Average Error: 0.0 → 0.0
Time: 11.7s
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 r442674 = 2.0;
        double r442675 = 1.0;
        double r442676 = x;
        double r442677 = r442675 - r442676;
        double r442678 = r442675 + r442676;
        double r442679 = r442677 / r442678;
        double r442680 = sqrt(r442679);
        double r442681 = atan(r442680);
        double r442682 = r442674 * r442681;
        return r442682;
}
↓
double f(double x) {
        double r442683 = 1.0;
        double r442684 = x;
        double r442685 = r442683 - r442684;
        double r442686 = r442683 + r442684;
        double r442687 = r442685 / r442686;
        double r442688 = sqrt(r442687);
        double r442689 = atan(r442688);
        double r442690 = 2.0;
        double r442691 = r442689 * r442690;
        return r442691;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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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 2019171 +o rules:numerics
(FPCore (x)
  :name "arccos"
  (* 2.0 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))