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 r66261 = 9.0;
        double r66262 = x;
        double r66263 = 4.0;
        double r66264 = pow(r66262, r66263);
        double r66265 = r66261 * r66264;
        double r66266 = y;
        double r66267 = pow(r66266, r66263);
        double r66268 = r66265 - r66267;
        double r66269 = 2.0;
        double r66270 = r66266 * r66266;
        double r66271 = r66269 * r66270;
        double r66272 = r66268 + r66271;
        return r66272;
}
↓
double f(double x, double y) {
        double r66273 = 9.0;
        double r66274 = x;
        double r66275 = 4.0;
        double r66276 = pow(r66274, r66275);
        double r66277 = r66273 * r66276;
        double r66278 = y;
        double r66279 = pow(r66278, r66275);
        double r66280 = r66277 - r66279;
        double r66281 = 3.0;
        double r66282 = pow(r66280, r66281);
        double r66283 = cbrt(r66282);
        double r66284 = 2.0;
        double r66285 = r66278 * r66278;
        double r66286 = r66284 * r66285;
        double r66287 = r66283 + r66286;
        return r66287;
}

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 2020056 
(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))))