Average Error: 0.0 → 0.0
Time: 5.2s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\cos x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt{\frac{\sinh y}{y}}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\left(\cos x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt{\frac{\sinh y}{y}}
double f(double x, double y) {
        double r160709 = x;
        double r160710 = cos(r160709);
        double r160711 = y;
        double r160712 = sinh(r160711);
        double r160713 = r160712 / r160711;
        double r160714 = r160710 * r160713;
        return r160714;
}
↓
double f(double x, double y) {
        double r160715 = x;
        double r160716 = cos(r160715);
        double r160717 = y;
        double r160718 = sinh(r160717);
        double r160719 = r160718 / r160717;
        double r160720 = sqrt(r160719);
        double r160721 = r160716 * r160720;
        double r160722 = r160721 * r160720;
        return r160722;
}

Error

Bits error versus x

Bits error versus y

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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. Applied associate-*r*0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020065 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))