Average Error: 0.0 → 0.0
Time: 9.5s
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 r571097 = 2.0;
        double r571098 = 1.0;
        double r571099 = x;
        double r571100 = r571098 - r571099;
        double r571101 = r571098 + r571099;
        double r571102 = r571100 / r571101;
        double r571103 = sqrt(r571102);
        double r571104 = atan(r571103);
        double r571105 = r571097 * r571104;
        return r571105;
}
↓
double f(double x) {
        double r571106 = 1.0;
        double r571107 = x;
        double r571108 = r571106 - r571107;
        double r571109 = r571106 + r571107;
        double r571110 = r571108 / r571109;
        double r571111 = sqrt(r571110);
        double r571112 = atan(r571111);
        double r571113 = 2.0;
        double r571114 = r571112 * r571113;
        return r571114;
}

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