This work studies hardware-specific optimization opportunities currently unexploited by HLS compilers. Some of these optimizations are specializations of floating-point operations that respect the usual semantics of the input program, without changing the numerical result. Some other optimizations, locally triggered by the programmer thanks to a pragma, assume a different semantics, where floating-point code is interpreted as the specification of computation with real numbers. The compiler is then in charge to ensure an application-level accuracy constraint expressed in the pragma, and has the freedom to use non-standard arithmetic hardware when more efficient. These two classes of optimizations are prototyped in the GeCoS source-to-source compiler, and evaluated on the Polybench and EEMBC benchmark suites. Latency is reduced by up to 93%, and resource usage is reduced by up to 58%.