Average Error: 52.0 → 52.0
Time: 27.3s
Precision: 64
\[x = 10864.0 \land y = 18817.0\]
\[\left(9.0 \cdot {x}^{4.0} - {y}^{4.0}\right) + 2.0 \cdot \left(y \cdot y\right)\]
↓
\[2.0 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4.0} \cdot 9.0 - {y}^{4.0}\right) \cdot \left(\left({x}^{4.0} \cdot 9.0 - {y}^{4.0}\right) \cdot \left({x}^{4.0} \cdot 9.0 - {y}^{4.0}\right)\right)}\]
\left(9.0 \cdot {x}^{4.0} - {y}^{4.0}\right) + 2.0 \cdot \left(y \cdot y\right)
↓
2.0 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4.0} \cdot 9.0 - {y}^{4.0}\right) \cdot \left(\left({x}^{4.0} \cdot 9.0 - {y}^{4.0}\right) \cdot \left({x}^{4.0} \cdot 9.0 - {y}^{4.0}\right)\right)}
double f(double x, double y) {
        double r2547495 = 9.0;
        double r2547496 = x;
        double r2547497 = 4.0;
        double r2547498 = pow(r2547496, r2547497);
        double r2547499 = r2547495 * r2547498;
        double r2547500 = y;
        double r2547501 = pow(r2547500, r2547497);
        double r2547502 = r2547499 - r2547501;
        double r2547503 = 2.0;
        double r2547504 = r2547500 * r2547500;
        double r2547505 = r2547503 * r2547504;
        double r2547506 = r2547502 + r2547505;
        return r2547506;
}
↓
double f(double x, double y) {
        double r2547507 = 2.0;
        double r2547508 = y;
        double r2547509 = r2547508 * r2547508;
        double r2547510 = r2547507 * r2547509;
        double r2547511 = x;
        double r2547512 = 4.0;
        double r2547513 = pow(r2547511, r2547512);
        double r2547514 = 9.0;
        double r2547515 = r2547513 * r2547514;
        double r2547516 = pow(r2547508, r2547512);
        double r2547517 = r2547515 - r2547516;
        double r2547518 = r2547517 * r2547517;
        double r2547519 = r2547517 * r2547518;
        double r2547520 = cbrt(r2547519);
        double r2547521 = r2547510 + r2547520;
        return r2547521;
}

Error

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Your Program's Arguments

Results

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Derivation

  1. Initial program 52.0

    \[\left(9.0 \cdot {x}^{4.0} - {y}^{4.0}\right) + 2.0 \cdot \left(y \cdot y\right)\]
  2. Using strategy rm

  3. Applied add-cbrt-cube52.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(9.0 \cdot {x}^{4.0} - {y}^{4.0}\right) \cdot \left(9.0 \cdot {x}^{4.0} - {y}^{4.0}\right)\right) \cdot \left(9.0 \cdot {x}^{4.0} - {y}^{4.0}\right)}} + 2.0 \cdot \left(y \cdot y\right)\]

  4. Final simplification52.0

    \[\leadsto 2.0 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4.0} \cdot 9.0 - {y}^{4.0}\right) \cdot \left(\left({x}^{4.0} \cdot 9.0 - {y}^{4.0}\right) \cdot \left({x}^{4.0} \cdot 9.0 - {y}^{4.0}\right)\right)}\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x y)
  :name "From Rump in a 1983 paper"
  :pre (and (== x 10864.0) (== y 18817.0))
  (+ (- (* 9.0 (pow x 4.0)) (pow y 4.0)) (* 2.0 (* y y))))