Average Error: 7.6 → 0.4
Time: 21.5s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\cosh x \cdot \frac{y}{x} \le -2.917391625482233487164607746012211025076 \cdot 10^{296} \lor \neg \left(\cosh x \cdot \frac{y}{x} \le 1.441100974532180611209834362198683583791 \cdot 10^{193}\right):\\ \;\;\;\;\frac{\frac{1}{2} \cdot \left(\left(e^{x} + e^{-x}\right) \cdot y\right)}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;\cosh x \cdot \frac{y}{x} \le -2.917391625482233487164607746012211025076 \cdot 10^{296} \lor \neg \left(\cosh x \cdot \frac{y}{x} \le 1.441100974532180611209834362198683583791 \cdot 10^{193}\right):\\
\;\;\;\;\frac{\frac{1}{2} \cdot \left(\left(e^{x} + e^{-x}\right) \cdot y\right)}{x \cdot z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r341753 = x;
        double r341754 = cosh(r341753);
        double r341755 = y;
        double r341756 = r341755 / r341753;
        double r341757 = r341754 * r341756;
        double r341758 = z;
        double r341759 = r341757 / r341758;
        return r341759;
}
↓
double f(double x, double y, double z) {
        double r341760 = x;
        double r341761 = cosh(r341760);
        double r341762 = y;
        double r341763 = r341762 / r341760;
        double r341764 = r341761 * r341763;
        double r341765 = -2.9173916254822335e+296;
        bool r341766 = r341764 <= r341765;
        double r341767 = 1.4411009745321806e+193;
        bool r341768 = r341764 <= r341767;
        double r341769 = !r341768;
        bool r341770 = r341766 || r341769;
        double r341771 = 0.5;
        double r341772 = exp(r341760);
        double r341773 = -r341760;
        double r341774 = exp(r341773);
        double r341775 = r341772 + r341774;
        double r341776 = r341775 * r341762;
        double r341777 = r341771 * r341776;
        double r341778 = z;
        double r341779 = r341760 * r341778;
        double r341780 = r341777 / r341779;
        double r341781 = r341761 * r341762;
        double r341782 = r341781 / r341760;
        double r341783 = r341782 / r341778;
        double r341784 = r341770 ? r341780 : r341783;
        return r341784;
}

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

Original7.6
Target0.4
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687041990497740832940559043667 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.038530535935153018369520384190862667426 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* (cosh x) (/ y x)) < -2.9173916254822335e+296 or 1.4411009745321806e+193 < (* (cosh x) (/ y x))

    1. Initial program 37.4

      \[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
    2. Using strategy rm

    3. Applied associate-*r/37.4

      \[\leadsto \frac{\color{blue}{\frac{\cosh x \cdot y}{x}}}{z}\]

    4. Taylor expanded around inf 0.9

      \[\leadsto \color{blue}{\frac{y \cdot \left(\frac{1}{2} \cdot e^{x} + \frac{1}{2} \cdot e^{-x}\right)}{x \cdot z}}\]

    5. Simplified0.9

      \[\leadsto \color{blue}{\frac{\frac{1}{2} \cdot \left(\left(e^{x} + e^{-x}\right) \cdot y\right)}{x \cdot z}}\]

    if -2.9173916254822335e+296 < (* (cosh x) (/ y x)) < 1.4411009745321806e+193

    1. Initial program 0.2

      \[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
    2. Using strategy rm

    3. Applied associate-*r/0.2

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\cosh x \cdot \frac{y}{x} \le -2.917391625482233487164607746012211025076 \cdot 10^{296} \lor \neg \left(\cosh x \cdot \frac{y}{x} \le 1.441100974532180611209834362198683583791 \cdot 10^{193}\right):\\ \;\;\;\;\frac{\frac{1}{2} \cdot \left(\left(e^{x} + e^{-x}\right) \cdot y\right)}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 
(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))