A method to transform the function of a programmable circuit (e.g. FPGA) for removing functional bugs or Hardware Trojans is provided. The method comprises: providing a lookup-table (LUT) mapped circuit representation derived from the programmable circuit being implemented with a first register-transfer level (RTL) document, the first RTL document being of an original specification; providing a second RTL document of the programmable circuit, the second RTL document being of a revised specification, wherein the revised specification is modified from the original specification and has a transformed function from the original specification; converting the LUT mapped circuit representation into a shadow netlist, the shadow netlist corresponding to a gate level (GTL) netlist representing the LUT mapped circuit representation; generating a second GTL netlist from the second RTL document; producing an engineering change order (ECO) patch to be completely merged inside the LUT mapped circuit representation based on a comparison of the shadow netlist with the second GTL netlist; and transforming the function of the programmable circuit by merging the ECO patch inside the LUT mapped circuit representation, wherein the merged LUT mapped circuit representation is equivalent to the second GTL netlist to perform same functions such that the programmable circuit can be reprogrammed in accordance with the revised specification by making use of free merging cost property of LUT structures. The method and corresponding systems reduce the time spent in ECO iterations in building programmable circuit, and also minimize the committed programmable circuit chip area after adding the ECO/HT-eliminating patches.