Average Error: 52.0 → 52.0
Time: 7.3s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[2 \cdot \left(y \cdot y\right) + \sqrt[3]{{\left({x}^{4} \cdot 9 - {y}^{4}\right)}^{3}}\]
\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)}^{3}}
double f(double x, double y) {
        double r43299 = 9.0;
        double r43300 = x;
        double r43301 = 4.0;
        double r43302 = pow(r43300, r43301);
        double r43303 = r43299 * r43302;
        double r43304 = y;
        double r43305 = pow(r43304, r43301);
        double r43306 = r43303 - r43305;
        double r43307 = 2.0;
        double r43308 = r43304 * r43304;
        double r43309 = r43307 * r43308;
        double r43310 = r43306 + r43309;
        return r43310;
}
↓
double f(double x, double y) {
        double r43311 = 2.0;
        double r43312 = y;
        double r43313 = r43312 * r43312;
        double r43314 = r43311 * r43313;
        double r43315 = x;
        double r43316 = 4.0;
        double r43317 = pow(r43315, r43316);
        double r43318 = 9.0;
        double r43319 = r43317 * r43318;
        double r43320 = pow(r43312, r43316);
        double r43321 = r43319 - r43320;
        double r43322 = 3.0;
        double r43323 = pow(r43321, r43322);
        double r43324 = cbrt(r43323);
        double r43325 = r43314 + r43324;
        return r43325;
}

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

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

  5. Final simplification52.0

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

Reproduce

herbie shell --seed 2019194 
(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))))