Average Error: 52.0 → 52.0
Time: 7.3s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} + 2 \cdot \left(y \cdot y\right)\]
\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 r44238 = 9.0;
        double r44239 = x;
        double r44240 = 4.0;
        double r44241 = pow(r44239, r44240);
        double r44242 = r44238 * r44241;
        double r44243 = y;
        double r44244 = pow(r44243, r44240);
        double r44245 = r44242 - r44244;
        double r44246 = 2.0;
        double r44247 = r44243 * r44243;
        double r44248 = r44246 * r44247;
        double r44249 = r44245 + r44248;
        return r44249;
}
↓
double f(double x, double y) {
        double r44250 = 9.0;
        double r44251 = x;
        double r44252 = 4.0;
        double r44253 = pow(r44251, r44252);
        double r44254 = r44250 * r44253;
        double r44255 = y;
        double r44256 = pow(r44255, r44252);
        double r44257 = r44254 - r44256;
        double r44258 = 3.0;
        double r44259 = pow(r44257, r44258);
        double r44260 = cbrt(r44259);
        double r44261 = 2.0;
        double r44262 = r44255 * r44255;
        double r44263 = r44261 * r44262;
        double r44264 = r44260 + r44263;
        return r44264;
}

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 2019212 
(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))))