Average Error: 52.0 → 52.0
Time: 13.1s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[2 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
2 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}
double f(double x, double y) {
        double r2787484 = 9.0;
        double r2787485 = x;
        double r2787486 = 4.0;
        double r2787487 = pow(r2787485, r2787486);
        double r2787488 = r2787484 * r2787487;
        double r2787489 = y;
        double r2787490 = pow(r2787489, r2787486);
        double r2787491 = r2787488 - r2787490;
        double r2787492 = 2.0;
        double r2787493 = r2787489 * r2787489;
        double r2787494 = r2787492 * r2787493;
        double r2787495 = r2787491 + r2787494;
        return r2787495;
}
↓
double f(double x, double y) {
        double r2787496 = 2.0;
        double r2787497 = y;
        double r2787498 = r2787497 * r2787497;
        double r2787499 = r2787496 * r2787498;
        double r2787500 = x;
        double r2787501 = 4.0;
        double r2787502 = pow(r2787500, r2787501);
        double r2787503 = 9.0;
        double r2787504 = r2787502 * r2787503;
        double r2787505 = pow(r2787497, r2787501);
        double r2787506 = r2787504 - r2787505;
        double r2787507 = r2787506 * r2787506;
        double r2787508 = r2787506 * r2787507;
        double r2787509 = cbrt(r2787508);
        double r2787510 = r2787499 + r2787509;
        return r2787510;
}

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. Final simplification52.0

    \[\leadsto 2 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}\]

Reproduce

herbie shell --seed 2019170 +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))))