Average Error: 0.0 → 0.0
Time: 7.1s
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 r180954 = 2.0;
        double r180955 = 1.0;
        double r180956 = x;
        double r180957 = r180955 - r180956;
        double r180958 = r180955 + r180956;
        double r180959 = r180957 / r180958;
        double r180960 = sqrt(r180959);
        double r180961 = atan(r180960);
        double r180962 = r180954 * r180961;
        return r180962;
}
↓
double f(double x) {
        double r180963 = 1.0;
        double r180964 = x;
        double r180965 = r180963 - r180964;
        double r180966 = r180963 + r180964;
        double r180967 = r180965 / r180966;
        double r180968 = sqrt(r180967);
        double r180969 = atan(r180968);
        double r180970 = 2.0;
        double r180971 = r180969 * r180970;
        return r180971;
}

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 2019154 
(FPCore (x)
  :name "arccos"
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))