Average Error: 0.0 → 0.0
Time: 9.8s
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 r503606 = 2.0;
        double r503607 = 1.0;
        double r503608 = x;
        double r503609 = r503607 - r503608;
        double r503610 = r503607 + r503608;
        double r503611 = r503609 / r503610;
        double r503612 = sqrt(r503611);
        double r503613 = atan(r503612);
        double r503614 = r503606 * r503613;
        return r503614;
}
↓
double f(double x) {
        double r503615 = 1.0;
        double r503616 = x;
        double r503617 = r503615 - r503616;
        double r503618 = r503615 + r503616;
        double r503619 = r503617 / r503618;
        double r503620 = sqrt(r503619);
        double r503621 = atan(r503620);
        double r503622 = 2.0;
        double r503623 = r503621 * r503622;
        return r503623;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x)
  :name "arccos"
  (* 2.0 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))