Average Error: 7.7 → 0.7
Time: 10.0s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.93577210121831744 \cdot 10^{80} \lor \neg \left(z \le 2.60686388496247717 \cdot 10^{-42}\right):\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x}{\frac{z}{y} \cdot x}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.93577210121831744 \cdot 10^{80} \lor \neg \left(z \le 2.60686388496247717 \cdot 10^{-42}\right):\\
\;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r523537 = x;
        double r523538 = cosh(r523537);
        double r523539 = y;
        double r523540 = r523539 / r523537;
        double r523541 = r523538 * r523540;
        double r523542 = z;
        double r523543 = r523541 / r523542;
        return r523543;
}
↓
double f(double x, double y, double z) {
        double r523544 = z;
        double r523545 = -1.9357721012183174e+80;
        bool r523546 = r523544 <= r523545;
        double r523547 = 2.6068638849624772e-42;
        bool r523548 = r523544 <= r523547;
        double r523549 = !r523548;
        bool r523550 = r523546 || r523549;
        double r523551 = x;
        double r523552 = cosh(r523551);
        double r523553 = y;
        double r523554 = r523551 * r523544;
        double r523555 = r523553 / r523554;
        double r523556 = r523552 * r523555;
        double r523557 = r523544 / r523553;
        double r523558 = r523557 * r523551;
        double r523559 = r523552 / r523558;
        double r523560 = r523550 ? r523556 : r523559;
        return r523560;
}

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

Original7.7
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 2 regimes

  2. if z < -1.9357721012183174e+80 or 2.6068638849624772e-42 < z

    1. Initial program 12.0

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

    3. Applied *-un-lft-identity12.0

      \[\leadsto \frac{\cosh x \cdot \frac{y}{x}}{\color{blue}{1 \cdot z}}\]

    4. Applied times-frac12.0

      \[\leadsto \color{blue}{\frac{\cosh x}{1} \cdot \frac{\frac{y}{x}}{z}}\]

    5. Simplified12.0

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

    6. Simplified0.4

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

    if -1.9357721012183174e+80 < z < 2.6068638849624772e-42

    1. Initial program 1.3

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

    3. Applied associate-/l*1.4

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

    4. Simplified1.2

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.93577210121831744 \cdot 10^{80} \lor \neg \left(z \le 2.60686388496247717 \cdot 10^{-42}\right):\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x}{\frac{z}{y} \cdot x}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(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))