Average Error: 0.0 → 0.0
Time: 3.6s
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 r12107 = 2.0;
        double r12108 = 1.0;
        double r12109 = x;
        double r12110 = r12108 - r12109;
        double r12111 = r12108 + r12109;
        double r12112 = r12110 / r12111;
        double r12113 = sqrt(r12112);
        double r12114 = atan(r12113);
        double r12115 = r12107 * r12114;
        return r12115;
}
↓
double f(double x) {
        double r12116 = 2.0;
        double r12117 = 1.0;
        double r12118 = x;
        double r12119 = r12117 - r12118;
        double r12120 = r12117 + r12118;
        double r12121 = r12119 / r12120;
        double r12122 = sqrt(r12121);
        double r12123 = atan(r12122);
        double r12124 = r12116 * r12123;
        return r12124;
}

Error

Bits error versus x

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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 2020033 
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))