The implementation has three branches; with $t = -x/\sqrt{2}$ in the lower tail and $u = x/\sqrt{2}$ in the upper one,

$$\log \Phi(x) = \begin{cases} \log\!\left(\tfrac{1}{2}\,\mathrm{erfcx}(t)\right) - t^2, & x < -1 \\[2pt] \log \Phi(x), & -1 \le x \le 2\sqrt{2} \\[2pt] \operatorname{log1p}\!\left( -\tfrac{1}{2}\,\mathrm{erfcx}(u)\, e^{-u^2}\right), & x > 2\sqrt{2}. \end{cases}$$

Between the cuts $0.16 \lesssim \Phi(x) \lesssim 0.998$, so the direct log(ndtr(x)) is safe. Below $x = -1$ the identity $\Phi(x) = \tfrac{1}{2}\,\mathrm{erfc}(t) = \tfrac{1}{2}\,\mathrm{erfcx}(t)\, e^{-t^2}$ is used: erfc(t) itself underflows to zero near $x = -13$ in float32 (and loses its relative precision well before that), while erfcx stays bounded and the Gaussian factor comes out exactly as $-t^2$.

The upper tail fails the other way round. There $\log \Phi(x) \approx -Q$ with $Q = 1 - \Phi(x)$ small, and forming $\Phi(x)$ first leaves $Q$ to rounding: float32 answered -2.98e-7 at $x = 5$ for -2.867e-7, and 0 from $x \approx 5.4$ on. Computing $Q = \tfrac{1}{2}\,\mathrm{erfcx}(u)\, e^{-u^2}$ directly and taking log1p of its negative keeps the relative precision until $Q$ itself underflows.