Average Error: 0.0 → 0.1
Time: 33.8s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\sin x \cdot \left(\left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right) \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)\]
\sin x \cdot \frac{\sinh y}{y}
↓
\sin x \cdot \left(\left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right) \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)
double f(double x, double y) {
        double r92906 = x;
        double r92907 = sin(r92906);
        double r92908 = y;
        double r92909 = sinh(r92908);
        double r92910 = r92909 / r92908;
        double r92911 = r92907 * r92910;
        return r92911;
}
↓
double f(double x, double y) {
        double r92912 = x;
        double r92913 = sin(r92912);
        double r92914 = y;
        double r92915 = sinh(r92914);
        double r92916 = r92915 / r92914;
        double r92917 = cbrt(r92916);
        double r92918 = r92917 * r92917;
        double r92919 = r92918 * r92917;
        double r92920 = r92913 * r92919;
        return r92920;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  3. Applied add-cube-cbrt0.1

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

  4. Final simplification0.1

    \[\leadsto \sin x \cdot \left(\left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right) \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)\]

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))