Henrywood and Agarwal, Equation (9a)

Percentage Accurate: 80.5% → 84.9%

Time: 13.0s

Alternatives: 8

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ w0 \cdot \sqrt{1 - {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}} \end{array} \]

FPCore

(FPCore (w0 M D h l d)
 :precision binary64
 (* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))))

C

double code(double w0, double M, double D, double h, double l, double d) {
	return w0 * sqrt((1.0 - (pow(((M * D) / (2.0 * d)), 2.0) * (h / l))));
}

Fortran

real(8) function code(w0, m, d, h, l, d_1)
    real(8), intent (in) :: w0
    real(8), intent (in) :: m
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: d_1
    code = w0 * sqrt((1.0d0 - ((((m * d) / (2.0d0 * d_1)) ** 2.0d0) * (h / l))))
end function

Java

public static double code(double w0, double M, double D, double h, double l, double d) {
	return w0 * Math.sqrt((1.0 - (Math.pow(((M * D) / (2.0 * d)), 2.0) * (h / l))));
}

Python

def code(w0, M, D, h, l, d):
	return w0 * math.sqrt((1.0 - (math.pow(((M * D) / (2.0 * d)), 2.0) * (h / l))))

Julia

function code(w0, M, D, h, l, d)
	return Float64(w0 * sqrt(Float64(1.0 - Float64((Float64(Float64(M * D) / Float64(2.0 * d)) ^ 2.0) * Float64(h / l)))))
end

MATLAB

function tmp = code(w0, M, D, h, l, d)
	tmp = w0 * sqrt((1.0 - ((((M * D) / (2.0 * d)) ^ 2.0) * (h / l))));
end

Wolfram

code[w0_, M_, D_, h_, l_, d_] := N[(w0 * N[Sqrt[N[(1.0 - N[(N[Power[N[(N[(M * D), $MachinePrecision] / N[(2.0 * d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * N[(h / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 80.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ w0 \cdot \sqrt{1 - {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}} \end{array} \]

FPCore

(FPCore (w0 M D h l d)
 :precision binary64
 (* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))))

C

double code(double w0, double M, double D, double h, double l, double d) {
	return w0 * sqrt((1.0 - (pow(((M * D) / (2.0 * d)), 2.0) * (h / l))));
}

Fortran

real(8) function code(w0, m, d, h, l, d_1)
    real(8), intent (in) :: w0
    real(8), intent (in) :: m
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: d_1
    code = w0 * sqrt((1.0d0 - ((((m * d) / (2.0d0 * d_1)) ** 2.0d0) * (h / l))))
end function

Java

public static double code(double w0, double M, double D, double h, double l, double d) {
	return w0 * Math.sqrt((1.0 - (Math.pow(((M * D) / (2.0 * d)), 2.0) * (h / l))));
}

Python

def code(w0, M, D, h, l, d):
	return w0 * math.sqrt((1.0 - (math.pow(((M * D) / (2.0 * d)), 2.0) * (h / l))))

Julia

function code(w0, M, D, h, l, d)
	return Float64(w0 * sqrt(Float64(1.0 - Float64((Float64(Float64(M * D) / Float64(2.0 * d)) ^ 2.0) * Float64(h / l)))))
end

MATLAB

function tmp = code(w0, M, D, h, l, d)
	tmp = w0 * sqrt((1.0 - ((((M * D) / (2.0 * d)) ^ 2.0) * (h / l))));
end

Wolfram

code[w0_, M_, D_, h_, l_, d_] := N[(w0 * N[Sqrt[N[(1.0 - N[(N[Power[N[(N[(M * D), $MachinePrecision] / N[(2.0 * d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * N[(h / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{+210}:\\ \;\;\;\;w0 \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;w0 \cdot \sqrt{1 - \frac{0.25}{\ell \cdot \frac{d \cdot \frac{d}{h}}{{\left(M \cdot D\right)}^{2}}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (w0 M D h l d)
 :precision binary64
 (let* ((t_0 (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
   (if (<= t_0 5e+210)
     (* w0 (sqrt t_0))
     (*
      w0
      (sqrt (- 1.0 (/ 0.25 (* l (/ (* d (/ d h)) (pow (* M D) 2.0))))))))))

