Average Error: 0.0 → 0.1
Time: 14.7s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \left(\left(\sqrt[3]{\sqrt{\frac{\sinh y}{y}}} \cdot \sqrt[3]{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt[3]{\sqrt{\frac{\sinh y}{y}}}\right)\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \left(\left(\sqrt[3]{\sqrt{\frac{\sinh y}{y}}} \cdot \sqrt[3]{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt[3]{\sqrt{\frac{\sinh y}{y}}}\right)
double f(double x, double y) {
        double r148975 = x;
        double r148976 = sin(r148975);
        double r148977 = y;
        double r148978 = sinh(r148977);
        double r148979 = r148978 / r148977;
        double r148980 = r148976 * r148979;
        return r148980;
}
↓
double f(double x, double y) {
        double r148981 = x;
        double r148982 = sin(r148981);
        double r148983 = y;
        double r148984 = sinh(r148983);
        double r148985 = r148984 / r148983;
        double r148986 = sqrt(r148985);
        double r148987 = r148982 * r148986;
        double r148988 = cbrt(r148986);
        double r148989 = r148988 * r148988;
        double r148990 = r148989 * r148988;
        double r148991 = r148987 * r148990;
        return r148991;
}

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. Applied associate-*r*0.0

    \[\leadsto \color{blue}{\left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt{\frac{\sinh y}{y}}}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))