Average Error: 0.0 → 0.0
Time: 13.2s
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 r688951 = 2.0;
        double r688952 = 1.0;
        double r688953 = x;
        double r688954 = r688952 - r688953;
        double r688955 = r688952 + r688953;
        double r688956 = r688954 / r688955;
        double r688957 = sqrt(r688956);
        double r688958 = atan(r688957);
        double r688959 = r688951 * r688958;
        return r688959;
}
↓
double f(double x) {
        double r688960 = 2.0;
        double r688961 = 1.0;
        double r688962 = x;
        double r688963 = r688961 - r688962;
        double r688964 = sqrt(r688963);
        double r688965 = r688961 + r688962;
        double r688966 = sqrt(r688965);
        double r688967 = r688964 / r688966;
        double r688968 = atan(r688967);
        double r688969 = r688960 * r688968;
        return r688969;
}

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 2019163 
(FPCore (x)
  :name "arccos"
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))