Average Error: 0.0 → 0.1
Time: 13.2s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\sin x \cdot \left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)\right)\]
\sin x \cdot \frac{\sinh y}{y}
↓
\sin x \cdot \left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)\right)
double f(double x, double y) {
        double r116670 = x;
        double r116671 = sin(r116670);
        double r116672 = y;
        double r116673 = sinh(r116672);
        double r116674 = r116673 / r116672;
        double r116675 = r116671 * r116674;
        return r116675;
}
↓
double f(double x, double y) {
        double r116676 = x;
        double r116677 = sin(r116676);
        double r116678 = y;
        double r116679 = sinh(r116678);
        double r116680 = r116679 / r116678;
        double r116681 = cbrt(r116680);
        double r116682 = r116681 * r116681;
        double r116683 = r116681 * r116682;
        double r116684 = r116677 * r116683;
        return r116684;
}

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-cube-cbrt0.1

    \[\leadsto \sin x \cdot \color{blue}{\left(\left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right) \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)}\]

  4. Final simplification0.1

    \[\leadsto \sin x \cdot \left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)\right)\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  (* (sin x) (/ (sinh y) y)))