Average Error: 7.3 → 0.3
Time: 17.3s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.0432260555262782 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \mathbf{elif}\;y \le 2922533292505.41:\\ \;\;\;\;\frac{\frac{y}{x} \cdot \cosh x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.0432260555262782 \cdot 10^{-16}:\\
\;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\

\mathbf{elif}\;y \le 2922533292505.41:\\
\;\;\;\;\frac{\frac{y}{x} \cdot \cosh x}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r21690432 = x;
        double r21690433 = cosh(r21690432);
        double r21690434 = y;
        double r21690435 = r21690434 / r21690432;
        double r21690436 = r21690433 * r21690435;
        double r21690437 = z;
        double r21690438 = r21690436 / r21690437;
        return r21690438;
}
↓
double f(double x, double y, double z) {
        double r21690439 = y;
        double r21690440 = -1.0432260555262782e-16;
        bool r21690441 = r21690439 <= r21690440;
        double r21690442 = x;
        double r21690443 = cosh(r21690442);
        double r21690444 = r21690443 * r21690439;
        double r21690445 = z;
        double r21690446 = r21690444 / r21690445;
        double r21690447 = r21690446 / r21690442;
        double r21690448 = 2922533292505.41;
        bool r21690449 = r21690439 <= r21690448;
        double r21690450 = r21690439 / r21690442;
        double r21690451 = r21690450 * r21690443;
        double r21690452 = r21690451 / r21690445;
        double r21690453 = r21690449 ? r21690452 : r21690447;
        double r21690454 = r21690441 ? r21690447 : r21690453;
        return r21690454;
}

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

Original7.3
Target0.5
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687042 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.038530535935153 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.0432260555262782e-16 or 2922533292505.41 < y

    1. Initial program 20.1

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

    3. Applied associate-*r/20.1

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

    4. Applied associate-/l/0.3

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

    6. Applied associate-/r*0.3

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

    if -1.0432260555262782e-16 < y < 2922533292505.41

    1. Initial program 0.3

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.0432260555262782 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \mathbf{elif}\;y \le 2922533292505.41:\\ \;\;\;\;\frac{\frac{y}{x} \cdot \cosh x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(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))