Average Error: 0.0 → 0.0
Time: 11.6s
Precision: 64
\[2.0 \cdot \tan^{-1} \left(\sqrt{\frac{1.0 - x}{1.0 + x}}\right)\]
↓
\[\tan^{-1} \left(\sqrt{\frac{1.0 - x}{1.0 + x}}\right) \cdot 2.0\]
2.0 \cdot \tan^{-1} \left(\sqrt{\frac{1.0 - x}{1.0 + x}}\right)
↓
\tan^{-1} \left(\sqrt{\frac{1.0 - x}{1.0 + x}}\right) \cdot 2.0
double f(double x) {
        double r125327 = 2.0;
        double r125328 = 1.0;
        double r125329 = x;
        double r125330 = r125328 - r125329;
        double r125331 = r125328 + r125329;
        double r125332 = r125330 / r125331;
        double r125333 = sqrt(r125332);
        double r125334 = atan(r125333);
        double r125335 = r125327 * r125334;
        return r125335;
}
↓
double f(double x) {
        double r125336 = 1.0;
        double r125337 = x;
        double r125338 = r125336 - r125337;
        double r125339 = r125336 + r125337;
        double r125340 = r125338 / r125339;
        double r125341 = sqrt(r125340);
        double r125342 = atan(r125341);
        double r125343 = 2.0;
        double r125344 = r125342 * r125343;
        return r125344;
}

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

    \[2.0 \cdot \tan^{-1} \left(\sqrt{\frac{1.0 - x}{1.0 + x}}\right)\]

  2. Final simplification0.0

    \[\leadsto \tan^{-1} \left(\sqrt{\frac{1.0 - x}{1.0 + x}}\right) \cdot 2.0\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x)
  :name "arccos"
  (* 2.0 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))