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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 r6512776 = 1.0;
        double r6512777 = s;
        double r6512778 = -r6512777;
        double r6512779 = exp(r6512778);
        double r6512780 = r6512776 + r6512779;
        double r6512781 = r6512776 / r6512780;
        double r6512782 = c_p;
        double r6512783 = pow(r6512781, r6512782);
        double r6512784 = r6512776 - r6512781;
        double r6512785 = c_n;
        double r6512786 = pow(r6512784, r6512785);
        double r6512787 = r6512783 * r6512786;
        double r6512788 = t;
        double r6512789 = -r6512788;
        double r6512790 = exp(r6512789);
        double r6512791 = r6512776 + r6512790;
        double r6512792 = r6512776 / r6512791;
        double r6512793 = pow(r6512792, r6512782);
        double r6512794 = r6512776 - r6512792;
        double r6512795 = pow(r6512794, r6512785);
        double r6512796 = r6512793 * r6512795;
        double r6512797 = r6512787 / r6512796;
        return r6512797;
}

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (c_p c_n t s)
  :name "Harley's example"
  :pre (and (< 0.0 c_p) (< 0.0 c_n))

  :herbie-target
  (* (pow (/ (+ 1.0 (exp (- t))) (+ 1.0 (exp (- s)))) c_p) (pow (/ (+ 1.0 (exp t)) (+ 1.0 (exp s))) c_n))

  (/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n))))