Average Error: 0.0 → 0.0
Time: 3.3s
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 r10592 = 2.0;
        double r10593 = 1.0;
        double r10594 = x;
        double r10595 = r10593 - r10594;
        double r10596 = r10593 + r10594;
        double r10597 = r10595 / r10596;
        double r10598 = sqrt(r10597);
        double r10599 = atan(r10598);
        double r10600 = r10592 * r10599;
        return r10600;
}
↓
double f(double x) {
        double r10601 = 2.0;
        double r10602 = 1.0;
        double r10603 = x;
        double r10604 = r10602 - r10603;
        double r10605 = r10602 + r10603;
        double r10606 = r10604 / r10605;
        double r10607 = sqrt(r10606);
        double r10608 = atan(r10607);
        double r10609 = r10601 * r10608;
        return r10609;
}

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))))))