Average Error: 0.0 → 0.1
Time: 4.3s
Precision: binary64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\cos x \cdot \sqrt[3]{{\left(\frac{\sinh y}{y}\right)}^{3}}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\cos x \cdot \sqrt[3]{{\left(\frac{\sinh y}{y}\right)}^{3}}
double code(double x, double y) {
	return ((double) (((double) cos(x)) * (((double) sinh(y)) / y)));
}
↓
double code(double x, double y) {
	return ((double) (((double) cos(x)) * ((double) cbrt(((double) pow((((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

    \[\cos x \cdot \frac{\sinh y}{y}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube41.9

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

  4. Applied add-cbrt-cube41.5

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

  5. Applied cbrt-undiv41.5

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020196 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))