2isqrt (example 3.6)

Percentage Accurate: 38.6% → 99.9%

Time: 10.9s

Alternatives: 6

Speedup: 2.0×

Specification

\[x > 1 \land x < 10^{+308}\]

Math

\[\begin{array}{l} \\ \frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

C

double code(double x) {
	return (1.0 / sqrt(x)) - (1.0 / sqrt((x + 1.0)));
}

Fortran

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

Java

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

Python

def code(x):
	return (1.0 / math.sqrt(x)) - (1.0 / math.sqrt((x + 1.0)))

Julia

function code(x)
	return Float64(Float64(1.0 / sqrt(x)) - Float64(1.0 / sqrt(Float64(x + 1.0))))
end

MATLAB

function tmp = code(x)
	tmp = (1.0 / sqrt(x)) - (1.0 / sqrt((x + 1.0)));
end

Wolfram

code[x_] := N[(N[(1.0 / N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(1.0 / N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 38.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

C

double code(double x) {
	return (1.0 / sqrt(x)) - (1.0 / sqrt((x + 1.0)));
}

Fortran

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

Java

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

Python

def code(x):
	return (1.0 / math.sqrt(x)) - (1.0 / math.sqrt((x + 1.0)))

Julia

function code(x)
	return Float64(Float64(1.0 / sqrt(x)) - Float64(1.0 / sqrt(Float64(x + 1.0))))
end

MATLAB

function tmp = code(x)
	tmp = (1.0 / sqrt(x)) - (1.0 / sqrt((x + 1.0)));
end

Wolfram

code[x_] := N[(N[(1.0 / N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(1.0 / N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}} \leq 0:\\ \;\;\;\;{x}^{-1.5} \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{{\left(1 + x\right)}^{0.5}}{\frac{\left(1 + x\right) - x}{x + {\left(x \cdot \left(1 + x\right)\right)}^{0.5}}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) 0.0)
   (* (pow x -1.5) 0.5)
   (/
    1.0
    (/
     (pow (+ 1.0 x) 0.5)
     (/ (- (+ 1.0 x) x) (+ x (pow (* x (+ 1.0 x)) 0.5)))))))

C

double code(double x) {
	double tmp;
	if (((1.0 / sqrt(x)) - (1.0 / sqrt((x + 1.0)))) <= 0.0) {
		tmp = pow(x, -1.5) * 0.5;
	} else {
		tmp = 1.0 / (pow((1.0 + x), 0.5) / (((1.0 + x) - x) / (x + pow((x * (1.0 + x)), 0.5))));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((1.0d0 / sqrt(x)) - (1.0d0 / sqrt((x + 1.0d0)))) <= 0.0d0) then
        tmp = (x ** (-1.5d0)) * 0.5d0
    else
        tmp = 1.0d0 / (((1.0d0 + x) ** 0.5d0) / (((1.0d0 + x) - x) / (x + ((x * (1.0d0 + x)) ** 0.5d0))))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((1.0 / Math.sqrt(x)) - (1.0 / Math.sqrt((x + 1.0)))) <= 0.0) {
		tmp = Math.pow(x, -1.5) * 0.5;
	} else {
		tmp = 1.0 / (Math.pow((1.0 + x), 0.5) / (((1.0 + x) - x) / (x + Math.pow((x * (1.0 + x)), 0.5))));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((1.0 / math.sqrt(x)) - (1.0 / math.sqrt((x + 1.0)))) <= 0.0:
		tmp = math.pow(x, -1.5) * 0.5
	else:
		tmp = 1.0 / (math.pow((1.0 + x), 0.5) / (((1.0 + x) - x) / (x + math.pow((x * (1.0 + x)), 0.5))))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(1.0 / sqrt(x)) - Float64(1.0 / sqrt(Float64(x + 1.0)))) <= 0.0)
		tmp = Float64((x ^ -1.5) * 0.5);
	else
		tmp = Float64(1.0 / Float64((Float64(1.0 + x) ^ 0.5) / Float64(Float64(Float64(1.0 + x) - x) / Float64(x + (Float64(x * Float64(1.0 + x)) ^ 0.5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((1.0 / sqrt(x)) - (1.0 / sqrt((x + 1.0)))) <= 0.0)
		tmp = (x ^ -1.5) * 0.5;
	else
		tmp = 1.0 / (((1.0 + x) ^ 0.5) / (((1.0 + x) - x) / (x + ((x * (1.0 + x)) ^ 0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(1.0 / N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(1.0 / N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0], N[(N[Power[x, -1.5], $MachinePrecision] * 0.5), $MachinePrecision], N[(1.0 / N[(N[Power[N[(1.0 + x), $MachinePrecision], 0.5], $MachinePrecision] / N[(N[(N[(1.0 + x), $MachinePrecision] - x), $MachinePrecision] / N[(x + N[Power[N[(x * N[(1.0 + x), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) < 0.0

