Average Error: 0.0 → 0.0
Time: 5.4s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\cos x \cdot \frac{1}{\sqrt{\frac{y}{\sinh y}} \cdot \sqrt{\frac{y}{\sinh y}}}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\cos x \cdot \frac{1}{\sqrt{\frac{y}{\sinh y}} \cdot \sqrt{\frac{y}{\sinh y}}}
double f(double x, double y) {
        double r132971 = x;
        double r132972 = cos(r132971);
        double r132973 = y;
        double r132974 = sinh(r132973);
        double r132975 = r132974 / r132973;
        double r132976 = r132972 * r132975;
        return r132976;
}
↓
double f(double x, double y) {
        double r132977 = x;
        double r132978 = cos(r132977);
        double r132979 = 1.0;
        double r132980 = y;
        double r132981 = sinh(r132980);
        double r132982 = r132980 / r132981;
        double r132983 = sqrt(r132982);
        double r132984 = r132983 * r132983;
        double r132985 = r132979 / r132984;
        double r132986 = r132978 * r132985;
        return r132986;
}

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 clear-num0.0

    \[\leadsto \cos x \cdot \color{blue}{\frac{1}{\frac{y}{\sinh y}}}\]
  4. Using strategy rm

  5. Applied add-sqr-sqrt0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020027 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))