?

Average Error: 0 → 0
Time: 3.2s
Precision: binary64
Cost: 6720

?

\[0 \leq x \land x \leq 10^{-9}\]
\[\sqrt{1 - x \cdot x} \]
\[\sqrt{1 - x \cdot x} \]
(FPCore (x) :precision binary64 (sqrt (- 1.0 (* x x))))
(FPCore (x) :precision binary64 (sqrt (- 1.0 (* x x))))
double code(double x) {
	return sqrt((1.0 - (x * x)));
}
double code(double x) {
	return sqrt((1.0 - (x * x)));
}
real(8) function code(x)
    real(8), intent (in) :: x
    code = sqrt((1.0d0 - (x * x)))
end function
real(8) function code(x)
    real(8), intent (in) :: x
    code = sqrt((1.0d0 - (x * x)))
end function
public static double code(double x) {
	return Math.sqrt((1.0 - (x * x)));
}
public static double code(double x) {
	return Math.sqrt((1.0 - (x * x)));
}
def code(x):
	return math.sqrt((1.0 - (x * x)))
def code(x):
	return math.sqrt((1.0 - (x * x)))
function code(x)
	return sqrt(Float64(1.0 - Float64(x * x)))
end
function code(x)
	return sqrt(Float64(1.0 - Float64(x * x)))
end
function tmp = code(x)
	tmp = sqrt((1.0 - (x * x)));
end
function tmp = code(x)
	tmp = sqrt((1.0 - (x * x)));
end
code[x_] := N[Sqrt[N[(1.0 - N[(x * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]
code[x_] := N[Sqrt[N[(1.0 - N[(x * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]
\sqrt{1 - x \cdot x}
\sqrt{1 - x \cdot x}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 0

    \[\sqrt{1 - x \cdot x} \]
  2. Final simplification0

    \[\leadsto \sqrt{1 - x \cdot x} \]

Reproduce?

herbie shell --seed 1 
(FPCore (x)
  :name "sqrt(1-x*x)"
  :precision binary64
  :pre (and (<= 0.0 x) (<= x 1e-9))
  (sqrt (- 1.0 (* x x))))