Average Error: 2.7 → 0.5
Time: 3.8s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -9143070719594530171069555313882934804480 \lor \neg \left(z \le 1.385132396102934305433311993086749775457 \cdot 10^{108}\right):\\ \;\;\;\;\left(x \cdot \frac{\sin y}{y}\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -9143070719594530171069555313882934804480 \lor \neg \left(z \le 1.385132396102934305433311993086749775457 \cdot 10^{108}\right):\\
\;\;\;\;\left(x \cdot \frac{\sin y}{y}\right) \cdot \frac{1}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r512905 = x;
        double r512906 = y;
        double r512907 = sin(r512906);
        double r512908 = r512907 / r512906;
        double r512909 = r512905 * r512908;
        double r512910 = z;
        double r512911 = r512909 / r512910;
        return r512911;
}
↓
double f(double x, double y, double z) {
        double r512912 = z;
        double r512913 = -9.14307071959453e+39;
        bool r512914 = r512912 <= r512913;
        double r512915 = 1.3851323961029343e+108;
        bool r512916 = r512912 <= r512915;
        double r512917 = !r512916;
        bool r512918 = r512914 || r512917;
        double r512919 = x;
        double r512920 = y;
        double r512921 = sin(r512920);
        double r512922 = r512921 / r512920;
        double r512923 = r512919 * r512922;
        double r512924 = 1.0;
        double r512925 = r512924 / r512912;
        double r512926 = r512923 * r512925;
        double r512927 = r512912 / r512922;
        double r512928 = r512919 / r512927;
        double r512929 = r512918 ? r512926 : r512928;
        return r512929;
}

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
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;z \lt -4.217372020342714661850238929213415773451 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -9.14307071959453e+39 or 1.3851323961029343e+108 < z

    1. Initial program 0.1

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

    3. Applied div-inv0.2

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

    if -9.14307071959453e+39 < z < 1.3851323961029343e+108

    1. Initial program 4.5

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

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

      \[\leadsto \frac{\color{blue}{1 \cdot \left(x \cdot \frac{\sin y}{y}\right)}}{z}\]
    4. Using strategy rm

    5. Applied clear-num4.8

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

    6. Simplified4.8

      \[\leadsto \frac{1}{\color{blue}{\frac{z}{x \cdot \frac{\sin y}{y}}}}\]
    7. Using strategy rm

    8. Applied *-un-lft-identity4.8

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

    9. Applied times-frac1.1

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

    10. Applied associate-/r*0.7

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

    11. Simplified0.6

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -9143070719594530171069555313882934804480 \lor \neg \left(z \le 1.385132396102934305433311993086749775457 \cdot 10^{108}\right):\\ \;\;\;\;\left(x \cdot \frac{\sin y}{y}\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 
(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))