In some cases I suspect it depends a lot on the hardware. I did a bit of research into the "Integer minimum" algorithm. Given the following straightforward implementation:

    int min(int x, int y) { return y < x ? y : x; }

..most compilers will produce something very much like the following for x86-64 (from Compiler Explorer https://gcc.godbolt.org using -Ofast -march=haswell):

    min(int, int):
        cmp     esi, edi
        mov     eax, edi
        cmovle  eax, esi
        ret

Compare that to the generated instructions for the algorithm listed in the "Integer minimum or maximum" section (x+(((y-x)>>(WORDBITS-1))&(y-x))):

    min(int, int):
        sub     esi, edi
        mov     eax, esi
        sar     eax, 31
        and     eax, esi
        add     eax, edi
        ret

It's not immediately obvious to me which one is likely to be faster (I'm not an expert on x86-64 assembly).