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Numerical simulations of 15 orbits of an equal-mass binary black hole systemare presented. Gravitational waveforms from these simulations, covering morethan 30 cycles and ending about 1.5 cycles before merger, are compared withthose from quasi-circular zero-spin post-Newtonian (PN) formulae. Thecumulative phase uncertainty of these comparisons is about 0.05 radians,dominated by effects arising from the small residual spins of the black holesand the small residual orbital eccentricity in the simulations. Matchingnumerical results to PN waveforms early in the run yields excellent agreement(within 0.05 radians) over the first $\sim 15$ cycles, thus validating thenumerical simulation and establishing a regime where PN theory is accurate. Inthe last 15 cycles to merger, however, {\em generic} time-domain Taylorapproximants build up phase differences of several radians. But, apparently bycoincidence, one specific post-Newtonian approximant, TaylorT4 at 3.5PN order,agrees much better with the numerical simulations, with accumulated phasedifferences of less than 0.05 radians over the 30-cycle waveform.Gravitational-wave amplitude comparisons are also done between numericalsimulations and post-Newtonian, and the agreement depends on the post-Newtonianorder of the amplitude expansion: the amplitude difference is about 6--7% forzeroth order and becomes smaller for increasing order. A newly derived 3.0PNamplitude correction improves agreement significantly ($<1%$ amplitudedifference throughout most of the run, increasing to 4% near merger) over thepreviously known 2.5PN amplitude terms.

High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions