Average Error: 0.0 → 0.0
Time: 9.4s
Precision: 64
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
↓
\[2 \cdot \tan^{-1} \left(\frac{\sqrt{1 - x}}{\sqrt{1 + x}}\right)\]
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
↓
2 \cdot \tan^{-1} \left(\frac{\sqrt{1 - x}}{\sqrt{1 + x}}\right)
double f(double x) {
        double r604889 = 2.0;
        double r604890 = 1.0;
        double r604891 = x;
        double r604892 = r604890 - r604891;
        double r604893 = r604890 + r604891;
        double r604894 = r604892 / r604893;
        double r604895 = sqrt(r604894);
        double r604896 = atan(r604895);
        double r604897 = r604889 * r604896;
        return r604897;
}
↓
double f(double x) {
        double r604898 = 2.0;
        double r604899 = 1.0;
        double r604900 = x;
        double r604901 = r604899 - r604900;
        double r604902 = sqrt(r604901);
        double r604903 = r604899 + r604900;
        double r604904 = sqrt(r604903);
        double r604905 = r604902 / r604904;
        double r604906 = atan(r604905);
        double r604907 = r604898 * r604906;
        return r604907;
}

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. Using strategy rm

  3. Applied sqrt-div0.0

    \[\leadsto 2 \cdot \tan^{-1} \color{blue}{\left(\frac{\sqrt{1 - x}}{\sqrt{1 + x}}\right)}\]

  4. Final simplification0.0

    \[\leadsto 2 \cdot \tan^{-1} \left(\frac{\sqrt{1 - x}}{\sqrt{1 + x}}\right)\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x)
  :name "arccos"
  (* 2.0 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))