Average Error: 0.0 → 0.0
Time: 7.1s
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 r185530 = 2.0;
        double r185531 = 1.0;
        double r185532 = x;
        double r185533 = r185531 - r185532;
        double r185534 = r185531 + r185532;
        double r185535 = r185533 / r185534;
        double r185536 = sqrt(r185535);
        double r185537 = atan(r185536);
        double r185538 = r185530 * r185537;
        return r185538;
}
↓
double f(double x) {
        double r185539 = 1.0;
        double r185540 = x;
        double r185541 = r185539 - r185540;
        double r185542 = r185539 + r185540;
        double r185543 = r185541 / r185542;
        double r185544 = sqrt(r185543);
        double r185545 = atan(r185544);
        double r185546 = 2.0;
        double r185547 = r185545 * r185546;
        return r185547;
}

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 2019152 
(FPCore (x)
  :name "arccos"
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))