A method, computer program product, and a computer system are disclosed for processing information using hardware instructions in a processor of a computer system by performing a hardware reduction instruction using an input to calculate at least one range reduction factor of the input; performing a hardware restoration instruction using the input to calculate at least one range restoration factor of the input; and performing a final fused multiply add (FMA) type of hardware instruction or a multiply (FM) hardware instruction by combining an approximation based on a value reduced by the at least one range reduction factor with the at least one range restoration factor.