Average Error: 0.0 → 0.0
Time: 10.5s
Precision: 64
\[\cos \left(\left(\cos^{-1} a - \cos^{-1} b\right) \cdot 0.5\right)\]
\[\cos \left(\left(\cos^{-1} a - \cos^{-1} b\right) \cdot 0.5\right)\]
\cos \left(\left(\cos^{-1} a - \cos^{-1} b\right) \cdot 0.5\right)
\cos \left(\left(\cos^{-1} a - \cos^{-1} b\right) \cdot 0.5\right)
double f(double a, double b) {
        double r21238 = a;
        double r21239 = acos(r21238);
        double r21240 = b;
        double r21241 = acos(r21240);
        double r21242 = r21239 - r21241;
        double r21243 = 0.5;
        double r21244 = r21242 * r21243;
        double r21245 = cos(r21244);
        return r21245;
}

double f(double a, double b) {
        double r21246 = a;
        double r21247 = acos(r21246);
        double r21248 = b;
        double r21249 = acos(r21248);
        double r21250 = r21247 - r21249;
        double r21251 = 0.5;
        double r21252 = r21250 * r21251;
        double r21253 = cos(r21252);
        return r21253;
}

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 0.0

    \[\cos \left(\left(\cos^{-1} a - \cos^{-1} b\right) \cdot 0.5\right)\]
  2. Final simplification0.0

    \[\leadsto \cos \left(\left(\cos^{-1} a - \cos^{-1} b\right) \cdot 0.5\right)\]

Reproduce

herbie shell --seed 1 
(FPCore (a b)
  :name "cos((acos(a) - acos(b)) * 0.5)"
  :precision binary64
  (cos (* (- (acos a) (acos b)) 0.5)))