Average Error: 2.5 → 1.7
Time: 3.8s
Precision: 64
\[\frac{x \cdot \frac{\sin y}{y}}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le 1.5167308587843438 \cdot 10^{54}:\\ \;\;\;\;x \cdot \left(\frac{\sin y}{y} \cdot \frac{1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x \cdot \sin y\right) \cdot \frac{1}{y}}{z}\\ \end{array}\]
\frac{x \cdot \frac{\sin y}{y}}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le 1.5167308587843438 \cdot 10^{54}:\\
\;\;\;\;x \cdot \left(\frac{\sin y}{y} \cdot \frac{1}{z}\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{\left(x \cdot \sin y\right) \cdot \frac{1}{y}}{z}\\

\end{array}
double f(double x, double y, double z) {
        double r527953 = x;
        double r527954 = y;
        double r527955 = sin(r527954);
        double r527956 = r527955 / r527954;
        double r527957 = r527953 * r527956;
        double r527958 = z;
        double r527959 = r527957 / r527958;
        return r527959;
}
↓
double f(double x, double y, double z) {
        double r527960 = x;
        double r527961 = 1.5167308587843438e+54;
        bool r527962 = r527960 <= r527961;
        double r527963 = y;
        double r527964 = sin(r527963);
        double r527965 = r527964 / r527963;
        double r527966 = 1.0;
        double r527967 = z;
        double r527968 = r527966 / r527967;
        double r527969 = r527965 * r527968;
        double r527970 = r527960 * r527969;
        double r527971 = r527960 * r527964;
        double r527972 = r527966 / r527963;
        double r527973 = r527971 * r527972;
        double r527974 = r527973 / r527967;
        double r527975 = r527962 ? r527970 : r527974;
        return r527975;
}

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

Original2.5
Target0.3
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;z \lt -4.21737202034271466 \cdot 10^{-29}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \mathbf{elif}\;z \lt 4.44670236911381103 \cdot 10^{64}:\\ \;\;\;\;\frac{x}{z \cdot \frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{1}{\frac{y}{\sin y}}}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < 1.5167308587843438e+54

    1. Initial program 3.0

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

    3. Applied div-inv3.1

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

    5. Applied associate-*l*2.0

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

    if 1.5167308587843438e+54 < x

    1. Initial program 0.2

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

    3. Applied div-inv0.3

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

    4. Applied associate-*r*0.4

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le 1.5167308587843438 \cdot 10^{54}:\\ \;\;\;\;x \cdot \left(\frac{\sin y}{y} \cdot \frac{1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x \cdot \sin y\right) \cdot \frac{1}{y}}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020039 
(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))