An original analog function synthesizer circuit with increased accuracy will be presented, allowing to implement a multitude of important continuous mathematical functions. The accuracy of the proposed structure is excellent and the range of the input variable is strongly extended as a result of the third-order approximation of the implemented functions. The circuit performance is expected to be stable against process corners as all functions exclusively depend on current ratios. The great advantages of the increased modularity and controllability and of the associated reduced design costs per function represent an immediate consequence of the multiple functions realized by the proposed structure. The function synthesizer circuit is designed for implementing in 0.18 mu m CMOS technology and it is supplied at 1.8V. The SPICE simulations confirm the estimated theoretical results, showing an approximating error smaller than 0.01% for the composing squaring block and smaller than 0.013% for the composing multiplier/divider block.