Average Error: 2.9 → 0.7
Time: 9.2s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -9.48611484393196181 \cdot 10^{-94} \lor \neg \left(z \le 1.43053913878422607 \cdot 10^{127}\right):\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{\sin y}{y}}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -9.48611484393196181 \cdot 10^{-94} \lor \neg \left(z \le 1.43053913878422607 \cdot 10^{127}\right):\\
\;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r598801 = x;
        double r598802 = y;
        double r598803 = sin(r598802);
        double r598804 = r598803 / r598802;
        double r598805 = r598801 * r598804;
        double r598806 = z;
        double r598807 = r598805 / r598806;
        return r598807;
}
↓
double f(double x, double y, double z) {
        double r598808 = z;
        double r598809 = -9.486114843931962e-94;
        bool r598810 = r598808 <= r598809;
        double r598811 = 1.430539138784226e+127;
        bool r598812 = r598808 <= r598811;
        double r598813 = !r598812;
        bool r598814 = r598810 || r598813;
        double r598815 = x;
        double r598816 = 1.0;
        double r598817 = y;
        double r598818 = sin(r598817);
        double r598819 = r598817 / r598818;
        double r598820 = r598816 / r598819;
        double r598821 = r598815 * r598820;
        double r598822 = r598821 / r598808;
        double r598823 = r598818 / r598817;
        double r598824 = r598823 / r598808;
        double r598825 = r598815 * r598824;
        double r598826 = r598814 ? r598822 : r598825;
        return r598826;
}

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
Target0.2
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -9.486114843931962e-94 or 1.430539138784226e+127 < z

    1. Initial program 0.6

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

    3. Applied clear-num0.6

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

    if -9.486114843931962e-94 < z < 1.430539138784226e+127

    1. Initial program 5.2

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

    3. Applied *-un-lft-identity5.2

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

    4. Applied times-frac0.7

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

    5. Simplified0.7

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -9.48611484393196181 \cdot 10^{-94} \lor \neg \left(z \le 1.43053913878422607 \cdot 10^{127}\right):\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{\sin y}{y}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(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))