Average Error: 52.0 → 52.0
Time: 13.8s
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 r3702273 = 9.0;
        double r3702274 = x;
        double r3702275 = 4.0;
        double r3702276 = pow(r3702274, r3702275);
        double r3702277 = r3702273 * r3702276;
        double r3702278 = y;
        double r3702279 = pow(r3702278, r3702275);
        double r3702280 = r3702277 - r3702279;
        double r3702281 = 2.0;
        double r3702282 = r3702278 * r3702278;
        double r3702283 = r3702281 * r3702282;
        double r3702284 = r3702280 + r3702283;
        return r3702284;
}
↓
double f(double x, double y) {
        double r3702285 = 2.0;
        double r3702286 = y;
        double r3702287 = r3702286 * r3702286;
        double r3702288 = r3702285 * r3702287;
        double r3702289 = x;
        double r3702290 = 4.0;
        double r3702291 = pow(r3702289, r3702290);
        double r3702292 = 9.0;
        double r3702293 = r3702291 * r3702292;
        double r3702294 = pow(r3702286, r3702290);
        double r3702295 = r3702293 - r3702294;
        double r3702296 = r3702295 * r3702295;
        double r3702297 = r3702295 * r3702296;
        double r3702298 = cbrt(r3702297);
        double r3702299 = r3702288 + r3702298;
        return r3702299;
}

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 2019170 
(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))))