Average Error: 2.7 → 1.3
Time: 16.8s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le 24.59938632289427218324817658867686986923:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le 24.59938632289427218324817658867686986923:\\
\;\;\;\;\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 r296779 = x;
        double r296780 = y;
        double r296781 = sin(r296780);
        double r296782 = r296781 / r296780;
        double r296783 = r296779 * r296782;
        double r296784 = z;
        double r296785 = r296783 / r296784;
        return r296785;
}
↓
double f(double x, double y, double z) {
        double r296786 = x;
        double r296787 = 24.599386322894272;
        bool r296788 = r296786 <= r296787;
        double r296789 = z;
        double r296790 = y;
        double r296791 = sin(r296790);
        double r296792 = r296791 / r296790;
        double r296793 = r296789 / r296792;
        double r296794 = r296786 / r296793;
        double r296795 = r296786 * r296791;
        double r296796 = r296795 / r296790;
        double r296797 = r296796 / r296789;
        double r296798 = r296788 ? r296794 : r296797;
        return r296798;
}

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
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;z \lt -4.217372020342714661850238929213415773451 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < 24.599386322894272

    1. Initial program 3.4

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

    3. Applied clear-num3.9

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

    5. Applied *-un-lft-identity3.9

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

    6. Applied times-frac2.3

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

    7. Applied associate-/r*1.7

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

    8. Simplified1.6

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

    if 24.599386322894272 < x

    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 associate-/r*0.2

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

    5. Simplified0.2

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le 24.59938632289427218324817658867686986923:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{\sin y}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \sin y}{y}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(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))