Average Error: 62.0 → 52.0
Time: 16.2s
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 r3077403 = 9.0;
        double r3077404 = x;
        double r3077405 = 4.0;
        double r3077406 = pow(r3077404, r3077405);
        double r3077407 = r3077403 * r3077406;
        double r3077408 = y;
        double r3077409 = r3077408 * r3077408;
        double r3077410 = 2.0;
        double r3077411 = r3077409 - r3077410;
        double r3077412 = r3077409 * r3077411;
        double r3077413 = r3077407 - r3077412;
        return r3077413;
}
↓
double f(double x, double y) {
        double r3077414 = x;
        double r3077415 = 4.0;
        double r3077416 = pow(r3077414, r3077415);
        double r3077417 = 9.0;
        double r3077418 = r3077416 * r3077417;
        double r3077419 = y;
        double r3077420 = r3077419 * r3077419;
        double r3077421 = r3077420 * r3077420;
        double r3077422 = r3077418 - r3077421;
        double r3077423 = r3077422 * r3077422;
        double r3077424 = r3077423 * r3077422;
        double r3077425 = cbrt(r3077424);
        double r3077426 = 2.0;
        double r3077427 = -r3077426;
        double r3077428 = r3077427 * r3077420;
        double r3077429 = r3077425 - r3077428;
        return r3077429;
}

Error

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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-rgt-in62.0

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

  5. Applied associate--r+52.0

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

  7. Applied add-cbrt-cube52.0

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

  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 2019192 
(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))))