Average Error: 2.8 → 0.5
Time: 4.3s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.0552052215129959 \cdot 10^{82}:\\ \;\;\;\;\left(x \cdot \frac{\sin y}{y}\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;x \le 3.1288782285340333 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.0552052215129959 \cdot 10^{82}:\\
\;\;\;\;\left(x \cdot \frac{\sin y}{y}\right) \cdot \frac{1}{z}\\

\mathbf{elif}\;x \le 3.1288782285340333 \cdot 10^{-49}:\\
\;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r331939 = x;
        double r331940 = y;
        double r331941 = sin(r331940);
        double r331942 = r331941 / r331940;
        double r331943 = r331939 * r331942;
        double r331944 = z;
        double r331945 = r331943 / r331944;
        return r331945;
}
↓
double f(double x, double y, double z) {
        double r331946 = x;
        double r331947 = -1.055205221512996e+82;
        bool r331948 = r331946 <= r331947;
        double r331949 = y;
        double r331950 = sin(r331949);
        double r331951 = r331950 / r331949;
        double r331952 = r331946 * r331951;
        double r331953 = 1.0;
        double r331954 = z;
        double r331955 = r331953 / r331954;
        double r331956 = r331952 * r331955;
        double r331957 = 3.1288782285340333e-49;
        bool r331958 = r331946 <= r331957;
        double r331959 = r331954 / r331951;
        double r331960 = r331946 / r331959;
        double r331961 = r331946 * r331950;
        double r331962 = r331961 / r331949;
        double r331963 = r331962 / r331954;
        double r331964 = r331958 ? r331960 : r331963;
        double r331965 = r331948 ? r331956 : r331964;
        return r331965;
}

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
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -1.055205221512996e+82

    1. Initial program 0.2

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

    3. Applied *-un-lft-identity0.2

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

    4. Applied times-frac6.9

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

    5. Simplified6.9

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

    7. Applied div-inv6.9

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

    8. Applied associate-*r*0.3

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

    if -1.055205221512996e+82 < x < 3.1288782285340333e-49

    1. Initial program 4.7

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

    3. Applied associate-/l*0.5

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

    if 3.1288782285340333e-49 < x

    1. Initial program 0.3

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

    3. Applied associate-*r/0.6

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.0552052215129959 \cdot 10^{82}:\\ \;\;\;\;\left(x \cdot \frac{\sin y}{y}\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;x \le 3.1288782285340333 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020003 
(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))