Variant of the Secant Method

[Albert Chan]

I extend previous post, with another round of iteration, using all points.
(First iteration matched previous post, done in double precision)

inverse-interpolation:
2.71131291035698220988289207111279
2.71131291035698331469084928874683

improved secant:
2.71131291035698244759230088334763
2.71131291035698331469084928874750

newton's method:
2.71131291035698307703744887554087
2.71131291035698331469084928874753