Average Error: 0.0 → 0.1
Time: 33.5s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sin x \cdot \left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)\right) \cdot \sqrt[3]{\frac{\sinh y}{y}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\sin x \cdot \left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)\right) \cdot \sqrt[3]{\frac{\sinh y}{y}}
double f(double x, double y) {
        double r129588 = x;
        double r129589 = sin(r129588);
        double r129590 = y;
        double r129591 = sinh(r129590);
        double r129592 = r129591 / r129590;
        double r129593 = r129589 * r129592;
        return r129593;
}
↓
double f(double x, double y) {
        double r129594 = x;
        double r129595 = sin(r129594);
        double r129596 = y;
        double r129597 = sinh(r129596);
        double r129598 = r129597 / r129596;
        double r129599 = cbrt(r129598);
        double r129600 = r129599 * r129599;
        double r129601 = r129595 * r129600;
        double r129602 = r129601 * r129599;
        return r129602;
}

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. Applied associate-*r*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019326 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))