Average Error: 2.8 → 0.3
Time: 8.3s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -4.99748861820327434 \cdot 10^{41} \lor \neg \left(z \le 5.7247708611607825 \cdot 10^{66}\right):\\ \;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -4.99748861820327434 \cdot 10^{41} \lor \neg \left(z \le 5.7247708611607825 \cdot 10^{66}\right):\\
\;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r539622 = x;
        double r539623 = y;
        double r539624 = sin(r539623);
        double r539625 = r539624 / r539623;
        double r539626 = r539622 * r539625;
        double r539627 = z;
        double r539628 = r539626 / r539627;
        return r539628;
}
↓
double f(double x, double y, double z) {
        double r539629 = z;
        double r539630 = -4.997488618203274e+41;
        bool r539631 = r539629 <= r539630;
        double r539632 = 5.7247708611607825e+66;
        bool r539633 = r539629 <= r539632;
        double r539634 = !r539633;
        bool r539635 = r539631 || r539634;
        double r539636 = x;
        double r539637 = y;
        double r539638 = sin(r539637);
        double r539639 = 1.0;
        double r539640 = r539639 / r539637;
        double r539641 = r539638 * r539640;
        double r539642 = r539636 * r539641;
        double r539643 = r539642 / r539629;
        double r539644 = r539637 / r539638;
        double r539645 = r539629 * r539644;
        double r539646 = r539636 / r539645;
        double r539647 = r539635 ? r539643 : r539646;
        return r539647;
}

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

Original2.8
Target0.3
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -4.997488618203274e+41 or 5.7247708611607825e+66 < z

    1. Initial program 0.1

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

    3. Applied div-inv0.2

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

    if -4.997488618203274e+41 < z < 5.7247708611607825e+66

    1. Initial program 5.0

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

    3. Applied associate-/l*0.4

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

    4. Simplified0.4

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -4.99748861820327434 \cdot 10^{41} \lor \neg \left(z \le 5.7247708611607825 \cdot 10^{66}\right):\\ \;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020043 +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))