Average Error: 0.0 → 0.0
Time: 5.8s
Precision: binary64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\sqrt[3]{\frac{\sinh y}{y}} \cdot \left(\left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right) \cdot \cos x\right)\]
\cos x \cdot \frac{\sinh y}{y}
↓
\sqrt[3]{\frac{\sinh y}{y}} \cdot \left(\left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right) \cdot \cos x\right)
(FPCore (x y) :precision binary64 (* (cos x) (/ (sinh y) y)))
↓
(FPCore (x y)
 :precision binary64
 (*
  (cbrt (/ (sinh y) y))
  (* (* (cbrt (/ (sinh y) y)) (cbrt (/ (sinh y) y))) (cos x))))
double code(double x, double y) {
	return cos(x) * (sinh(y) / y);
}
↓
double code(double x, double y) {
	return cbrt(sinh(y) / y) * ((cbrt(sinh(y) / y) * cbrt(sinh(y) / y)) * cos(x));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  3. Applied add-cube-cbrt_binary640.0

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

  4. Applied associate-*r*_binary640.0

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

  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

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

Reproduce

herbie shell --seed 2020260 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))