Average Error: 0.0 → 0.0
Time: 22.2s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sin x\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sin x
double f(double x, double y) {
        double r7455796 = x;
        double r7455797 = sin(r7455796);
        double r7455798 = y;
        double r7455799 = sinh(r7455798);
        double r7455800 = r7455799 / r7455798;
        double r7455801 = r7455797 * r7455800;
        return r7455801;
}
↓
double f(double x, double y) {
        double r7455802 = y;
        double r7455803 = sinh(r7455802);
        double r7455804 = r7455803 / r7455802;
        double r7455805 = sqrt(r7455804);
        double r7455806 = r7455805 * r7455805;
        double r7455807 = x;
        double r7455808 = sin(r7455807);
        double r7455809 = r7455806 * r7455808;
        return r7455809;
}

Error

Bits error versus x

Bits error versus y

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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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  (* (sin x) (/ (sinh y) y)))