Average Error: 52.0 → 52.0
Time: 2.8s
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 r59951 = 9.0;
        double r59952 = x;
        double r59953 = 4.0;
        double r59954 = pow(r59952, r59953);
        double r59955 = r59951 * r59954;
        double r59956 = y;
        double r59957 = pow(r59956, r59953);
        double r59958 = r59955 - r59957;
        double r59959 = 2.0;
        double r59960 = r59956 * r59956;
        double r59961 = r59959 * r59960;
        double r59962 = r59958 + r59961;
        return r59962;
}
↓
double f(double x, double y) {
        double r59963 = 9.0;
        double r59964 = x;
        double r59965 = 4.0;
        double r59966 = pow(r59964, r59965);
        double r59967 = r59963 * r59966;
        double r59968 = y;
        double r59969 = pow(r59968, r59965);
        double r59970 = r59967 - r59969;
        double r59971 = 3.0;
        double r59972 = pow(r59970, r59971);
        double r59973 = cbrt(r59972);
        double r59974 = 2.0;
        double r59975 = r59968 * r59968;
        double r59976 = r59974 * r59975;
        double r59977 = r59973 + r59976;
        return r59977;
}

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 2020046 
(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))))