# ?

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}


# Try it out?

Results

 In Out
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))))