Average Error: 52.0 → 52.0
Time: 21.7s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\sqrt[3]{\left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)} + 2 \cdot \left(y \cdot y\right)\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
\sqrt[3]{\left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)} + 2 \cdot \left(y \cdot y\right)
double f(double x, double y) {
        double r2909310 = 9.0;
        double r2909311 = x;
        double r2909312 = 4.0;
        double r2909313 = pow(r2909311, r2909312);
        double r2909314 = r2909310 * r2909313;
        double r2909315 = y;
        double r2909316 = pow(r2909315, r2909312);
        double r2909317 = r2909314 - r2909316;
        double r2909318 = 2.0;
        double r2909319 = r2909315 * r2909315;
        double r2909320 = r2909318 * r2909319;
        double r2909321 = r2909317 + r2909320;
        return r2909321;
}
↓
double f(double x, double y) {
        double r2909322 = x;
        double r2909323 = 4.0;
        double r2909324 = pow(r2909322, r2909323);
        double r2909325 = 9.0;
        double r2909326 = r2909324 * r2909325;
        double r2909327 = y;
        double r2909328 = pow(r2909327, r2909323);
        double r2909329 = r2909326 - r2909328;
        double r2909330 = r2909329 * r2909329;
        double r2909331 = r2909330 * r2909329;
        double r2909332 = cbrt(r2909331);
        double r2909333 = 2.0;
        double r2909334 = r2909327 * r2909327;
        double r2909335 = r2909333 * r2909334;
        double r2909336 = r2909332 + r2909335;
        return r2909336;
}

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

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(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))))