Average Error: 0.0 → 0.0
Time: 10.2s
Precision: 64
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
↓
\[\tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right) \cdot 2\]
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
↓
\tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right) \cdot 2
double f(double x) {
        double r604673 = 2.0;
        double r604674 = 1.0;
        double r604675 = x;
        double r604676 = r604674 - r604675;
        double r604677 = r604674 + r604675;
        double r604678 = r604676 / r604677;
        double r604679 = sqrt(r604678);
        double r604680 = atan(r604679);
        double r604681 = r604673 * r604680;
        return r604681;
}
↓
double f(double x) {
        double r604682 = 1.0;
        double r604683 = x;
        double r604684 = r604682 - r604683;
        double r604685 = r604682 + r604683;
        double r604686 = r604684 / r604685;
        double r604687 = sqrt(r604686);
        double r604688 = atan(r604687);
        double r604689 = 2.0;
        double r604690 = r604688 * r604689;
        return r604690;
}

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

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x)
  :name "arccos"
  (* 2.0 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))