Average Error: 62.0 → 0
Time: 1.8s
Precision: binary64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right) \]
↓
\[\mathsf{fma}\left(y, -y \cdot \mathsf{fma}\left(y, y, -2\right), 9 \cdot {x}^{4}\right) \]
(FPCore (x y)
 :precision binary64
 (- (* 9.0 (pow x 4.0)) (* (* y y) (- (* y y) 2.0))))
↓
(FPCore (x y)
 :precision binary64
 (fma y (- (* y (fma y y -2.0))) (* 9.0 (pow x 4.0))))
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(y, -(y * fma(y, y, -2.0)), (9.0 * pow(x, 4.0)));
}

function code(x, y)
	return Float64(Float64(9.0 * (x ^ 4.0)) - Float64(Float64(y * y) * Float64(Float64(y * y) - 2.0)))
end
↓
function code(x, y)
	return fma(y, Float64(-Float64(y * fma(y, y, -2.0))), Float64(9.0 * (x ^ 4.0)))
end

code[x_, y_] := N[(N[(9.0 * N[Power[x, 4.0], $MachinePrecision]), $MachinePrecision] - N[(N[(y * y), $MachinePrecision] * N[(N[(y * y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(y * (-N[(y * N[(y * y + -2.0), $MachinePrecision]), $MachinePrecision]) + N[(9.0 * N[Power[x, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

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

Error

Derivation

  1. Initial program 62.0

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

  2. Simplified62.0

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

  3. Applied egg-rr0

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

  4. Final simplification0

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

Reproduce

herbie shell --seed 2022140 
(FPCore (x y)
  :name "From Rump in a 1983 paper, rewritten"
  :precision binary64
  :pre (and (== x 10864.0) (== y 18817.0))
  (- (* 9.0 (pow x 4.0)) (* (* y y) (- (* y y) 2.0))))