Average Error: 62.0 → 52.0
Time: 7.8s
Precision: 64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} - \left(y \cdot y\right) \cdot \left(-2\right)\]
9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} - \left(y \cdot y\right) \cdot \left(-2\right)
double f(double x, double y) {
        double r42488 = 9.0;
        double r42489 = x;
        double r42490 = 4.0;
        double r42491 = pow(r42489, r42490);
        double r42492 = r42488 * r42491;
        double r42493 = y;
        double r42494 = r42493 * r42493;
        double r42495 = 2.0;
        double r42496 = r42494 - r42495;
        double r42497 = r42494 * r42496;
        double r42498 = r42492 - r42497;
        return r42498;
}
↓
double f(double x, double y) {
        double r42499 = 9.0;
        double r42500 = x;
        double r42501 = 4.0;
        double r42502 = pow(r42500, r42501);
        double r42503 = r42499 * r42502;
        double r42504 = y;
        double r42505 = 4.0;
        double r42506 = pow(r42504, r42505);
        double r42507 = r42503 - r42506;
        double r42508 = 3.0;
        double r42509 = pow(r42507, r42508);
        double r42510 = cbrt(r42509);
        double r42511 = r42504 * r42504;
        double r42512 = 2.0;
        double r42513 = -r42512;
        double r42514 = r42511 * r42513;
        double r42515 = r42510 - r42514;
        return r42515;
}

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. Simplified52.0

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

  8. Applied add-cbrt-cube52.0

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

  9. Simplified52.0

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

  10. Final simplification52.0

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

Reproduce

herbie shell --seed 2019209 
(FPCore (x y)
  :name "From Rump in a 1983 paper, rewritten"
  :precision binary64
  :pre (and (== x 10864) (== y 18817))
  (- (* 9 (pow x 4)) (* (* y y) (- (* y y) 2))))