Average Error: 0.0 → 0.1
Time: 12.2s
Precision: binary64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\sin x \cdot \sqrt[3]{{\left(\frac{\sinh y}{y}\right)}^{3}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\sin x \cdot \sqrt[3]{{\left(\frac{\sinh y}{y}\right)}^{3}}
double code(double x, double y) {
	return ((double) (((double) sin(x)) * ((double) (((double) sinh(y)) / y))));
}
↓
double code(double x, double y) {
	return ((double) (((double) sin(x)) * ((double) cbrt(((double) pow(((double) (((double) sinh(y)) / y)), 3.0))))));
}

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-cube41.5

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

  4. Applied add-cbrt-cube41.0

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

  5. Applied cbrt-undiv41.0

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020163 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))