Is the product of metric and semi-metric functions a semi metric?

Question

I have a function - $B_{DGC}(x,y) = K_{(x,y)} \times e^{-(\frac{(I_x - I_y)^2}{2\sigma^2})}\times \frac{1}{d(x,y)} \times \frac{1}{\delta(x,y)_{DGC}}$. The components $K_{(x,y)}$ and $\frac{1}{\delta(x,y)_{DGC}}$ are semi metric, $\frac{1}{d(x,y)}$ is metric and $e^{-(\frac{(I_x - I_y)^2}{2\sigma^2})}$ is quasi metric. Is $B_{DGC}(x,y)$ a semi metric?