Average Error: 0.0 → 0.0
Time: 1.9s
Precision: binary64
\[2 \cdot \left(x \cdot x + x \cdot y\right) \]
↓
\[\left(y + x\right) \cdot \left(x \cdot 2\right) \]
(FPCore (x y) :precision binary64 (* 2.0 (+ (* x x) (* x y))))
↓
(FPCore (x y) :precision binary64 (* (+ y x) (* x 2.0)))
double code(double x, double y) {
	return 2.0 * ((x * x) + (x * y));
}
↓
double code(double x, double y) {
	return (y + x) * (x * 2.0);
}

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

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

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

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

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

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

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Taylor expanded in x around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2022210 
(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))))