Average Error: 2.7 → 1.0
Time: 4.5s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -6.9358893171807734 \cdot 10^{55} \lor \neg \left(z \le 3.7079327528267037 \cdot 10^{92}\right):\\ \;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{\sin y}{y}}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -6.9358893171807734 \cdot 10^{55} \lor \neg \left(z \le 3.7079327528267037 \cdot 10^{92}\right):\\
\;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r494770 = x;
        double r494771 = y;
        double r494772 = sin(r494771);
        double r494773 = r494772 / r494771;
        double r494774 = r494770 * r494773;
        double r494775 = z;
        double r494776 = r494774 / r494775;
        return r494776;
}
↓
double f(double x, double y, double z) {
        double r494777 = z;
        double r494778 = -6.935889317180773e+55;
        bool r494779 = r494777 <= r494778;
        double r494780 = 3.7079327528267037e+92;
        bool r494781 = r494777 <= r494780;
        double r494782 = !r494781;
        bool r494783 = r494779 || r494782;
        double r494784 = x;
        double r494785 = y;
        double r494786 = sin(r494785);
        double r494787 = r494784 * r494786;
        double r494788 = r494787 / r494785;
        double r494789 = r494788 / r494777;
        double r494790 = r494786 / r494785;
        double r494791 = r494790 / r494777;
        double r494792 = r494784 * r494791;
        double r494793 = r494783 ? r494789 : r494792;
        return r494793;
}

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
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -6.935889317180773e+55 or 3.7079327528267037e+92 < z

    1. Initial program 0.1

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

    3. Applied associate-*r/1.6

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

    if -6.935889317180773e+55 < z < 3.7079327528267037e+92

    1. Initial program 4.5

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

    3. Applied *-un-lft-identity4.5

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

    4. Applied times-frac0.6

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

    5. Simplified0.6

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.9358893171807734 \cdot 10^{55} \lor \neg \left(z \le 3.7079327528267037 \cdot 10^{92}\right):\\ \;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{\sin y}{y}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 +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))