Average Error: 0.0 → 0.0
Time: 8.3s
Precision: binary64
Cost: 6976
\[\left(x + y\right) \cdot \left(x + y\right) \]
↓
\[\mathsf{fma}\left(x + y, y, \left(x + y\right) \cdot x\right) \]
(FPCore (x y) :precision binary64 (* (+ x y) (+ x y)))
↓
(FPCore (x y) :precision binary64 (fma (+ x y) y (* (+ x y) x)))
double code(double x, double y) {
	return (x + y) * (x + y);
}
↓
double code(double x, double y) {
	return fma((x + y), y, ((x + y) * x));
}

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

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

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

Error

Target

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

Derivation

  1. Initial program 0.0

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

  2. Applied egg-rr0.0

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

Alternatives

Alternative 1
Error12.7
Cost712
\[\begin{array}{l} t_0 := x \cdot \left(\left(y + y\right) + x\right)\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{-23}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \left(\left(x + x\right) + y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 2
Error0.0
Cost704
\[y \cdot y + x \cdot \left(\left(x + y\right) + y\right) \]
Alternative 3
Error0.0
Cost704
\[\left(x + y\right) \cdot y + \left(x + y\right) \cdot x \]
Alternative 4
Error12.8
Cost580
\[\begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(\left(y + y\right) + x\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-96}:\\ \;\;\;\;y \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]
Alternative 5
Error13.0
Cost456
\[\begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{-21}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-96}:\\ \;\;\;\;y \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]
Alternative 6
Error0.0
Cost448
\[\left(x + y\right) \cdot \left(x + y\right) \]
Alternative 7
Error28.1
Cost192
\[x \cdot x \]

Error

Reproduce

herbie shell --seed 2023010 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f3 from sbv-4.4"
  :precision binary64

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

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