Average Error: 0.0 → 0.0
Time: 5.1s
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 r10579 = 2.0;
        double r10580 = 1.0;
        double r10581 = x;
        double r10582 = r10580 - r10581;
        double r10583 = r10580 + r10581;
        double r10584 = r10582 / r10583;
        double r10585 = sqrt(r10584);
        double r10586 = atan(r10585);
        double r10587 = r10579 * r10586;
        return r10587;
}
↓
double f(double x) {
        double r10588 = 2.0;
        double r10589 = 1.0;
        double r10590 = x;
        double r10591 = r10589 - r10590;
        double r10592 = r10589 + r10590;
        double r10593 = r10591 / r10592;
        double r10594 = sqrt(r10593);
        double r10595 = atan(r10594);
        double r10596 = r10588 * r10595;
        return r10596;
}

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