Average Error: 0.0 → 0.0
Time: 8.5s
Precision: 64
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
↓
\[\tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right) \cdot 2\]
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
↓
\tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right) \cdot 2
double f(double x) {
        double r323434 = 2.0;
        double r323435 = 1.0;
        double r323436 = x;
        double r323437 = r323435 - r323436;
        double r323438 = r323435 + r323436;
        double r323439 = r323437 / r323438;
        double r323440 = sqrt(r323439);
        double r323441 = atan(r323440);
        double r323442 = r323434 * r323441;
        return r323442;
}
↓
double f(double x) {
        double r323443 = 1.0;
        double r323444 = x;
        double r323445 = r323443 - r323444;
        double r323446 = r323443 + r323444;
        double r323447 = r323445 / r323446;
        double r323448 = sqrt(r323447);
        double r323449 = atan(r323448);
        double r323450 = 2.0;
        double r323451 = r323449 * r323450;
        return r323451;
}

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. Taylor expanded around 0 0.0

    \[\leadsto 2 \cdot \color{blue}{\tan^{-1} \left(\sqrt{\frac{1 - x}{x + 1}}\right)}\]

  3. Final simplification0.0

    \[\leadsto \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right) \cdot 2\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x)
  :name "arccos"
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))