Average Error: 52.0 → 52.0
Time: 13.3s
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 r54874 = 9.0;
        double r54875 = x;
        double r54876 = 4.0;
        double r54877 = pow(r54875, r54876);
        double r54878 = r54874 * r54877;
        double r54879 = y;
        double r54880 = pow(r54879, r54876);
        double r54881 = r54878 - r54880;
        double r54882 = 2.0;
        double r54883 = r54879 * r54879;
        double r54884 = r54882 * r54883;
        double r54885 = r54881 + r54884;
        return r54885;
}
↓
double f(double x, double y) {
        double r54886 = 9.0;
        double r54887 = x;
        double r54888 = 4.0;
        double r54889 = pow(r54887, r54888);
        double r54890 = r54886 * r54889;
        double r54891 = y;
        double r54892 = pow(r54891, r54888);
        double r54893 = r54890 - r54892;
        double r54894 = 3.0;
        double r54895 = pow(r54893, r54894);
        double r54896 = cbrt(r54895);
        double r54897 = 2.0;
        double r54898 = r54891 * r54891;
        double r54899 = r54897 * r54898;
        double r54900 = r54896 + r54899;
        return r54900;
}

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

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

  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 2019323 
(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))))