   1. Initial program 38.1%

      \[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if 0.0 < (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

   1. Initial program 59.1%

      \[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}} \leq 0:\\ \;\;\;\;{x}^{-1.5} \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(1 + x\right) - x}{x + {\left(x \cdot \left(1 + x\right)\right)}^{0.5}}}{{\left(1 + x\right)}^{0.5}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) 0.0)
   (* (pow x -1.5) 0.5)
   (/
    (/ (- (+ 1.0 x) x) (+ x (pow (* x (+ 1.0 x)) 0.5)))
    (pow (+ 1.0 x) 0.5))))

C

double code(double x) {
	double tmp;
	if (((1.0 / sqrt(x)) - (1.0 / sqrt((x + 1.0)))) <= 0.0) {
		tmp = pow(x, -1.5) * 0.5;
	} else {
		tmp = (((1.0 + x) - x) / (x + pow((x * (1.0 + x)), 0.5))) / pow((1.0 + x), 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((1.0d0 / sqrt(x)) - (1.0d0 / sqrt((x + 1.0d0)))) <= 0.0d0) then
        tmp = (x ** (-1.5d0)) * 0.5d0
    else
        tmp = (((1.0d0 + x) - x) / (x + ((x * (1.0d0 + x)) ** 0.5d0))) / ((1.0d0 + x) ** 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((1.0 / Math.sqrt(x)) - (1.0 / Math.sqrt((x + 1.0)))) <= 0.0) {
		tmp = Math.pow(x, -1.5) * 0.5;
	} else {
		tmp = (((1.0 + x) - x) / (x + Math.pow((x * (1.0 + x)), 0.5))) / Math.pow((1.0 + x), 0.5);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((1.0 / math.sqrt(x)) - (1.0 / math.sqrt((x + 1.0)))) <= 0.0:
		tmp = math.pow(x, -1.5) * 0.5
	else:
		tmp = (((1.0 + x) - x) / (x + math.pow((x * (1.0 + x)), 0.5))) / math.pow((1.0 + x), 0.5)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(1.0 / sqrt(x)) - Float64(1.0 / sqrt(Float64(x + 1.0)))) <= 0.0)
		tmp = Float64((x ^ -1.5) * 0.5);
	else
		tmp = Float64(Float64(Float64(Float64(1.0 + x) - x) / Float64(x + (Float64(x * Float64(1.0 + x)) ^ 0.5))) / (Float64(1.0 + x) ^ 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((1.0 / sqrt(x)) - (1.0 / sqrt((x + 1.0)))) <= 0.0)
		tmp = (x ^ -1.5) * 0.5;
	else
		tmp = (((1.0 + x) - x) / (x + ((x * (1.0 + x)) ^ 0.5))) / ((1.0 + x) ^ 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(1.0 / N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(1.0 / N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0], N[(N[Power[x, -1.5], $MachinePrecision] * 0.5), $MachinePrecision], N[(N[(N[(N[(1.0 + x), $MachinePrecision] - x), $MachinePrecision] / N[(x + N[Power[N[(x * N[(1.0 + x), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Power[N[(1.0 + x), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) < 0.0

