The output of the op amp (green) is either a diode drop above or a diode drop below the output of the rectifier circuit.  The transitions between these states are limited by the op amp slew rate.  I measured about 600 mV/µsec, which is what the MCP6002 op amp I'm using is specified to have as a slew rate (I measured before looking it up, to keep from being biased by the correct answer).