Average Error: 52.0 → 52.0
Time: 13.0s
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 r49294 = 9.0;
        double r49295 = x;
        double r49296 = 4.0;
        double r49297 = pow(r49295, r49296);
        double r49298 = r49294 * r49297;
        double r49299 = y;
        double r49300 = pow(r49299, r49296);
        double r49301 = r49298 - r49300;
        double r49302 = 2.0;
        double r49303 = r49299 * r49299;
        double r49304 = r49302 * r49303;
        double r49305 = r49301 + r49304;
        return r49305;
}
↓
double f(double x, double y) {
        double r49306 = 9.0;
        double r49307 = x;
        double r49308 = 4.0;
        double r49309 = pow(r49307, r49308);
        double r49310 = r49306 * r49309;
        double r49311 = y;
        double r49312 = pow(r49311, r49308);
        double r49313 = r49310 - r49312;
        double r49314 = 3.0;
        double r49315 = pow(r49313, r49314);
        double r49316 = cbrt(r49315);
        double r49317 = 2.0;
        double r49318 = r49311 * r49311;
        double r49319 = r49317 * r49318;
        double r49320 = r49316 + r49319;
        return r49320;
}

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))))