Average Error: 62.0 → 62.0
Time: 12.1s
Precision: 64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[\left(\left(y \cdot y\right) \cdot 2 + 9 \cdot {x}^{4}\right) - {y}^{4}\]
9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
\left(\left(y \cdot y\right) \cdot 2 + 9 \cdot {x}^{4}\right) - {y}^{4}
double f(double x, double y) {
        double r53586 = 9.0;
        double r53587 = x;
        double r53588 = 4.0;
        double r53589 = pow(r53587, r53588);
        double r53590 = r53586 * r53589;
        double r53591 = y;
        double r53592 = r53591 * r53591;
        double r53593 = 2.0;
        double r53594 = r53592 - r53593;
        double r53595 = r53592 * r53594;
        double r53596 = r53590 - r53595;
        return r53596;
}
↓
double f(double x, double y) {
        double r53597 = y;
        double r53598 = r53597 * r53597;
        double r53599 = 2.0;
        double r53600 = r53598 * r53599;
        double r53601 = 9.0;
        double r53602 = x;
        double r53603 = 4.0;
        double r53604 = pow(r53602, r53603);
        double r53605 = r53601 * r53604;
        double r53606 = r53600 + r53605;
        double r53607 = 4.0;
        double r53608 = pow(r53597, r53607);
        double r53609 = r53606 - r53608;
        return r53609;
}

Error

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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. Simplified52.0

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

  9. Final simplification62.0

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

Reproduce

herbie shell --seed 2019303 
(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))))