Average Error: 0.0 → 0.0
Time: 42.5s
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 r214724 = 2.0;
        double r214725 = 1.0;
        double r214726 = x;
        double r214727 = r214725 - r214726;
        double r214728 = r214725 + r214726;
        double r214729 = r214727 / r214728;
        double r214730 = sqrt(r214729);
        double r214731 = atan(r214730);
        double r214732 = r214724 * r214731;
        return r214732;
}
↓
double f(double x) {
        double r214733 = 1.0;
        double r214734 = x;
        double r214735 = r214733 - r214734;
        double r214736 = r214733 + r214734;
        double r214737 = r214735 / r214736;
        double r214738 = sqrt(r214737);
        double r214739 = atan(r214738);
        double r214740 = 2.0;
        double r214741 = r214739 * r214740;
        return r214741;
}

Error

Bits error versus x

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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 2019142 
(FPCore (x)
  :name "arccos"
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))