Average Error: 62.0 → 0
Time: 4.3s
Precision: binary64
Cost: 14848
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right) \]
↓
\[\begin{array}{l} t_0 := \left(y \cdot y\right) \cdot \left(y \cdot y + -2\right)\\ \mathsf{fma}\left(2 - y \cdot y, y \cdot y, t_0\right) + \left(9 \cdot {x}^{4} - t_0\right) \end{array} \]
(FPCore (x y)
 :precision binary64
 (- (* 9.0 (pow x 4.0)) (* (* y y) (- (* y y) 2.0))))
↓
(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (* y y) (+ (* y y) -2.0))))
   (+ (fma (- 2.0 (* y y)) (* y y) t_0) (- (* 9.0 (pow x 4.0)) t_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) {
	double t_0 = (y * y) * ((y * y) + -2.0);
	return fma((2.0 - (y * y)), (y * y), t_0) + ((9.0 * pow(x, 4.0)) - t_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)
	t_0 = Float64(Float64(y * y) * Float64(Float64(y * y) + -2.0))
	return Float64(fma(Float64(2.0 - Float64(y * y)), Float64(y * y), t_0) + Float64(Float64(9.0 * (x ^ 4.0)) - t_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_] := Block[{t$95$0 = N[(N[(y * y), $MachinePrecision] * N[(N[(y * y), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(2.0 - N[(y * y), $MachinePrecision]), $MachinePrecision] * N[(y * y), $MachinePrecision] + t$95$0), $MachinePrecision] + N[(N[(9.0 * N[Power[x, 4.0], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]), $MachinePrecision]]

9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
\begin{array}{l}
t_0 := \left(y \cdot y\right) \cdot \left(y \cdot y + -2\right)\\
\mathsf{fma}\left(2 - y \cdot y, y \cdot y, t_0\right) + \left(9 \cdot {x}^{4} - t_0\right)
\end{array}

Error

Derivation

  1. Initial program 62.0

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

  2. Applied egg-rr0

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

  3. Final simplification0

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

Alternatives

Alternative 1
Error52.0
Cost7552
\[\left(9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right) + 2 \cdot \left(y \cdot y\right) \]
Alternative 2
Error57.8
Cost6656
\[9 \cdot {x}^{4} \]
Alternative 3
Error57.9
Cost1600
\[\begin{array}{l} t_0 := y \cdot y + 3 \cdot \left(x \cdot x\right)\\ 2 \cdot \left(y \cdot y\right) + t_0 \cdot t_0 \end{array} \]

Error

Reproduce

herbie shell --seed 2023011 
(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))))