Average Error: 0.0 → 0.0
Time: 3.7s
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 r11753 = 2.0;
        double r11754 = 1.0;
        double r11755 = x;
        double r11756 = r11754 - r11755;
        double r11757 = r11754 + r11755;
        double r11758 = r11756 / r11757;
        double r11759 = sqrt(r11758);
        double r11760 = atan(r11759);
        double r11761 = r11753 * r11760;
        return r11761;
}
↓
double f(double x) {
        double r11762 = 2.0;
        double r11763 = 1.0;
        double r11764 = x;
        double r11765 = r11763 - r11764;
        double r11766 = r11763 + r11764;
        double r11767 = r11765 / r11766;
        double r11768 = sqrt(r11767);
        double r11769 = atan(r11768);
        double r11770 = r11762 * r11769;
        return r11770;
}

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 2019354 
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))