Average Error: 0.0 → 0.0
Time: 4.9s
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 r10553 = 2.0;
        double r10554 = 1.0;
        double r10555 = x;
        double r10556 = r10554 - r10555;
        double r10557 = r10554 + r10555;
        double r10558 = r10556 / r10557;
        double r10559 = sqrt(r10558);
        double r10560 = atan(r10559);
        double r10561 = r10553 * r10560;
        return r10561;
}
↓
double f(double x) {
        double r10562 = 2.0;
        double r10563 = 1.0;
        double r10564 = x;
        double r10565 = r10563 - r10564;
        double r10566 = r10563 + r10564;
        double r10567 = r10565 / r10566;
        double r10568 = sqrt(r10567);
        double r10569 = atan(r10568);
        double r10570 = r10562 * r10569;
        return r10570;
}

Error

Bits error versus x

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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 2019304 
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))