C

double code(double w0, double M, double D, double h, double l, double d) {
	double t_0 = 1.0 - (pow(((M * D) / (2.0 * d)), 2.0) * (h / l));
	double tmp;
	if (t_0 <= 5e+210) {
		tmp = w0 * sqrt(t_0);
	} else {
		tmp = w0 * sqrt((1.0 - (0.25 / (l * ((d * (d / h)) / pow((M * D), 2.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(w0, m, d, h, l, d_1)
    real(8), intent (in) :: w0
    real(8), intent (in) :: m
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: d_1
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - ((((m * d) / (2.0d0 * d_1)) ** 2.0d0) * (h / l))
    if (t_0 <= 5d+210) then
        tmp = w0 * sqrt(t_0)
    else
        tmp = w0 * sqrt((1.0d0 - (0.25d0 / (l * ((d_1 * (d_1 / h)) / ((m * d) ** 2.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double w0, double M, double D, double h, double l, double d) {
	double t_0 = 1.0 - (Math.pow(((M * D) / (2.0 * d)), 2.0) * (h / l));
	double tmp;
	if (t_0 <= 5e+210) {
		tmp = w0 * Math.sqrt(t_0);
	} else {
		tmp = w0 * Math.sqrt((1.0 - (0.25 / (l * ((d * (d / h)) / Math.pow((M * D), 2.0))))));
	}
	return tmp;
}

Python

def code(w0, M, D, h, l, d):
	t_0 = 1.0 - (math.pow(((M * D) / (2.0 * d)), 2.0) * (h / l))
	tmp = 0
	if t_0 <= 5e+210:
		tmp = w0 * math.sqrt(t_0)
	else:
		tmp = w0 * math.sqrt((1.0 - (0.25 / (l * ((d * (d / h)) / math.pow((M * D), 2.0))))))
	return tmp

Julia

function code(w0, M, D, h, l, d)
	t_0 = Float64(1.0 - Float64((Float64(Float64(M * D) / Float64(2.0 * d)) ^ 2.0) * Float64(h / l)))
	tmp = 0.0
	if (t_0 <= 5e+210)
		tmp = Float64(w0 * sqrt(t_0));
	else
		tmp = Float64(w0 * sqrt(Float64(1.0 - Float64(0.25 / Float64(l * Float64(Float64(d * Float64(d / h)) / (Float64(M * D) ^ 2.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w0, M, D, h, l, d)
	t_0 = 1.0 - ((((M * D) / (2.0 * d)) ^ 2.0) * (h / l));
	tmp = 0.0;
	if (t_0 <= 5e+210)
		tmp = w0 * sqrt(t_0);
	else
		tmp = w0 * sqrt((1.0 - (0.25 / (l * ((d * (d / h)) / ((M * D) ^ 2.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[w0_, M_, D_, h_, l_, d_] := Block[{t$95$0 = N[(1.0 - N[(N[Power[N[(N[(M * D), $MachinePrecision] / N[(2.0 * d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * N[(h / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 5e+210], N[(w0 * N[Sqrt[t$95$0], $MachinePrecision]), $MachinePrecision], N[(w0 * N[Sqrt[N[(1.0 - N[(0.25 / N[(l * N[(N[(d * N[(d / h), $MachinePrecision]), $MachinePrecision] / N[Power[N[(M * D), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 85.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{+210}:\\ \;\;\;\;w0 \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;w0 \cdot \sqrt{1 - \frac{0.25}{\ell} \cdot \left(\frac{h}{d} \cdot \frac{{\left(M \cdot D\right)}^{2}}{d}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (w0 M D h l d)
 :precision binary64
 (let* ((t_0 (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
   (if (<= t_0 5e+210)
     (* w0 (sqrt t_0))
     (*
      w0
      (sqrt (- 1.0 (* (/ 0.25 l) (* (/ h d) (/ (pow (* M D) 2.0) d)))))))))

