Average Error: 0.0 → 0.1
Time: 4.0s
Precision: binary64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\sqrt[3]{\frac{\sinh y}{y}} \cdot \left(\sin x \cdot \left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)\right)\]
\sin x \cdot \frac{\sinh y}{y}
↓
\sqrt[3]{\frac{\sinh y}{y}} \cdot \left(\sin x \cdot \left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)\right)
double code(double x, double y) {
	return ((double) (((double) sin(x)) * (((double) sinh(y)) / y)));
}
↓
double code(double x, double y) {
	return ((double) (((double) cbrt((((double) sinh(y)) / y))) * ((double) (((double) sin(x)) * ((double) (((double) cbrt((((double) sinh(y)) / y))) * ((double) cbrt((((double) sinh(y)) / y)))))))));
}

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 Error: 0.0 bits

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

  3. Applied add-cube-cbrtError: 0.1 bits

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

  4. Applied associate-*r*Error: 0.1 bits

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

  5. Final simplificationError: 0.1 bits

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

Reproduce

herbie shell --seed 2020200 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))