Simply moving a 32-bit value to a 64-bit register and back to 32-bit will not change it’s value.
That’s interesting, I wasn’t aware that Julia used the SIMD instructions (which don’t convert to the 80-bit format) to multiply scalar values. I haven’t been able to track down yet how Intel operates on the 32-bit FP values internally though, they may still get widened before the operation for a guard digit for rounding.