Average Error: 2.7 → 0.2
Time: 5.5s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.3341519654404754 \cdot 10^{-26}:\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{elif}\;z \le 90893168842109888:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{\sin y}}}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -3.3341519654404754 \cdot 10^{-26}:\\
\;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\

\mathbf{elif}\;z \le 90893168842109888:\\
\;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r550346 = x;
        double r550347 = y;
        double r550348 = sin(r550347);
        double r550349 = r550348 / r550347;
        double r550350 = r550346 * r550349;
        double r550351 = z;
        double r550352 = r550350 / r550351;
        return r550352;
}
↓
double f(double x, double y, double z) {
        double r550353 = z;
        double r550354 = -3.3341519654404754e-26;
        bool r550355 = r550353 <= r550354;
        double r550356 = x;
        double r550357 = y;
        double r550358 = sin(r550357);
        double r550359 = r550358 / r550357;
        double r550360 = r550356 * r550359;
        double r550361 = r550360 / r550353;
        double r550362 = 9.089316884210989e+16;
        bool r550363 = r550353 <= r550362;
        double r550364 = r550357 / r550358;
        double r550365 = r550353 * r550364;
        double r550366 = r550356 / r550365;
        double r550367 = r550356 / r550364;
        double r550368 = r550367 / r550353;
        double r550369 = r550363 ? r550366 : r550368;
        double r550370 = r550355 ? r550361 : r550369;
        return r550370;
}

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

Original2.7
Target0.3
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -3.3341519654404754e-26

    1. Initial program 0.1

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

    if -3.3341519654404754e-26 < z < 9.089316884210989e+16

    1. Initial program 5.9

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

    3. Applied clear-num5.9

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

    5. Applied *-un-lft-identity5.9

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

    6. Applied associate-/r*5.9

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

    7. Simplified5.9

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

    9. Applied div-inv5.9

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

    10. Applied associate-/l*0.3

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

    11. Simplified0.2

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

    if 9.089316884210989e+16 < z

    1. Initial program 0.1

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

    3. Applied clear-num0.2

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

    5. Applied *-un-lft-identity0.2

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

    6. Applied associate-/r*0.2

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

    7. Simplified0.1

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.3341519654404754 \cdot 10^{-26}:\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{elif}\;z \le 90893168842109888:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 
(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))