Average Error: 2.6 → 0.2
Time: 16.4s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1396587271183383937052376781815808:\\ \;\;\;\;\frac{1}{z} \cdot \left(x \cdot \frac{\sin y}{y}\right)\\ \mathbf{elif}\;z \le 1119859951.5625312328338623046875:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \left(x \cdot \frac{\sin y}{y}\right)\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1396587271183383937052376781815808:\\
\;\;\;\;\frac{1}{z} \cdot \left(x \cdot \frac{\sin y}{y}\right)\\

\mathbf{elif}\;z \le 1119859951.5625312328338623046875:\\
\;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{z} \cdot \left(x \cdot \frac{\sin y}{y}\right)\\

\end{array}
double f(double x, double y, double z) {
        double r36330285 = x;
        double r36330286 = y;
        double r36330287 = sin(r36330286);
        double r36330288 = r36330287 / r36330286;
        double r36330289 = r36330285 * r36330288;
        double r36330290 = z;
        double r36330291 = r36330289 / r36330290;
        return r36330291;
}
↓
double f(double x, double y, double z) {
        double r36330292 = z;
        double r36330293 = -1.396587271183384e+33;
        bool r36330294 = r36330292 <= r36330293;
        double r36330295 = 1.0;
        double r36330296 = r36330295 / r36330292;
        double r36330297 = x;
        double r36330298 = y;
        double r36330299 = sin(r36330298);
        double r36330300 = r36330299 / r36330298;
        double r36330301 = r36330297 * r36330300;
        double r36330302 = r36330296 * r36330301;
        double r36330303 = 1119859951.5625312;
        bool r36330304 = r36330292 <= r36330303;
        double r36330305 = r36330292 / r36330300;
        double r36330306 = r36330297 / r36330305;
        double r36330307 = r36330304 ? r36330306 : r36330302;
        double r36330308 = r36330294 ? r36330302 : r36330307;
        return r36330308;
}

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
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;z \lt -4.217372020342714661850238929213415773451 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.396587271183384e+33 or 1119859951.5625312 < z

    1. Initial program 0.1

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

    3. Applied div-inv0.2

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

    if -1.396587271183384e+33 < z < 1119859951.5625312

    1. Initial program 5.1

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

    3. Applied div-inv5.3

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

    5. Applied associate-*r/5.1

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

    6. Simplified5.2

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

    8. Applied div-inv5.2

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

    9. Applied associate-/l*0.3

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

    10. Simplified0.3

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1396587271183383937052376781815808:\\ \;\;\;\;\frac{1}{z} \cdot \left(x \cdot \frac{\sin y}{y}\right)\\ \mathbf{elif}\;z \le 1119859951.5625312328338623046875:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \left(x \cdot \frac{\sin y}{y}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"

  :herbie-target
  (if (< z -4.2173720203427147e-29) (/ (* x (/ 1.0 (/ y (sin y)))) z) (if (< z 4.446702369113811e+64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1.0 (/ y (sin y)))) z)))

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