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 r49351 = 9.0;
        double r49352 = x;
        double r49353 = 4.0;
        double r49354 = pow(r49352, r49353);
        double r49355 = r49351 * r49354;
        double r49356 = y;
        double r49357 = pow(r49356, r49353);
        double r49358 = r49355 - r49357;
        double r49359 = 2.0;
        double r49360 = r49356 * r49356;
        double r49361 = r49359 * r49360;
        double r49362 = r49358 + r49361;
        return r49362;
}
↓
double f(double x, double y) {
        double r49363 = 9.0;
        double r49364 = x;
        double r49365 = 4.0;
        double r49366 = pow(r49364, r49365);
        double r49367 = r49363 * r49366;
        double r49368 = y;
        double r49369 = pow(r49368, r49365);
        double r49370 = r49367 - r49369;
        double r49371 = 3.0;
        double r49372 = pow(r49370, r49371);
        double r49373 = cbrt(r49372);
        double r49374 = 2.0;
        double r49375 = r49368 * r49368;
        double r49376 = r49374 * r49375;
        double r49377 = r49373 + r49376;
        return r49377;
}

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 2020003 +o rules:numerics
(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))))