Average Error: 0.0 → 0.1
Time: 17.3s
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 r8075742 = x;
        double r8075743 = sin(r8075742);
        double r8075744 = y;
        double r8075745 = sinh(r8075744);
        double r8075746 = r8075745 / r8075744;
        double r8075747 = r8075743 * r8075746;
        return r8075747;
}
↓
double f(double x, double y) {
        double r8075748 = x;
        double r8075749 = sin(r8075748);
        double r8075750 = y;
        double r8075751 = sinh(r8075750);
        double r8075752 = r8075750 / r8075751;
        double r8075753 = r8075752 * r8075752;
        double r8075754 = r8075752 * r8075753;
        double r8075755 = cbrt(r8075754);
        double r8075756 = r8075749 / r8075755;
        return r8075756;
}

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-cbrt-cube40.4

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

  4. Applied add-cbrt-cube40.3

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

  5. Applied cbrt-undiv40.3

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

  6. Applied add-cbrt-cube47.2

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

  7. Applied cbrt-unprod47.2

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

  8. Simplified19.6

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

  10. Applied frac-times19.6

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

  11. Applied frac-times19.7

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

  12. Applied cbrt-div19.7

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

  13. Simplified0.1

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

  14. 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 2019168 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  (* (sin x) (/ (sinh y) y)))