Average Error: 2.6 → 0.4
Time: 20.2s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \frac{\sin y}{y}}{z} \le -4.797944114414283853740653503155849375579 \cdot 10^{-317} \lor \neg \left(\frac{x \cdot \frac{\sin y}{y}}{z} \le -0.0\right):\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{\frac{\sin y}{y}}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \frac{\sin y}{y}}{z} \le -4.797944114414283853740653503155849375579 \cdot 10^{-317} \lor \neg \left(\frac{x \cdot \frac{\sin y}{y}}{z} \le -0.0\right):\\
\;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{\frac{z}{x}}{\frac{\sin y}{y}}}\\

\end{array}
double f(double x, double y, double z) {
        double r353218 = x;
        double r353219 = y;
        double r353220 = sin(r353219);
        double r353221 = r353220 / r353219;
        double r353222 = r353218 * r353221;
        double r353223 = z;
        double r353224 = r353222 / r353223;
        return r353224;
}
↓
double f(double x, double y, double z) {
        double r353225 = x;
        double r353226 = y;
        double r353227 = sin(r353226);
        double r353228 = r353227 / r353226;
        double r353229 = r353225 * r353228;
        double r353230 = z;
        double r353231 = r353229 / r353230;
        double r353232 = -4.7979441144143e-317;
        bool r353233 = r353231 <= r353232;
        double r353234 = -0.0;
        bool r353235 = r353231 <= r353234;
        double r353236 = !r353235;
        bool r353237 = r353233 || r353236;
        double r353238 = 1.0;
        double r353239 = r353230 / r353225;
        double r353240 = r353239 / r353228;
        double r353241 = r353238 / r353240;
        double r353242 = r353237 ? r353231 : r353241;
        return r353242;
}

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
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;z \lt -4.217372020342714661850238929213415773451 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (/ (sin y) y)) z) < -4.7979441144143e-317 or -0.0 < (/ (* x (/ (sin y) y)) z)

    1. Initial program 0.4

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

    if -4.7979441144143e-317 < (/ (* x (/ (sin y) y)) z) < -0.0

    1. Initial program 8.9

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

    3. Applied clear-num9.0

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x \cdot \frac{\sin y}{y}}}}\]
    4. Using strategy rm

    5. Applied associate-/r*0.5

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{z}{x}}{\frac{\sin y}{y}}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \frac{\sin y}{y}}{z} \le -4.797944114414283853740653503155849375579 \cdot 10^{-317} \lor \neg \left(\frac{x \cdot \frac{\sin y}{y}}{z} \le -0.0\right):\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{\frac{\sin y}{y}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 
(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))