Average Error: 62.0 → 0
Time: 4.8s
Precision: 64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[\mathsf{fma}\left(y \cdot \mathsf{fma}\left(y, -y, 2\right), y, 9 \cdot {x}^{4}\right)\]
9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
\mathsf{fma}\left(y \cdot \mathsf{fma}\left(y, -y, 2\right), y, 9 \cdot {x}^{4}\right)
double f(double x, double y) {
        double r38852 = 9.0;
        double r38853 = x;
        double r38854 = 4.0;
        double r38855 = pow(r38853, r38854);
        double r38856 = r38852 * r38855;
        double r38857 = y;
        double r38858 = r38857 * r38857;
        double r38859 = 2.0;
        double r38860 = r38858 - r38859;
        double r38861 = r38858 * r38860;
        double r38862 = r38856 - r38861;
        return r38862;
}
↓
double f(double x, double y) {
        double r38863 = y;
        double r38864 = -r38863;
        double r38865 = 2.0;
        double r38866 = fma(r38863, r38864, r38865);
        double r38867 = r38863 * r38866;
        double r38868 = 9.0;
        double r38869 = x;
        double r38870 = 4.0;
        double r38871 = pow(r38869, r38870);
        double r38872 = r38868 * r38871;
        double r38873 = fma(r38867, r38863, r38872);
        return r38873;
}

Error

Derivation

  1. Initial program 62.0

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(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))))