Average Error: 0.0 → 0.0

Time: 2.2s

Precision: binary64

Cost: 448

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

↓

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

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

↓

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

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

↓

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

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 = (x - y) * (2.0d0 * x)
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 (x - y) * (2.0 * x);
}

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

↓

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

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

↓

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

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

↓

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

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

↓

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

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

↓

\left(x - y\right) \cdot \left(2 \cdot x\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
\[2 \cdot \left(x \cdot x - x \cdot y\right) \]
Simplified0.0
\[\leadsto \color{blue}{\left(2 \cdot x\right) \cdot \left(x - y\right)} \]
Proof
(*.f64 (*.f64 2 x) (-.f64 x y)): 0 points increase in error, 0 points decrease in error
(Rewrite<= associate-*r*_binary64 (*.f64 2 (*.f64 x (-.f64 x y)))): 0 points increase in error, 0 points decrease in error
(*.f64 2 (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 x x) (*.f64 x y)))): 4 points increase in error, 4 points decrease in error
Final simplification0.0
\[\leadsto \left(x - y\right) \cdot \left(2 \cdot x\right) \]

Alternatives

Alternative 1
Error	7.9
Cost	584

\[\begin{array}{l} t_0 := -2 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -2.3833745838419967 \cdot 10^{-56}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9.232376549514604 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(2 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	32.7
Cost	320

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

Reproduce

herbie shell --seed 2022294 
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, A"
  :precision binary64

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

  (* 2.0 (- (* x x) (* x y))))