Average Error: 7.8 → 0.7
Time: 14.6s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.912986458297726092960347241480881860468 \cdot 10^{82} \lor \neg \left(z \le 10075888755760661719987257344\right):\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y \cdot \cosh x\right) \cdot \frac{1}{x}}{z}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -5.912986458297726092960347241480881860468 \cdot 10^{82} \lor \neg \left(z \le 10075888755760661719987257344\right):\\
\;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r401110 = x;
        double r401111 = cosh(r401110);
        double r401112 = y;
        double r401113 = r401112 / r401110;
        double r401114 = r401111 * r401113;
        double r401115 = z;
        double r401116 = r401114 / r401115;
        return r401116;
}
↓
double f(double x, double y, double z) {
        double r401117 = z;
        double r401118 = -5.912986458297726e+82;
        bool r401119 = r401117 <= r401118;
        double r401120 = 1.0075888755760662e+28;
        bool r401121 = r401117 <= r401120;
        double r401122 = !r401121;
        bool r401123 = r401119 || r401122;
        double r401124 = x;
        double r401125 = cosh(r401124);
        double r401126 = y;
        double r401127 = r401124 * r401117;
        double r401128 = r401126 / r401127;
        double r401129 = r401125 * r401128;
        double r401130 = r401126 * r401125;
        double r401131 = 1.0;
        double r401132 = r401131 / r401124;
        double r401133 = r401130 * r401132;
        double r401134 = r401133 / r401117;
        double r401135 = r401123 ? r401129 : r401134;
        return r401135;
}

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

Original7.8
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 z < -5.912986458297726e+82 or 1.0075888755760662e+28 < z

    1. Initial program 13.3

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

    2. Simplified0.3

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

    if -5.912986458297726e+82 < z < 1.0075888755760662e+28

    1. Initial program 1.1

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

    3. Applied div-inv1.2

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

    4. Applied associate-*r*1.2

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

    5. Simplified1.2

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.912986458297726092960347241480881860468 \cdot 10^{82} \lor \neg \left(z \le 10075888755760661719987257344\right):\\ \;\;\;\;\cosh x \cdot \frac{y}{x \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y \cdot \cosh x\right) \cdot \frac{1}{x}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019195 
(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))