Average Error: 0.0 → 0.0
Time: 4.7s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\frac{\cos x}{\frac{y}{\sinh y}}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\frac{\cos x}{\frac{y}{\sinh y}}
double f(double x, double y) {
        double r126601 = x;
        double r126602 = cos(r126601);
        double r126603 = y;
        double r126604 = sinh(r126603);
        double r126605 = r126604 / r126603;
        double r126606 = r126602 * r126605;
        return r126606;
}
↓
double f(double x, double y) {
        double r126607 = x;
        double r126608 = cos(r126607);
        double r126609 = y;
        double r126610 = sinh(r126609);
        double r126611 = r126609 / r126610;
        double r126612 = r126608 / r126611;
        return r126612;
}

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 associate-*r/0.1

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

  5. Applied associate-/l*0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020081 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))