Average Error: 2.8 → 0.3
Time: 4.2s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.3412211236133659 \cdot 10^{-51} \lor \neg \left(z \le 9.6931285533073065 \cdot 10^{-43}\right):\\ \;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{\sin y}{y}}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.3412211236133659 \cdot 10^{-51} \lor \neg \left(z \le 9.6931285533073065 \cdot 10^{-43}\right):\\
\;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r525826 = x;
        double r525827 = y;
        double r525828 = sin(r525827);
        double r525829 = r525828 / r525827;
        double r525830 = r525826 * r525829;
        double r525831 = z;
        double r525832 = r525830 / r525831;
        return r525832;
}
↓
double f(double x, double y, double z) {
        double r525833 = z;
        double r525834 = -2.341221123613366e-51;
        bool r525835 = r525833 <= r525834;
        double r525836 = 9.693128553307307e-43;
        bool r525837 = r525833 <= r525836;
        double r525838 = !r525837;
        bool r525839 = r525835 || r525838;
        double r525840 = x;
        double r525841 = y;
        double r525842 = sin(r525841);
        double r525843 = 1.0;
        double r525844 = r525843 / r525841;
        double r525845 = r525842 * r525844;
        double r525846 = r525840 * r525845;
        double r525847 = r525846 / r525833;
        double r525848 = r525842 / r525841;
        double r525849 = r525848 / r525833;
        double r525850 = r525840 * r525849;
        double r525851 = r525839 ? r525847 : r525850;
        return r525851;
}

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

Original2.8
Target0.3
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.341221123613366e-51 or 9.693128553307307e-43 < z

    1. Initial program 0.3

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

    3. Applied div-inv0.4

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

    if -2.341221123613366e-51 < z < 9.693128553307307e-43

    1. Initial program 6.9

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

    3. Applied *-un-lft-identity6.9

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

    4. Applied times-frac0.3

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

    5. Simplified0.3

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.3412211236133659 \cdot 10^{-51} \lor \neg \left(z \le 9.6931285533073065 \cdot 10^{-43}\right):\\ \;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{\sin y}{y}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020083 
(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))