Average Error: 2.9 → 1.2
Time: 8.7s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -5.83744516104687908 \cdot 10^{-226} \lor \neg \left(x \le 2.8660794228489788 \cdot 10^{-87}\right):\\ \;\;\;\;\frac{x \cdot \frac{\sqrt[3]{1}}{\frac{y}{\sin y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -5.83744516104687908 \cdot 10^{-226} \lor \neg \left(x \le 2.8660794228489788 \cdot 10^{-87}\right):\\
\;\;\;\;\frac{x \cdot \frac{\sqrt[3]{1}}{\frac{y}{\sin y}}}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r422068 = x;
        double r422069 = y;
        double r422070 = sin(r422069);
        double r422071 = r422070 / r422069;
        double r422072 = r422068 * r422071;
        double r422073 = z;
        double r422074 = r422072 / r422073;
        return r422074;
}
↓
double f(double x, double y, double z) {
        double r422075 = x;
        double r422076 = -5.837445161046879e-226;
        bool r422077 = r422075 <= r422076;
        double r422078 = 2.866079422848979e-87;
        bool r422079 = r422075 <= r422078;
        double r422080 = !r422079;
        bool r422081 = r422077 || r422080;
        double r422082 = 1.0;
        double r422083 = cbrt(r422082);
        double r422084 = y;
        double r422085 = sin(r422084);
        double r422086 = r422084 / r422085;
        double r422087 = r422083 / r422086;
        double r422088 = r422075 * r422087;
        double r422089 = z;
        double r422090 = r422088 / r422089;
        double r422091 = r422082 / r422086;
        double r422092 = r422091 / r422089;
        double r422093 = r422075 * r422092;
        double r422094 = r422081 ? r422090 : r422093;
        return r422094;
}

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

Original2.9
Target0.3
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -5.837445161046879e-226 or 2.866079422848979e-87 < x

    1. Initial program 1.5

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

    3. Applied clear-num1.6

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

    5. Applied *-un-lft-identity1.6

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

    6. Applied *-un-lft-identity1.6

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

    7. Applied times-frac1.6

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

    8. Applied add-cube-cbrt1.6

      \[\leadsto \frac{x \cdot \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{1}{1} \cdot \frac{y}{\sin y}}}{z}\]

    9. Applied times-frac1.6

      \[\leadsto \frac{x \cdot \color{blue}{\left(\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{1}{1}} \cdot \frac{\sqrt[3]{1}}{\frac{y}{\sin y}}\right)}}{z}\]

    10. Applied associate-*r*1.6

      \[\leadsto \frac{\color{blue}{\left(x \cdot \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{1}{1}}\right) \cdot \frac{\sqrt[3]{1}}{\frac{y}{\sin y}}}}{z}\]

    11. Simplified1.6

      \[\leadsto \frac{\color{blue}{x} \cdot \frac{\sqrt[3]{1}}{\frac{y}{\sin y}}}{z}\]

    if -5.837445161046879e-226 < x < 2.866079422848979e-87

    1. Initial program 6.7

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

    3. Applied *-un-lft-identity6.7

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

    4. Applied times-frac0.2

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

    5. Simplified0.2

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

    7. Applied clear-num0.2

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -5.83744516104687908 \cdot 10^{-226} \lor \neg \left(x \le 2.8660794228489788 \cdot 10^{-87}\right):\\ \;\;\;\;\frac{x \cdot \frac{\sqrt[3]{1}}{\frac{y}{\sin y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 
(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))