Average Error: 0.0 → 0.0
Time: 9.1s
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 r18932 = 2.0;
        double r18933 = 1.0;
        double r18934 = x;
        double r18935 = r18933 - r18934;
        double r18936 = r18933 + r18934;
        double r18937 = r18935 / r18936;
        double r18938 = sqrt(r18937);
        double r18939 = atan(r18938);
        double r18940 = r18932 * r18939;
        return r18940;
}
↓
double f(double x) {
        double r18941 = 2.0;
        double r18942 = 1.0;
        double r18943 = x;
        double r18944 = r18942 - r18943;
        double r18945 = r18942 + r18943;
        double r18946 = r18944 / r18945;
        double r18947 = sqrt(r18946);
        double r18948 = atan(r18947);
        double r18949 = r18941 * r18948;
        return r18949;
}

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 2019347 
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))