Average Error: 62.0 → 62.0
Time: 11.9s
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 r55605 = 9.0;
        double r55606 = x;
        double r55607 = 4.0;
        double r55608 = pow(r55606, r55607);
        double r55609 = r55605 * r55608;
        double r55610 = y;
        double r55611 = r55610 * r55610;
        double r55612 = 2.0;
        double r55613 = r55611 - r55612;
        double r55614 = r55611 * r55613;
        double r55615 = r55609 - r55614;
        return r55615;
}
↓
double f(double x, double y) {
        double r55616 = y;
        double r55617 = r55616 * r55616;
        double r55618 = 2.0;
        double r55619 = r55617 * r55618;
        double r55620 = 9.0;
        double r55621 = x;
        double r55622 = 4.0;
        double r55623 = pow(r55621, r55622);
        double r55624 = r55620 * r55623;
        double r55625 = r55619 + r55624;
        double r55626 = 4.0;
        double r55627 = pow(r55616, r55626);
        double r55628 = r55625 - r55627;
        return r55628;
}

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 2019297 
(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))))