Average Error: 0.1 → 0.1
Time: 7.3s
Precision: binary64
\[\tan^{-1} \left(\frac{\sqrt{{\left(\cos a \cdot \cos b\right)}^{2} + {\left(\cos a \cdot \sin b\right)}^{2}}}{\sin a}\right)\]
↓
\[\tan^{-1} \left(\frac{\sqrt{{\left(\cos a \cdot \cos b\right)}^{2} + {\left(\cos a \cdot \sin b\right)}^{2}}}{\sin a}\right)\]
\tan^{-1} \left(\frac{\sqrt{{\left(\cos a \cdot \cos b\right)}^{2} + {\left(\cos a \cdot \sin b\right)}^{2}}}{\sin a}\right)
↓
\tan^{-1} \left(\frac{\sqrt{{\left(\cos a \cdot \cos b\right)}^{2} + {\left(\cos a \cdot \sin b\right)}^{2}}}{\sin a}\right)
double code(double a, double b) {
	return ((double) atan(((double) (((double) sqrt(((double) (((double) pow(((double) (((double) cos(a)) * ((double) cos(b)))), 2.0)) + ((double) pow(((double) (((double) cos(a)) * ((double) sin(b)))), 2.0)))))) / ((double) sin(a))))));
}
↓
double code(double a, double b) {
	return ((double) atan(((double) (((double) sqrt(((double) (((double) pow(((double) (((double) cos(a)) * ((double) cos(b)))), 2.0)) + ((double) pow(((double) (((double) cos(a)) * ((double) sin(b)))), 2.0)))))) / ((double) sin(a))))));
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\tan^{-1} \left(\frac{\sqrt{{\left(\cos a \cdot \cos b\right)}^{2} + {\left(\cos a \cdot \sin b\right)}^{2}}}{\sin a}\right)\]

  2. Final simplification0.1

    \[\leadsto \tan^{-1} \left(\frac{\sqrt{{\left(\cos a \cdot \cos b\right)}^{2} + {\left(\cos a \cdot \sin b\right)}^{2}}}{\sin a}\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (a b)
  :name "(atan (/ (sqrt (+ (pow (* (cos a) (cos b)) 2) (pow (* (cos a) (sin b)) 2))) (sin a)))"
  :precision binary64
  (atan (/ (sqrt (+ (pow (* (cos a) (cos b)) 2.0) (pow (* (cos a) (sin b)) 2.0))) (sin a))))