Average Error: 0.3 → 0.3
Time: 1.6s
Precision: binary64
\[\frac{\cos^{-1} \left(\frac{x}{y}\right)}{y \cdot \sin \left(\cos^{-1} \left(\frac{x}{y}\right)\right)}\]
↓
\[\frac{\cos^{-1} \left(\frac{x}{y}\right)}{y \cdot \sin \left(\cos^{-1} \left(\frac{x}{y}\right)\right)}\]
\frac{\cos^{-1} \left(\frac{x}{y}\right)}{y \cdot \sin \left(\cos^{-1} \left(\frac{x}{y}\right)\right)}
↓
\frac{\cos^{-1} \left(\frac{x}{y}\right)}{y \cdot \sin \left(\cos^{-1} \left(\frac{x}{y}\right)\right)}
double code(double x, double y) {
	return ((double) (((double) acos(((double) (x / y)))) / ((double) (y * ((double) sin(((double) acos(((double) (x / y))))))))));
}
↓
double code(double x, double y) {
	return ((double) (((double) acos(((double) (x / y)))) / ((double) (y * ((double) sin(((double) acos(((double) (x / 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 0.3

    \[\frac{\cos^{-1} \left(\frac{x}{y}\right)}{y \cdot \sin \left(\cos^{-1} \left(\frac{x}{y}\right)\right)}\]

  2. Final simplification0.3

    \[\leadsto \frac{\cos^{-1} \left(\frac{x}{y}\right)}{y \cdot \sin \left(\cos^{-1} \left(\frac{x}{y}\right)\right)}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x y)
  :name "(/ (acos (/ x y)) (* y (sin (acos (/ x y)))))"
  :precision binary64
  (/ (acos (/ x y)) (* y (sin (acos (/ x y))))))