We consider unconstrained derivative-free optimization problems in which only inexact function evaluations are available. Specifically, we study the setting where the oracle returns function values with partially controllable inexactness, with the error bounded linearly by a user-specified accuracy parameter, but with an unknown proportionality constant. This framework captures optimization problems arising from approximate simulations or experimental evaluations with adjustable accuracy. We propose a variant of the Stochastic Three Points method (SIAM J. Optim. 30, 1–25, 2020) that jointly updates oracle accuracy and stepsizes without requiring prior knowledge of the error bound. Assuming that the objective function has a Lipschitz continuous gradient, we show that the proposed method requires at most $\mathcal{O}\bigl(n|\ln(\epsilon)|^{2}\epsilon^{-2}\bigr)$ calls to the inexact oracle to find a point whose expected gradient norm is below $\epsilon$, where $n$ is the number of variables. As an application, we study model-free steady-state optimization in control systems and show that it can be addressed using the proposed method.