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We describe a modification of a fourth-order accurate ``moving puncture''evolution code, where by replacing spatial fourth-order accurate differencingoperators in the bulk of the grid by a specific choice of sixth-order accuratestencils we gain significant improvements in accuracy. We illustrate theperformance of the modified algorithm with an equal-mass simulation coveringnine orbits.

Reducing phase error in long numerical binary black hole evolutions with sixth order finite differencing