C

double code(double w0, double M, double D, double h, double l, double d) {
	double t_0 = 1.0 - (pow(((M * D) / (2.0 * d)), 2.0) * (h / l));
	double tmp;
	if (t_0 <= 5e+210) {
		tmp = w0 * sqrt(t_0);
	} else {
		tmp = w0 * sqrt((1.0 - ((0.25 / l) * ((h / d) * (pow((M * D), 2.0) / d)))));
	}
	return tmp;
}

Fortran

real(8) function code(w0, m, d, h, l, d_1)
    real(8), intent (in) :: w0
    real(8), intent (in) :: m
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: d_1
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - ((((m * d) / (2.0d0 * d_1)) ** 2.0d0) * (h / l))
    if (t_0 <= 5d+210) then
        tmp = w0 * sqrt(t_0)
    else
        tmp = w0 * sqrt((1.0d0 - ((0.25d0 / l) * ((h / d_1) * (((m * d) ** 2.0d0) / d_1)))))
    end if
    code = tmp
end function

Java

public static double code(double w0, double M, double D, double h, double l, double d) {
	double t_0 = 1.0 - (Math.pow(((M * D) / (2.0 * d)), 2.0) * (h / l));
	double tmp;
	if (t_0 <= 5e+210) {
		tmp = w0 * Math.sqrt(t_0);
	} else {
		tmp = w0 * Math.sqrt((1.0 - ((0.25 / l) * ((h / d) * (Math.pow((M * D), 2.0) / d)))));
	}
	return tmp;
}

Python

def code(w0, M, D, h, l, d):
	t_0 = 1.0 - (math.pow(((M * D) / (2.0 * d)), 2.0) * (h / l))
	tmp = 0
	if t_0 <= 5e+210:
		tmp = w0 * math.sqrt(t_0)
	else:
		tmp = w0 * math.sqrt((1.0 - ((0.25 / l) * ((h / d) * (math.pow((M * D), 2.0) / d)))))
	return tmp

Julia

function code(w0, M, D, h, l, d)
	t_0 = Float64(1.0 - Float64((Float64(Float64(M * D) / Float64(2.0 * d)) ^ 2.0) * Float64(h / l)))
	tmp = 0.0
	if (t_0 <= 5e+210)
		tmp = Float64(w0 * sqrt(t_0));
	else
		tmp = Float64(w0 * sqrt(Float64(1.0 - Float64(Float64(0.25 / l) * Float64(Float64(h / d) * Float64((Float64(M * D) ^ 2.0) / d))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w0, M, D, h, l, d)
	t_0 = 1.0 - ((((M * D) / (2.0 * d)) ^ 2.0) * (h / l));
	tmp = 0.0;
	if (t_0 <= 5e+210)
		tmp = w0 * sqrt(t_0);
	else
		tmp = w0 * sqrt((1.0 - ((0.25 / l) * ((h / d) * (((M * D) ^ 2.0) / d)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[w0_, M_, D_, h_, l_, d_] := Block[{t$95$0 = N[(1.0 - N[(N[Power[N[(N[(M * D), $MachinePrecision] / N[(2.0 * d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * N[(h / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 5e+210], N[(w0 * N[Sqrt[t$95$0], $MachinePrecision]), $MachinePrecision], N[(w0 * N[Sqrt[N[(1.0 - N[(N[(0.25 / l), $MachinePrecision] * N[(N[(h / d), $MachinePrecision] * N[(N[Power[N[(M * D), $MachinePrecision], 2.0], $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 85.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{+210}:\\ \;\;\;\;w0 \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;w0 \cdot \sqrt{1 - \frac{0.25}{\ell} \cdot \frac{{\left(M \cdot D\right)}^{2} \cdot \frac{h}{d}}{d}}\\ \end{array} \end{array} \]

FPCore

(FPCore (w0 M D h l d)
 :precision binary64
 (let* ((t_0 (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
   (if (<= t_0 5e+210)
     (* w0 (sqrt t_0))
     (*
      w0
      (sqrt (- 1.0 (* (/ 0.25 l) (/ (* (pow (* M D) 2.0) (/ h d)) d))))))))

