Average Error: 2.6 → 0.5
Time: 19.0s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \le -1.667800433775549790266656174829587494332 \cdot 10^{-292} \lor \neg \left(x \cdot \frac{\sin y}{y} \le 0.0\right):\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \sin y}{z \cdot y}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot \frac{\sin y}{y} \le -1.667800433775549790266656174829587494332 \cdot 10^{-292} \lor \neg \left(x \cdot \frac{\sin y}{y} \le 0.0\right):\\
\;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r439050 = x;
        double r439051 = y;
        double r439052 = sin(r439051);
        double r439053 = r439052 / r439051;
        double r439054 = r439050 * r439053;
        double r439055 = z;
        double r439056 = r439054 / r439055;
        return r439056;
}
↓
double f(double x, double y, double z) {
        double r439057 = x;
        double r439058 = y;
        double r439059 = sin(r439058);
        double r439060 = r439059 / r439058;
        double r439061 = r439057 * r439060;
        double r439062 = -1.6678004337755498e-292;
        bool r439063 = r439061 <= r439062;
        double r439064 = 0.0;
        bool r439065 = r439061 <= r439064;
        double r439066 = !r439065;
        bool r439067 = r439063 || r439066;
        double r439068 = z;
        double r439069 = r439061 / r439068;
        double r439070 = r439057 * r439059;
        double r439071 = r439068 * r439058;
        double r439072 = r439070 / r439071;
        double r439073 = r439067 ? r439069 : r439072;
        return r439073;
}

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
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;z \lt -4.217372020342714661850238929213415773451 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x (/ (sin y) y)) < -1.6678004337755498e-292 or 0.0 < (* x (/ (sin y) y))

    1. Initial program 1.5

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

    3. Applied add-cube-cbrt2.4

      \[\leadsto \frac{x \cdot \frac{\sin y}{y}}{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\]

    4. Applied times-frac3.2

      \[\leadsto \color{blue}{\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{\frac{\sin y}{y}}{\sqrt[3]{z}}}\]
    5. Using strategy rm

    6. Applied frac-times2.4

      \[\leadsto \color{blue}{\frac{x \cdot \frac{\sin y}{y}}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\]

    7. Simplified1.5

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

    if -1.6678004337755498e-292 < (* x (/ (sin y) y)) < 0.0

    1. Initial program 14.5

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

    3. Applied add-cube-cbrt14.6

      \[\leadsto \frac{x \cdot \frac{\sin y}{y}}{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\]

    4. Applied times-frac0.5

      \[\leadsto \color{blue}{\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{\frac{\sin y}{y}}{\sqrt[3]{z}}}\]
    5. Using strategy rm

    6. Applied frac-times14.6

      \[\leadsto \color{blue}{\frac{x \cdot \frac{\sin y}{y}}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\]

    7. Simplified14.5

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

    9. Applied div-inv14.5

      \[\leadsto \color{blue}{\left(x \cdot \frac{\sin y}{y}\right) \cdot \frac{1}{z}}\]
    10. Using strategy rm

    11. Applied associate-*r/17.9

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

    12. Applied frac-times3.6

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

    13. Simplified3.6

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

    14. Simplified3.6

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \le -1.667800433775549790266656174829587494332 \cdot 10^{-292} \lor \neg \left(x \cdot \frac{\sin y}{y} \le 0.0\right):\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \sin y}{z \cdot y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< z -4.21737202034271466e-29) (/ (* x (/ 1 (/ y (sin y)))) z) (if (< z 4.44670236911381103e64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1 (/ y (sin y)))) z)))

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