Average Error: 2.7 → 2.0
Time: 4.2s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -4.40806905865946009 \cdot 10^{69}:\\ \;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -4.40806905865946009 \cdot 10^{69}:\\
\;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r458873 = x;
        double r458874 = y;
        double r458875 = sin(r458874);
        double r458876 = r458875 / r458874;
        double r458877 = r458873 * r458876;
        double r458878 = z;
        double r458879 = r458877 / r458878;
        return r458879;
}
↓
double f(double x, double y, double z) {
        double r458880 = z;
        double r458881 = -4.40806905865946e+69;
        bool r458882 = r458880 <= r458881;
        double r458883 = x;
        double r458884 = y;
        double r458885 = sin(r458884);
        double r458886 = r458883 * r458885;
        double r458887 = r458886 / r458884;
        double r458888 = r458887 / r458880;
        double r458889 = r458885 / r458884;
        double r458890 = r458880 / r458889;
        double r458891 = r458883 / r458890;
        double r458892 = r458882 ? r458888 : r458891;
        return r458892;
}

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
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -4.40806905865946e+69

    1. Initial program 0.1

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

    3. Applied associate-*r/1.7

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

    if -4.40806905865946e+69 < z

    1. Initial program 3.3

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

    3. Applied associate-/l*2.0

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

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -4.40806905865946009 \cdot 10^{69}:\\ \;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 +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))