Average Error: 2.6 → 0.5
Time: 20.3s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \le -1.667800433775549790266656174829587494332 \cdot 10^{-292} \lor \neg \left(x \cdot \frac{\sin y}{y} \le 0.0\right):\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \sin y}{z \cdot y}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot \frac{\sin y}{y} \le -1.667800433775549790266656174829587494332 \cdot 10^{-292} \lor \neg \left(x \cdot \frac{\sin y}{y} \le 0.0\right):\\
\;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r318464 = x;
        double r318465 = y;
        double r318466 = sin(r318465);
        double r318467 = r318466 / r318465;
        double r318468 = r318464 * r318467;
        double r318469 = z;
        double r318470 = r318468 / r318469;
        return r318470;
}
↓
double f(double x, double y, double z) {
        double r318471 = x;
        double r318472 = y;
        double r318473 = sin(r318472);
        double r318474 = r318473 / r318472;
        double r318475 = r318471 * r318474;
        double r318476 = -1.6678004337755498e-292;
        bool r318477 = r318475 <= r318476;
        double r318478 = 0.0;
        bool r318479 = r318475 <= r318478;
        double r318480 = !r318479;
        bool r318481 = r318477 || r318480;
        double r318482 = z;
        double r318483 = r318475 / r318482;
        double r318484 = r318471 * r318473;
        double r318485 = r318482 * r318472;
        double r318486 = r318484 / r318485;
        double r318487 = r318481 ? r318483 : r318486;
        return r318487;
}

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
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;z \lt -4.217372020342714661850238929213415773451 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x (/ (sin y) y)) < -1.6678004337755498e-292 or 0.0 < (* x (/ (sin y) y))

    1. Initial program 1.5

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

    3. Applied add-cube-cbrt2.4

      \[\leadsto \frac{x \cdot \frac{\sin y}{y}}{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\]

    4. Applied times-frac3.2

      \[\leadsto \color{blue}{\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{\frac{\sin y}{y}}{\sqrt[3]{z}}}\]
    5. Using strategy rm

    6. Applied frac-times2.4

      \[\leadsto \color{blue}{\frac{x \cdot \frac{\sin y}{y}}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\]

    7. Simplified1.5

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

    if -1.6678004337755498e-292 < (* x (/ (sin y) y)) < 0.0

    1. Initial program 14.5

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

    3. Applied add-cube-cbrt14.6

      \[\leadsto \frac{x \cdot \frac{\sin y}{y}}{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\]

    4. Applied times-frac0.5

      \[\leadsto \color{blue}{\frac{x}{\sqrt[3]{z} \cdot \sqrt[3]{z}} \cdot \frac{\frac{\sin y}{y}}{\sqrt[3]{z}}}\]
    5. Using strategy rm

    6. Applied frac-times14.6

      \[\leadsto \color{blue}{\frac{x \cdot \frac{\sin y}{y}}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}\]

    7. Simplified14.5

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

    9. Applied associate-*r/17.9

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

    10. Applied associate-/l/3.6

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \frac{\sin y}{y} \le -1.667800433775549790266656174829587494332 \cdot 10^{-292} \lor \neg \left(x \cdot \frac{\sin y}{y} \le 0.0\right):\\ \;\;\;\;\frac{x \cdot \frac{\sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \sin y}{z \cdot y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< z -4.21737202034271466e-29) (/ (* x (/ 1 (/ y (sin y)))) z) (if (< z 4.44670236911381103e64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1 (/ y (sin y)))) z)))

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