?

Average Error: 0.0 → 0.0
Time: 8.0s
Precision: binary64
Cost: 13120

?

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

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 0.0

    \[\sqrt{x + 1} - \sqrt{x} \]
  2. Final simplification0.0

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

Alternatives

Alternative 1
Error0.7
Cost6848
\[x \cdot 0.5 + \left(1 - \sqrt{x}\right) \]
Alternative 2
Error0.7
Cost6848
\[1 + \left(x \cdot 0.5 - \sqrt{x}\right) \]
Alternative 3
Error2.9
Cost64
\[1 \]

Error

Reproduce?

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