Average Error: 8.0 → 0.5
Time: 15.2s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -8.710586004282429932361687759696753237551 \cdot 10^{-56} \lor \neg \left(y \le 3.814137150824676695755918942870868365663 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{x} \cdot \left(\cosh x \cdot y\right)}{z}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;y \le -8.710586004282429932361687759696753237551 \cdot 10^{-56} \lor \neg \left(y \le 3.814137150824676695755918942870868365663 \cdot 10^{-28}\right):\\
\;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{1}{x} \cdot \left(\cosh x \cdot y\right)}{z}\\

\end{array}
double f(double x, double y, double z) {
        double r397521 = x;
        double r397522 = cosh(r397521);
        double r397523 = y;
        double r397524 = r397523 / r397521;
        double r397525 = r397522 * r397524;
        double r397526 = z;
        double r397527 = r397525 / r397526;
        return r397527;
}
↓
double f(double x, double y, double z) {
        double r397528 = y;
        double r397529 = -8.71058600428243e-56;
        bool r397530 = r397528 <= r397529;
        double r397531 = 3.8141371508246767e-28;
        bool r397532 = r397528 <= r397531;
        double r397533 = !r397532;
        bool r397534 = r397530 || r397533;
        double r397535 = x;
        double r397536 = cosh(r397535);
        double r397537 = r397536 * r397528;
        double r397538 = z;
        double r397539 = r397535 * r397538;
        double r397540 = r397537 / r397539;
        double r397541 = 1.0;
        double r397542 = r397541 / r397535;
        double r397543 = r397542 * r397537;
        double r397544 = r397543 / r397538;
        double r397545 = r397534 ? r397540 : r397544;
        return r397545;
}

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

Original8.0
Target0.4
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687041990497740832940559043667 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.038530535935153018369520384190862667426 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -8.71058600428243e-56 or 3.8141371508246767e-28 < y

    1. Initial program 18.2

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

    3. Applied associate-*r/18.2

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

    4. Applied associate-/l/0.7

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

    5. Simplified0.7

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

    if -8.71058600428243e-56 < y < 3.8141371508246767e-28

    1. Initial program 0.3

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

    3. Applied div-inv0.4

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

    4. Applied associate-*r*0.4

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -8.710586004282429932361687759696753237551 \cdot 10^{-56} \lor \neg \left(y \le 3.814137150824676695755918942870868365663 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{x} \cdot \left(\cosh x \cdot y\right)}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(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))