SC51Z | Preparation for Complex Conformal Radiotherapy                                                  |  25349 |  672.505  |      1.70473e+07 |  37 |
| OP    | Outpatient                | SC52Z | Preparation for Complex Conformal Radiotherapy, with Technical Support                          |   2524 |  844.509  |      2.13154e+06 |  36 |
| OP    | Outpatient                | SC53Z | Preparation for Intraluminal Brachytherapy                                                      |    523 |  251.418  | 131492           |   6 |
| OP    | Outpatient                | SC54Z | Preparation for Intracavitary Brachytherapy                                                     |   2000 |  813.972  |      1.62794e+06 |  21 |
| OP    | Outpatient                | SC55Z | Preparation for Interstitial Brachytherapy                                                      |    977 |  817.17   | 798375           |  15 |
| OP    | Outpatient                | SC56Z | Other External Beam Radiotherapy Preparation                                                    |    793 |  327.056  | 259355           |   7 |
| OP    | Outpatient                | SC57Z | Other Brachytherapy Preparation                                                                 |      1 | 3273.01   |   3273.01        |   1 |
| OP    | Outpatient                | SC97Z | Same Day Radiotherapy Admission or Attendance (excluding Brachytherapy)                         | 687284 |    0      |      0           |  19 |
| Oth   | Other                     | SC21Z | Deliver a Fraction of Treatment on a Superficial or Orthovoltage Machine                        |   1567 |  119.6    | 187413           |   1 |
| Oth   | Other                     | SC22Z | Deliver a Fraction of Treatment on a Megavoltage Machine                                        |  12808 |  130.339  |      1.66938e+06 |   3 |
| Oth   | Other                     | SC23Z | Deliver a Fraction of Complex Treatment on a Megavoltage Machine                                |  46577 |  162.492  |      7.56837e+06 |   3 |
| Oth   | Other                     | SC25Z | Deliver a Fraction of Total Body Irradiation                                                    |     30 | 1010.11   |  30303.3         |   1 |
| Oth   | Other                     | SC26Z | Deliver a Fraction of Intracavitary Radiotherapy without General Anaesthetic                    |    723 |  257.913  | 186471           |   3 |
| Oth   | Other                     | SC27Z | Deliver a Fraction of Intracavitary Radiotherapy with General Anaesthetic                       |    106 |  874.027  |  92646.8         |   3 |
| Oth   | Other                     | SC28Z | Deliver a Fraction of Interstitial Radiotherapy                                                 |    158 | 3596.49   | 568245           |   3 |
| Oth   | Other                     | SC29Z | Other Radiotherapy Treatment                                                                    |   1004 |  339.775  | 341134           |   2 |
| Oth   | Other                     | SC31Z | Deliver a Fraction of Adaptive Radiotherapy on a Megavoltage Machine                            |  71207 |  170.002  |      1.21053e+07 |   3 |
| Oth   | Other                     | SC40Z | Preparation for Intensity Modulated Radiation Therapy                                           |   2920 | 1694.74   |      4.94863e+06 |   4 |
| Oth   | Other                     | SC41Z | Preparation for Intensity Modulated Radiation Therapy, with Technical Support                   |   1218 | 3174.26   |      3.86624e+06 |   4 |
| Oth   | Other                     | SC42Z | Preparation for Total Body Irradiation                                                          |     18 | 5005.09   |  90091.7         |   2 |
| Oth   | Other                     | SC45Z | Preparation for Simple Radiotherapy with Imaging and Dosimetry                                  |   1997 |  720.877  |      1.43959e+06 |   3 |
| Oth   | Other                     | SC46Z | Preparation for Simple Radiotherapy with Imaging and Dosimetry, with Technical Support          |    661 |  678.509  | 448495           |   3 |
| Oth   | Other                     | SC47Z | Preparation for Simple Radiotherapy with Imaging and Simple Calculation                         |    750 |  304.507  | 228380           |   4 |
| Oth   | Other                     | SC48Z | Preparation for Simple Radiotherapy with Imaging and Simple Calculation, with Technical Support |    311 |  579.578  | 180249           |   4 |
| Oth   | Other                     | SC49Z | Preparation for Superficial Radiotherapy with Simple Calculation                                |    595 |  447.754  | 266413           |   2 |
| Oth   | Other                     | SC50Z | Preparation for Superficial Radiotherapy with Simple Calculation, with Technical Support        |    552 |  396.814  | 219041           |   2 |
| Oth   | Other                     | SC51Z | Preparation for Complex Conformal Radiotherapy                                                  |   2905 | 1045.04   |      3.03586e+06 |   4 |
| Oth   | Other                     | SC52Z | Preparation for Complex Conformal Radiotherapy, with Technical Support                          |    433 | 1919.63   | 831198           |   4 |
| Oth   | Other                     | SC54Z | Preparation for Intracavitary Brachytherapy                                                     |    292 |  565.818  | 165219           |   3 |
| Oth   | Other                     | SC55Z | Preparation for Interstitial Brachytherapy                                                      |     96 | 1073.39   | 103045           |   2 |
| Oth   | Other                     | SC56Z | Other External Beam Radiotherapy Preparation                                                    |    114 |  298.86   |  34070           |   1 |



label: F=G/E
labeled_formulas: F=G/E
output: {"Arithmetic-Relationship": ["F=G/E"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_569640___xlsx_2a0660bf37fd14e87caa1993fb32590edcebd5ff.xlsx___line_173