Average Error: 2.6 → 0.4
Time: 21.4s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \frac{\sin y}{y}}{z} \le -4.797944114414283853740653503155849375579 \cdot 10^{-317} \lor \neg \left(\frac{x \cdot \frac{\sin y}{y}}{z} \le -0.0\right):\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{\frac{\sin y}{y}}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \frac{\sin y}{y}}{z} \le -4.797944114414283853740653503155849375579 \cdot 10^{-317} \lor \neg \left(\frac{x \cdot \frac{\sin y}{y}}{z} \le -0.0\right):\\
\;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{\frac{z}{x}}{\frac{\sin y}{y}}}\\

\end{array}
double f(double x, double y, double z) {
        double r330859 = x;
        double r330860 = y;
        double r330861 = sin(r330860);
        double r330862 = r330861 / r330860;
        double r330863 = r330859 * r330862;
        double r330864 = z;
        double r330865 = r330863 / r330864;
        return r330865;
}
↓
double f(double x, double y, double z) {
        double r330866 = x;
        double r330867 = y;
        double r330868 = sin(r330867);
        double r330869 = r330868 / r330867;
        double r330870 = r330866 * r330869;
        double r330871 = z;
        double r330872 = r330870 / r330871;
        double r330873 = -4.7979441144143e-317;
        bool r330874 = r330872 <= r330873;
        double r330875 = -0.0;
        bool r330876 = r330872 <= r330875;
        double r330877 = !r330876;
        bool r330878 = r330874 || r330877;
        double r330879 = 1.0;
        double r330880 = r330871 / r330866;
        double r330881 = r330880 / r330869;
        double r330882 = r330879 / r330881;
        double r330883 = r330878 ? r330872 : r330882;
        return r330883;
}

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

Original2.6
Target0.3
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;z \lt -4.217372020342714661850238929213415773451 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (/ (sin y) y)) z) < -4.7979441144143e-317 or -0.0 < (/ (* x (/ (sin y) y)) z)

    1. Initial program 1.6

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

    if -4.7979441144143e-317 < (/ (* x (/ (sin y) y)) z) < -0.0

    1. Initial program 9.4

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

    3. Applied clear-num9.7

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x \cdot \frac{\sin y}{y}}}}\]
    4. Using strategy rm

    5. Applied associate-/r*0.6

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{z}{x}}{\frac{\sin y}{y}}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \frac{\sin y}{y}}{z} \le -4.797944114414283853740653503155849375579 \cdot 10^{-317} \lor \neg \left(\frac{x \cdot \frac{\sin y}{y}}{z} \le -0.0\right):\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{\frac{\sin y}{y}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< z -4.2173720203427147e-29) (/ (* x (/ 1 (/ y (sin y)))) z) (if (< z 4.446702369113811e+64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1 (/ y (sin y)))) z)))

  (/ (* x (/ (sin y) y)) z))