Average Error: 52.0 → 52.0
Time: 2.4s
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 r47305 = 9.0;
        double r47306 = x;
        double r47307 = 4.0;
        double r47308 = pow(r47306, r47307);
        double r47309 = r47305 * r47308;
        double r47310 = y;
        double r47311 = pow(r47310, r47307);
        double r47312 = r47309 - r47311;
        double r47313 = 2.0;
        double r47314 = r47310 * r47310;
        double r47315 = r47313 * r47314;
        double r47316 = r47312 + r47315;
        return r47316;
}
↓
double f(double x, double y) {
        double r47317 = 9.0;
        double r47318 = x;
        double r47319 = 4.0;
        double r47320 = pow(r47318, r47319);
        double r47321 = r47317 * r47320;
        double r47322 = y;
        double r47323 = pow(r47322, r47319);
        double r47324 = r47321 - r47323;
        double r47325 = 3.0;
        double r47326 = pow(r47324, r47325);
        double r47327 = cbrt(r47326);
        double r47328 = 2.0;
        double r47329 = r47322 * r47322;
        double r47330 = r47328 * r47329;
        double r47331 = r47327 + r47330;
        return r47331;
}

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 2020060 
(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))))