Average Error: 0.0 → 0.0
Time: 22.7s
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 r7860050 = x;
        double r7860051 = sin(r7860050);
        double r7860052 = y;
        double r7860053 = sinh(r7860052);
        double r7860054 = r7860053 / r7860052;
        double r7860055 = r7860051 * r7860054;
        return r7860055;
}
↓
double f(double x, double y) {
        double r7860056 = y;
        double r7860057 = sinh(r7860056);
        double r7860058 = r7860057 / r7860056;
        double r7860059 = sqrt(r7860058);
        double r7860060 = r7860059 * r7860059;
        double r7860061 = x;
        double r7860062 = sin(r7860061);
        double r7860063 = r7860060 * r7860062;
        return r7860063;
}

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 2019162 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  (* (sin x) (/ (sinh y) y)))