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

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

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

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

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

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

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

\left(x + y\right) \cdot \left(x + y\right)
↓
2 \cdot \left(y \cdot x\right) + \left({y}^{2} + {x}^{2}\right)

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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

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

  3. Taylor expanded in x around 0 0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2022210 
(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)))