Average Error: 2.9 → 0.7
Time: 8.3s
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 r583124 = x;
        double r583125 = y;
        double r583126 = sin(r583125);
        double r583127 = r583126 / r583125;
        double r583128 = r583124 * r583127;
        double r583129 = z;
        double r583130 = r583128 / r583129;
        return r583130;
}
↓
double f(double x, double y, double z) {
        double r583131 = z;
        double r583132 = -9.486114843931962e-94;
        bool r583133 = r583131 <= r583132;
        double r583134 = 1.430539138784226e+127;
        bool r583135 = r583131 <= r583134;
        double r583136 = !r583135;
        bool r583137 = r583133 || r583136;
        double r583138 = x;
        double r583139 = 1.0;
        double r583140 = y;
        double r583141 = sin(r583140);
        double r583142 = r583140 / r583141;
        double r583143 = r583139 / r583142;
        double r583144 = r583138 * r583143;
        double r583145 = r583144 / r583131;
        double r583146 = r583141 / r583140;
        double r583147 = r583146 / r583131;
        double r583148 = r583138 * r583147;
        double r583149 = r583137 ? r583145 : r583148;
        return r583149;
}

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))