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 r47964 = 9.0;
        double r47965 = x;
        double r47966 = 4.0;
        double r47967 = pow(r47965, r47966);
        double r47968 = r47964 * r47967;
        double r47969 = y;
        double r47970 = pow(r47969, r47966);
        double r47971 = r47968 - r47970;
        double r47972 = 2.0;
        double r47973 = r47969 * r47969;
        double r47974 = r47972 * r47973;
        double r47975 = r47971 + r47974;
        return r47975;
}
↓
double f(double x, double y) {
        double r47976 = 9.0;
        double r47977 = x;
        double r47978 = 4.0;
        double r47979 = pow(r47977, r47978);
        double r47980 = r47976 * r47979;
        double r47981 = y;
        double r47982 = pow(r47981, r47978);
        double r47983 = r47980 - r47982;
        double r47984 = 3.0;
        double r47985 = pow(r47983, r47984);
        double r47986 = cbrt(r47985);
        double r47987 = 2.0;
        double r47988 = r47981 * r47981;
        double r47989 = r47987 * r47988;
        double r47990 = r47986 + r47989;
        return r47990;
}

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 2020081 
(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))))