Average Error: 52.0 → 52.0
Time: 13.8s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} + 2 \cdot \left(y \cdot y\right)\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} + 2 \cdot \left(y \cdot y\right)
double f(double x, double y) {
        double r47239 = 9.0;
        double r47240 = x;
        double r47241 = 4.0;
        double r47242 = pow(r47240, r47241);
        double r47243 = r47239 * r47242;
        double r47244 = y;
        double r47245 = pow(r47244, r47241);
        double r47246 = r47243 - r47245;
        double r47247 = 2.0;
        double r47248 = r47244 * r47244;
        double r47249 = r47247 * r47248;
        double r47250 = r47246 + r47249;
        return r47250;
}
↓
double f(double x, double y) {
        double r47251 = 9.0;
        double r47252 = x;
        double r47253 = 4.0;
        double r47254 = pow(r47252, r47253);
        double r47255 = r47251 * r47254;
        double r47256 = y;
        double r47257 = pow(r47256, r47253);
        double r47258 = r47255 - r47257;
        double r47259 = 3.0;
        double r47260 = pow(r47258, r47259);
        double r47261 = cbrt(r47260);
        double r47262 = 2.0;
        double r47263 = r47256 * r47256;
        double r47264 = r47262 * r47263;
        double r47265 = r47261 + r47264;
        return r47265;
}

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

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

  5. Final simplification52.0

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

Reproduce

herbie shell --seed 2019325 
(FPCore (x y)
  :name "From Rump in a 1983 paper"
  :precision binary64
  :pre (and (== x 10864) (== y 18817))
  (+ (- (* 9 (pow x 4)) (pow y 4)) (* 2 (* y y))))