Let $X$ and $Y$ be two projective irreductive algebraic varieties of dimension $3$ and let $f:X\dashrightarrow Y$ be a pseudo isomorphism, i.e. a birational map which restricts to an isomorphism outside a union of curves.
I consider a divisor $E$ on a blow-up $p: Z\rightarrow X$ and look at the discrepancy of $E$ with respect to $p$ that I want to compare with the discrepancy of $E$ with respect to $fp$ (if $fp$ is not a morphism we just blow up a bit, or define the discrepancy locally)
Can we find an example where the two discrepancies are distinct and where $X$ and $Y$ are both smooth? If yes, I would be happy to see a simple example.