Average Error: 0.0 → 0.0
Time: 15.2s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\sqrt[3]{\frac{\sinh y}{y}} \cdot \left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \cos x\right)\right)\]
\cos x \cdot \frac{\sinh y}{y}
↓
\sqrt[3]{\frac{\sinh y}{y}} \cdot \left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \cos x\right)\right)
double f(double x, double y) {
        double r83927 = x;
        double r83928 = cos(r83927);
        double r83929 = y;
        double r83930 = sinh(r83929);
        double r83931 = r83930 / r83929;
        double r83932 = r83928 * r83931;
        return r83932;
}
↓
double f(double x, double y) {
        double r83933 = y;
        double r83934 = sinh(r83933);
        double r83935 = r83934 / r83933;
        double r83936 = cbrt(r83935);
        double r83937 = x;
        double r83938 = cos(r83937);
        double r83939 = r83936 * r83938;
        double r83940 = r83936 * r83939;
        double r83941 = r83936 * r83940;
        return r83941;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

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Derivation

  1. Initial program 0.0

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

  3. Applied add-cube-cbrt0.0

    \[\leadsto \cos x \cdot \color{blue}{\left(\left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right) \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)}\]
  4. Using strategy rm

  5. Applied associate-*r*0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  (* (cos x) (/ (sinh y) y)))