Average Error: 0.0 → 0.1
Time: 15.6s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\cos x \cdot \sqrt[3]{{\left(\frac{\sinh y}{y}\right)}^{3}}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\cos x \cdot \sqrt[3]{{\left(\frac{\sinh y}{y}\right)}^{3}}
double f(double x, double y) {
        double r116896 = x;
        double r116897 = cos(r116896);
        double r116898 = y;
        double r116899 = sinh(r116898);
        double r116900 = r116899 / r116898;
        double r116901 = r116897 * r116900;
        return r116901;
}
↓
double f(double x, double y) {
        double r116902 = x;
        double r116903 = cos(r116902);
        double r116904 = y;
        double r116905 = sinh(r116904);
        double r116906 = r116905 / r116904;
        double r116907 = 3.0;
        double r116908 = pow(r116906, r116907);
        double r116909 = cbrt(r116908);
        double r116910 = r116903 * r116909;
        return r116910;
}

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

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

  3. Applied add-cbrt-cube42.0

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

  4. Applied add-cbrt-cube41.5

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

  5. Applied cbrt-undiv41.5

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  (* (cos x) (/ (sinh y) y)))