Average Error: 0.0 → 0.0
Time: 2.4s
Precision: binary64
Cost: 6976
\[\left(x + y\right) \cdot \left(x + y\right) \]
↓
\[\mathsf{fma}\left(x + y, x, y \cdot \left(x + y\right)\right) \]
(FPCore (x y) :precision binary64 (* (+ x y) (+ x y)))
↓
(FPCore (x y) :precision binary64 (fma (+ x y) x (* y (+ x y))))
double code(double x, double y) {
	return (x + y) * (x + y);
}
↓
double code(double x, double y) {
	return fma((x + y), x, (y * (x + y)));
}

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

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

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

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

  3. Final simplification0.0

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

Alternatives

Alternative 1
Error0.0
Cost704
\[y \cdot \left(x + y\right) + x \cdot \left(x + y\right) \]
Alternative 2
Error20.6
Cost580
\[\begin{array}{l} \mathbf{if}\;y \leq 8.6 \cdot 10^{-137}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y + x \cdot 2\right)\\ \end{array} \]
Alternative 3
Error0.0
Cost448
\[\left(x + y\right) \cdot \left(x + y\right) \]
Alternative 4
Error20.7
Cost324
\[\begin{array}{l} \mathbf{if}\;y \leq 8.6 \cdot 10^{-137}:\\ \;\;\;\;x \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot y\\ \end{array} \]
Alternative 5
Error28.1
Cost192
\[x \cdot x \]

Error

Reproduce

herbie shell --seed 2022329 
(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)))