Average Error: 52.0 → 52.0
Time: 11.4s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\mathsf{fma}\left(2 \cdot y, y, \sqrt[3]{{\left(\mathsf{fma}\left({x}^{4}, 9, -{y}^{4}\right)\right)}^{3}}\right)\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
\mathsf{fma}\left(2 \cdot y, y, \sqrt[3]{{\left(\mathsf{fma}\left({x}^{4}, 9, -{y}^{4}\right)\right)}^{3}}\right)
double f(double x, double y) {
        double r49634 = 9.0;
        double r49635 = x;
        double r49636 = 4.0;
        double r49637 = pow(r49635, r49636);
        double r49638 = r49634 * r49637;
        double r49639 = y;
        double r49640 = pow(r49639, r49636);
        double r49641 = r49638 - r49640;
        double r49642 = 2.0;
        double r49643 = r49639 * r49639;
        double r49644 = r49642 * r49643;
        double r49645 = r49641 + r49644;
        return r49645;
}
↓
double f(double x, double y) {
        double r49646 = 2.0;
        double r49647 = y;
        double r49648 = r49646 * r49647;
        double r49649 = x;
        double r49650 = 4.0;
        double r49651 = pow(r49649, r49650);
        double r49652 = 9.0;
        double r49653 = pow(r49647, r49650);
        double r49654 = -r49653;
        double r49655 = fma(r49651, r49652, r49654);
        double r49656 = 3.0;
        double r49657 = pow(r49655, r49656);
        double r49658 = cbrt(r49657);
        double r49659 = fma(r49648, r49647, r49658);
        return r49659;
}

Error

Derivation

  1. Initial program 52.0

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

  2. Simplified52.0

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

  4. Applied add-cbrt-cube52.0

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

  5. Simplified52.0

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

  6. Final simplification52.0

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

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x y)
  :name "From Rump in a 1983 paper"
  :precision binary64
  :pre (and (== x 10864) (== y 18817))
  (+ (- (* 9 (pow x 4)) (pow y 4)) (* 2 (* y y))))