Average Error: 0.0 → 0.0
Time: 2.7s
Precision: 64
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
↓
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
↓
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
double f(double x) {
        double r10925 = 2.0;
        double r10926 = 1.0;
        double r10927 = x;
        double r10928 = r10926 - r10927;
        double r10929 = r10926 + r10927;
        double r10930 = r10928 / r10929;
        double r10931 = sqrt(r10930);
        double r10932 = atan(r10931);
        double r10933 = r10925 * r10932;
        return r10933;
}
↓
double f(double x) {
        double r10934 = 2.0;
        double r10935 = 1.0;
        double r10936 = x;
        double r10937 = r10935 - r10936;
        double r10938 = r10935 + r10936;
        double r10939 = r10937 / r10938;
        double r10940 = sqrt(r10939);
        double r10941 = atan(r10940);
        double r10942 = r10934 * r10941;
        return r10942;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2020024 
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))