Average Error: 0.0 → 0.0
Time: 17.3s
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 r403719 = 2.0;
        double r403720 = 1.0;
        double r403721 = x;
        double r403722 = r403720 - r403721;
        double r403723 = r403720 + r403721;
        double r403724 = r403722 / r403723;
        double r403725 = sqrt(r403724);
        double r403726 = atan(r403725);
        double r403727 = r403719 * r403726;
        return r403727;
}
↓
double f(double x) {
        double r403728 = 2.0;
        double r403729 = 1.0;
        double r403730 = x;
        double r403731 = r403729 - r403730;
        double r403732 = sqrt(r403731);
        double r403733 = r403729 + r403730;
        double r403734 = sqrt(r403733);
        double r403735 = r403732 / r403734;
        double r403736 = atan(r403735);
        double r403737 = r403728 * r403736;
        return r403737;
}

Error

Bits error versus x

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Your Program's Arguments

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 2019128 
(FPCore (x)
  :name "arccos"
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))