Average Error: 7.7 → 0.7
Time: 19.5s
Precision: 64
\[\frac{\cosh x \cdot \frac{y}{x}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1748856571088665297207486973462200713216 \lor \neg \left(z \le 247753.5478154585871379822492599487304688\right):\\ \;\;\;\;\frac{\frac{1}{2} \cdot \left({x}^{2} \cdot y\right) + y}{z \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \end{array}\]
\frac{\cosh x \cdot \frac{y}{x}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1748856571088665297207486973462200713216 \lor \neg \left(z \le 247753.5478154585871379822492599487304688\right):\\
\;\;\;\;\frac{\frac{1}{2} \cdot \left({x}^{2} \cdot y\right) + y}{z \cdot x}\\

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

\end{array}
double f(double x, double y, double z) {
        double r265124 = x;
        double r265125 = cosh(r265124);
        double r265126 = y;
        double r265127 = r265126 / r265124;
        double r265128 = r265125 * r265127;
        double r265129 = z;
        double r265130 = r265128 / r265129;
        return r265130;
}
↓
double f(double x, double y, double z) {
        double r265131 = z;
        double r265132 = -1.7488565710886653e+39;
        bool r265133 = r265131 <= r265132;
        double r265134 = 247753.5478154586;
        bool r265135 = r265131 <= r265134;
        double r265136 = !r265135;
        bool r265137 = r265133 || r265136;
        double r265138 = 0.5;
        double r265139 = x;
        double r265140 = 2.0;
        double r265141 = pow(r265139, r265140);
        double r265142 = y;
        double r265143 = r265141 * r265142;
        double r265144 = r265138 * r265143;
        double r265145 = r265144 + r265142;
        double r265146 = r265131 * r265139;
        double r265147 = r265145 / r265146;
        double r265148 = cosh(r265139);
        double r265149 = r265148 * r265142;
        double r265150 = r265149 / r265131;
        double r265151 = r265150 / r265139;
        double r265152 = r265137 ? r265147 : r265151;
        return r265152;
}

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
Target0.5
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 < -1.7488565710886653e+39 or 247753.5478154586 < z

    1. Initial program 12.6

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

    3. Applied associate-*r/12.6

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

    4. Applied associate-/l/0.3

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

    5. Taylor expanded around 0 1.0

      \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot \left({x}^{2} \cdot y\right) + y}}{z \cdot x}\]

    if -1.7488565710886653e+39 < z < 247753.5478154586

    1. Initial program 0.4

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

    3. Applied associate-*r/0.4

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

    4. Applied associate-/l/17.3

      \[\leadsto \color{blue}{\frac{\cosh x \cdot y}{z \cdot x}}\]
    5. Using strategy rm

    6. Applied associate-/r*0.4

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1748856571088665297207486973462200713216 \lor \neg \left(z \le 247753.5478154585871379822492599487304688\right):\\ \;\;\;\;\frac{\frac{1}{2} \cdot \left({x}^{2} \cdot y\right) + y}{z \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\cosh x \cdot y}{z}}{x}\\ \end{array}\]

Reproduce

herbie shell --seed 2019325 
(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 1.038530535935153e-39) (/ (/ (* (cosh x) y) x) z) (* (/ (/ y z) x) (cosh x))))

  (/ (* (cosh x) (/ y x)) z))