In the recent decade, precision tuning becomes one of the key techniques to obtain significant gains in performance and energy efficiency. This process consists of substituting smaller data types to the original data types assigned to floating-point variables in numerical programs in such a way that accuracy requirements remain fulfilled. In face of the huge amount of precision tuning tools, we present in this article a survey on the approaches proposed in the bibliography. Besides, we point out the differences between these approaches and our own tool POP which avoids the usual trial-and-fail paradigm. POP implements a static analysis method relying on constraints derived from the modelling of the program errors propagation and accuracy specifications. We also extend the functionalities of POP by experimenting several optimization criteria to our system of constraints as a means to achieve the best performance improvements. We validate our results on a new set of numerical benchmarks and we report that in all cases we are able to accomplish better optimization by keeping the introduced numerical error below the given tolerance threshold.