Average Error: 2.9 → 0.4
Time: 10.3s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -4.807101316999124 \cdot 10^{+93}:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;x \le 0.0015208711258388175:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{y}{\sin y}} \cdot x}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -4.807101316999124 \cdot 10^{+93}:\\
\;\;\;\;\frac{\frac{x}{\frac{y}{\sin y}}}{z}\\

\mathbf{elif}\;x \le 0.0015208711258388175:\\
\;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r8652524 = x;
        double r8652525 = y;
        double r8652526 = sin(r8652525);
        double r8652527 = r8652526 / r8652525;
        double r8652528 = r8652524 * r8652527;
        double r8652529 = z;
        double r8652530 = r8652528 / r8652529;
        return r8652530;
}
↓
double f(double x, double y, double z) {
        double r8652531 = x;
        double r8652532 = -4.807101316999124e+93;
        bool r8652533 = r8652531 <= r8652532;
        double r8652534 = y;
        double r8652535 = sin(r8652534);
        double r8652536 = r8652534 / r8652535;
        double r8652537 = r8652531 / r8652536;
        double r8652538 = z;
        double r8652539 = r8652537 / r8652538;
        double r8652540 = 0.0015208711258388175;
        bool r8652541 = r8652531 <= r8652540;
        double r8652542 = r8652535 / r8652534;
        double r8652543 = r8652538 / r8652542;
        double r8652544 = r8652531 / r8652543;
        double r8652545 = 1.0;
        double r8652546 = r8652545 / r8652536;
        double r8652547 = r8652546 * r8652531;
        double r8652548 = r8652547 / r8652538;
        double r8652549 = r8652541 ? r8652544 : r8652548;
        double r8652550 = r8652533 ? r8652539 : r8652549;
        return r8652550;
}

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

Original2.9
Target0.3
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;z \lt -4.2173720203427147 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -4.807101316999124e+93

    1. Initial program 0.2

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

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

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

    4. Applied times-frac8.5

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

    5. Simplified8.5

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

    7. Applied div-inv8.5

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

    9. Applied associate-*r/8.5

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

    10. Applied associate-*r/0.2

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

    11. Simplified0.3

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

    if -4.807101316999124e+93 < x < 0.0015208711258388175

    1. Initial program 4.4

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

    3. Applied associate-/l*0.4

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

    if 0.0015208711258388175 < x

    1. Initial program 0.2

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

    3. Applied clear-num0.3

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -4.807101316999124 \cdot 10^{+93}:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;x \le 0.0015208711258388175:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{y}{\sin y}} \cdot x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"

  :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))