Making explicit something I said in passing elsewhere: it seems not-impossible that the sequence might be best looked at in reverse order, since mapping x to 1-(x/2)^2 or (1-x^2)/2 is somewhat more natural than going the other way. However, it does look rather as if there might be some accumulation of roundoff error in the forward direction, which if true would argue for reading it forwards rather than backwards.
Making explicit something I said in passing elsewhere: it seems not-impossible that the sequence might be best looked at in reverse order, since mapping x to 1-(x/2)^2 or (1-x^2)/2 is somewhat more natural than going the other way. However, it does look rather as if there might be some accumulation of roundoff error in the forward direction, which if true would argue for reading it forwards rather than backwards.