Average Error: 2.9 → 0.9
Time: 8.2s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -6.6091788831885175 \cdot 10^{198}:\\ \;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\ \mathbf{elif}\;z \le 8.27444862348079715 \cdot 10^{120}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -6.6091788831885175 \cdot 10^{198}:\\
\;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\

\mathbf{elif}\;z \le 8.27444862348079715 \cdot 10^{120}:\\
\;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r483543 = x;
        double r483544 = y;
        double r483545 = sin(r483544);
        double r483546 = r483545 / r483544;
        double r483547 = r483543 * r483546;
        double r483548 = z;
        double r483549 = r483547 / r483548;
        return r483549;
}
↓
double f(double x, double y, double z) {
        double r483550 = z;
        double r483551 = -6.609178883188517e+198;
        bool r483552 = r483550 <= r483551;
        double r483553 = x;
        double r483554 = y;
        double r483555 = sin(r483554);
        double r483556 = 1.0;
        double r483557 = r483556 / r483554;
        double r483558 = r483555 * r483557;
        double r483559 = r483553 * r483558;
        double r483560 = r483559 / r483550;
        double r483561 = 8.274448623480797e+120;
        bool r483562 = r483550 <= r483561;
        double r483563 = r483555 / r483554;
        double r483564 = r483550 / r483563;
        double r483565 = r483553 / r483564;
        double r483566 = r483554 / r483555;
        double r483567 = r483556 / r483566;
        double r483568 = r483553 * r483567;
        double r483569 = r483568 / r483550;
        double r483570 = r483562 ? r483565 : r483569;
        double r483571 = r483552 ? r483560 : r483570;
        return r483571;
}

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
Target0.2
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -6.609178883188517e+198

    1. Initial program 0.1

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

    3. Applied div-inv0.1

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

    if -6.609178883188517e+198 < z < 8.274448623480797e+120

    1. Initial program 3.9

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

    3. Applied clear-num3.9

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

    5. Applied associate-/l*1.3

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

    6. Simplified1.2

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

    if 8.274448623480797e+120 < z

    1. Initial program 0.1

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

    3. Applied clear-num0.1

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.6091788831885175 \cdot 10^{198}:\\ \;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\ \mathbf{elif}\;z \le 8.27444862348079715 \cdot 10^{120}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(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))