Average Error: 52.0 → 52.0
Time: 13.7s
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 r2949007 = 9.0;
        double r2949008 = x;
        double r2949009 = 4.0;
        double r2949010 = pow(r2949008, r2949009);
        double r2949011 = r2949007 * r2949010;
        double r2949012 = y;
        double r2949013 = pow(r2949012, r2949009);
        double r2949014 = r2949011 - r2949013;
        double r2949015 = 2.0;
        double r2949016 = r2949012 * r2949012;
        double r2949017 = r2949015 * r2949016;
        double r2949018 = r2949014 + r2949017;
        return r2949018;
}
↓
double f(double x, double y) {
        double r2949019 = 2.0;
        double r2949020 = y;
        double r2949021 = r2949020 * r2949020;
        double r2949022 = r2949019 * r2949021;
        double r2949023 = x;
        double r2949024 = 4.0;
        double r2949025 = pow(r2949023, r2949024);
        double r2949026 = 9.0;
        double r2949027 = r2949025 * r2949026;
        double r2949028 = pow(r2949020, r2949024);
        double r2949029 = r2949027 - r2949028;
        double r2949030 = r2949029 * r2949029;
        double r2949031 = r2949029 * r2949030;
        double r2949032 = cbrt(r2949031);
        double r2949033 = r2949022 + r2949032;
        return r2949033;
}

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 2019172 
(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))))