Average Error: 0.0 → 0.0
Time: 26.3s
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 r930568 = 2.0;
        double r930569 = 1.0;
        double r930570 = x;
        double r930571 = r930569 - r930570;
        double r930572 = r930569 + r930570;
        double r930573 = r930571 / r930572;
        double r930574 = sqrt(r930573);
        double r930575 = atan(r930574);
        double r930576 = r930568 * r930575;
        return r930576;
}
↓
double f(double x) {
        double r930577 = 1.0;
        double r930578 = x;
        double r930579 = r930577 - r930578;
        double r930580 = r930577 + r930578;
        double r930581 = r930579 / r930580;
        double r930582 = sqrt(r930581);
        double r930583 = atan(r930582);
        double r930584 = 2.0;
        double r930585 = r930583 * r930584;
        return r930585;
}

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 2019120 
(FPCore (x)
  :name "arccos"
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))