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 r242962 = 2.0;
        double r242963 = 1.0;
        double r242964 = x;
        double r242965 = r242963 - r242964;
        double r242966 = r242963 + r242964;
        double r242967 = r242965 / r242966;
        double r242968 = sqrt(r242967);
        double r242969 = atan(r242968);
        double r242970 = r242962 * r242969;
        return r242970;
}
↓
double f(double x) {
        double r242971 = 1.0;
        double r242972 = x;
        double r242973 = r242971 - r242972;
        double r242974 = r242971 + r242972;
        double r242975 = r242973 / r242974;
        double r242976 = sqrt(r242975);
        double r242977 = atan(r242976);
        double r242978 = 2.0;
        double r242979 = r242977 * r242978;
        return r242979;
}

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 2019152 
(FPCore (x)
  :name "arccos"
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))