Average Error: 16.0 → 16.0
Time: 4.8s
Precision: binary64
\[\tan^{-1} \left(\sqrt{\tan \left(\frac{s}{2}\right) \cdot \tan \left(\frac{s - a}{2}\right)}\right)\]
↓
\[\tan^{-1} \left(\sqrt{\tan \left(\frac{s}{2}\right) \cdot \tan \left(\frac{s - a}{2}\right)}\right)\]
\tan^{-1} \left(\sqrt{\tan \left(\frac{s}{2}\right) \cdot \tan \left(\frac{s - a}{2}\right)}\right)
↓
\tan^{-1} \left(\sqrt{\tan \left(\frac{s}{2}\right) \cdot \tan \left(\frac{s - a}{2}\right)}\right)
double code(double s, double a) {
	return ((double) atan(((double) sqrt(((double) (((double) tan(((double) (s / 2.0)))) * ((double) tan(((double) (((double) (s - a)) / 2.0))))))))));
}
↓
double code(double s, double a) {
	return ((double) atan(((double) sqrt(((double) (((double) tan(((double) (s / 2.0)))) * ((double) tan(((double) (((double) (s - a)) / 2.0))))))))));
}

Error

Bits error versus s

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.0

    \[\tan^{-1} \left(\sqrt{\tan \left(\frac{s}{2}\right) \cdot \tan \left(\frac{s - a}{2}\right)}\right)\]

  2. Final simplification16.0

    \[\leadsto \tan^{-1} \left(\sqrt{\tan \left(\frac{s}{2}\right) \cdot \tan \left(\frac{s - a}{2}\right)}\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (s a)
  :name "(atan (sqrt (* (tan (/ s 2)) (tan (/ (- s a) 2)))))"
  :precision binary64
  (atan (sqrt (* (tan (/ s 2.0)) (tan (/ (- s a) 2.0))))))