Average Error: 0.1 → 0.1
Time: 5.6s
Precision: binary64
Cost: 13504
\[0 \leq x \land x \leq 1000\]
\[\sqrt{x + 1} - \sqrt{x} \]
\[\frac{x + \left(1 - x\right)}{\sqrt{x + 1} + \sqrt{x}} \]
(FPCore (x) :precision binary64 (- (sqrt (+ x 1.0)) (sqrt x)))
(FPCore (x)
 :precision binary64
 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x))))
double code(double x) {
	return sqrt((x + 1.0)) - sqrt(x);
}
double code(double x) {
	return (x + (1.0 - x)) / (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 = (x + (1.0d0 - x)) / (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 (x + (1.0 - x)) / (Math.sqrt((x + 1.0)) + Math.sqrt(x));
}
def code(x):
	return math.sqrt((x + 1.0)) - math.sqrt(x)
def code(x):
	return (x + (1.0 - x)) / (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(Float64(x + Float64(1.0 - x)) / 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 = (x + (1.0 - x)) / (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[(x + N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] + N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\sqrt{x + 1} - \sqrt{x}
\frac{x + \left(1 - x\right)}{\sqrt{x + 1} + \sqrt{x}}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\sqrt{x + 1} - \sqrt{x} \]
  2. Applied egg-rr0.1

    \[\leadsto \color{blue}{\frac{x + \left(1 - x\right)}{\sqrt{x + 1} + \sqrt{x}}} \]
  3. Final simplification0.1

    \[\leadsto \frac{x + \left(1 - x\right)}{\sqrt{x + 1} + \sqrt{x}} \]

Alternatives

Alternative 1
Error0.1
Cost13120
\[\sqrt{x + 1} - \sqrt{x} \]
Alternative 2
Error1.2
Cost7232
\[\frac{x + \left(1 - x\right)}{\sqrt{x} + \left(1 + x \cdot 0.5\right)} \]
Alternative 3
Error1.2
Cost6848
\[1 + \left(x \cdot 0.5 - \sqrt{x}\right) \]
Alternative 4
Error3.3
Cost64
\[1 \]

Error

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "sqrt(x+1)-sqrt(x)"
  :precision binary64
  :pre (and (<= 0.0 x) (<= x 1000.0))
  (- (sqrt (+ x 1.0)) (sqrt x)))