Average Error: 0.0 → 0.1
Time: 31.5s
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 r93677 = x;
        double r93678 = sin(r93677);
        double r93679 = y;
        double r93680 = sinh(r93679);
        double r93681 = r93680 / r93679;
        double r93682 = r93678 * r93681;
        return r93682;
}
↓
double f(double x, double y) {
        double r93683 = x;
        double r93684 = sin(r93683);
        double r93685 = y;
        double r93686 = sinh(r93685);
        double r93687 = r93686 / r93685;
        double r93688 = cbrt(r93687);
        double r93689 = r93688 * r93688;
        double r93690 = r93684 * r93689;
        double r93691 = r93690 * r93688;
        return r93691;
}

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 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))