Average Error: 52.0 → 52.0
Time: 2.5s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} + 2 \cdot \left(y \cdot y\right)\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} + 2 \cdot \left(y \cdot y\right)
double f(double x, double y) {
        double r53847 = 9.0;
        double r53848 = x;
        double r53849 = 4.0;
        double r53850 = pow(r53848, r53849);
        double r53851 = r53847 * r53850;
        double r53852 = y;
        double r53853 = pow(r53852, r53849);
        double r53854 = r53851 - r53853;
        double r53855 = 2.0;
        double r53856 = r53852 * r53852;
        double r53857 = r53855 * r53856;
        double r53858 = r53854 + r53857;
        return r53858;
}
↓
double f(double x, double y) {
        double r53859 = 9.0;
        double r53860 = x;
        double r53861 = 4.0;
        double r53862 = pow(r53860, r53861);
        double r53863 = r53859 * r53862;
        double r53864 = y;
        double r53865 = pow(r53864, r53861);
        double r53866 = r53863 - r53865;
        double r53867 = 3.0;
        double r53868 = pow(r53866, r53867);
        double r53869 = cbrt(r53868);
        double r53870 = 2.0;
        double r53871 = r53864 * r53864;
        double r53872 = r53870 * r53871;
        double r53873 = r53869 + r53872;
        return r53873;
}

Error

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 52.0

    \[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
  2. Using strategy rm

  3. Applied add-cbrt-cube52.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(9 \cdot {x}^{4} - {y}^{4}\right) \cdot \left(9 \cdot {x}^{4} - {y}^{4}\right)\right) \cdot \left(9 \cdot {x}^{4} - {y}^{4}\right)}} + 2 \cdot \left(y \cdot y\right)\]

  4. Simplified52.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}}} + 2 \cdot \left(y \cdot y\right)\]

  5. Final simplification52.0

    \[\leadsto \sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} + 2 \cdot \left(y \cdot y\right)\]

Reproduce

herbie shell --seed 2020020 
(FPCore (x y)
  :name "From Rump in a 1983 paper"
  :precision binary64
  :pre (and (== x 10864) (== y 18817))
  (+ (- (* 9 (pow x 4)) (pow y 4)) (* 2 (* y y))))