Average Error: 7.7 → 0.3
Time: 34.4s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\cosh x \cdot \frac{y}{x} = -\infty \lor \neg \left(\cosh x \cdot \frac{y}{x} \le 6.555653103340297262881216521095130213881 \cdot 10^{295}\right):\\ \;\;\;\;\frac{1}{2} \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;\cosh x \cdot \frac{y}{x} = -\infty \lor \neg \left(\cosh x \cdot \frac{y}{x} \le 6.555653103340297262881216521095130213881 \cdot 10^{295}\right):\\
\;\;\;\;\frac{1}{2} \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}\\

\mathbf{else}:\\
\;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\

\end{array}
double f(double x, double y, double z) {
        double r341807 = x;
        double r341808 = cosh(r341807);
        double r341809 = y;
        double r341810 = r341809 / r341807;
        double r341811 = r341808 * r341810;
        double r341812 = z;
        double r341813 = r341811 / r341812;
        return r341813;
}
↓
double f(double x, double y, double z) {
        double r341814 = x;
        double r341815 = cosh(r341814);
        double r341816 = y;
        double r341817 = r341816 / r341814;
        double r341818 = r341815 * r341817;
        double r341819 = -inf.0;
        bool r341820 = r341818 <= r341819;
        double r341821 = 6.555653103340297e+295;
        bool r341822 = r341818 <= r341821;
        double r341823 = !r341822;
        bool r341824 = r341820 || r341823;
        double r341825 = 0.5;
        double r341826 = r341814 * r341816;
        double r341827 = z;
        double r341828 = r341826 / r341827;
        double r341829 = r341825 * r341828;
        double r341830 = r341814 * r341827;
        double r341831 = r341816 / r341830;
        double r341832 = r341829 + r341831;
        double r341833 = r341818 / r341827;
        double r341834 = r341824 ? r341832 : r341833;
        return r341834;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.7
Target0.5
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687041990497740832940559043667 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.038530535935153018369520384190862667426 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* (cosh x) (/ y x)) < -inf.0 or 6.555653103340297e+295 < (* (cosh x) (/ y x))

    1. Initial program 59.0

      \[\frac{\cosh x \cdot \frac{y}{x}}{z}\]

    2. Taylor expanded around 0 1.0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}}\]

    if -inf.0 < (* (cosh x) (/ y x)) < 6.555653103340297e+295

    1. Initial program 0.3

      \[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\cosh x \cdot \frac{y}{x} = -\infty \lor \neg \left(\cosh x \cdot \frac{y}{x} \le 6.555653103340297262881216521095130213881 \cdot 10^{295}\right):\\ \;\;\;\;\frac{1}{2} \cdot \frac{x \cdot y}{z} + \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019322 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctan from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< y -4.618902267687042e-52) (* (/ (/ y z) x) (cosh x)) (if (< y 1.038530535935153e-39) (/ (/ (* (cosh x) y) x) z) (* (/ (/ y z) x) (cosh x))))

  (/ (* (cosh x) (/ y x)) z))