Average Error: 7.7 → 0.7
Time: 20.0s
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 r334939 = x;
        double r334940 = cosh(r334939);
        double r334941 = y;
        double r334942 = r334941 / r334939;
        double r334943 = r334940 * r334942;
        double r334944 = z;
        double r334945 = r334943 / r334944;
        return r334945;
}
↓
double f(double x, double y, double z) {
        double r334946 = z;
        double r334947 = -1.7488565710886653e+39;
        bool r334948 = r334946 <= r334947;
        double r334949 = 247753.5478154586;
        bool r334950 = r334946 <= r334949;
        double r334951 = !r334950;
        bool r334952 = r334948 || r334951;
        double r334953 = 0.5;
        double r334954 = x;
        double r334955 = 2.0;
        double r334956 = pow(r334954, r334955);
        double r334957 = y;
        double r334958 = r334956 * r334957;
        double r334959 = r334953 * r334958;
        double r334960 = r334959 + r334957;
        double r334961 = r334946 * r334954;
        double r334962 = r334960 / r334961;
        double r334963 = cosh(r334954);
        double r334964 = r334963 * r334957;
        double r334965 = r334964 / r334946;
        double r334966 = r334965 / r334954;
        double r334967 = r334952 ? r334962 : r334966;
        return r334967;
}

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))