Average Error: 62.0 → 52.0
Time: 15.6s
Precision: 64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[\sqrt[3]{\left(\left({x}^{4} \cdot 9 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right) \cdot \left({x}^{4} \cdot 9 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right) \cdot \left({x}^{4} \cdot 9 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)} - \left(-2\right) \cdot \left(y \cdot y\right)\]
9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
\sqrt[3]{\left(\left({x}^{4} \cdot 9 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right) \cdot \left({x}^{4} \cdot 9 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right) \cdot \left({x}^{4} \cdot 9 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)} - \left(-2\right) \cdot \left(y \cdot y\right)
double f(double x, double y) {
        double r3131338 = 9.0;
        double r3131339 = x;
        double r3131340 = 4.0;
        double r3131341 = pow(r3131339, r3131340);
        double r3131342 = r3131338 * r3131341;
        double r3131343 = y;
        double r3131344 = r3131343 * r3131343;
        double r3131345 = 2.0;
        double r3131346 = r3131344 - r3131345;
        double r3131347 = r3131344 * r3131346;
        double r3131348 = r3131342 - r3131347;
        return r3131348;
}
↓
double f(double x, double y) {
        double r3131349 = x;
        double r3131350 = 4.0;
        double r3131351 = pow(r3131349, r3131350);
        double r3131352 = 9.0;
        double r3131353 = r3131351 * r3131352;
        double r3131354 = y;
        double r3131355 = r3131354 * r3131354;
        double r3131356 = r3131355 * r3131355;
        double r3131357 = r3131353 - r3131356;
        double r3131358 = r3131357 * r3131357;
        double r3131359 = r3131358 * r3131357;
        double r3131360 = cbrt(r3131359);
        double r3131361 = 2.0;
        double r3131362 = -r3131361;
        double r3131363 = r3131362 * r3131355;
        double r3131364 = r3131360 - r3131363;
        return r3131364;
}

Error

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Your Program's Arguments

Results

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Derivation

  1. Initial program 62.0

    \[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
  2. Using strategy rm

  3. Applied sub-neg62.0

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

  4. Applied distribute-lft-in62.0

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

  5. Applied associate--r+52.0

    \[\leadsto \color{blue}{\left(9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right) - \left(y \cdot y\right) \cdot \left(-2\right)}\]
  6. Using strategy rm

  7. Applied add-cbrt-cube52.0

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

  8. Final simplification52.0

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x y)
  :name "From Rump in a 1983 paper, rewritten"
  :pre (and (== x 10864.0) (== y 18817.0))
  (- (* 9.0 (pow x 4.0)) (* (* y y) (- (* y y) 2.0))))