C

double code(double w0, double M, double D, double h, double l, double d) {
	double t_0 = 1.0 - (pow(((M * D) / (2.0 * d)), 2.0) * (h / l));
	double tmp;
	if (t_0 <= 5e+210) {
		tmp = w0 * sqrt(t_0);
	} else {
		tmp = w0 * sqrt((1.0 - ((0.25 / l) * ((pow((M * D), 2.0) * (h / d)) / d))));
	}
	return tmp;
}

Fortran

real(8) function code(w0, m, d, h, l, d_1)
    real(8), intent (in) :: w0
    real(8), intent (in) :: m
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: d_1
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - ((((m * d) / (2.0d0 * d_1)) ** 2.0d0) * (h / l))
    if (t_0 <= 5d+210) then
        tmp = w0 * sqrt(t_0)
    else
        tmp = w0 * sqrt((1.0d0 - ((0.25d0 / l) * ((((m * d) ** 2.0d0) * (h / d_1)) / d_1))))
    end if
    code = tmp
end function

Java

public static double code(double w0, double M, double D, double h, double l, double d) {
	double t_0 = 1.0 - (Math.pow(((M * D) / (2.0 * d)), 2.0) * (h / l));
	double tmp;
	if (t_0 <= 5e+210) {
		tmp = w0 * Math.sqrt(t_0);
	} else {
		tmp = w0 * Math.sqrt((1.0 - ((0.25 / l) * ((Math.pow((M * D), 2.0) * (h / d)) / d))));
	}
	return tmp;
}

Python

def code(w0, M, D, h, l, d):
	t_0 = 1.0 - (math.pow(((M * D) / (2.0 * d)), 2.0) * (h / l))
	tmp = 0
	if t_0 <= 5e+210:
		tmp = w0 * math.sqrt(t_0)
	else:
		tmp = w0 * math.sqrt((1.0 - ((0.25 / l) * ((math.pow((M * D), 2.0) * (h / d)) / d))))
	return tmp

Julia

function code(w0, M, D, h, l, d)
	t_0 = Float64(1.0 - Float64((Float64(Float64(M * D) / Float64(2.0 * d)) ^ 2.0) * Float64(h / l)))
	tmp = 0.0
	if (t_0 <= 5e+210)
		tmp = Float64(w0 * sqrt(t_0));
	else
		tmp = Float64(w0 * sqrt(Float64(1.0 - Float64(Float64(0.25 / l) * Float64(Float64((Float64(M * D) ^ 2.0) * Float64(h / d)) / d)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w0, M, D, h, l, d)
	t_0 = 1.0 - ((((M * D) / (2.0 * d)) ^ 2.0) * (h / l));
	tmp = 0.0;
	if (t_0 <= 5e+210)
		tmp = w0 * sqrt(t_0);
	else
		tmp = w0 * sqrt((1.0 - ((0.25 / l) * ((((M * D) ^ 2.0) * (h / d)) / d))));
	end
	tmp_2 = tmp;
end

Wolfram

code[w0_, M_, D_, h_, l_, d_] := Block[{t$95$0 = N[(1.0 - N[(N[Power[N[(N[(M * D), $MachinePrecision] / N[(2.0 * d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * N[(h / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 5e+210], N[(w0 * N[Sqrt[t$95$0], $MachinePrecision]), $MachinePrecision], N[(w0 * N[Sqrt[N[(1.0 - N[(N[(0.25 / l), $MachinePrecision] * N[(N[(N[Power[N[(M * D), $MachinePrecision], 2.0], $MachinePrecision] * N[(h / d), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 86.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}\\ \mathbf{if}\;t_0 \leq \infty:\\ \;\;\;\;w0 \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;w0\\ \end{array} \end{array} \]

FPCore

(FPCore (w0 M D h l d)
 :precision binary64
 (let* ((t_0 (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
   (if (<= t_0 INFINITY) (* w0 (sqrt t_0)) w0)))

