Average Error: 0.0 → 0.0
Time: 27.8s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\sqrt{\frac{\sinh y}{y}} \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \sin x\right)\]
\sin x \cdot \frac{\sinh y}{y}
↓
\sqrt{\frac{\sinh y}{y}} \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \sin x\right)
double f(double x, double y) {
        double r8050897 = x;
        double r8050898 = sin(r8050897);
        double r8050899 = y;
        double r8050900 = sinh(r8050899);
        double r8050901 = r8050900 / r8050899;
        double r8050902 = r8050898 * r8050901;
        return r8050902;
}
↓
double f(double x, double y) {
        double r8050903 = y;
        double r8050904 = sinh(r8050903);
        double r8050905 = r8050904 / r8050903;
        double r8050906 = sqrt(r8050905);
        double r8050907 = x;
        double r8050908 = sin(r8050907);
        double r8050909 = r8050906 * r8050908;
        double r8050910 = r8050906 * r8050909;
        return r8050910;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Derivation

  1. Initial program 0.0

    \[\sin x \cdot \frac{\sinh y}{y}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

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

  4. Applied associate-*r*0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  (* (sin x) (/ (sinh y) y)))