?

Average Error: 58.6 → 0.0
Time: 7.0s
Precision: binary64
Cost: 6976

?

\[0 \leq x \land x \leq 1\]
\[\sqrt{x + 1} - 1 \]
\[x \cdot \frac{1}{1 + \sqrt{x + 1}} \]
(FPCore (x) :precision binary64 (- (sqrt (+ x 1.0)) 1.0))
(FPCore (x) :precision binary64 (* x (/ 1.0 (+ 1.0 (sqrt (+ x 1.0))))))
double code(double x) {
	return sqrt((x + 1.0)) - 1.0;
}
double code(double x) {
	return x * (1.0 / (1.0 + sqrt((x + 1.0))));
}
real(8) function code(x)
    real(8), intent (in) :: x
    code = sqrt((x + 1.0d0)) - 1.0d0
end function
real(8) function code(x)
    real(8), intent (in) :: x
    code = x * (1.0d0 / (1.0d0 + sqrt((x + 1.0d0))))
end function
public static double code(double x) {
	return Math.sqrt((x + 1.0)) - 1.0;
}
public static double code(double x) {
	return x * (1.0 / (1.0 + Math.sqrt((x + 1.0))));
}
def code(x):
	return math.sqrt((x + 1.0)) - 1.0
def code(x):
	return x * (1.0 / (1.0 + math.sqrt((x + 1.0))))
function code(x)
	return Float64(sqrt(Float64(x + 1.0)) - 1.0)
end
function code(x)
	return Float64(x * Float64(1.0 / Float64(1.0 + sqrt(Float64(x + 1.0)))))
end
function tmp = code(x)
	tmp = sqrt((x + 1.0)) - 1.0;
end
function tmp = code(x)
	tmp = x * (1.0 / (1.0 + sqrt((x + 1.0))));
end
code[x_] := N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] - 1.0), $MachinePrecision]
code[x_] := N[(x * N[(1.0 / N[(1.0 + N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\sqrt{x + 1} - 1
x \cdot \frac{1}{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

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

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

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

Alternatives

Alternative 1
Error0.0
Cost6848
\[\frac{x}{1 + \sqrt{x + 1}} \]
Alternative 2
Error0.6
Cost448
\[x \cdot \left(0.5 + x \cdot -0.125\right) \]
Alternative 3
Error0.6
Cost448
\[\frac{x}{x \cdot 0.5 + 2} \]
Alternative 4
Error1.3
Cost192
\[x \cdot 0.5 \]

Error

Reproduce?

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