In this paper, we study the convergence rate of an Embedded exponential-type low-regularity integrator (ELRI) for the Korteweg-de Vries equation. We develop some new harmonic analysis techniques to handle the "stability" issue. In particular, we use a new stability estimate which allows us to avoid the use of the fractional Leibniz inequality,
![1614068076263070.png image.png](https://admin.global-sci.org/uploads/ueditor/image/20210223/1614068076263070.png)
and replace it by suitable inequalities without loss of regularity. Based on these techniques, we prove that the ELRI scheme proposed in [41] provides $\frac12$-order convergence accuracy in $H^\gamma$ for any initial data belonging to $H^\gamma$ with $\gamma >\frac32$, which does not require any additional derivative assumptions.