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\[0.0 \lt c_p \land 0.0 \lt c_n\]
\[\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c_p} \cdot {\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c_n}}\]
\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c_p} \cdot {\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c_n}}
double f(double c_p, double c_n, double t, double s) {
        double r117758 = 1.0;
        double r117759 = s;
        double r117760 = -r117759;
        double r117761 = exp(r117760);
        double r117762 = r117758 + r117761;
        double r117763 = r117758 / r117762;
        double r117764 = c_p;
        double r117765 = pow(r117763, r117764);
        double r117766 = r117758 - r117763;
        double r117767 = c_n;
        double r117768 = pow(r117766, r117767);
        double r117769 = r117765 * r117768;
        double r117770 = t;
        double r117771 = -r117770;
        double r117772 = exp(r117771);
        double r117773 = r117758 + r117772;
        double r117774 = r117758 / r117773;
        double r117775 = pow(r117774, r117764);
        double r117776 = r117758 - r117774;
        double r117777 = pow(r117776, r117767);
        double r117778 = r117775 * r117777;
        double r117779 = r117769 / r117778;
        return r117779;
}

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (c_p c_n t s)
  :name "Harley's example"
  :precision binary64
  :pre (and (< 0.0 c_p) (< 0.0 c_n))

  :herbie-target
  (* (pow (/ (+ 1 (exp (- t))) (+ 1 (exp (- s)))) c_p) (pow (/ (+ 1 (exp t)) (+ 1 (exp s))) c_n))

  (/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n))))