Average Error: 16.7 → 16.7
Time: 8.4s
Precision: binary64
\[\cos^{-1} \left(\sin x \cdot \sin x2 + \left(\cos x \cdot \cos x2\right) \cdot \cos \left(y - y2\right)\right)\]
↓
\[\cos^{-1} \left(\sin x \cdot \sin x2 + \left(\cos x \cdot \cos x2\right) \cdot \cos \left(y - y2\right)\right)\]
\cos^{-1} \left(\sin x \cdot \sin x2 + \left(\cos x \cdot \cos x2\right) \cdot \cos \left(y - y2\right)\right)
↓
\cos^{-1} \left(\sin x \cdot \sin x2 + \left(\cos x \cdot \cos x2\right) \cdot \cos \left(y - y2\right)\right)
double code(double x, double x2, double y, double y2) {
	return ((double) acos(((double) (((double) (((double) sin(x)) * ((double) sin(x2)))) + ((double) (((double) (((double) cos(x)) * ((double) cos(x2)))) * ((double) cos(((double) (y - y2))))))))));
}
↓
double code(double x, double x2, double y, double y2) {
	return ((double) acos(((double) (((double) (((double) sin(x)) * ((double) sin(x2)))) + ((double) (((double) (((double) cos(x)) * ((double) cos(x2)))) * ((double) cos(((double) (y - y2))))))))));
}

Error

Bits error versus x

Bits error versus x2

Bits error versus y

Bits error versus y2

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.7

    \[\cos^{-1} \left(\sin x \cdot \sin x2 + \left(\cos x \cdot \cos x2\right) \cdot \cos \left(y - y2\right)\right)\]

  2. Final simplification16.7

    \[\leadsto \cos^{-1} \left(\sin x \cdot \sin x2 + \left(\cos x \cdot \cos x2\right) \cdot \cos \left(y - y2\right)\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x x2 y y2)
  :name "(acos (+ (* (sin x) (sin x2)) (* (* (cos x) (cos x2)) (cos (- y y2)))))"
  :precision binary64
  (acos (+ (* (sin x) (sin x2)) (* (* (cos x) (cos x2)) (cos (- y y2))))))