Average Error: 0.0 → 0.0
Time: 3.2s
Precision: 64
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
↓
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 \cdot 1 - x \cdot x} \cdot \left(1 - x\right)}\right)\]
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
↓
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 \cdot 1 - x \cdot x} \cdot \left(1 - x\right)}\right)
double f(double x) {
        double r11700 = 2.0;
        double r11701 = 1.0;
        double r11702 = x;
        double r11703 = r11701 - r11702;
        double r11704 = r11701 + r11702;
        double r11705 = r11703 / r11704;
        double r11706 = sqrt(r11705);
        double r11707 = atan(r11706);
        double r11708 = r11700 * r11707;
        return r11708;
}
↓
double f(double x) {
        double r11709 = 2.0;
        double r11710 = 1.0;
        double r11711 = x;
        double r11712 = r11710 - r11711;
        double r11713 = r11710 * r11710;
        double r11714 = r11711 * r11711;
        double r11715 = r11713 - r11714;
        double r11716 = r11712 / r11715;
        double r11717 = r11716 * r11712;
        double r11718 = sqrt(r11717);
        double r11719 = atan(r11718);
        double r11720 = r11709 * r11719;
        return r11720;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
  2. Using strategy rm

  3. Applied flip-+0.0

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

  4. Applied associate-/r/0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020018 
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))