  The existence of a quantum butterfly effect in the form of exponential
sensitivity to small perturbations has been under debate for a long time.
Lately, this question gained increased interest due to the proposal to probe
chaotic dynamics and scrambling using out-of-time-order correlators. In this
work we study echo dynamics in the Sachdev-Ye-Kitaev model under effective time
reversal in a semiclassical approach. We demonstrate that small imperfections
introduced in the time-reversal procedure result in an exponential divergence
from the perfect echo, which allows to identify a Lyapunov exponent
$\lambda_L$. In particular, we find that $\lambda_L$ is twice the Lyapunov
exponent of the semiclassical equations of motion. This behavior is attributed
to the growth of an out-of-time-order double commutator that resembles an
out-of-time-order correlator.
