Average Error: 0.0 → 0.0
Time: 5.2s
Precision: binary64
Cost: 6848
\[\left(x \cdot 2 + x \cdot x\right) + y \cdot y \]
↓
\[\mathsf{fma}\left(y, y, x \cdot \left(x + 2\right)\right) \]
(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)

Error

Target

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

Derivation

  1. Initial program 0.0

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

  2. Applied egg-rr0.0

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

  3. Final simplification0.0

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

Alternatives

Alternative 1
Error23.6
Cost984
\[\begin{array}{l} \mathbf{if}\;x \leq -206656834.59811637:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq -1.0328821791116344 \cdot 10^{-188}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;x \leq -3.618042442110372 \cdot 10^{-210}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 4.8519513807725224 \cdot 10^{-244}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;x \leq 4.4091860649209813 \cdot 10^{-20}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 768591552366115.8:\\ \;\;\;\;y \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]
Alternative 2
Error10.4
Cost712
\[\begin{array}{l} \mathbf{if}\;y \leq -1.9500649546564696 \cdot 10^{-42}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;y \leq 3.4981477904657354 \cdot 10^{-69}:\\ \;\;\;\;x \cdot x + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;y \cdot y\\ \end{array} \]
Alternative 3
Error3.9
Cost712
\[\begin{array}{l} t_0 := x \cdot x + y \cdot y\\ \mathbf{if}\;y \leq -3.0383785291965773 \cdot 10^{-87}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.6171712579822924 \cdot 10^{-85}:\\ \;\;\;\;x \cdot x + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 4
Error1.3
Cost712
\[\begin{array}{l} t_0 := x \cdot x + y \cdot y\\ \mathbf{if}\;x \leq -111.87953993195254:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.34999229671614995:\\ \;\;\;\;y \cdot y + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 5
Error0.0
Cost704
\[y \cdot y + \left(x \cdot x + x \cdot 2\right) \]
Alternative 6
Error10.4
Cost584
\[\begin{array}{l} \mathbf{if}\;y \leq -1.9500649546564696 \cdot 10^{-42}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;y \leq 3.4981477904657354 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(x + 2\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot y\\ \end{array} \]
Alternative 7
Error0.0
Cost576
\[x \cdot \left(x + 2\right) + y \cdot y \]
Alternative 8
Error21.5
Cost456
\[\begin{array}{l} \mathbf{if}\;y \leq -3.0383785291965773 \cdot 10^{-87}:\\ \;\;\;\;y \cdot y\\ \mathbf{elif}\;y \leq 4.6171712579822924 \cdot 10^{-85}:\\ \;\;\;\;x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;y \cdot y\\ \end{array} \]
Alternative 9
Error42.2
Cost192
\[x \cdot 2 \]

Error

Reproduce

herbie shell --seed 2022297 
(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)))