C

double code(double w0, double M, double D, double h, double l, double d) {
	double t_0 = 1.0 - (pow(((M * D) / (2.0 * d)), 2.0) * (h / l));
	double tmp;
	if (t_0 <= ((double) INFINITY)) {
		tmp = w0 * sqrt(t_0);
	} else {
		tmp = w0;
	}
	return tmp;
}

Java

public static double code(double w0, double M, double D, double h, double l, double d) {
	double t_0 = 1.0 - (Math.pow(((M * D) / (2.0 * d)), 2.0) * (h / l));
	double tmp;
	if (t_0 <= Double.POSITIVE_INFINITY) {
		tmp = w0 * Math.sqrt(t_0);
	} else {
		tmp = w0;
	}
	return tmp;
}

Python

def code(w0, M, D, h, l, d):
	t_0 = 1.0 - (math.pow(((M * D) / (2.0 * d)), 2.0) * (h / l))
	tmp = 0
	if t_0 <= math.inf:
		tmp = w0 * math.sqrt(t_0)
	else:
		tmp = w0
	return tmp

Julia

function code(w0, M, D, h, l, d)
	t_0 = Float64(1.0 - Float64((Float64(Float64(M * D) / Float64(2.0 * d)) ^ 2.0) * Float64(h / l)))
	tmp = 0.0
	if (t_0 <= Inf)
		tmp = Float64(w0 * sqrt(t_0));
	else
		tmp = w0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(w0, M, D, h, l, d)
	t_0 = 1.0 - ((((M * D) / (2.0 * d)) ^ 2.0) * (h / l));
	tmp = 0.0;
	if (t_0 <= Inf)
		tmp = w0 * sqrt(t_0);
	else
		tmp = w0;
	end
	tmp_2 = tmp;
end

Wolfram

code[w0_, M_, D_, h_, l_, d_] := Block[{t$95$0 = N[(1.0 - N[(N[Power[N[(N[(M * D), $MachinePrecision] / N[(2.0 * d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * N[(h / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, Infinity], N[(w0 * N[Sqrt[t$95$0], $MachinePrecision]), $MachinePrecision], w0]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 86.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{+256}:\\ \;\;\;\;w0 \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;w0 \cdot \sqrt{1 - \frac{h \cdot {\left(M \cdot \left(D \cdot \frac{0.5}{d}\right)\right)}^{2}}{\ell}}\\ \end{array} \end{array} \]

FPCore

(FPCore (w0 M D h l d)
 :precision binary64
 (let* ((t_0 (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
   (if (<= t_0 5e+256)
     (* w0 (sqrt t_0))
     (* w0 (sqrt (- 1.0 (/ (* h (pow (* M (* D (/ 0.5 d))) 2.0)) l)))))))

C

double code(double w0, double M, double D, double h, double l, double d) {
	double t_0 = 1.0 - (pow(((M * D) / (2.0 * d)), 2.0) * (h / l));
	double tmp;
	if (t_0 <= 5e+256) {
		tmp = w0 * sqrt(t_0);
	} else {
		tmp = w0 * sqrt((1.0 - ((h * pow((M * (D * (0.5 / d))), 2.0)) / l)));
	}
	return tmp;
}

Fortran

real(8) function code(w0, m, d, h, l, d_1)
    real(8), intent (in) :: w0
    real(8), intent (in) :: m
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: d_1
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - ((((m * d) / (2.0d0 * d_1)) ** 2.0d0) * (h / l))
    if (t_0 <= 5d+256) then
        tmp = w0 * sqrt(t_0)
    else
        tmp = w0 * sqrt((1.0d0 - ((h * ((m * (d * (0.5d0 / d_1))) ** 2.0d0)) / l)))
    end if
    code = tmp
end function

Java

public static double code(double w0, double M, double D, double h, double l, double d) {
	double t_0 = 1.0 - (Math.pow(((M * D) / (2.0 * d)), 2.0) * (h / l));
	double tmp;
	if (t_0 <= 5e+256) {
		tmp = w0 * Math.sqrt(t_0);
	} else {
		tmp = w0 * Math.sqrt((1.0 - ((h * Math.pow((M * (D * (0.5 / d))), 2.0)) / l)));
	}
	return tmp;
}

