Average Error: 7.3 → 0.3
Time: 16.4s
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 r21964569 = x;
        double r21964570 = cosh(r21964569);
        double r21964571 = y;
        double r21964572 = r21964571 / r21964569;
        double r21964573 = r21964570 * r21964572;
        double r21964574 = z;
        double r21964575 = r21964573 / r21964574;
        return r21964575;
}
↓
double f(double x, double y, double z) {
        double r21964576 = y;
        double r21964577 = -1.0432260555262782e-16;
        bool r21964578 = r21964576 <= r21964577;
        double r21964579 = x;
        double r21964580 = cosh(r21964579);
        double r21964581 = r21964580 * r21964576;
        double r21964582 = z;
        double r21964583 = r21964581 / r21964582;
        double r21964584 = r21964583 / r21964579;
        double r21964585 = 2922533292505.41;
        bool r21964586 = r21964576 <= r21964585;
        double r21964587 = r21964576 / r21964579;
        double r21964588 = r21964587 * r21964580;
        double r21964589 = r21964588 / r21964582;
        double r21964590 = r21964586 ? r21964589 : r21964584;
        double r21964591 = r21964578 ? r21964584 : r21964590;
        return r21964591;
}

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))