Average Error: 7.6 → 0.7
Time: 5.7s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.3159694493115124 \cdot 10^{88}:\\ \;\;\;\;\frac{\cosh x \cdot y}{z \cdot x}\\ \mathbf{elif}\;z \le 3.7391398403450612 \cdot 10^{37}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\cosh x}{z \cdot x}}{\frac{1}{y}}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.3159694493115124 \cdot 10^{88}:\\
\;\;\;\;\frac{\cosh x \cdot y}{z \cdot x}\\

\mathbf{elif}\;z \le 3.7391398403450612 \cdot 10^{37}:\\
\;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{\cosh x}{z \cdot x}}{\frac{1}{y}}\\

\end{array}
double f(double x, double y, double z) {
        double r2686 = x;
        double r2687 = cosh(r2686);
        double r2688 = y;
        double r2689 = r2688 / r2686;
        double r2690 = r2687 * r2689;
        double r2691 = z;
        double r2692 = r2690 / r2691;
        return r2692;
}
↓
double f(double x, double y, double z) {
        double r2693 = z;
        double r2694 = -1.3159694493115124e+88;
        bool r2695 = r2693 <= r2694;
        double r2696 = x;
        double r2697 = cosh(r2696);
        double r2698 = y;
        double r2699 = r2697 * r2698;
        double r2700 = r2693 * r2696;
        double r2701 = r2699 / r2700;
        double r2702 = 3.739139840345061e+37;
        bool r2703 = r2693 <= r2702;
        double r2704 = r2699 / r2693;
        double r2705 = r2704 / r2696;
        double r2706 = r2697 / r2700;
        double r2707 = 1.0;
        double r2708 = r2707 / r2698;
        double r2709 = r2706 / r2708;
        double r2710 = r2703 ? r2705 : r2709;
        double r2711 = r2695 ? r2701 : r2710;
        return r2711;
}

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
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687042 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.0385305359351529 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -1.3159694493115124e+88

    1. Initial program 13.4

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

    3. Applied associate-*r/13.4

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

    4. Applied associate-/l/0.4

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

    if -1.3159694493115124e+88 < z < 3.739139840345061e+37

    1. Initial program 1.5

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

    3. Applied associate-*r/1.5

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

    4. Applied associate-/l/14.2

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

    6. Applied associate-/r*1.1

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

    if 3.739139840345061e+37 < z

    1. Initial program 12.8

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

    3. Applied associate-*r/12.8

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

    4. Applied associate-/l/0.3

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

    6. Applied associate-/l*0.8

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

    8. Applied div-inv0.9

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

    9. Applied associate-/r*0.5

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.3159694493115124 \cdot 10^{88}:\\ \;\;\;\;\frac{\cosh x \cdot y}{z \cdot x}\\ \mathbf{elif}\;z \le 3.7391398403450612 \cdot 10^{37}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\cosh x}{z \cdot x}}{\frac{1}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(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 1.0385305359351529e-39) (/ (/ (* (cosh x) y) x) z) (* (/ (/ y z) x) (cosh x))))

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