Python

def code(w0, M, D, h, l, d):
	t_0 = 1.0 - (math.pow(((M * D) / (2.0 * d)), 2.0) * (h / l))
	tmp = 0
	if t_0 <= 5e+256:
		tmp = w0 * math.sqrt(t_0)
	else:
		tmp = w0 * math.sqrt((1.0 - ((h * math.pow((M * (D * (0.5 / d))), 2.0)) / l)))
	return tmp

Julia

function code(w0, M, D, h, l, d)
	t_0 = Float64(1.0 - Float64((Float64(Float64(M * D) / Float64(2.0 * d)) ^ 2.0) * Float64(h / l)))
	tmp = 0.0
	if (t_0 <= 5e+256)
		tmp = Float64(w0 * sqrt(t_0));
	else
		tmp = Float64(w0 * sqrt(Float64(1.0 - Float64(Float64(h * (Float64(M * Float64(D * Float64(0.5 / d))) ^ 2.0)) / l))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w0, M, D, h, l, d)
	t_0 = 1.0 - ((((M * D) / (2.0 * d)) ^ 2.0) * (h / l));
	tmp = 0.0;
	if (t_0 <= 5e+256)
		tmp = w0 * sqrt(t_0);
	else
		tmp = w0 * sqrt((1.0 - ((h * ((M * (D * (0.5 / d))) ^ 2.0)) / l)));
	end
	tmp_2 = tmp;
end

Wolfram

code[w0_, M_, D_, h_, l_, d_] := Block[{t$95$0 = N[(1.0 - N[(N[Power[N[(N[(M * D), $MachinePrecision] / N[(2.0 * d), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * N[(h / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 5e+256], N[(w0 * N[Sqrt[t$95$0], $MachinePrecision]), $MachinePrecision], N[(w0 * N[Sqrt[N[(1.0 - N[(N[(h * N[Power[N[(M * N[(D * N[(0.5 / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 83.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{h}{\ell} \leq -7.2 \cdot 10^{-287}:\\ \;\;\;\;w0 \cdot \sqrt{1 - \frac{h}{\ell} \cdot {\left(D \cdot \frac{M}{2 \cdot d}\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;w0\\ \end{array} \end{array} \]

FPCore

(FPCore (w0 M D h l d)
 :precision binary64
 (if (<= (/ h l) -7.2e-287)
   (* w0 (sqrt (- 1.0 (* (/ h l) (pow (* D (/ M (* 2.0 d))) 2.0)))))
   w0))

C

double code(double w0, double M, double D, double h, double l, double d) {
	double tmp;
	if ((h / l) <= -7.2e-287) {
		tmp = w0 * sqrt((1.0 - ((h / l) * pow((D * (M / (2.0 * d))), 2.0))));
	} else {
		tmp = w0;
	}
	return tmp;
}

Fortran

real(8) function code(w0, m, d, h, l, d_1)
    real(8), intent (in) :: w0
    real(8), intent (in) :: m
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: d_1
    real(8) :: tmp
    if ((h / l) <= (-7.2d-287)) then
        tmp = w0 * sqrt((1.0d0 - ((h / l) * ((d * (m / (2.0d0 * d_1))) ** 2.0d0))))
    else
        tmp = w0
    end if
    code = tmp
end function

Java

public static double code(double w0, double M, double D, double h, double l, double d) {
	double tmp;
	if ((h / l) <= -7.2e-287) {
		tmp = w0 * Math.sqrt((1.0 - ((h / l) * Math.pow((D * (M / (2.0 * d))), 2.0))));
	} else {
		tmp = w0;
	}
	return tmp;
}

Python

def code(w0, M, D, h, l, d):
	tmp = 0
	if (h / l) <= -7.2e-287:
		tmp = w0 * math.sqrt((1.0 - ((h / l) * math.pow((D * (M / (2.0 * d))), 2.0))))
	else:
		tmp = w0
	return tmp

