Average Error: 0.0 → 0.0
Time: 2.8s
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 r11094 = 2.0;
        double r11095 = 1.0;
        double r11096 = x;
        double r11097 = r11095 - r11096;
        double r11098 = r11095 + r11096;
        double r11099 = r11097 / r11098;
        double r11100 = sqrt(r11099);
        double r11101 = atan(r11100);
        double r11102 = r11094 * r11101;
        return r11102;
}
↓
double f(double x) {
        double r11103 = 2.0;
        double r11104 = 1.0;
        double r11105 = x;
        double r11106 = r11104 - r11105;
        double r11107 = r11104 + r11105;
        double r11108 = r11106 / r11107;
        double r11109 = sqrt(r11108);
        double r11110 = atan(r11109);
        double r11111 = r11103 * r11110;
        return r11111;
}

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 2020024 +o rules:numerics
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))