Average Error: 62.0 → 52.0
Time: 15.2s
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 r3512520 = 9.0;
        double r3512521 = x;
        double r3512522 = 4.0;
        double r3512523 = pow(r3512521, r3512522);
        double r3512524 = r3512520 * r3512523;
        double r3512525 = y;
        double r3512526 = r3512525 * r3512525;
        double r3512527 = 2.0;
        double r3512528 = r3512526 - r3512527;
        double r3512529 = r3512526 * r3512528;
        double r3512530 = r3512524 - r3512529;
        return r3512530;
}
↓
double f(double x, double y) {
        double r3512531 = x;
        double r3512532 = 4.0;
        double r3512533 = pow(r3512531, r3512532);
        double r3512534 = 9.0;
        double r3512535 = r3512533 * r3512534;
        double r3512536 = y;
        double r3512537 = r3512536 * r3512536;
        double r3512538 = r3512537 * r3512537;
        double r3512539 = r3512535 - r3512538;
        double r3512540 = r3512539 * r3512539;
        double r3512541 = r3512540 * r3512539;
        double r3512542 = cbrt(r3512541);
        double r3512543 = 2.0;
        double r3512544 = -r3512543;
        double r3512545 = r3512544 * r3512537;
        double r3512546 = r3512542 - r3512545;
        return r3512546;
}

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-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 2019171 
(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))))