Can someone explain to me why this precision rectifier circuit isn't fully rectifying the signal? It seems to work well until the crest of the non-inverted sine wave signal. I've been trying to understand it but the only thing I can think of is that it might be the breakdown voltage of the diodes? That said, it doesn't seems like voltage would be the issue here.
U3 output can't get close enough to the negative rail
try increasing the supply voltage (you can go to +/-15V on this part) or reducing the input signal amplitude.
The data sheet wants you to keep the output voltage at-least 2V away from the supply rails for best performance, and with only a 9V supply this circuit looks to be going less than 0.5V from the negative rail on U3 output when the input is +8V.