Average Error: 0.0 → 0.0

Time: 2.6s

Precision: binary64

Cost: 576

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

↓

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

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

↓

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

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

↓

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

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 2.0d0 * ((x * x) + (x * y))
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 2.0d0 * ((x * x) + (x * y))
end function

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

↓

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

def code(x, y):
	return 2.0 * ((x * x) + (x * y))

↓

def code(x, y):
	return 2.0 * ((x * x) + (x * y))

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

↓

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

function tmp = code(x, y)
	tmp = 2.0 * ((x * x) + (x * y));
end

↓

function tmp = code(x, y)
	tmp = 2.0 * ((x * x) + (x * y));
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[(N[(x * x), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

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

↓

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

Try it out

In
Out

Enter valid numbers for all inputs

Target

Original	0.0
Target	0.0
Herbie	0.0

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

Derivation

Initial program 0.0
\[2 \cdot \left(x \cdot x + x \cdot y\right) \]
Final simplification0.0
\[\leadsto 2 \cdot \left(x \cdot x + x \cdot y\right) \]

Alternatives

Alternative 1
Error	7.4
Cost	584

\[\begin{array}{l} t_0 := y \cdot \left(2 \cdot x\right)\\ \mathbf{if}\;y \leq -3.5054404949919658 \cdot 10^{-15}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.5479429605238394 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(2 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	0.0
Cost	448

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

Alternative 3
Error	22.1
Cost	320

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

Reproduce

herbie shell --seed 2022308 
(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))))