# ?

Average Error: 0.4 → 0.4
Time: 10.4s
Precision: binary64
Cost: 13120

# ?

$\left(0 \leq x \land x \leq 1.79 \cdot 10^{+308}\right) \land \left(0 \leq y \land y \leq 1\right)$
$\frac{1}{\sqrt{x} \cdot \sqrt{y}}$
${y}^{-0.5} \cdot {x}^{-0.5}$
(FPCore (x y) :precision binary64 (/ 1.0 (* (sqrt x) (sqrt y))))
(FPCore (x y) :precision binary64 (* (pow y -0.5) (pow x -0.5)))
double code(double x, double y) {
return 1.0 / (sqrt(x) * sqrt(y));
}

double code(double x, double y) {
return pow(y, -0.5) * pow(x, -0.5);
}

real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = 1.0d0 / (sqrt(x) * sqrt(y))
end function

real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (y ** (-0.5d0)) * (x ** (-0.5d0))
end function

public static double code(double x, double y) {
return 1.0 / (Math.sqrt(x) * Math.sqrt(y));
}

public static double code(double x, double y) {
return Math.pow(y, -0.5) * Math.pow(x, -0.5);
}

def code(x, y):
return 1.0 / (math.sqrt(x) * math.sqrt(y))

def code(x, y):
return math.pow(y, -0.5) * math.pow(x, -0.5)

function code(x, y)
return Float64(1.0 / Float64(sqrt(x) * sqrt(y)))
end

function code(x, y)
return Float64((y ^ -0.5) * (x ^ -0.5))
end

function tmp = code(x, y)
tmp = 1.0 / (sqrt(x) * sqrt(y));
end

function tmp = code(x, y)
tmp = (y ^ -0.5) * (x ^ -0.5);
end

code[x_, y_] := N[(1.0 / N[(N[Sqrt[x], $MachinePrecision] * N[Sqrt[y],$MachinePrecision]), $MachinePrecision]),$MachinePrecision]

code[x_, y_] := N[(N[Power[y, -0.5], $MachinePrecision] * N[Power[x, -0.5],$MachinePrecision]), \$MachinePrecision]

\frac{1}{\sqrt{x} \cdot \sqrt{y}}

{y}^{-0.5} \cdot {x}^{-0.5}


# Try it out?

Your Program's Arguments

Results

 In Out
Enter valid numbers for all inputs

# Derivation?

1. Initial program 0.4

$\frac{1}{\sqrt{x} \cdot \sqrt{y}}$
2. Applied egg-rr0.4

$\leadsto \color{blue}{{x}^{-0.5} \cdot \frac{1}{\sqrt{y}}}$
3. Simplified0.3

$\leadsto \color{blue}{\frac{{x}^{-0.5}}{\sqrt{y}}}$
Proof
[Start]0.4 ${x}^{-0.5} \cdot \frac{1}{\sqrt{y}}$ $\color{blue}{\frac{{x}^{-0.5} \cdot 1}{\sqrt{y}}}$ $\frac{\color{blue}{{x}^{-0.5}}}{\sqrt{y}}$
4. Applied egg-rr0.4

$\leadsto \color{blue}{{y}^{-0.5} \cdot {x}^{-0.5}}$
5. Final simplification0.4

$\leadsto {y}^{-0.5} \cdot {x}^{-0.5}$

# Alternatives

Alternative 1
Error0.3
Cost13056
$\frac{{x}^{-0.5}}{\sqrt{y}}$
Alternative 2
Error14.8
Cost6656
${\left(y \cdot x\right)}^{-0.5}$

# Reproduce?

herbie shell --seed 1
(FPCore (x y)
:name "1/(sqrt(x)*sqrt(y))"
:precision binary64
:pre (and (and (<= 0.0 x) (<= x 1.79e+308)) (and (<= 0.0 y) (<= y 1.0)))
(/ 1.0 (* (sqrt x) (sqrt y))))