Average Error: 7.8 → 0.7
Time: 14.8s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.56082919711251703348519476677496253443 \cdot 10^{-15} \lor \neg \left(z \le 4.489894380771518759583953311198839017656 \cdot 10^{-96}\right):\\ \;\;\;\;\frac{y \cdot \cosh x}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.56082919711251703348519476677496253443 \cdot 10^{-15} \lor \neg \left(z \le 4.489894380771518759583953311198839017656 \cdot 10^{-96}\right):\\
\;\;\;\;\frac{y \cdot \cosh x}{x \cdot z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r371802 = x;
        double r371803 = cosh(r371802);
        double r371804 = y;
        double r371805 = r371804 / r371802;
        double r371806 = r371803 * r371805;
        double r371807 = z;
        double r371808 = r371806 / r371807;
        return r371808;
}
↓
double f(double x, double y, double z) {
        double r371809 = z;
        double r371810 = -2.560829197112517e-15;
        bool r371811 = r371809 <= r371810;
        double r371812 = 4.489894380771519e-96;
        bool r371813 = r371809 <= r371812;
        double r371814 = !r371813;
        bool r371815 = r371811 || r371814;
        double r371816 = y;
        double r371817 = x;
        double r371818 = cosh(r371817);
        double r371819 = r371816 * r371818;
        double r371820 = r371817 * r371809;
        double r371821 = r371819 / r371820;
        double r371822 = r371816 / r371809;
        double r371823 = r371822 / r371817;
        double r371824 = r371818 * r371823;
        double r371825 = r371815 ? r371821 : r371824;
        return r371825;
}

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

Original7.8
Target0.5
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687041990497740832940559043667 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.038530535935153018369520384190862667426 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.560829197112517e-15 or 4.489894380771519e-96 < z

    1. Initial program 10.5

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

    2. Simplified0.9

      \[\leadsto \color{blue}{\frac{y}{z \cdot x} \cdot \cosh x}\]
    3. Using strategy rm

    4. Applied associate-*l/0.9

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

    if -2.560829197112517e-15 < z < 4.489894380771519e-96

    1. Initial program 0.3

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

    2. Simplified23.8

      \[\leadsto \color{blue}{\frac{y}{z \cdot x} \cdot \cosh x}\]
    3. Using strategy rm

    4. Applied *-un-lft-identity23.8

      \[\leadsto \color{blue}{\left(1 \cdot \frac{y}{z \cdot x}\right)} \cdot \cosh x\]

    5. Applied associate-*l*23.8

      \[\leadsto \color{blue}{1 \cdot \left(\frac{y}{z \cdot x} \cdot \cosh x\right)}\]

    6. Simplified0.3

      \[\leadsto 1 \cdot \color{blue}{\left(\frac{\frac{y}{z}}{x} \cdot \cosh x\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.56082919711251703348519476677496253443 \cdot 10^{-15} \lor \neg \left(z \le 4.489894380771518759583953311198839017656 \cdot 10^{-96}\right):\\ \;\;\;\;\frac{y \cdot \cosh x}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{z}}{x}\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctan from linear-1.19.1.3"

  :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))