Julia

function code(w0, M, D, h, l, d)
	tmp = 0.0
	if (Float64(h / l) <= -7.2e-287)
		tmp = Float64(w0 * sqrt(Float64(1.0 - Float64(Float64(h / l) * (Float64(D * Float64(M / Float64(2.0 * d))) ^ 2.0)))));
	else
		tmp = w0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(w0, M, D, h, l, d)
	tmp = 0.0;
	if ((h / l) <= -7.2e-287)
		tmp = w0 * sqrt((1.0 - ((h / l) * ((D * (M / (2.0 * d))) ^ 2.0))));
	else
		tmp = w0;
	end
	tmp_2 = tmp;
end

Wolfram

code[w0_, M_, D_, h_, l_, d_] := If[LessEqual[N[(h / l), $MachinePrecision], -7.2e-287], N[(w0 * N[Sqrt[N[(1.0 - N[(N[(h / l), $MachinePrecision] * N[Power[N[(D * N[(M / N[(2.0 * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], w0]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 63.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;M \leq 9.5 \cdot 10^{+52}:\\ \;\;\;\;w0\\ \mathbf{else}:\\ \;\;\;\;\log \left(e^{w0}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (w0 M D h l d)
 :precision binary64
 (if (<= M 9.5e+52) w0 (log (exp w0))))

C

double code(double w0, double M, double D, double h, double l, double d) {
	double tmp;
	if (M <= 9.5e+52) {
		tmp = w0;
	} else {
		tmp = log(exp(w0));
	}
	return tmp;
}

Fortran

real(8) function code(w0, m, d, h, l, d_1)
    real(8), intent (in) :: w0
    real(8), intent (in) :: m
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: d_1
    real(8) :: tmp
    if (m <= 9.5d+52) then
        tmp = w0
    else
        tmp = log(exp(w0))
    end if
    code = tmp
end function

Java

public static double code(double w0, double M, double D, double h, double l, double d) {
	double tmp;
	if (M <= 9.5e+52) {
		tmp = w0;
	} else {
		tmp = Math.log(Math.exp(w0));
	}
	return tmp;
}

Python

def code(w0, M, D, h, l, d):
	tmp = 0
	if M <= 9.5e+52:
		tmp = w0
	else:
		tmp = math.log(math.exp(w0))
	return tmp

Julia

function code(w0, M, D, h, l, d)
	tmp = 0.0
	if (M <= 9.5e+52)
		tmp = w0;
	else
		tmp = log(exp(w0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(w0, M, D, h, l, d)
	tmp = 0.0;
	if (M <= 9.5e+52)
		tmp = w0;
	else
		tmp = log(exp(w0));
	end
	tmp_2 = tmp;
end

Wolfram

code[w0_, M_, D_, h_, l_, d_] := If[LessEqual[M, 9.5e+52], w0, N[Log[N[Exp[w0], $MachinePrecision]], $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 67.7% accurate, 216.0× speedup

Math

\[\begin{array}{l} \\ w0 \end{array} \]

FPCore

(FPCore (w0 M D h l d) :precision binary64 w0)

C

double code(double w0, double M, double D, double h, double l, double d) {
	return w0;
}

Fortran

real(8) function code(w0, m, d, h, l, d_1)
    real(8), intent (in) :: w0
    real(8), intent (in) :: m
    real(8), intent (in) :: d
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: d_1
    code = w0
end function

Java

public static double code(double w0, double M, double D, double h, double l, double d) {
	return w0;
}

Python

def code(w0, M, D, h, l, d):
	return w0

Julia

function code(w0, M, D, h, l, d)
	return w0
end

MATLAB

function tmp = code(w0, M, D, h, l, d)
	tmp = w0;
end

Wolfram

code[w0_, M_, D_, h_, l_, d_] := w0

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2023342 
(FPCore (w0 M D h l d)
  :name "Henrywood and Agarwal, Equation (9a)"
  :precision binary64
  (* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))))