Average Error: 62.0 → 0
Time: 1.1s
Precision: 64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[\mathsf{fma}\left({y}^{2}, 2 - {y}^{2}, 9 \cdot {x}^{4}\right) + \left(y \cdot \left(y \cdot y - 2\right)\right) \cdot \left(\left(-y\right) + y\right)\]
9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
\mathsf{fma}\left({y}^{2}, 2 - {y}^{2}, 9 \cdot {x}^{4}\right) + \left(y \cdot \left(y \cdot y - 2\right)\right) \cdot \left(\left(-y\right) + y\right)
double code(double x, double y) {
	return ((9.0 * pow(x, 4.0)) - ((y * y) * ((y * y) - 2.0)));
}
↓
double code(double x, double y) {
	return (fma(pow(y, 2.0), (2.0 - pow(y, 2.0)), (9.0 * pow(x, 4.0))) + ((y * ((y * y) - 2.0)) * (-y + y)));
}

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 prod-diff0

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

  4. Simplified52.0

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

  5. Simplified0

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

  6. Final simplification0

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

Reproduce

herbie shell --seed 2020071 +o rules:numerics
(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))))