Average Error: 30.0 → 0.1
Time: 6.5s
Precision: binary64
Cost: 13248
\[0 \leq x \land x \leq 1.79 \cdot 10^{+308}\]
\[\sqrt{x + 1.002} - \sqrt{x} \]
\[\frac{1.002}{\sqrt{1.002 + x} + \sqrt{x}} \]
(FPCore (x) :precision binary64 (- (sqrt (+ x 1.002)) (sqrt x)))
(FPCore (x) :precision binary64 (/ 1.002 (+ (sqrt (+ 1.002 x)) (sqrt x))))
double code(double x) {
	return sqrt((x + 1.002)) - sqrt(x);
}
double code(double x) {
	return 1.002 / (sqrt((1.002 + x)) + sqrt(x));
}
real(8) function code(x)
    real(8), intent (in) :: x
    code = sqrt((x + 1.002d0)) - sqrt(x)
end function
real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.002d0 / (sqrt((1.002d0 + x)) + sqrt(x))
end function
public static double code(double x) {
	return Math.sqrt((x + 1.002)) - Math.sqrt(x);
}
public static double code(double x) {
	return 1.002 / (Math.sqrt((1.002 + x)) + Math.sqrt(x));
}
def code(x):
	return math.sqrt((x + 1.002)) - math.sqrt(x)
def code(x):
	return 1.002 / (math.sqrt((1.002 + x)) + math.sqrt(x))
function code(x)
	return Float64(sqrt(Float64(x + 1.002)) - sqrt(x))
end
function code(x)
	return Float64(1.002 / Float64(sqrt(Float64(1.002 + x)) + sqrt(x)))
end
function tmp = code(x)
	tmp = sqrt((x + 1.002)) - sqrt(x);
end
function tmp = code(x)
	tmp = 1.002 / (sqrt((1.002 + x)) + sqrt(x));
end
code[x_] := N[(N[Sqrt[N[(x + 1.002), $MachinePrecision]], $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision]
code[x_] := N[(1.002 / N[(N[Sqrt[N[(1.002 + x), $MachinePrecision]], $MachinePrecision] + N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\sqrt{x + 1.002} - \sqrt{x}
\frac{1.002}{\sqrt{1.002 + x} + \sqrt{x}}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.0

    \[\sqrt{x + 1.002} - \sqrt{x} \]
  2. Applied egg-rr30.0

    \[\leadsto \color{blue}{\frac{x + \left(1.002 - x\right)}{\sqrt{x + 1.002} + \sqrt{x}}} \]
  3. Taylor expanded in x around 0 0.1

    \[\leadsto \frac{\color{blue}{1.002}}{\sqrt{x + 1.002} + \sqrt{x}} \]
  4. Final simplification0.1

    \[\leadsto \frac{1.002}{\sqrt{1.002 + x} + \sqrt{x}} \]

Alternatives

Alternative 1
Error30.0
Cost13184
\[{\left(1.002 + x\right)}^{0.5} - \sqrt{x} \]
Alternative 2
Error30.0
Cost13120
\[\sqrt{1.002 + x} - \sqrt{x} \]
Alternative 3
Error31.2
Cost6464
\[\sqrt{1.002} \]

Error

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "sqrt(x + 1.002) - sqrt(x)"
  :precision binary64
  :pre (and (<= 0.0 x) (<= x 1.79e+308))
  (- (sqrt (+ x 1.002)) (sqrt x)))