Average Error: 52.0 → 52.0
Time: 13.6s
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 r49950 = 9.0;
        double r49951 = x;
        double r49952 = 4.0;
        double r49953 = pow(r49951, r49952);
        double r49954 = r49950 * r49953;
        double r49955 = y;
        double r49956 = pow(r49955, r49952);
        double r49957 = r49954 - r49956;
        double r49958 = 2.0;
        double r49959 = r49955 * r49955;
        double r49960 = r49958 * r49959;
        double r49961 = r49957 + r49960;
        return r49961;
}
↓
double f(double x, double y) {
        double r49962 = 9.0;
        double r49963 = x;
        double r49964 = 4.0;
        double r49965 = pow(r49963, r49964);
        double r49966 = r49962 * r49965;
        double r49967 = y;
        double r49968 = pow(r49967, r49964);
        double r49969 = r49966 - r49968;
        double r49970 = 3.0;
        double r49971 = pow(r49969, r49970);
        double r49972 = cbrt(r49971);
        double r49973 = 2.0;
        double r49974 = r49967 * r49967;
        double r49975 = r49973 * r49974;
        double r49976 = r49972 + r49975;
        return r49976;
}

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))))