Question: From July 27, 2025 to August 13, 2025, what proportion of days had the 5, 20, 60-day Hull Moving Average lines of Williams-Sonoma in long alignment? (Unit: %) Using unadjusted prices, write down the indicator formula, collect the raw data, calculate the answer, and keep four decimal places. Please list the raw data and key calculation process.
Formula: HMA = WMA_{\sqrt{n}}(2 * WMA_{n/2}(P) - WMA_n(P))
Data:
date,close,high,open
2025-03-18,172.27999877929688,176.25,171.14999389648438
2025-03-19,166.27000427246094,167.16000366210938,157.8000030517578
2025-03-20,164.99000549316406,170.3300018310547,165.05999755859375
2025-03-21,163.64999389648438,165.2899932861328,161.13999938964844
2025-03-24,170.3000030517578,171.0800018310547,166.5800018310547
2025-03-25,169.1699981689453,171.2899932861328,170.0
2025-03-26,165.36000061035156,169.8800048828125,169.3000030517578
2025-03-27,164.4199981689453,167.86000061035156,163.8800048828125
2025-03-28,158.97999572753906,164.35000610351562,163.10000610351562
2025-03-31,158.10000610351562,159.72000122070312,155.4600067138672
2025-04-01,158.8699951171875,160.72999572753906,157.52000427246094
2025-04-02,165.00999450683594,166.33999633789062,156.6300048828125
2025-04-03,138.86000061035156,143.1699981689453,142.35000610351562
2025-04-04,141.67999267578125,150.55999755859375,131.55999755859375
2025-04-07,145.08999633789062,152.9199981689453,140.5399932861328
2025-04-08,139.2100067138672,152.80999755859375,149.5
2025-04-09,158.25,160.88999938964844,138.00999450683594
2025-04-10,147.88999938964844,153.22000122070312,153.22000122070312
2025-04-11,148.25,149.30999755859375,147.88999938964844
2025-04-14,145.25999450683594,155.7100067138672,151.94000244140625
2025-04-15,142.89999389648438,147.0,144.85000610351562
2025-04-16,137.6199951171875,142.32000732421875,141.13999938964844
2025-04-17,139.2100067138672,140.14999389648438,138.2100067138672
2025-04-21,137.8699951171875,138.8699951171875,137.07000732421875
2025-04-22,141.92999267578125,144.8000030517578,139.4199981689453
2025-04-23,145.8800048828125,156.50999450683594,148.44000244140625
2025-04-24,151.39999389648438,151.69000244140625,145.82000732421875
2025-04-25,151.19000244140625,153.22999572753906,152.5500030517578
2025-04-28,152.5399932861328,154.36000061035156,153.3300018310547
2025-04-29,153.39999389648438,153.86000061035156,151.05999755859375
2025-04-30,154.47000122070312,154.88999938964844,150.52999877929688
2025-05-01,155.82000732421875,159.0800018310547,157.99000549316406
2025-05-02,160.55999755859375,162.10000610351562,158.4600067138672
2025-05-05,158.38999938964844,159.83999633789062,158.3800048828125
2025-05-06,154.41000366210938,157.27999877929688,155.8300018310547
2025-05-07,157.63999938964844,158.47000122070312,155.6999969482422
2025-05-08,160.88999938964844,162.13999938964844,160.0399932861328
2025-05-09,160.30999755859375,161.99000549316406,161.19000244140625
2025-05-12,173.8000030517578,180.07000732421875,173.25999450683594
2025-05-13,174.44000244140625,176.19000244140625,176.0800018310547
2025-05-14,171.6199951171875,175.91000366210938,173.0800018310547
2025-05-15,171.6699981689453,172.58999633789062,168.27999877929688
2025-05-16,173.83999633789062,175.0500030517578,172.1999969482422
2025-05-19,174.27999877929688,175.2899932861328,169.41000366210938
2025-05-20,172.52000427246094,177.2899932861328,173.8699951171875
2025-05-21,167.9199981689453,171.47000122070312,170.2899932861328
2025-05-22,160.38999938964844,162.6300048828125,156.5
2025-05-23,157.85000610351562,161.60000610351562,158.1300048828125
2025-05-27,166.8300018310547,166.8300018310547,160.63999938964844
2025-05-28,164.50999450683594,168.3300018310547,167.0500030517578
2025-05-29,164.50999450683594,166.6699981689453,165.8300018310547
2025-05-30,161.75999450683594,164.38999938964844,163.5399932861328
2025-06-02,158.22000122070312,161.27000427246094,160.88999938964844
2025-06-03,161.5399932861328,162.47999572753906,158.35000610351562
2025-06-04,159.97000122070312,162.42999267578125,161.1699981689453
2025-06-05,157.97999572753906,160.8300018310547,159.60000610351562
2025-06-06,157.8000030517578,160.50999450683594,159.5
2025-06-09,156.74000549316406,159.22999572753906,159.22999572753906
2025-06-10,158.10000610351562,159.02999877929688,159.02999877929688
2025-06-11,155.5800018310547,162.55999755859375,160.3000030517578
2025-06-12,154.80999755859375,155.94000244140625,155.52999877929688
2025-06-13,153.9600067138672,161.1999969482422,153.82000732421875
2025-06-16,158.14999389648438,158.36000061035156,156.16000366210938
2025-06-17,156.92999267578125,161.1300048828125,156.9499969482422
2025-06-18,160.44000244140625,163.0,157.4499969482422
2025-06-20,158.83999633789062,162.66000366210938,160.97000122070312
2025-06-23,157.88999938964844,158.57000732421875,157.0500030517578
2025-06-24,157.8800048828125,159.57000732421875,159.19000244140625
