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

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.0

$x \cdot x - y \cdot y$
2. Applied egg-rr0.0

$\leadsto \color{blue}{\left(x + y\right) \cdot \left(x - y\right)}$
3. Final simplification0.0

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

# Alternatives

Alternative 1
Error9.7
Cost1036
$\begin{array}{l} t_0 := y \cdot \left(-y\right)\\ \mathbf{if}\;x \cdot x \leq 2.0894288403 \cdot 10^{-314}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \cdot x \leq 1.6779288059284855 \cdot 10^{-263}:\\ \;\;\;\;x \cdot x\\ \mathbf{elif}\;x \cdot x \leq 2.887445983802016 \cdot 10^{-216}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot x\\ \end{array}$
Alternative 2
Error23.1
Cost192
$x \cdot x$

# 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)))