Average Error: 0.0 → 0.0
Time: 4.5s
Precision: binary64
Cost: 13120
\[\left(-1.79 \cdot 10^{+308} \leq x \land x \leq 1.79 \cdot 10^{+308}\right) \land \left(-1 \leq X \land X \leq 1000000000\right)\]
\[\sqrt{x + 1} - \sqrt{X} \]
↓
\[\sqrt{x + 1} - \sqrt{X} \]
(FPCore (x X) :precision binary64 (- (sqrt (+ x 1.0)) (sqrt X)))
↓
(FPCore (x X) :precision binary64 (- (sqrt (+ x 1.0)) (sqrt X)))
double code(double x, double X) {
	return sqrt((x + 1.0)) - sqrt(X);
}
↓
double code(double x, double X) {
	return sqrt((x + 1.0)) - sqrt(X);
}

real(8) function code(x, x_1)
    real(8), intent (in) :: x
    real(8), intent (in) :: x_1
    code = sqrt((x + 1.0d0)) - sqrt(x_1)
end function
↓
real(8) function code(x, x_1)
    real(8), intent (in) :: x
    real(8), intent (in) :: x_1
    code = sqrt((x + 1.0d0)) - sqrt(x_1)
end function

public static double code(double x, double X) {
	return Math.sqrt((x + 1.0)) - Math.sqrt(X);
}
↓
public static double code(double x, double X) {
	return Math.sqrt((x + 1.0)) - Math.sqrt(X);
}

def code(x, X):
	return math.sqrt((x + 1.0)) - math.sqrt(X)
↓
def code(x, X):
	return math.sqrt((x + 1.0)) - math.sqrt(X)

function code(x, X)
	return Float64(sqrt(Float64(x + 1.0)) - sqrt(X))
end
↓
function code(x, X)
	return Float64(sqrt(Float64(x + 1.0)) - sqrt(X))
end

function tmp = code(x, X)
	tmp = sqrt((x + 1.0)) - sqrt(X);
end
↓
function tmp = code(x, X)
	tmp = sqrt((x + 1.0)) - sqrt(X);
end

code[x_, X_] := N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[X], $MachinePrecision]), $MachinePrecision]
↓
code[x_, 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
Error0.4
Cost6980
\[\begin{array}{l} \mathbf{if}\;x \leq 5.841605225893026 \cdot 10^{-14}:\\ \;\;\;\;\left(1 + x \cdot 0.5\right) - \sqrt{X}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x + 1}\\ \end{array} \]
Alternative 2
Error0.7
Cost6724
\[\begin{array}{l} \mathbf{if}\;x \leq 1.780146019877377 \cdot 10^{-22}:\\ \;\;\;\;1 - \sqrt{X}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x + 1}\\ \end{array} \]
Alternative 3
Error20.7
Cost6592
\[1 - \sqrt{X} \]
Alternative 4
Error23.0
Cost320
\[1 + x \cdot 0.5 \]
Alternative 5
Error23.5
Cost64
\[1 \]

Error

Reproduce

herbie shell --seed 1 
(FPCore (x X)
  :name "sqrt(x+1)-sqrt(X)"
  :precision binary64
  :pre (and (and (<= -1.79e+308 x) (<= x 1.79e+308)) (and (<= -1.0 X) (<= X 1000000000.0)))
  (- (sqrt (+ x 1.0)) (sqrt X)))