delta = 1e-06

local function bisect (f, a, b, fa, fb)
   local c = (a + b) / 2
   io.write (n, " c=", c, " a=", a, " b=", b, "\n")
   if (c == a or c == b) or math.abs (a - b) < delta then
      return c, b - a
   end
   n = n + 1
   local fc = f (c)
   if fa * fc < 0 then
      return bisect (f, a, c, fa, fc)
   else
      return bisect (f, c, b, fc, fb)
   end
end



local function f (x)
   return ((x * x) * x - x) - 1
end

local __v4f, __v3a, __v1b = f, 1, 2

n = 0

local __v2z, __v5e = bisect (__v4f, __v3a, __v1b, __v4f (__v3a), __v4f (__v1b))

io.write (string.format ("after %d steps, root is %.17g with error %.1e, f=%.1e\n", n, __v2z, __v5e, __v4f (__v2z)))