Average Error: 52.0 → 52.0
Time: 26.4s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[2 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}\]
\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) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}
double f(double x, double y) {
        double r3795005 = 9.0;
        double r3795006 = x;
        double r3795007 = 4.0;
        double r3795008 = pow(r3795006, r3795007);
        double r3795009 = r3795005 * r3795008;
        double r3795010 = y;
        double r3795011 = pow(r3795010, r3795007);
        double r3795012 = r3795009 - r3795011;
        double r3795013 = 2.0;
        double r3795014 = r3795010 * r3795010;
        double r3795015 = r3795013 * r3795014;
        double r3795016 = r3795012 + r3795015;
        return r3795016;
}
↓
double f(double x, double y) {
        double r3795017 = 2.0;
        double r3795018 = y;
        double r3795019 = r3795018 * r3795018;
        double r3795020 = r3795017 * r3795019;
        double r3795021 = x;
        double r3795022 = 4.0;
        double r3795023 = pow(r3795021, r3795022);
        double r3795024 = 9.0;
        double r3795025 = r3795023 * r3795024;
        double r3795026 = pow(r3795018, r3795022);
        double r3795027 = r3795025 - r3795026;
        double r3795028 = r3795027 * r3795027;
        double r3795029 = r3795027 * r3795028;
        double r3795030 = cbrt(r3795029);
        double r3795031 = r3795020 + r3795030;
        return r3795031;
}

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. Final simplification52.0

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

Reproduce

herbie shell --seed 2019168 
(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))))