With[{minimizer =
NelderMeadMinimize`Dump`CompiledNelderMead[
Function[{a, b, c, d},
Block[{x = Range@Length[data]},
Norm[data - (a + b x + c x^2 + d x^3)]]], {a, b, c, d},
"ReturnValues" -> "OptimizedParameters"],
epsilon = $MachineEpsilon},
parallelFitter =
Compile[{{data, _Real, 1}},
minimizer[RandomReal[{0, 1}, {4 + 1, 4}], epsilon, -1],
CompilationOptions -> {"InlineCompiledFunctions" -> True},
RuntimeOptions -> {"Speed", "EvaluateSymbolically" -> False},