Average Error: 0.0 → 0.0
Time: 2.8s
Precision: 64
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
↓
\[2 \cdot \tan^{-1} \left(\sqrt{\sqrt[3]{{\left(\frac{1 - x}{1 + x}\right)}^{3}}}\right)\]
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
↓
2 \cdot \tan^{-1} \left(\sqrt{\sqrt[3]{{\left(\frac{1 - x}{1 + x}\right)}^{3}}}\right)
double f(double x) {
        double r8012 = 2.0;
        double r8013 = 1.0;
        double r8014 = x;
        double r8015 = r8013 - r8014;
        double r8016 = r8013 + r8014;
        double r8017 = r8015 / r8016;
        double r8018 = sqrt(r8017);
        double r8019 = atan(r8018);
        double r8020 = r8012 * r8019;
        return r8020;
}
↓
double f(double x) {
        double r8021 = 2.0;
        double r8022 = 1.0;
        double r8023 = x;
        double r8024 = r8022 - r8023;
        double r8025 = r8022 + r8023;
        double r8026 = r8024 / r8025;
        double r8027 = 3.0;
        double r8028 = pow(r8026, r8027);
        double r8029 = cbrt(r8028);
        double r8030 = sqrt(r8029);
        double r8031 = atan(r8030);
        double r8032 = r8021 * r8031;
        return r8032;
}

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

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

  4. Applied add-cbrt-cube0.0

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

  5. Applied cbrt-undiv0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020002 
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))