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 r5252 = 2.0;
        double r5253 = 1.0;
        double r5254 = x;
        double r5255 = r5253 - r5254;
        double r5256 = r5253 + r5254;
        double r5257 = r5255 / r5256;
        double r5258 = sqrt(r5257);
        double r5259 = atan(r5258);
        double r5260 = r5252 * r5259;
        return r5260;
}
↓
double f(double x) {
        double r5261 = 2.0;
        double r5262 = 1.0;
        double r5263 = x;
        double r5264 = r5262 - r5263;
        double r5265 = r5262 + r5263;
        double r5266 = r5264 / r5265;
        double r5267 = sqrt(r5266);
        double r5268 = atan(r5267);
        double r5269 = r5261 * r5268;
        return r5269;
}

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 2020089 +o rules:numerics
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))