Average Error: 0.0 → 0.0
Time: 11.8s
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 r18045 = 2.0;
        double r18046 = 1.0;
        double r18047 = x;
        double r18048 = r18046 - r18047;
        double r18049 = r18046 + r18047;
        double r18050 = r18048 / r18049;
        double r18051 = sqrt(r18050);
        double r18052 = atan(r18051);
        double r18053 = r18045 * r18052;
        return r18053;
}
↓
double f(double x) {
        double r18054 = 2.0;
        double r18055 = 1.0;
        double r18056 = x;
        double r18057 = r18055 - r18056;
        double r18058 = r18055 + r18056;
        double r18059 = r18057 / r18058;
        double r18060 = 3.0;
        double r18061 = pow(r18059, r18060);
        double r18062 = cbrt(r18061);
        double r18063 = sqrt(r18062);
        double r18064 = atan(r18063);
        double r18065 = r18054 * r18064;
        return r18065;
}

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

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

  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 2019297 
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))