Average Error: 0.0 → 0.0
Time: 26.8s
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 r138032 = x;
        double r138033 = cos(r138032);
        double r138034 = y;
        double r138035 = sinh(r138034);
        double r138036 = r138035 / r138034;
        double r138037 = r138033 * r138036;
        return r138037;
}
↓
double f(double x, double y) {
        double r138038 = x;
        double r138039 = cos(r138038);
        double r138040 = y;
        double r138041 = sinh(r138040);
        double r138042 = r138040 / r138041;
        double r138043 = r138039 / r138042;
        return r138043;
}

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 *-un-lft-identity0.0

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

  4. Applied associate-*l*0.0

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

  5. Simplified0.0

    \[\leadsto 1 \cdot \color{blue}{\frac{\cos x}{\frac{y}{\sinh y}}}\]

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))