Average Error: 0.0 → 0.0
Time: 10.5s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\frac{1}{\sqrt{\frac{y}{\sinh y}} \cdot \sqrt{\frac{y}{\sinh y}}} \cdot \cos x\]
\cos x \cdot \frac{\sinh y}{y}
↓
\frac{1}{\sqrt{\frac{y}{\sinh y}} \cdot \sqrt{\frac{y}{\sinh y}}} \cdot \cos x
double f(double x, double y) {
        double r1739024 = x;
        double r1739025 = cos(r1739024);
        double r1739026 = y;
        double r1739027 = sinh(r1739026);
        double r1739028 = r1739027 / r1739026;
        double r1739029 = r1739025 * r1739028;
        return r1739029;
}
↓
double f(double x, double y) {
        double r1739030 = 1.0;
        double r1739031 = y;
        double r1739032 = sinh(r1739031);
        double r1739033 = r1739031 / r1739032;
        double r1739034 = sqrt(r1739033);
        double r1739035 = r1739034 * r1739034;
        double r1739036 = r1739030 / r1739035;
        double r1739037 = x;
        double r1739038 = cos(r1739037);
        double r1739039 = r1739036 * r1739038;
        return r1739039;
}

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

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

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  (* (cos x) (/ (sinh y) y)))