Average Error: 0.0 → 0.0
Time: 3.1s
Precision: 64
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
↓
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
↓
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
double f(double x) {
        double r8500 = 2.0;
        double r8501 = 1.0;
        double r8502 = x;
        double r8503 = r8501 - r8502;
        double r8504 = r8501 + r8502;
        double r8505 = r8503 / r8504;
        double r8506 = sqrt(r8505);
        double r8507 = atan(r8506);
        double r8508 = r8500 * r8507;
        return r8508;
}
↓
double f(double x) {
        double r8509 = 2.0;
        double r8510 = 1.0;
        double r8511 = x;
        double r8512 = r8510 - r8511;
        double r8513 = r8510 + r8511;
        double r8514 = r8512 / r8513;
        double r8515 = sqrt(r8514);
        double r8516 = atan(r8515);
        double r8517 = r8509 * r8516;
        return r8517;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020100 
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))