So why does the harmonic distortion increase when it gets close to the rails?
As with any amplifier, when the output swings near the rails, the output
transistors approach saturation. Saturation is a “soft” limit, which introduces
distortion to the waveform as the output approaches the rail. For the AD8476,
best distortion performance is achieved by keeping the outputs 500mV from each
rail. See figures 39 and 40 in the data sheet for details.