Average Error: 2.8 → 0.3
Time: 7.6s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -4.99748861820327434 \cdot 10^{41} \lor \neg \left(z \le 5.7247708611607825 \cdot 10^{66}\right):\\ \;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -4.99748861820327434 \cdot 10^{41} \lor \neg \left(z \le 5.7247708611607825 \cdot 10^{66}\right):\\
\;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r649651 = x;
        double r649652 = y;
        double r649653 = sin(r649652);
        double r649654 = r649653 / r649652;
        double r649655 = r649651 * r649654;
        double r649656 = z;
        double r649657 = r649655 / r649656;
        return r649657;
}
↓
double f(double x, double y, double z) {
        double r649658 = z;
        double r649659 = -4.997488618203274e+41;
        bool r649660 = r649658 <= r649659;
        double r649661 = 5.7247708611607825e+66;
        bool r649662 = r649658 <= r649661;
        double r649663 = !r649662;
        bool r649664 = r649660 || r649663;
        double r649665 = x;
        double r649666 = y;
        double r649667 = sin(r649666);
        double r649668 = 1.0;
        double r649669 = r649668 / r649666;
        double r649670 = r649667 * r649669;
        double r649671 = r649665 * r649670;
        double r649672 = r649671 / r649658;
        double r649673 = r649666 / r649667;
        double r649674 = r649658 * r649673;
        double r649675 = r649665 / r649674;
        double r649676 = r649664 ? r649672 : r649675;
        return r649676;
}

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
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -4.997488618203274e+41 or 5.7247708611607825e+66 < z

    1. Initial program 0.1

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

    3. Applied div-inv0.2

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

    if -4.997488618203274e+41 < z < 5.7247708611607825e+66

    1. Initial program 5.0

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

    3. Applied associate-/l*0.4

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

    4. Simplified0.4

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -4.99748861820327434 \cdot 10^{41} \lor \neg \left(z \le 5.7247708611607825 \cdot 10^{66}\right):\\ \;\;\;\;\frac{x \cdot \left(\sin y \cdot \frac{1}{y}\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020043 
(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))