Average Error: 0.0 → 0.0

Time: 3.0s

Precision: binary64

Cost: 448

\[\left(-1000000000 \leq x \land x \leq 1000000000\right) \land \left(-1000000000 \leq y \land y \leq 1000000000\right)\]

\[x \cdot x - y \cdot y \]

↓

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

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

↓

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

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

↓

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

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * x) - (y * y)
end function

↓

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

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

↓

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

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

↓

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

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

↓

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

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

↓

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

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

↓

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

x \cdot x - y \cdot y

↓

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

Try it out

In
Out

Enter valid numbers for all inputs

Derivation

Initial program 0.0
\[x \cdot x - y \cdot y \]
Applied egg-rr0.0
\[\leadsto \color{blue}{\left(x + y\right) \cdot \left(x - y\right)} \]
Final simplification0.0
\[\leadsto \left(x + y\right) \cdot \left(x - y\right) \]

Alternatives

Alternative 1
Error	9.7
Cost	1036

\[\begin{array}{l} t_0 := y \cdot \left(-y\right)\\ \mathbf{if}\;x \cdot x \leq 2.0894288403 \cdot 10^{-314}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \cdot x \leq 1.6779288059284855 \cdot 10^{-263}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \cdot x \leq 2.887445983802016 \cdot 10^{-216}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array} \]

Alternative 2
Error	23.1
Cost	192

\[x \cdot x \]

Reproduce

herbie shell --seed 1 
(FPCore (x y)
  :name "x*x -y*y"
  :precision binary64
  :pre (and (and (<= -1000000000.0 x) (<= x 1000000000.0)) (and (<= -1000000000.0 y) (<= y 1000000000.0)))
  (- (* x x) (* y y)))