Average Error: 7.7 → 0.3
Time: 21.0s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -0.001616770998561857129380281428154830791755 \lor \neg \left(y \le 7.142361989502533093026412822345017131219 \cdot 10^{-24}\right):\\ \;\;\;\;\cosh x \cdot \frac{y}{z \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} \cdot \cosh x}{z}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;y \le -0.001616770998561857129380281428154830791755 \lor \neg \left(y \le 7.142361989502533093026412822345017131219 \cdot 10^{-24}\right):\\
\;\;\;\;\cosh x \cdot \frac{y}{z \cdot x}\\

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

\end{array}
double f(double x, double y, double z) {
        double r337346 = x;
        double r337347 = cosh(r337346);
        double r337348 = y;
        double r337349 = r337348 / r337346;
        double r337350 = r337347 * r337349;
        double r337351 = z;
        double r337352 = r337350 / r337351;
        return r337352;
}
↓
double f(double x, double y, double z) {
        double r337353 = y;
        double r337354 = -0.0016167709985618571;
        bool r337355 = r337353 <= r337354;
        double r337356 = 7.142361989502533e-24;
        bool r337357 = r337353 <= r337356;
        double r337358 = !r337357;
        bool r337359 = r337355 || r337358;
        double r337360 = x;
        double r337361 = cosh(r337360);
        double r337362 = z;
        double r337363 = r337362 * r337360;
        double r337364 = r337353 / r337363;
        double r337365 = r337361 * r337364;
        double r337366 = r337353 / r337360;
        double r337367 = r337366 * r337361;
        double r337368 = r337367 / r337362;
        double r337369 = r337359 ? r337365 : r337368;
        return r337369;
}

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
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687041990497740832940559043667 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.038530535935153018369520384190862667426 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -0.0016167709985618571 or 7.142361989502533e-24 < y

    1. Initial program 19.9

      \[\frac{\cosh x \cdot \frac{y}{x}}{z}\]

    2. Simplified0.4

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

    if -0.0016167709985618571 < y < 7.142361989502533e-24

    1. Initial program 0.3

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -0.001616770998561857129380281428154830791755 \lor \neg \left(y \le 7.142361989502533093026412822345017131219 \cdot 10^{-24}\right):\\ \;\;\;\;\cosh x \cdot \frac{y}{z \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{x} \cdot \cosh x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019196 
(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))