Average Error: 0.0 → 0.0
Time: 17.7s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sqrt{\frac{\sinh y}{y}} \cdot \cos x\right) \cdot \sqrt{\frac{\sinh y}{y}}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\left(\sqrt{\frac{\sinh y}{y}} \cdot \cos x\right) \cdot \sqrt{\frac{\sinh y}{y}}
double f(double x, double y) {
        double r133783 = x;
        double r133784 = cos(r133783);
        double r133785 = y;
        double r133786 = sinh(r133785);
        double r133787 = r133786 / r133785;
        double r133788 = r133784 * r133787;
        return r133788;
}
↓
double f(double x, double y) {
        double r133789 = y;
        double r133790 = sinh(r133789);
        double r133791 = r133790 / r133789;
        double r133792 = sqrt(r133791);
        double r133793 = x;
        double r133794 = cos(r133793);
        double r133795 = r133792 * r133794;
        double r133796 = r133795 * r133792;
        return r133796;
}

Error

Bits error versus x

Bits error versus y

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Results

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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. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019198 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  (* (cos x) (/ (sinh y) y)))