Average Error: 0.0 → 0.3
Time: 17.1s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sinh y \cdot \cos x\right) \cdot \frac{1}{y}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\left(\sinh y \cdot \cos x\right) \cdot \frac{1}{y}
double f(double x, double y) {
        double r125055 = x;
        double r125056 = cos(r125055);
        double r125057 = y;
        double r125058 = sinh(r125057);
        double r125059 = r125058 / r125057;
        double r125060 = r125056 * r125059;
        return r125060;
}
↓
double f(double x, double y) {
        double r125061 = y;
        double r125062 = sinh(r125061);
        double r125063 = x;
        double r125064 = cos(r125063);
        double r125065 = r125062 * r125064;
        double r125066 = 1.0;
        double r125067 = r125066 / r125061;
        double r125068 = r125065 * r125067;
        return r125068;
}

Error

Bits error versus x

Bits error versus y

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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 div-inv0.2

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

  4. Applied associate-*r*0.3

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

  5. Simplified0.3

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

  6. Final simplification0.3

    \[\leadsto \left(\sinh y \cdot \cos x\right) \cdot \frac{1}{y}\]

Reproduce

herbie shell --seed 2019208 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))