Average Error: 0.0 → 0.0
Time: 8.6s
Precision: binary64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right) \cdot \cos x\right) \cdot \sqrt[3]{\frac{\sinh y}{y}}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\left(\left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right) \cdot \cos x\right) \cdot \sqrt[3]{\frac{\sinh y}{y}}
double code(double x, double y) {
	return ((double) (((double) cos(x)) * (((double) sinh(y)) / y)));
}
↓
double code(double x, double y) {
	return ((double) (((double) (((double) (((double) cbrt((((double) sinh(y)) / y))) * ((double) cbrt((((double) sinh(y)) / y))))) * ((double) cos(x)))) * ((double) cbrt((((double) sinh(y)) / y)))));
}

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-cube-cbrt0.0

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

  4. Applied associate-*r*0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020182 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))