This work studies hardware-specific optimization opportunities currently unexploited by HLS compilers. Some of these optimizations are specializations of floating-point operations. They respect the usual semantics of the input program. Other optimizations do not, assuming instead that a floating-point computation is actually intended to compute with real numbers. What matters then is to respect application-level accuracy constraints, expressed as pragmas in the source code. This provides the compiler with freedom to use non-standard arithmetic when more efficient. A source-to-source compiler is used to prototype the proposed optimizations and evaluate them on relevant benchmarks.