Average Error: 8.0 → 0.4
Time: 4.1s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\cosh x \cdot \frac{y}{x} \le -2.12049539930230558 \cdot 10^{286} \lor \neg \left(\cosh x \cdot \frac{y}{x} \le 1.8941550272477898 \cdot 10^{193}\right):\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;\cosh x \cdot \frac{y}{x} \le -2.12049539930230558 \cdot 10^{286} \lor \neg \left(\cosh x \cdot \frac{y}{x} \le 1.8941550272477898 \cdot 10^{193}\right):\\
\;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r606348 = x;
        double r606349 = cosh(r606348);
        double r606350 = y;
        double r606351 = r606350 / r606348;
        double r606352 = r606349 * r606351;
        double r606353 = z;
        double r606354 = r606352 / r606353;
        return r606354;
}
↓
double f(double x, double y, double z) {
        double r606355 = x;
        double r606356 = cosh(r606355);
        double r606357 = y;
        double r606358 = r606357 / r606355;
        double r606359 = r606356 * r606358;
        double r606360 = -2.1204953993023056e+286;
        bool r606361 = r606359 <= r606360;
        double r606362 = 1.8941550272477898e+193;
        bool r606363 = r606359 <= r606362;
        double r606364 = !r606363;
        bool r606365 = r606361 || r606364;
        double r606366 = z;
        double r606367 = r606355 * r606366;
        double r606368 = r606357 / r606367;
        double r606369 = r606356 * r606368;
        double r606370 = r606359 / r606366;
        double r606371 = r606365 ? r606369 : r606370;
        return r606371;
}

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
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687042 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.0385305359351529 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* (cosh x) (/ y x)) < -2.1204953993023056e+286 or 1.8941550272477898e+193 < (* (cosh x) (/ y x))

    1. Initial program 37.3

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

    3. Applied *-un-lft-identity37.3

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

    4. Applied times-frac37.1

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

    5. Simplified37.1

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

    6. Simplified0.9

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

    if -2.1204953993023056e+286 < (* (cosh x) (/ y x)) < 1.8941550272477898e+193

    1. Initial program 0.2

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\cosh x \cdot \frac{y}{x} \le -2.12049539930230558 \cdot 10^{286} \lor \neg \left(\cosh x \cdot \frac{y}{x} \le 1.8941550272477898 \cdot 10^{193}\right):\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot \frac{y}{x}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020057 +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))