Average Error: 2.9 → 1.5
Time: 8.1s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \frac{\sin y}{y}}{z} \le -7.27792199657957297 \cdot 10^{48}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{y}{\sin y}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \frac{\sin y}{y}}{z} \le -7.27792199657957297 \cdot 10^{48}:\\
\;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r501827 = x;
        double r501828 = y;
        double r501829 = sin(r501828);
        double r501830 = r501829 / r501828;
        double r501831 = r501827 * r501830;
        double r501832 = z;
        double r501833 = r501831 / r501832;
        return r501833;
}
↓
double f(double x, double y, double z) {
        double r501834 = x;
        double r501835 = y;
        double r501836 = sin(r501835);
        double r501837 = r501836 / r501835;
        double r501838 = r501834 * r501837;
        double r501839 = z;
        double r501840 = r501838 / r501839;
        double r501841 = -7.277921996579573e+48;
        bool r501842 = r501840 <= r501841;
        double r501843 = r501835 / r501836;
        double r501844 = r501839 * r501843;
        double r501845 = r501834 / r501844;
        double r501846 = r501834 / r501839;
        double r501847 = r501846 / r501843;
        double r501848 = r501842 ? r501845 : r501847;
        return r501848;
}

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

Original2.9
Target0.3
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (/ (sin y) y)) z) < -7.277921996579573e+48

    1. Initial program 0.2

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

    3. Applied associate-/l*0.2

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

    4. Simplified0.2

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

    if -7.277921996579573e+48 < (/ (* x (/ (sin y) y)) z)

    1. Initial program 3.3

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

    3. Applied associate-/l*3.2

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

    4. Simplified3.3

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

    6. Applied associate-/r*1.7

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \frac{\sin y}{y}}{z} \le -7.27792199657957297 \cdot 10^{48}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{y}{\sin y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 
(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))