?

Average Error: 58.6 → 0.0
Time: 11.4s
Precision: binary64
Cost: 6848

?

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

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 58.6

    \[\sqrt{1 + x} - 1 \]
  2. Applied egg-rr0.0

    \[\leadsto \color{blue}{\frac{x}{\sqrt{1 + x} - -1}} \]
  3. Final simplification0.0

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

Alternatives

Alternative 1
Error0.5
Cost832
\[\frac{1}{x \cdot -0.125 + \left(0.5 + 2 \cdot \frac{1}{x}\right)} \]
Alternative 2
Error0.6
Cost448
\[x \cdot \left(x \cdot -0.125 + 0.5\right) \]
Alternative 3
Error0.6
Cost448
\[\frac{x}{2 + x \cdot 0.5} \]
Alternative 4
Error1.3
Cost192
\[x \cdot 0.5 \]

Error

Reproduce?

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