2025-06-25,158.89999389648438,159.1199951171875,158.57000732421875
2025-06-26,161.92999267578125,162.25999450683594,159.47999572753906
2025-06-27,164.22000122070312,165.41000366210938,162.66000366210938
2025-06-30,163.3699951171875,165.3699951171875,164.74000549316406
2025-07-01,169.19000244140625,172.63999938964844,163.3699951171875
2025-07-02,173.17999267578125,174.27999877929688,169.63999938964844
2025-07-03,173.19000244140625,173.9499969482422,172.60000610351562
2025-07-07,169.2100067138672,172.75999450683594,172.49000549316406
2025-07-08,169.2100067138672,170.82000732421875,169.6300048828125
2025-07-09,173.72999572753906,174.07000732421875,170.75999450683594
2025-07-10,176.5,178.1699981689453,174.13999938964844
2025-07-11,174.82000732421875,176.38999938964844,174.39999389648438
2025-07-14,170.4600067138672,175.67999267578125,173.88999938964844
2025-07-15,163.6199951171875,172.1999969482422,171.0
2025-07-16,165.00999450683594,165.5399932861328,164.52999877929688
2025-07-17,170.1999969482422,171.32000732421875,165.5800018310547
2025-07-18,170.38999938964844,171.1300048828125,171.1300048828125
2025-07-21,172.1999969482422,174.74000549316406,171.72999572753906
2025-07-22,178.61000061035156,179.3300018310547,173.91000366210938
2025-07-23,183.6499938964844,185.27999877929688,183.08999633789065
2025-07-24,180.5399932861328,183.9600067138672,182.0
2025-07-25,181.7100067138672,182.4900054931641,181.8999938964844
2025-07-28,188.22999572753903,188.91000366210935,182.8800048828125
2025-07-29,187.1100006103516,188.55999755859372,188.55999755859372
2025-07-30,190.52999877929688,192.3800048828125,188.2899932861328
2025-07-31,187.0500030517578,191.3300018310547,189.88999938964844
2025-08-01,187.6699981689453,189.4499969482422,184.1999969482422
2025-08-04,200.5200042724609,201.1000061035156,191.72000122070312
2025-08-05,203.77999877929688,204.58999633789065,201.66000366210935
2025-08-06,200.75,205.3500061035156,202.82000732421875
2025-08-07,199.6000061035156,206.3699951171875,204.5399932861328
2025-08-08,199.4199981689453,201.16000366210935,201.0399932861328
2025-08-11,200.0,201.0,200.1499938964844
2025-08-12,206.97000122070312,207.3500061035156,202.22000122070312
2025-08-13,210.1999969482422,210.58999633789065,207.6999969482422

Indicator data:
date,5-day,20-day,60-day
2025-06-20,160.4306660970052,155.90131785867533,162.51094213484134
2025-06-23,158.67355448404948,156.55115745049017,161.87501217169026
2025-06-24,157.56622551812066,157.09690563713835,161.24838958003056
2025-06-25,158.2042215983073,157.6139734679383,160.6479909226005
2025-06-26,161.04821404351128,158.46281357802354,160.1463208749676
2025-06-27,164.51444023980034,159.7288521684919,159.79778872760318
2025-06-30,165.18510911729598,161.0501654627416,159.56213903861084
2025-07-01,167.99333360460068,162.83992128116228,159.57345751665633
2025-07-02,173.49710828993057,165.2094259108506,159.8943732259328
2025-07-03,175.75910915798613,167.77066261588752,160.46942167282825
2025-07-07,172.23111707899307,169.85159242902483,161.14422831942517
2025-07-08,168.72400953504777,171.32801403095195,161.87676233114536
2025-07-09,171.2517791748047,172.70263171835896,162.73536704004027
2025-07-10,176.33999633789065,174.22159409163837,163.73619236283403
2025-07-11,177.23555874294706,175.5524521468522,164.7860549222435
2025-07-14,172.7062310112847,176.0985801122096,165.75473457209242
2025-07-15,164.69755655924482,175.20936030202097,166.4877684642168
2025-07-16,161.4348812527127,173.4778697640555,167.05760927614583
2025-07-17,166.49488186306422,171.9480567403686,167.60457978056112
2025-07-18,171.2244422064887,170.86373344850745,168.13066439216377
2025-07-21,173.03377651638456,170.45670419602166,168.68884760734701
2025-07-22,177.61422186957466,171.11258070578305,169.44082789552567
2025-07-23,184.2984412299262,172.86413961237125,170.48130357115073
2025-07-24,184.8353257921007,174.91804322081722,171.67237906750302
2025-07-25,182.58711174858942,177.14764208112442,172.97364160307603
2025-07-28,186.2417799207899,179.99214206249684,174.47335900722672
2025-07-29,189.3004438612196,182.9285010551684,176.06722688082465
2025-07-30,190.89088812934028,186.03157568399007,177.76841042761103
2025-07-31,189.57377929687496,188.4763934108189,179.42260155820568
2025-08-01,187.46777852376303,190.19309182435404,181.01310817030418
2025-08-04,195.82911309136287,192.61710876795124,182.83783943464647
2025-08-05,205.97466803656687,195.65358418452274,184.894906180966
2025-08-06,206.04755486382382,198.6026498782996,187.02202913815952
2025-08-07,201.48622572157117,201.04962386160187,189.14065438641583
2025-08-08,199.01311340332032,202.69013870371367,191.1973248473225
2025-08-11,199.18777669270833,203.67600621607394,193.1738512213008
2025-08-12,204.55822211371526,204.9774173654003,195.19502613681172
2025-08-13,211.0911095513238,206.75694055004038,197.26723720919125

Answer: 57.8947