?

Average Error: 0.1 → 0.0
Time: 2.3s
Precision: binary64
Cost: 6528

?

\[0 \leq x \land x \leq 1.79 \cdot 10^{+308}\]
\[\sqrt{\sqrt{x}} \]
\[{x}^{0.25} \]
(FPCore (x) :precision binary64 (sqrt (sqrt x)))
(FPCore (x) :precision binary64 (pow x 0.25))
double code(double x) {
	return sqrt(sqrt(x));
}
double code(double x) {
	return pow(x, 0.25);
}
real(8) function code(x)
    real(8), intent (in) :: x
    code = sqrt(sqrt(x))
end function
real(8) function code(x)
    real(8), intent (in) :: x
    code = x ** 0.25d0
end function
public static double code(double x) {
	return Math.sqrt(Math.sqrt(x));
}
public static double code(double x) {
	return Math.pow(x, 0.25);
}
def code(x):
	return math.sqrt(math.sqrt(x))
def code(x):
	return math.pow(x, 0.25)
function code(x)
	return sqrt(sqrt(x))
end
function code(x)
	return x ^ 0.25
end
function tmp = code(x)
	tmp = sqrt(sqrt(x));
end
function tmp = code(x)
	tmp = x ^ 0.25;
end
code[x_] := N[Sqrt[N[Sqrt[x], $MachinePrecision]], $MachinePrecision]
code[x_] := N[Power[x, 0.25], $MachinePrecision]
\sqrt{\sqrt{x}}
{x}^{0.25}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 0.1

    \[\sqrt{\sqrt{x}} \]
  2. Taylor expanded in x around 0 0.0

    \[\leadsto \color{blue}{{x}^{0.25}} \]
  3. Final simplification0.0

    \[\leadsto {x}^{0.25} \]

Reproduce?

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