Average Error: 0.0 → 0.0
Time: 1.9s
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 r4583 = 2.0;
        double r4584 = 1.0;
        double r4585 = x;
        double r4586 = r4584 - r4585;
        double r4587 = r4584 + r4585;
        double r4588 = r4586 / r4587;
        double r4589 = sqrt(r4588);
        double r4590 = atan(r4589);
        double r4591 = r4583 * r4590;
        return r4591;
}
↓
double f(double x) {
        double r4592 = 2.0;
        double r4593 = 1.0;
        double r4594 = x;
        double r4595 = r4593 - r4594;
        double r4596 = r4593 * r4593;
        double r4597 = r4594 * r4594;
        double r4598 = r4596 - r4597;
        double r4599 = r4595 / r4598;
        double r4600 = r4599 * r4595;
        double r4601 = sqrt(r4600);
        double r4602 = atan(r4601);
        double r4603 = r4592 * r4602;
        return r4603;
}

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 2020025 
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))