?

Average Error: 0.2 → 0.0
Time: 2.1s
Precision: binary64
Cost: 6528

?

\[1.79 \cdot 10^{-308} \leq x \land x \leq 1.79 \cdot 10^{+308}\]
\[\frac{1}{\sqrt{x}} \]
\[{x}^{-0.5} \]
(FPCore (x) :precision binary64 (/ 1.0 (sqrt x)))
(FPCore (x) :precision binary64 (pow x -0.5))
double code(double x) {
	return 1.0 / sqrt(x);
}
double code(double x) {
	return pow(x, -0.5);
}
real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 / sqrt(x)
end function
real(8) function code(x)
    real(8), intent (in) :: x
    code = x ** (-0.5d0)
end function
public static double code(double x) {
	return 1.0 / Math.sqrt(x);
}
public static double code(double x) {
	return Math.pow(x, -0.5);
}
def code(x):
	return 1.0 / math.sqrt(x)
def code(x):
	return math.pow(x, -0.5)
function code(x)
	return Float64(1.0 / sqrt(x))
end
function code(x)
	return x ^ -0.5
end
function tmp = code(x)
	tmp = 1.0 / sqrt(x);
end
function tmp = code(x)
	tmp = x ^ -0.5;
end
code[x_] := N[(1.0 / N[Sqrt[x], $MachinePrecision]), $MachinePrecision]
code[x_] := N[Power[x, -0.5], $MachinePrecision]
\frac{1}{\sqrt{x}}
{x}^{-0.5}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 0.2

    \[\frac{1}{\sqrt{x}} \]
  2. Applied egg-rr29.1

    \[\leadsto \color{blue}{\left(1 + {x}^{-0.5}\right) - 1} \]
  3. Simplified0.0

    \[\leadsto \color{blue}{{x}^{-0.5}} \]
    Proof

    [Start]29.1

    \[ \left(1 + {x}^{-0.5}\right) - 1 \]

    +-commutative [=>]29.1

    \[ \color{blue}{\left({x}^{-0.5} + 1\right)} - 1 \]

    associate--l+ [=>]0.0

    \[ \color{blue}{{x}^{-0.5} + \left(1 - 1\right)} \]

    metadata-eval [=>]0.0

    \[ {x}^{-0.5} + \color{blue}{0} \]

    +-rgt-identity [=>]0.0

    \[ \color{blue}{{x}^{-0.5}} \]
  4. Final simplification0.0

    \[\leadsto {x}^{-0.5} \]

Reproduce?

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