Average Error: 0.0 → 0.1
Time: 22.6s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\frac{\sin x}{\sqrt[3]{\frac{y}{\sinh y} \cdot \left(\frac{y}{\sinh y} \cdot \frac{y}{\sinh y}\right)}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\frac{\sin x}{\sqrt[3]{\frac{y}{\sinh y} \cdot \left(\frac{y}{\sinh y} \cdot \frac{y}{\sinh y}\right)}}
double f(double x, double y) {
        double r9683684 = x;
        double r9683685 = sin(r9683684);
        double r9683686 = y;
        double r9683687 = sinh(r9683686);
        double r9683688 = r9683687 / r9683686;
        double r9683689 = r9683685 * r9683688;
        return r9683689;
}
↓
double f(double x, double y) {
        double r9683690 = x;
        double r9683691 = sin(r9683690);
        double r9683692 = y;
        double r9683693 = sinh(r9683692);
        double r9683694 = r9683692 / r9683693;
        double r9683695 = r9683694 * r9683694;
        double r9683696 = r9683694 * r9683695;
        double r9683697 = cbrt(r9683696);
        double r9683698 = r9683691 / r9683697;
        return r9683698;
}

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. Taylor expanded around inf 58.7

    \[\leadsto \color{blue}{\frac{\frac{1}{2} \cdot \left(\sin x \cdot e^{y}\right) - \frac{1}{2} \cdot \left(\sin x \cdot e^{-y}\right)}{y}}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{\frac{\sin x}{\frac{y}{\sinh y}}}\]
  4. Using strategy rm

  5. Applied add-cbrt-cube39.9

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

  6. Applied add-cbrt-cube40.3

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

  7. Applied cbrt-undiv40.3

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  (* (sin x) (/ (sinh y) y)))