Average Error: 0.0 → 0.0
Time: 4.4s
Precision: 64
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
↓
\[2 \cdot \tan^{-1} \left(\sqrt[3]{{\left(\sqrt{\frac{1 - x}{1 + x}}\right)}^{3}}\right)\]
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
↓
2 \cdot \tan^{-1} \left(\sqrt[3]{{\left(\sqrt{\frac{1 - x}{1 + x}}\right)}^{3}}\right)
double f(double x) {
        double r9400 = 2.0;
        double r9401 = 1.0;
        double r9402 = x;
        double r9403 = r9401 - r9402;
        double r9404 = r9401 + r9402;
        double r9405 = r9403 / r9404;
        double r9406 = sqrt(r9405);
        double r9407 = atan(r9406);
        double r9408 = r9400 * r9407;
        return r9408;
}
↓
double f(double x) {
        double r9409 = 2.0;
        double r9410 = 1.0;
        double r9411 = x;
        double r9412 = r9410 - r9411;
        double r9413 = r9410 + r9411;
        double r9414 = r9412 / r9413;
        double r9415 = sqrt(r9414);
        double r9416 = 3.0;
        double r9417 = pow(r9415, r9416);
        double r9418 = cbrt(r9417);
        double r9419 = atan(r9418);
        double r9420 = r9409 * r9419;
        return r9420;
}

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. Using strategy rm

  3. Applied add-cbrt-cube0.0

    \[\leadsto 2 \cdot \tan^{-1} \color{blue}{\left(\sqrt[3]{\left(\sqrt{\frac{1 - x}{1 + x}} \cdot \sqrt{\frac{1 - x}{1 + x}}\right) \cdot \sqrt{\frac{1 - x}{1 + x}}}\right)}\]

  4. Simplified0.0

    \[\leadsto 2 \cdot \tan^{-1} \left(\sqrt[3]{\color{blue}{{\left(\sqrt{\frac{1 - x}{1 + x}}\right)}^{3}}}\right)\]

  5. Final simplification0.0

    \[\leadsto 2 \cdot \tan^{-1} \left(\sqrt[3]{{\left(\sqrt{\frac{1 - x}{1 + x}}\right)}^{3}}\right)\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))