Average Error: 52.0 → 52.0
Time: 13.9s
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 r2949009 = 9.0;
        double r2949010 = x;
        double r2949011 = 4.0;
        double r2949012 = pow(r2949010, r2949011);
        double r2949013 = r2949009 * r2949012;
        double r2949014 = y;
        double r2949015 = pow(r2949014, r2949011);
        double r2949016 = r2949013 - r2949015;
        double r2949017 = 2.0;
        double r2949018 = r2949014 * r2949014;
        double r2949019 = r2949017 * r2949018;
        double r2949020 = r2949016 + r2949019;
        return r2949020;
}
↓
double f(double x, double y) {
        double r2949021 = 2.0;
        double r2949022 = y;
        double r2949023 = r2949022 * r2949022;
        double r2949024 = r2949021 * r2949023;
        double r2949025 = x;
        double r2949026 = 4.0;
        double r2949027 = pow(r2949025, r2949026);
        double r2949028 = 9.0;
        double r2949029 = r2949027 * r2949028;
        double r2949030 = pow(r2949022, r2949026);
        double r2949031 = r2949029 - r2949030;
        double r2949032 = r2949031 * r2949031;
        double r2949033 = r2949031 * r2949032;
        double r2949034 = cbrt(r2949033);
        double r2949035 = r2949024 + r2949034;
        return r2949035;
}

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))))