?

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}

Error?

Try it out?

Your Program's Arguments

Results

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

    \[ {x}^{-0.5} \cdot \frac{1}{\sqrt{y}} \]

    associate-*r/ [=>]0.3

    \[ \color{blue}{\frac{{x}^{-0.5} \cdot 1}{\sqrt{y}}} \]

    *-rgt-identity [=>]0.3

    \[ \frac{\color{blue}{{x}^{-0.5}}}{\sqrt{y}} \]
  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
\[{\left(y \cdot x\right)}^{-0.5} \]

Error

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))))