   1. Initial program 38.1%

      \[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if 0.0 < (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

   1. Initial program 59.1%

      \[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}} \leq 0:\\ \;\;\;\;{x}^{-1.5} \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(1 + x\right) - x}{x + {\left(x \cdot \left(1 + x\right)\right)}^{0.5}} \cdot {\left(1 + x\right)}^{-0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) 0.0)
   (* (pow x -1.5) 0.5)
   (*
    (/ (- (+ 1.0 x) x) (+ x (pow (* x (+ 1.0 x)) 0.5)))
    (pow (+ 1.0 x) -0.5))))

C

double code(double x) {
	double tmp;
	if (((1.0 / sqrt(x)) - (1.0 / sqrt((x + 1.0)))) <= 0.0) {
		tmp = pow(x, -1.5) * 0.5;
	} else {
		tmp = (((1.0 + x) - x) / (x + pow((x * (1.0 + x)), 0.5))) * pow((1.0 + x), -0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((1.0d0 / sqrt(x)) - (1.0d0 / sqrt((x + 1.0d0)))) <= 0.0d0) then
        tmp = (x ** (-1.5d0)) * 0.5d0
    else
        tmp = (((1.0d0 + x) - x) / (x + ((x * (1.0d0 + x)) ** 0.5d0))) * ((1.0d0 + x) ** (-0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((1.0 / Math.sqrt(x)) - (1.0 / Math.sqrt((x + 1.0)))) <= 0.0) {
		tmp = Math.pow(x, -1.5) * 0.5;
	} else {
		tmp = (((1.0 + x) - x) / (x + Math.pow((x * (1.0 + x)), 0.5))) * Math.pow((1.0 + x), -0.5);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((1.0 / math.sqrt(x)) - (1.0 / math.sqrt((x + 1.0)))) <= 0.0:
		tmp = math.pow(x, -1.5) * 0.5
	else:
		tmp = (((1.0 + x) - x) / (x + math.pow((x * (1.0 + x)), 0.5))) * math.pow((1.0 + x), -0.5)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(1.0 / sqrt(x)) - Float64(1.0 / sqrt(Float64(x + 1.0)))) <= 0.0)
		tmp = Float64((x ^ -1.5) * 0.5);
	else
		tmp = Float64(Float64(Float64(Float64(1.0 + x) - x) / Float64(x + (Float64(x * Float64(1.0 + x)) ^ 0.5))) * (Float64(1.0 + x) ^ -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((1.0 / sqrt(x)) - (1.0 / sqrt((x + 1.0)))) <= 0.0)
		tmp = (x ^ -1.5) * 0.5;
	else
		tmp = (((1.0 + x) - x) / (x + ((x * (1.0 + x)) ^ 0.5))) * ((1.0 + x) ^ -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(1.0 / N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(1.0 / N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0], N[(N[Power[x, -1.5], $MachinePrecision] * 0.5), $MachinePrecision], N[(N[(N[(N[(1.0 + x), $MachinePrecision] - x), $MachinePrecision] / N[(x + N[Power[N[(x * N[(1.0 + x), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Power[N[(1.0 + x), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) < 0.0

   1. Initial program 38.1%

      \[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if 0.0 < (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

   1. Initial program 59.1%

      \[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}} \]
   2. Add Preprocessing

   4. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 97.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \frac{{x}^{-1.5} \cdot \frac{x + -1}{x}}{2} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ (* (pow x -1.5) (/ (+ x -1.0) x)) 2.0))

C

double code(double x) {
	return (pow(x, -1.5) * ((x + -1.0) / x)) / 2.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((x ** (-1.5d0)) * ((x + (-1.0d0)) / x)) / 2.0d0
end function

