Average Error: 0.0 → 0.0
Time: 13.8s
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 r605424 = 2.0;
        double r605425 = 1.0;
        double r605426 = x;
        double r605427 = r605425 - r605426;
        double r605428 = r605425 + r605426;
        double r605429 = r605427 / r605428;
        double r605430 = sqrt(r605429);
        double r605431 = atan(r605430);
        double r605432 = r605424 * r605431;
        return r605432;
}
↓
double f(double x) {
        double r605433 = 2.0;
        double r605434 = 1.0;
        double r605435 = x;
        double r605436 = r605434 - r605435;
        double r605437 = sqrt(r605436);
        double r605438 = r605434 + r605435;
        double r605439 = sqrt(r605438);
        double r605440 = r605437 / r605439;
        double r605441 = atan(r605440);
        double r605442 = r605433 * r605441;
        return r605442;
}

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 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))))))