[jlgustafson]

The real hope is that 32-bit posits (with 512-bit quire for exact dot products and exact sums) can replace 64-bit floats where users hope 15-decimal accuracy in every variable means they don't have to learn numerical analysis. When you can do all your linear algebra to 8-decimal accuracy with 32-bit posits, the need for 64-bit representation starts to look expensive and unnecessary.

Also, please note that all traditional algorithms are wary of the disasters of overflow to infinity and underflow to zero, so they tend to manage the magnitudes of numbers to prevent that. Posits take advantage of that by decreasing relative error when the exponent scaling is not extreme. Standard 64-bit posits (2 exponent bits) have 60-bit significands, versus 53-bit significands for IEEE floats, for values between 1/16 and 16 in magnitude. And floats do not have anything like the quire, since an exact dot product accumulator for 64-bit IEEE floats has to be something like 4,664 bits wide (an ugly number) and has no provisions for infinities and NaN values.