Java

public static double code(double x) {
	return (Math.pow(x, -1.5) * ((x + -1.0) / x)) / 2.0;
}

Python

def code(x):
	return (math.pow(x, -1.5) * ((x + -1.0) / x)) / 2.0

Julia

function code(x)
	return Float64(Float64((x ^ -1.5) * Float64(Float64(x + -1.0) / x)) / 2.0)
end

MATLAB

function tmp = code(x)
	tmp = ((x ^ -1.5) * ((x + -1.0) / x)) / 2.0;
end

Wolfram

code[x_] := N[(N[(N[Power[x, -1.5], $MachinePrecision] * N[(N[(x + -1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]

Derivation

1. Initial program 39.1%

   \[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

7. Applied egg-rr 0

   \[\leadsto expr\]

9. Applied egg-rr 0

   \[\leadsto expr\]
10. Add Preprocessing

Alternative 5: 97.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ {x}^{-1.5} \cdot 0.5 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (pow x -1.5) 0.5))

C

double code(double x) {
	return pow(x, -1.5) * 0.5;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x ** (-1.5d0)) * 0.5d0
end function

Java

public static double code(double x) {
	return Math.pow(x, -1.5) * 0.5;
}

Python

def code(x):
	return math.pow(x, -1.5) * 0.5

Julia

function code(x)
	return Float64((x ^ -1.5) * 0.5)
end

MATLAB

function tmp = code(x)
	tmp = (x ^ -1.5) * 0.5;
end

Wolfram

code[x_] := N[(N[Power[x, -1.5], $MachinePrecision] * 0.5), $MachinePrecision]

Derivation

1. Initial program 39.1%

   \[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

7. Applied egg-rr 0

   \[\leadsto expr\]
8. Add Preprocessing

Alternative 6: 35.5% accurate, 209.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x) :precision binary64 0.0)

C

double code(double x) {
	return 0.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 0.0d0
end function

Java

public static double code(double x) {
	return 0.0;
}

Python

def code(x):
	return 0.0

Julia

function code(x)
	return 0.0
end

MATLAB

function tmp = code(x)
	tmp = 0.0;
end

Wolfram

code[x_] := 0.0

Derivation

1. Initial program 39.1%

   \[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

7. Applied egg-rr 0

   \[\leadsto expr\]
8. Add Preprocessing

Developer Target 1: 98.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\left(x + 1\right) \cdot \sqrt{x} + x \cdot \sqrt{x + 1}} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (/ 1.0 (+ (* (+ x 1.0) (sqrt x)) (* x (sqrt (+ x 1.0))))))

C

double code(double x) {
	return 1.0 / (((x + 1.0) * sqrt(x)) + (x * sqrt((x + 1.0))));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 / (((x + 1.0d0) * sqrt(x)) + (x * sqrt((x + 1.0d0))))
end function

Java

public static double code(double x) {
	return 1.0 / (((x + 1.0) * Math.sqrt(x)) + (x * Math.sqrt((x + 1.0))));
}

Python

def code(x):
	return 1.0 / (((x + 1.0) * math.sqrt(x)) + (x * math.sqrt((x + 1.0))))

Julia

function code(x)
	return Float64(1.0 / Float64(Float64(Float64(x + 1.0) * sqrt(x)) + Float64(x * sqrt(Float64(x + 1.0)))))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 / (((x + 1.0) * sqrt(x)) + (x * sqrt((x + 1.0))));
end

Wolfram

code[x_] := N[(1.0 / N[(N[(N[(x + 1.0), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] + N[(x * N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024111 
(FPCore (x)
  :name "2isqrt (example 3.6)"
  :precision binary64
  :pre (and (> x 1.0) (< x 1e+308))

  :alt
  (! :herbie-platform default (/ 1 (+ (* (+ x 1) (sqrt x)) (* x (sqrt (+ x 1))))))

  (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))