Average Error: 7.5 → 0.7
Time: 18.0s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -13294780528925495035856397041561239552:\\ \;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\ \mathbf{elif}\;y \le 1.449820321413413963499843591018471786151 \cdot 10^{72}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;y \le -13294780528925495035856397041561239552:\\
\;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\

\mathbf{elif}\;y \le 1.449820321413413963499843591018471786151 \cdot 10^{72}:\\
\;\;\;\;\cosh x \cdot \frac{\frac{y}{x}}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r18208245 = x;
        double r18208246 = cosh(r18208245);
        double r18208247 = y;
        double r18208248 = r18208247 / r18208245;
        double r18208249 = r18208246 * r18208248;
        double r18208250 = z;
        double r18208251 = r18208249 / r18208250;
        return r18208251;
}
↓
double f(double x, double y, double z) {
        double r18208252 = y;
        double r18208253 = -1.3294780528925495e+37;
        bool r18208254 = r18208252 <= r18208253;
        double r18208255 = x;
        double r18208256 = cosh(r18208255);
        double r18208257 = r18208256 * r18208252;
        double r18208258 = z;
        double r18208259 = r18208255 * r18208258;
        double r18208260 = r18208257 / r18208259;
        double r18208261 = 1.449820321413414e+72;
        bool r18208262 = r18208252 <= r18208261;
        double r18208263 = r18208252 / r18208255;
        double r18208264 = r18208263 / r18208258;
        double r18208265 = r18208256 * r18208264;
        double r18208266 = r18208262 ? r18208265 : r18208260;
        double r18208267 = r18208254 ? r18208260 : r18208266;
        return r18208267;
}

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

Original7.5
Target0.4
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;y \lt -4.618902267687041990497740832940559043667 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \mathbf{elif}\;y \lt 1.038530535935153018369520384190862667426 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{x} \cdot \cosh x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.3294780528925495e+37 or 1.449820321413414e+72 < y

    1. Initial program 26.9

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

    3. Applied associate-*r/26.9

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

    4. Applied associate-/l/0.4

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

    if -1.3294780528925495e+37 < y < 1.449820321413414e+72

    1. Initial program 0.8

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

    3. Applied *-un-lft-identity0.8

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

    4. Applied times-frac0.8

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

    5. Simplified0.8

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -13294780528925495035856397041561239552:\\ \;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\ \mathbf{elif}\;y \le 1.449820321413413963499843591018471786151 \cdot 10^{72}:\\ \;\;\;\;\cosh x \cdot \frac{\frac{y}{x}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cosh x \cdot y}{x \cdot z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(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))