Average Error: 0.0 → 0.0
Time: 2.7s
Precision: 64
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
↓
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
↓
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
double f(double x) {
        double r9408 = 2.0;
        double r9409 = 1.0;
        double r9410 = x;
        double r9411 = r9409 - r9410;
        double r9412 = r9409 + r9410;
        double r9413 = r9411 / r9412;
        double r9414 = sqrt(r9413);
        double r9415 = atan(r9414);
        double r9416 = r9408 * r9415;
        return r9416;
}
↓
double f(double x) {
        double r9417 = 2.0;
        double r9418 = 1.0;
        double r9419 = x;
        double r9420 = r9418 - r9419;
        double r9421 = r9418 + r9419;
        double r9422 = r9420 / r9421;
        double r9423 = sqrt(r9422);
        double r9424 = atan(r9423);
        double r9425 = r9417 * r9424;
        return r9425;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))