Average Error: 0.0 → 0.0
Time: 5.8s
Precision: binary64
Cost: 6848
\[2 \cdot \left(x \cdot x + x \cdot y\right) \]
↓
\[2 \cdot \mathsf{fma}\left(y, x, x \cdot x\right) \]
(FPCore (x y) :precision binary64 (* 2.0 (+ (* x x) (* x y))))
↓
(FPCore (x y) :precision binary64 (* 2.0 (fma y x (* x x))))
double code(double x, double y) {
	return 2.0 * ((x * x) + (x * y));
}
↓
double code(double x, double y) {
	return 2.0 * fma(y, x, (x * x));
}

function code(x, y)
	return Float64(2.0 * Float64(Float64(x * x) + Float64(x * y)))
end
↓
function code(x, y)
	return Float64(2.0 * fma(y, x, Float64(x * x)))
end

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

2 \cdot \left(x \cdot x + x \cdot y\right)
↓
2 \cdot \mathsf{fma}\left(y, x, x \cdot x\right)

Error

Target

Original0.0
Target0.0
Herbie0.0
\[\left(x \cdot 2\right) \cdot \left(x + y\right) \]

Derivation

  1. Initial program 0.0

    \[2 \cdot \left(x \cdot x + x \cdot y\right) \]

  2. Applied egg-rr0.0

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

  3. Final simplification0.0

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

Alternatives

Alternative 1
Error15.2
Cost1112
\[\begin{array}{l} t_0 := x \cdot \left(2 \cdot x\right)\\ t_1 := x \cdot \left(2 \cdot y\right)\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+68}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -9.2550700171727 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.8599552550718737 \cdot 10^{-17}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.8559982809127606 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.7658802787410023 \cdot 10^{+47}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 2
Error0.0
Cost448
\[2 \cdot \left(x \cdot \left(y + x\right)\right) \]
Alternative 3
Error21.8
Cost320
\[x \cdot \left(2 \cdot y\right) \]

Error

Reproduce

herbie shell --seed 2022300 
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (* (* x 2.0) (+ x y))

  (* 2.0 (+ (* x x) (* x y))))