Precision rectifier doesn't give expected output
Precision rectifiers need fast opamps. I'm guessing this one isn't.
This is because, when the diode is reverse-biased, the opamp operates open-loop. Thus, when V1 goes -ve, U1 output swings hard -ve and settles at (or close to) V-. The -ve input is uncontrolled after that.
When V1 becomes +ve again, or at least more +ve than In-, there is a considerable lag before the opamp returns to linear operation again.
You can mitigate this with another diode from the opamp output to In-, limiting the open loop operation to 1.2V pk-pk.



simulate this circuit &ndash; Schematic created using CircuitLab
Now, when IN goes -ve, D2 controls the opamp IN- and limits the output swing. And R2 provides some isolation between all that and OUT. There is usually a large capacitor on OUT, R2 will drain in ... slowly. If too fast, increase R2.