Average Error: 0.0 → 0.0
Time: 19.3s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \cos x\]
\cos x \cdot \frac{\sinh y}{y}
↓
\left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \cos x
double f(double x, double y) {
        double r5088323 = x;
        double r5088324 = cos(r5088323);
        double r5088325 = y;
        double r5088326 = sinh(r5088325);
        double r5088327 = r5088326 / r5088325;
        double r5088328 = r5088324 * r5088327;
        return r5088328;
}
↓
double f(double x, double y) {
        double r5088329 = y;
        double r5088330 = sinh(r5088329);
        double r5088331 = r5088330 / r5088329;
        double r5088332 = sqrt(r5088331);
        double r5088333 = r5088332 * r5088332;
        double r5088334 = x;
        double r5088335 = cos(r5088334);
        double r5088336 = r5088333 * r5088335;
        return r5088336;
}

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 add-sqr-sqrt0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  (* (cos x) (/ (sinh y) y)))