Average Error: 2.9 → 0.2
Time: 39.0s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\sin y}{y} \cdot x \le -4.625916909407842 \cdot 10^{-220}:\\ \;\;\;\;\frac{\frac{\sin y}{y} \cdot x}{z}\\ \mathbf{elif}\;\frac{\sin y}{y} \cdot x \le 3.125262785899896 \cdot 10^{-309}:\\ \;\;\;\;\sin y \cdot \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\sin y}{y} \cdot x}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\sin y}{y} \cdot x \le -4.625916909407842 \cdot 10^{-220}:\\
\;\;\;\;\frac{\frac{\sin y}{y} \cdot x}{z}\\

\mathbf{elif}\;\frac{\sin y}{y} \cdot x \le 3.125262785899896 \cdot 10^{-309}:\\
\;\;\;\;\sin y \cdot \frac{\frac{x}{z}}{y}\\

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

\end{array}
double f(double x, double y, double z) {
        double r24181979 = x;
        double r24181980 = y;
        double r24181981 = sin(r24181980);
        double r24181982 = r24181981 / r24181980;
        double r24181983 = r24181979 * r24181982;
        double r24181984 = z;
        double r24181985 = r24181983 / r24181984;
        return r24181985;
}
↓
double f(double x, double y, double z) {
        double r24181986 = y;
        double r24181987 = sin(r24181986);
        double r24181988 = r24181987 / r24181986;
        double r24181989 = x;
        double r24181990 = r24181988 * r24181989;
        double r24181991 = -4.625916909407842e-220;
        bool r24181992 = r24181990 <= r24181991;
        double r24181993 = z;
        double r24181994 = r24181990 / r24181993;
        double r24181995 = 3.125262785899896e-309;
        bool r24181996 = r24181990 <= r24181995;
        double r24181997 = r24181989 / r24181993;
        double r24181998 = r24181997 / r24181986;
        double r24181999 = r24181987 * r24181998;
        double r24182000 = r24181996 ? r24181999 : r24181994;
        double r24182001 = r24181992 ? r24181994 : r24182000;
        return r24182001;
}

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
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;z \lt -4.2173720203427147 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1.0}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1.0}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x (/ (sin y) y)) < -4.625916909407842e-220 or 3.125262785899896e-309 < (* x (/ (sin y) y))

    1. Initial program 0.2

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

    if -4.625916909407842e-220 < (* x (/ (sin y) y)) < 3.125262785899896e-309

    1. Initial program 12.5

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

    3. Applied associate-/l*0.2

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

    5. Applied div-inv0.2

      \[\leadsto \frac{x}{\frac{z}{\color{blue}{\sin y \cdot \frac{1}{y}}}}\]

    6. Applied *-un-lft-identity0.2

      \[\leadsto \frac{x}{\frac{\color{blue}{1 \cdot z}}{\sin y \cdot \frac{1}{y}}}\]

    7. Applied times-frac2.6

      \[\leadsto \frac{x}{\color{blue}{\frac{1}{\sin y} \cdot \frac{z}{\frac{1}{y}}}}\]

    8. Applied *-un-lft-identity2.6

      \[\leadsto \frac{\color{blue}{1 \cdot x}}{\frac{1}{\sin y} \cdot \frac{z}{\frac{1}{y}}}\]

    9. Applied times-frac2.6

      \[\leadsto \color{blue}{\frac{1}{\frac{1}{\sin y}} \cdot \frac{x}{\frac{z}{\frac{1}{y}}}}\]

    10. Simplified2.6

      \[\leadsto \color{blue}{\sin y} \cdot \frac{x}{\frac{z}{\frac{1}{y}}}\]

    11. Simplified0.3

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\sin y}{y} \cdot x \le -4.625916909407842 \cdot 10^{-220}:\\ \;\;\;\;\frac{\frac{\sin y}{y} \cdot x}{z}\\ \mathbf{elif}\;\frac{\sin y}{y} \cdot x \le 3.125262785899896 \cdot 10^{-309}:\\ \;\;\;\;\sin y \cdot \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\sin y}{y} \cdot x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"

  :herbie-target
  (if (< z -4.2173720203427147e-29) (/ (* x (/ 1.0 (/ y (sin y)))) z) (if (< z 4.446702369113811e+64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1.0 (/ y (sin y)))) z)))

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