NoICE

function solve(x,solver)
 local result=solver[0]
 for i=1,#solver//2 do
  result=result*(x-solver[i*2-1])+solver[i*2]
 end
 return result
end

function f(x)
 return x*x-2*math.abs(x)+1
end

function getStart(xs)
 local t={}
 for i=1,#xs do
  t[i]=f(xs[i])
 end
 return t
end

function table.print(t,n)
 local n=n or #t
 for i=1,n do
  print(t[i])
 end
end

function getSolver(xs)
 local t=getStart(xs)
 local n=#t
 local solver={}
 solver[n*2-2]=t[1]
 for i=1,n-1 do
  for j=1,n-i do
   t[j]=(t[j+1]-t[j])/(xs[j+i]-xs[j])
  end
  solver[(n-i)*2-2]=t[1]
  solver[(n-i)*2-1]=xs[i]
 end
 return solver
end

function getR(solver,xs)
 local max=0
 for i=1,#xs-1 do
  local x=(xs[i]+xs[i+1])/2
  local err=solve(x,solver)-f(x)
  if math.abs(err)>math.abs(max) then
   max=err
   print(x)
  end
 end
 return max
end

local xs1={}
for i=0,10 do
 xs1[i+1]=i*0.4-2
end
local xs2={}
for i=0,25 do
 xs2[i+1]=i*0.16-2
end
local xs3={}
for i=0,50 do
 xs3[i+1]=i*0.8-2
end
local solver1=getSolver(xs1)
print(getR(solver1,xs1))
local solver2=getSolver(xs2)
print(getR(solver2,xs2))
local solver3=getSolver(xs3)
print(getR(solver3,xs3))