rf1b[f_, sx_, a_, n_Integer] := (AccuracyGoal -> n; PrecisionGoal -> n; 
     WorkingPrecision -> n + 7; Module[{u, zx, du, b, fe, fe2, st15, st16}, 
      b = a; st16 = N[sbx[{{D[f, x1], D[f, x2], D[f, x3], D[f, x4], D[f, x5], 
            D[f, x6], D[f, x7], D[f, x8], D[f, x9], D[f, x10], D[f, x11], 
            D[f, x12], D[f, x13], D[f, x14], D[f, x15]}, f}, sx], n]; 
       st16 = Rationalize[st16, 1/10^(n + 2)]; {st15, fe} = st16; 
       du = sqsum[st15]; u = -(fe/du); Goto[o2]; Label[o1]; b = (2*b)/3; 
       Label[o2]; zx = N[sx + b*u*st15, n]; fe2 = N[sbx[f, zx], n]; 
       If[fe2 < fe, Goto[o3]]; If[b < 6^(-n), Return[gonetoosmall]]; 
       Goto[o1]; Label[o3]; Return[zx]; Null; ])