Average Error: 2.7 → 3.2
Time: 43.6s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.614448996584022 \cdot 10^{+210}:\\ \;\;\;\;\frac{\frac{\sin y}{\frac{y}{x}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{1}{\frac{y}{\sin y}}}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.614448996584022 \cdot 10^{+210}:\\
\;\;\;\;\frac{\frac{\sin y}{\frac{y}{x}}}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r23866760 = x;
        double r23866761 = y;
        double r23866762 = sin(r23866761);
        double r23866763 = r23866762 / r23866761;
        double r23866764 = r23866760 * r23866763;
        double r23866765 = z;
        double r23866766 = r23866764 / r23866765;
        return r23866766;
}
↓
double f(double x, double y, double z) {
        double r23866767 = z;
        double r23866768 = -1.614448996584022e+210;
        bool r23866769 = r23866767 <= r23866768;
        double r23866770 = y;
        double r23866771 = sin(r23866770);
        double r23866772 = x;
        double r23866773 = r23866770 / r23866772;
        double r23866774 = r23866771 / r23866773;
        double r23866775 = r23866774 / r23866767;
        double r23866776 = 1.0;
        double r23866777 = r23866770 / r23866771;
        double r23866778 = r23866776 / r23866777;
        double r23866779 = r23866767 / r23866778;
        double r23866780 = r23866772 / r23866779;
        double r23866781 = r23866769 ? r23866775 : r23866780;
        return r23866781;
}

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

Original2.7
Target0.3
Herbie3.2
\[\begin{array}{l} \mathbf{if}\;z \lt -4.2173720203427147 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.614448996584022e+210

    1. Initial program 0.1

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

    3. Applied *-un-lft-identity0.1

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

    4. Applied associate-/r*0.1

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

    5. Simplified8.4

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

    if -1.614448996584022e+210 < z

    1. Initial program 3.0

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

    3. Applied associate-/l*2.7

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

    5. Applied clear-num2.7

      \[\leadsto \frac{x}{\frac{z}{\color{blue}{\frac{1}{\frac{y}{\sin y}}}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.614448996584022 \cdot 10^{+210}:\\ \;\;\;\;\frac{\frac{\sin y}{\frac{y}{x}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{1}{\frac{y}{\sin y}}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(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))