Average Error: 0.0 → 0.0
Time: 4.0s
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 r9558 = 2.0;
        double r9559 = 1.0;
        double r9560 = x;
        double r9561 = r9559 - r9560;
        double r9562 = r9559 + r9560;
        double r9563 = r9561 / r9562;
        double r9564 = sqrt(r9563);
        double r9565 = atan(r9564);
        double r9566 = r9558 * r9565;
        return r9566;
}
↓
double f(double x) {
        double r9567 = 2.0;
        double r9568 = 1.0;
        double r9569 = x;
        double r9570 = r9568 - r9569;
        double r9571 = r9568 + r9569;
        double r9572 = r9570 / r9571;
        double r9573 = sqrt(r9572);
        double r9574 = 3.0;
        double r9575 = pow(r9573, r9574);
        double r9576 = cbrt(r9575);
        double r9577 = atan(r9576);
        double r9578 = r9567 * r9577;
        return r9578;
}

Error

Bits error versus x

Try it out

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))))))