Average Error: 0.0 → 0.0
Time: 5.6s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\frac{\sin x}{\frac{y}{\sinh y}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\frac{\sin x}{\frac{y}{\sinh y}}
double f(double x, double y) {
        double r122912 = x;
        double r122913 = sin(r122912);
        double r122914 = y;
        double r122915 = sinh(r122914);
        double r122916 = r122915 / r122914;
        double r122917 = r122913 * r122916;
        return r122917;
}
↓
double f(double x, double y) {
        double r122918 = x;
        double r122919 = sin(r122918);
        double r122920 = y;
        double r122921 = sinh(r122920);
        double r122922 = r122920 / r122921;
        double r122923 = r122919 / r122922;
        return r122923;
}

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 associate-*r/14.0

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

  5. Applied associate-/l*0.0

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

  6. Final simplification0.0

    \[\leadsto \frac{\sin x}{\frac{y}{\sinh y}}\]

Reproduce

herbie shell --seed 2020089 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))