Average Error: 62.0 → 52.0
Time: 3.1s
Precision: 64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[\mathsf{fma}\left({y}^{2}, 2, \sqrt[3]{{\left(9 \cdot \left({\left(\frac{1}{{-1}^{4}}\right)}^{1} \cdot {x}^{4}\right) - {y}^{4}\right)}^{3}}\right)\]
9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
\mathsf{fma}\left({y}^{2}, 2, \sqrt[3]{{\left(9 \cdot \left({\left(\frac{1}{{-1}^{4}}\right)}^{1} \cdot {x}^{4}\right) - {y}^{4}\right)}^{3}}\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, cbrt(pow(((9.0 * (pow((1.0 / pow(-1.0, 4.0)), 1.0) * pow(x, 4.0))) - pow(y, 4.0)), 3.0)));
}

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. Taylor expanded around -inf 62.0

    \[\leadsto \color{blue}{\left(2 \cdot {y}^{2} + 9 \cdot \left({\left(\frac{1}{{-1}^{4}}\right)}^{1} \cdot {x}^{4}\right)\right) - {y}^{4}}\]

  3. Simplified52.0

    \[\leadsto \color{blue}{\mathsf{fma}\left({y}^{2}, 2, 9 \cdot \left({\left(\frac{1}{{-1}^{4}}\right)}^{1} \cdot {x}^{4}\right) - {y}^{4}\right)}\]
  4. Using strategy rm

  5. Applied add-cbrt-cube52.0

    \[\leadsto \mathsf{fma}\left({y}^{2}, 2, \color{blue}{\sqrt[3]{\left(\left(9 \cdot \left({\left(\frac{1}{{-1}^{4}}\right)}^{1} \cdot {x}^{4}\right) - {y}^{4}\right) \cdot \left(9 \cdot \left({\left(\frac{1}{{-1}^{4}}\right)}^{1} \cdot {x}^{4}\right) - {y}^{4}\right)\right) \cdot \left(9 \cdot \left({\left(\frac{1}{{-1}^{4}}\right)}^{1} \cdot {x}^{4}\right) - {y}^{4}\right)}}\right)\]

  6. Simplified52.0

    \[\leadsto \mathsf{fma}\left({y}^{2}, 2, \sqrt[3]{\color{blue}{{\left(9 \cdot \left({\left(\frac{1}{{-1}^{4}}\right)}^{1} \cdot {x}^{4}\right) - {y}^{4}\right)}^{3}}}\right)\]

  7. Final simplification52.0

    \[\leadsto \mathsf{fma}\left({y}^{2}, 2, \sqrt[3]{{\left(9 \cdot \left({\left(\frac{1}{{-1}^{4}}\right)}^{1} \cdot {x}^{4}\right) - {y}^{4}\right)}^{3}}\right)\]

Reproduce

herbie shell --seed 2020078 +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))))