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

↓

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

(FPCore (x y) :precision binary64 (+ (+ (* x 2.0) (* x x)) (* y y)))

↓

(FPCore (x y) :precision binary64 (fma y y (* x (+ x 2.0))))

double code(double x, double y) {
	return ((x * 2.0) + (x * x)) + (y * y);
}

↓

double code(double x, double y) {
	return fma(y, y, (x * (x + 2.0)));
}

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

↓

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

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

↓

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

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

↓

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

Original	0.0
Target	0.0
Herbie	0.0

Derivation

Initial program 0.0
\[\left(x \cdot 2 + x \cdot x\right) + y \cdot y \]
Applied egg-rr0.0
\[\leadsto \color{blue}{\mathsf{fma}\left(y, y, x \cdot \left(x + 2\right)\right)} \]
Final simplification0.0
\[\leadsto \mathsf{fma}\left(y, y, x \cdot \left(x + 2\right)\right) \]

Alternatives

Alternative 1
Error	22.2
Cost	984

\[\begin{array}{l} \mathbf{if}\;y \leq -2.0473755703022338 \cdot 10^{-48}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;y \leq -1.1425786832006367 \cdot 10^{-60}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;y \leq -1.9627365448322503 \cdot 10^{-76}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;y \leq -2.4615407341997716 \cdot 10^{-144}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;y \leq -2.7112890487471582 \cdot 10^{-182}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;y \leq 2.1421365959341102 \cdot 10^{-96}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;y \cdot y\\ \end{array} \]

Alternative 2
Error	4.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;x \leq -0.007314762397706714:\\ \;\;\;\;x \cdot \left(x + 2\right)\\ \mathbf{elif}\;x \leq 5.555247080015769 \cdot 10^{-19}:\\ \;\;\;\;y \cdot y + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot x + x \cdot 2\\ \end{array} \]

Alternative 3
Error	1.6
Cost	712

\[\begin{array}{l} t_0 := x \cdot x + y \cdot y\\ \mathbf{if}\;x \leq -26400793.338923223:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.727645131349073 \cdot 10^{-7}:\\ \;\;\;\;y \cdot y + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	0.0
Cost	704

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

Alternative 5
Error	10.1
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1.4630840755337115 \cdot 10^{-44}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;y \leq 3.7438811464537276 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(x + 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot y\\ \end{array} \]

Alternative 6
Error	21.6
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1.4630840755337115 \cdot 10^{-44}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;y \leq 2.1421365959341102 \cdot 10^{-96}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;y \cdot y\\ \end{array} \]

Alternative 7
Error	42.0
Cost	192

\[x \cdot 2 \]

Reproduce

herbie shell --seed 2022300 
(FPCore (x y)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, A"
  :precision binary64

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

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

Error

Target

Derivation

Alternatives

Error

Reproduce