Average Error: 2.6 → 0.7
Time: 14.0s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.090910714546979714783795734486200807187 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{\sin y}{y} \cdot x}{z}\\ \mathbf{elif}\;z \le 4.576842764057799981661987703139532669264 \cdot 10^{-157}:\\ \;\;\;\;\left(\frac{1}{z} \cdot \frac{\sin y}{y}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{\sin y}{y}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -5.090910714546979714783795734486200807187 \cdot 10^{-38}:\\
\;\;\;\;\frac{\frac{\sin y}{y} \cdot x}{z}\\

\mathbf{elif}\;z \le 4.576842764057799981661987703139532669264 \cdot 10^{-157}:\\
\;\;\;\;\left(\frac{1}{z} \cdot \frac{\sin y}{y}\right) \cdot x\\

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

\end{array}
double f(double x, double y, double z) {
        double r1000468 = x;
        double r1000469 = y;
        double r1000470 = sin(r1000469);
        double r1000471 = r1000470 / r1000469;
        double r1000472 = r1000468 * r1000471;
        double r1000473 = z;
        double r1000474 = r1000472 / r1000473;
        return r1000474;
}
↓
double f(double x, double y, double z) {
        double r1000475 = z;
        double r1000476 = -5.09091071454698e-38;
        bool r1000477 = r1000475 <= r1000476;
        double r1000478 = y;
        double r1000479 = sin(r1000478);
        double r1000480 = r1000479 / r1000478;
        double r1000481 = x;
        double r1000482 = r1000480 * r1000481;
        double r1000483 = r1000482 / r1000475;
        double r1000484 = 4.5768427640578e-157;
        bool r1000485 = r1000475 <= r1000484;
        double r1000486 = 1.0;
        double r1000487 = r1000486 / r1000475;
        double r1000488 = r1000487 * r1000480;
        double r1000489 = r1000488 * r1000481;
        double r1000490 = r1000481 / r1000475;
        double r1000491 = r1000490 * r1000480;
        double r1000492 = r1000485 ? r1000489 : r1000491;
        double r1000493 = r1000477 ? r1000483 : r1000492;
        return r1000493;
}

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
Target0.2
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;z \lt -4.217372020342714661850238929213415773451 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -5.09091071454698e-38

    1. Initial program 0.1

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

    2. Simplified4.6

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

    4. Applied div-inv4.6

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

    6. Applied un-div-inv4.6

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

    7. Applied associate-*r/0.1

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

    8. Simplified0.1

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

    if -5.09091071454698e-38 < z < 4.5768427640578e-157

    1. Initial program 7.1

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

    2. Simplified0.3

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

    4. Applied div-inv0.4

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

    if 4.5768427640578e-157 < z

    1. Initial program 1.1

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

    2. Simplified3.6

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

    4. Applied add-cube-cbrt3.8

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

    6. Applied *-un-lft-identity3.8

      \[\leadsto \color{blue}{\left(1 \cdot x\right)} \cdot \frac{\left(\sqrt[3]{\frac{\sin y}{y}} \cdot \sqrt[3]{\frac{\sin y}{y}}\right) \cdot \sqrt[3]{\frac{\sin y}{y}}}{z}\]

    7. Applied associate-*l*3.8

      \[\leadsto \color{blue}{1 \cdot \left(x \cdot \frac{\left(\sqrt[3]{\frac{\sin y}{y}} \cdot \sqrt[3]{\frac{\sin y}{y}}\right) \cdot \sqrt[3]{\frac{\sin y}{y}}}{z}\right)}\]

    8. Simplified1.3

      \[\leadsto 1 \cdot \color{blue}{\left(\frac{\sin y}{y} \cdot \frac{x}{z}\right)}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.090910714546979714783795734486200807187 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{\sin y}{y} \cdot x}{z}\\ \mathbf{elif}\;z \le 4.576842764057799981661987703139532669264 \cdot 10^{-157}:\\ \;\;\;\;\left(\frac{1}{z} \cdot \frac{\sin y}{y}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{\sin y}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(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))