Average Error: 0.0 → 0.0
Time: 14.0s
Precision: 64
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
↓
\[2 \cdot \tan^{-1} \left(\frac{\sqrt{1 - x}}{\sqrt{1 + x}}\right)\]
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
↓
2 \cdot \tan^{-1} \left(\frac{\sqrt{1 - x}}{\sqrt{1 + x}}\right)
double f(double x) {
        double r547254 = 2.0;
        double r547255 = 1.0;
        double r547256 = x;
        double r547257 = r547255 - r547256;
        double r547258 = r547255 + r547256;
        double r547259 = r547257 / r547258;
        double r547260 = sqrt(r547259);
        double r547261 = atan(r547260);
        double r547262 = r547254 * r547261;
        return r547262;
}
↓
double f(double x) {
        double r547263 = 2.0;
        double r547264 = 1.0;
        double r547265 = x;
        double r547266 = r547264 - r547265;
        double r547267 = sqrt(r547266);
        double r547268 = r547264 + r547265;
        double r547269 = sqrt(r547268);
        double r547270 = r547267 / r547269;
        double r547271 = atan(r547270);
        double r547272 = r547263 * r547271;
        return r547272;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Derivation

  1. Initial program 0.0

    \[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
  2. Using strategy rm

  3. Applied sqrt-div0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x)
  :name "arccos"
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))