Mathematicians vs Computer / Systems Engineers. The machine only has so much space, so it's best to imagine every value also has a corresponding error range attached and that managing the growth of that error range so that it remains under the target value is key.

Usually, it's not worth the effort of converting microcode into discrete logic to get performance. Among other things, it's a mess to try to fix a bug.

A few exceptions: The different models of the IBM System/360 mainframe are almost all microcoded, except for the high-end machines, which were hard-wired for performance. The design of the Apollo Guidance Computer is microcode, but the implementation is discrete logic. The 8086 and derivatives are microcoded, except NEC created a faster hard-wired version, the V33.

This is exactly the theory of the RISC and VLIW processors, which replaced, respectively, the vertical microprograms and the horizontal microprograms stored in ROMs, which were used in the processors of the seventies, with normal programs with simple instructions, which were normally executed from fast cache memories, thus achieving the same speed as microprograms.

However, when the 8087 was designed, RISC and VLIW processors were still in the future, because a fast cache memory allowing the execution of an instruction per clock cycle was still far too expensive in comparison with a microprogram ROM.

Most earlier floating-point accelerators were microprogrammed like 8087, with the microprograms stored in a ROM. However, there existed FPS AP-120B, introduced by the company Floating Point Systems in 1976. This was a floating-point accelerator for minicomputers, like DEC PDP-11 or VAX, which was marketed as a "supercomputer for the poor".

FPS AP-120B was a VLIW processor launched 7 years before the term "VLIW" was coined. This means that it was a horizontally microprogrammed processor (i.e. with multiple concurrent operations specified by each microinstruction), where the microprogram was not stored in a ROM, but it was fed into the accelerator by the host computer. Therefore the user could write directly such microprograms for it, to implement optimized computational algorithms.

Nevertheless, while FPS AP-120B was said to be a "supercomputer for the poor", "poor" was meant only in comparison with those who could afford to buy a Cray-1. Such a "cheap" array processor still had a price more than 100 times greater than an Intel 8087.

By the time when RISC and VLIW CPUs became fashionable, using microinstructions as simple as those of Intel 8087 for implementing floating-point operations was no longer acceptable, because having to execute tens or hundreds of simple instructions for each FP operation was deemed too slow. Therefore the instruction sets of RISC and VLIW CPUs were eventually extended to include FP operations as single instructions, which had to be implemented in complex hardware in order to achieve an execution throughput of one instruction per clock cycle.

That's basically the RISC approach, using simple one-clock instructions instead of complex microcoded instructions. In the case of the 8087, it made sense to use microcode because the 8087 is running in parallel with the regular 8086 processor. If the 8087 is constantly fetching micro-instructions from RAM, it will get in the way of the 8086. (Note that RISC chips rapidly added floating-point units, even though that goes against the strict RISC ideology.)

You're them moving and storing a lot of repetitive instruction data.