Average Error: 52.0 → 52.0
Time: 7.4s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[2 \cdot \left(y \cdot y\right) + \sqrt[3]{{\left({x}^{4} \cdot 9 - {y}^{4}\right)}^{3}}\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
2 \cdot \left(y \cdot y\right) + \sqrt[3]{{\left({x}^{4} \cdot 9 - {y}^{4}\right)}^{3}}
double f(double x, double y) {
        double r46838 = 9.0;
        double r46839 = x;
        double r46840 = 4.0;
        double r46841 = pow(r46839, r46840);
        double r46842 = r46838 * r46841;
        double r46843 = y;
        double r46844 = pow(r46843, r46840);
        double r46845 = r46842 - r46844;
        double r46846 = 2.0;
        double r46847 = r46843 * r46843;
        double r46848 = r46846 * r46847;
        double r46849 = r46845 + r46848;
        return r46849;
}
↓
double f(double x, double y) {
        double r46850 = 2.0;
        double r46851 = y;
        double r46852 = r46851 * r46851;
        double r46853 = r46850 * r46852;
        double r46854 = x;
        double r46855 = 4.0;
        double r46856 = pow(r46854, r46855);
        double r46857 = 9.0;
        double r46858 = r46856 * r46857;
        double r46859 = pow(r46851, r46855);
        double r46860 = r46858 - r46859;
        double r46861 = 3.0;
        double r46862 = pow(r46860, r46861);
        double r46863 = cbrt(r46862);
        double r46864 = r46853 + r46863;
        return r46864;
}

Error

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Your Program's Arguments

Results

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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

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

  5. Final simplification52.0

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y)
  :name "From Rump in a 1983 paper"
  :pre (and (== x 10864.0) (== y 18817.0))
  (+ (- (* 9.0 (pow x 4.0)) (pow y 4.0)) (* 2.0 (* y y))))