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 r9095 = 2.0;
        double r9096 = 1.0;
        double r9097 = x;
        double r9098 = r9096 - r9097;
        double r9099 = r9096 + r9097;
        double r9100 = r9098 / r9099;
        double r9101 = sqrt(r9100);
        double r9102 = atan(r9101);
        double r9103 = r9095 * r9102;
        return r9103;
}
↓
double f(double x) {
        double r9104 = 2.0;
        double r9105 = 1.0;
        double r9106 = x;
        double r9107 = r9105 - r9106;
        double r9108 = r9105 + r9106;
        double r9109 = r9107 / r9108;
        double r9110 = sqrt(r9109);
        double r9111 = atan(r9110);
        double r9112 = r9104 * r9111;
        return r9112;
}

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