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 r9123 = 2.0;
        double r9124 = 1.0;
        double r9125 = x;
        double r9126 = r9124 - r9125;
        double r9127 = r9124 + r9125;
        double r9128 = r9126 / r9127;
        double r9129 = sqrt(r9128);
        double r9130 = atan(r9129);
        double r9131 = r9123 * r9130;
        return r9131;
}
↓
double f(double x) {
        double r9132 = 2.0;
        double r9133 = 1.0;
        double r9134 = x;
        double r9135 = r9133 - r9134;
        double r9136 = r9133 + r9134;
        double r9137 = r9135 / r9136;
        double r9138 = sqrt(r9137);
        double r9139 = atan(r9138);
        double r9140 = r9132 * r9139;
        return r9140;
}

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 2019235 +o rules:numerics
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))