The floating-point format on the ZX Spectrum has the unusual feature of special-casing small integers: Why does Sinclair BASIC have two formats for storing numbers in the same structure?
There are excellent and sufficient reasons for this. Basic programming tends to be casual about types; many variables that could hold a floating-point number, in fact only hold small integers. The machine had no FP hardware; floating-point calculations were much slower than integer calculations. The upshot was that this design decision made many programs run a lot faster.
No one repeats it nowadays because there's no point. All modern general-purpose computers have floating-point hardware.
It seems to me there was an intermediate time, in the sixties for mainframes, seventies for minicomputers, eighties for microcomputers, when it could've made sense because floating-point hardware was possible but unusual. For example the IBM PC could have an 8087 installed, but most of them didn't.
The common strategy in this situation was to just go ahead and use IEEE format as though a coprocessor were expected: https://en.wikipedia.org/wiki/Standard_Apple_Numerics_Environment
Some programs used a different format designed for software floating-point: Did any PC software floating point use non-IEEE format?
But as far as I can tell, nothing else used a format that treated integers as a special case and made an effort to run them faster.
Was there ever any floating-point format designed (unlike the Spectrum) on the basis that hardware support was possible but uncommon, that was designed to fast-track operations when the operands happened to be small integers?