Average Error: 0.0 → 0.0
Time: 9.5s
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 r292175 = 2.0;
        double r292176 = 1.0;
        double r292177 = x;
        double r292178 = r292176 - r292177;
        double r292179 = r292176 + r292177;
        double r292180 = r292178 / r292179;
        double r292181 = sqrt(r292180);
        double r292182 = atan(r292181);
        double r292183 = r292175 * r292182;
        return r292183;
}
↓
double f(double x) {
        double r292184 = 1.0;
        double r292185 = x;
        double r292186 = r292184 - r292185;
        double r292187 = r292184 + r292185;
        double r292188 = r292186 / r292187;
        double r292189 = sqrt(r292188);
        double r292190 = atan(r292189);
        double r292191 = 2.0;
        double r292192 = r292190 * r292191;
        return r292192;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 0.0

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

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2019132 
(FPCore (x)
  :name "arccos"
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))