Average Error: 0.0 → 0.0
Time: 5.2s
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 r223137 = 2.0;
        double r223138 = 1.0;
        double r223139 = x;
        double r223140 = r223138 - r223139;
        double r223141 = r223138 + r223139;
        double r223142 = r223140 / r223141;
        double r223143 = sqrt(r223142);
        double r223144 = atan(r223143);
        double r223145 = r223137 * r223144;
        return r223145;
}
↓
double f(double x) {
        double r223146 = 1.0;
        double r223147 = x;
        double r223148 = r223146 - r223147;
        double r223149 = r223146 + r223147;
        double r223150 = r223148 / r223149;
        double r223151 = sqrt(r223150);
        double r223152 = atan(r223151);
        double r223153 = 2.0;
        double r223154 = r223152 * r223153;
        return r223154;
}

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 2019165 
(FPCore (x)
  :name "arccos"
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))