arcsinc( 1-y ), for small y
07-06-2018, 03:22 PM (This post was last modified: 10-01-2019 10:54 PM by Albert Chan.)
Post: #2
 Albert Chan Senior Member Posts: 2,103 Joined: Jul 2018
RE: arcsinc( 1-y ), for small y
This new formula is slightly more accurate, and just as simple:

For small y: arcsinc( 1-y ) ~ √(6y) / (1 - 0.15 y)

arcsinc(1 - 1/5281) ~ √(6/5281) / (1 - 0.15/5281) = 0.033707 75877

Example:
y = 1 - sin(x) / x = 0.001665833532

Old formula, x ~ √(6y) * (1 + 0.15 y) = 0.099999 98408
New formula, x ~ √(6y) / (1 - 0.15 y) = 0.099999 99033

Update: newer formula from post #11

x ~$$\large \sqrt{6y ÷ \sqrt{1 + 0.6 y}}$$ = 0.099999 99997 // almost round-trip!
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 Messages In This Thread arcsinc( 1-y ), for small y - Albert Chan - 07-05-2018, 11:43 PM RE: arcsinc( 1-y ), for small y - Albert Chan - 07-06-2018 03:22 PM RE: arcsinc( 1-y ), for small y - Thomas Klemm - 07-06-2018, 09:07 PM RE: arcsinc( 1-y ), for small y - Albert Chan - 07-06-2018, 11:17 PM RE: arcsinc( 1-y ), for small y - Albert Chan - 07-07-2018, 06:11 AM RE: arcsinc( 1-y ), for small y - Albert Chan - 07-07-2018, 06:04 PM RE: arcsinc( 1-y ), for small y - Albert Chan - 07-08-2018, 03:28 AM RE: arcsinc( 1-y ), for small y - Albert Chan - 07-09-2018, 01:12 AM RE: arcsinc( 1-y ), for small y - Albert Chan - 07-12-2018, 05:26 PM RE: arcsinc( 1-y ), for small y - Albert Chan - 08-20-2018, 02:20 PM RE: arcsinc( 1-y ), for small y - Albert Chan - 08-20-2018, 03:23 PM RE: arcsinc( 1-y ), for small y - Albert Chan - 08-25-2018, 03:51 PM RE: arcsinc( 1-y ), for small y - Albert Chan - 10-01-2019, 06:03 PM RE: arcsinc( 1-y ), for small y - Albert Chan - 06-18-2020, 11:54 PM

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