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\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{-im} - e^{im}\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{-im} - e^{im}\right)
double f(double re, double im) {
        double r234759 = 0.5;
        double r234760 = re;
        double r234761 = sin(r234760);
        double r234762 = r234759 * r234761;
        double r234763 = im;
        double r234764 = -r234763;
        double r234765 = exp(r234764);
        double r234766 = exp(r234763);
        double r234767 = r234765 - r234766;
        double r234768 = r234762 * r234767;
        return r234768;
}

Reproduce

herbie shell --seed 2020046 
(FPCore (re im)
  :name "math.cos on complex, imaginary part"
  :precision binary64

  :herbie-target
  (if (< (fabs im) 1) (- (* (sin re) (+ (+ im (* (* (* 0.16666666666666666 im) im) im)) (* (* (* (* (* 0.008333333333333333 im) im) im) im) im)))) (* (* 0.5 (sin re)) (- (exp (- im)) (exp im))))

  (* (* 0.5 (sin re)) (- (exp (- im)) (exp im))))