Average Error: 2.8 → 1.5
Time: 18.5s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -7744513270.8935337066650390625:\\ \;\;\;\;\frac{\frac{\sin y \cdot x}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;-x \cdot \frac{\frac{\sin y}{y}}{-z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -7744513270.8935337066650390625:\\
\;\;\;\;\frac{\frac{\sin y \cdot x}{y}}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r681657 = x;
        double r681658 = y;
        double r681659 = sin(r681658);
        double r681660 = r681659 / r681658;
        double r681661 = r681657 * r681660;
        double r681662 = z;
        double r681663 = r681661 / r681662;
        return r681663;
}
↓
double f(double x, double y, double z) {
        double r681664 = x;
        double r681665 = -7744513270.893534;
        bool r681666 = r681664 <= r681665;
        double r681667 = y;
        double r681668 = sin(r681667);
        double r681669 = r681668 * r681664;
        double r681670 = r681669 / r681667;
        double r681671 = z;
        double r681672 = r681670 / r681671;
        double r681673 = r681668 / r681667;
        double r681674 = -r681671;
        double r681675 = r681673 / r681674;
        double r681676 = r681664 * r681675;
        double r681677 = -r681676;
        double r681678 = r681666 ? r681672 : r681677;
        return r681678;
}

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
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;z \lt -4.217372020342714661850238929213415773451 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.446702369113811028051510715777703865332 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -7744513270.893534

    1. Initial program 0.2

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

    3. Applied associate-*r/0.3

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

    if -7744513270.893534 < x

    1. Initial program 3.5

      \[\frac{x \cdot \frac{\sin y}{y}}{z}\]

    2. Simplified1.9

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

    4. Applied frac-2neg1.9

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

    5. Simplified1.9

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -7744513270.8935337066650390625:\\ \;\;\;\;\frac{\frac{\sin y \cdot x}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;-x \cdot \frac{\frac{\sin y}{y}}{-z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"

  :herbie-target
  (if (< z -4.2173720203427147e-29) (/ (* x (/ 1.0 (/ y (sin y)))) z) (if (< z 4.446702369113811e+64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1.0 (/ y (sin y)))) z)))

  (/ (* x (/ (sin y) y)) z))