Henrywood and Agarwal, Equation (9a)

Percentage Accurate: 80.2% → 87.6%

Time: 15.2s

Alternatives: 6

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: 80.2% 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: 87.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ D_m = \left|D\right| \\ d_m = \left|d\right| \\ w0_m = \left|w0\right| \\ w0_s = \mathsf{copysign}\left(1, w0\right) \\ [w0_m, M_m, D_m, h, l, d_m] = \mathsf{sort}([w0_m, M_m, D_m, h, l, d_m])\\ \\ w0_s \cdot \begin{array}{l} \mathbf{if}\;\frac{M_m \cdot D_m}{2 \cdot d_m} \leq 5 \cdot 10^{+162}:\\ \;\;\;\;w0_m \cdot \sqrt{1 - \frac{\frac{h \cdot {\left(\frac{M_m}{d_m} \cdot \frac{D_m}{2}\right)}^{2}}{{\left(\sqrt[3]{\ell}\right)}^{2}}}{\sqrt[3]{\ell}}}\\ \mathbf{else}:\\ \;\;\;\;{\left(\sqrt{w0_m} \cdot e^{0.25 \cdot \left(\left(\log \left(0.25 \cdot \frac{h \cdot \left(-{M_m}^{2}\right)}{\ell}\right) + -2 \cdot \log d_m\right) + -2 \cdot \log \left(\frac{1}{D_m}\right)\right)}\right)}^{2}\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
D_m = (fabs.f64 D)
d_m = (fabs.f64 d)
w0_m = (fabs.f64 w0)
w0_s = (copysign.f64 1 w0)
NOTE: w0_m, M_m, D_m, h, l, and d_m should be sorted in increasing order before calling this function.
(FPCore (w0_s w0_m M_m D_m h l d_m)
 :precision binary64
 (*
  w0_s
  (if (<= (/ (* M_m D_m) (* 2.0 d_m)) 5e+162)
    (*
     w0_m
     (sqrt
      (-
       1.0
       (/
        (/ (* h (pow (* (/ M_m d_m) (/ D_m 2.0)) 2.0)) (pow (cbrt l) 2.0))
        (cbrt l)))))
    (pow
     (*
      (sqrt w0_m)
      (exp
       (*
        0.25
        (+
         (+ (log (* 0.25 (/ (* h (- (pow M_m 2.0))) l))) (* -2.0 (log d_m)))
         (* -2.0 (log (/ 1.0 D_m)))))))
     2.0))))

C

M_m = fabs(M);
D_m = fabs(D);
d_m = fabs(d);
w0_m = fabs(w0);
w0_s = copysign(1.0, w0);
assert(w0_m < M_m && M_m < D_m && D_m < h && h < l && l < d_m);
double code(double w0_s, double w0_m, double M_m, double D_m, double h, double l, double d_m) {
	double tmp;
	if (((M_m * D_m) / (2.0 * d_m)) <= 5e+162) {
		tmp = w0_m * sqrt((1.0 - (((h * pow(((M_m / d_m) * (D_m / 2.0)), 2.0)) / pow(cbrt(l), 2.0)) / cbrt(l))));
	} else {
		tmp = pow((sqrt(w0_m) * exp((0.25 * ((log((0.25 * ((h * -pow(M_m, 2.0)) / l))) + (-2.0 * log(d_m))) + (-2.0 * log((1.0 / D_m))))))), 2.0);
	}
	return w0_s * tmp;
}

Java

M_m = Math.abs(M);
D_m = Math.abs(D);
d_m = Math.abs(d);
w0_m = Math.abs(w0);
w0_s = Math.copySign(1.0, w0);
assert w0_m < M_m && M_m < D_m && D_m < h && h < l && l < d_m;
public static double code(double w0_s, double w0_m, double M_m, double D_m, double h, double l, double d_m) {
	double tmp;
	if (((M_m * D_m) / (2.0 * d_m)) <= 5e+162) {
		tmp = w0_m * Math.sqrt((1.0 - (((h * Math.pow(((M_m / d_m) * (D_m / 2.0)), 2.0)) / Math.pow(Math.cbrt(l), 2.0)) / Math.cbrt(l))));
	} else {
		tmp = Math.pow((Math.sqrt(w0_m) * Math.exp((0.25 * ((Math.log((0.25 * ((h * -Math.pow(M_m, 2.0)) / l))) + (-2.0 * Math.log(d_m))) + (-2.0 * Math.log((1.0 / D_m))))))), 2.0);
	}
	return w0_s * tmp;
}

Julia

M_m = abs(M)
D_m = abs(D)
d_m = abs(d)
w0_m = abs(w0)
w0_s = copysign(1.0, w0)
w0_m, M_m, D_m, h, l, d_m = sort([w0_m, M_m, D_m, h, l, d_m])
function code(w0_s, w0_m, M_m, D_m, h, l, d_m)
	tmp = 0.0
	if (Float64(Float64(M_m * D_m) / Float64(2.0 * d_m)) <= 5e+162)
		tmp = Float64(w0_m * sqrt(Float64(1.0 - Float64(Float64(Float64(h * (Float64(Float64(M_m / d_m) * Float64(D_m / 2.0)) ^ 2.0)) / (cbrt(l) ^ 2.0)) / cbrt(l)))));
	else
		tmp = Float64(sqrt(w0_m) * exp(Float64(0.25 * Float64(Float64(log(Float64(0.25 * Float64(Float64(h * Float64(-(M_m ^ 2.0))) / l))) + Float64(-2.0 * log(d_m))) + Float64(-2.0 * log(Float64(1.0 / D_m))))))) ^ 2.0;
	end
	return Float64(w0_s * tmp)
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
D_m = N[Abs[D], $MachinePrecision]
d_m = N[Abs[d], $MachinePrecision]
w0_m = N[Abs[w0], $MachinePrecision]
w0_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[w0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: w0_m, M_m, D_m, h, l, and d_m should be sorted in increasing order before calling this function.
code[w0$95$s_, w0$95$m_, M$95$m_, D$95$m_, h_, l_, d$95$m_] := N[(w0$95$s * If[LessEqual[N[(N[(M$95$m * D$95$m), $MachinePrecision] / N[(2.0 * d$95$m), $MachinePrecision]), $MachinePrecision], 5e+162], N[(w0$95$m * N[Sqrt[N[(1.0 - N[(N[(N[(h * N[Power[N[(N[(M$95$m / d$95$m), $MachinePrecision] * N[(D$95$m / 2.0), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[Power[N[Power[l, 1/3], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[Power[l, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Power[N[(N[Sqrt[w0$95$m], $MachinePrecision] * N[Exp[N[(0.25 * N[(N[(N[Log[N[(0.25 * N[(N[(h * (-N[Power[M$95$m, 2.0], $MachinePrecision])), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[(-2.0 * N[Log[d$95$m], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-2.0 * N[Log[N[(1.0 / D$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 2: 86.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ D_m = \left|D\right| \\ d_m = \left|d\right| \\ w0_m = \left|w0\right| \\ w0_s = \mathsf{copysign}\left(1, w0\right) \\ [w0_m, M_m, D_m, h, l, d_m] = \mathsf{sort}([w0_m, M_m, D_m, h, l, d_m])\\ \\ w0_s \cdot \left(w0_m \cdot \sqrt{1 - \frac{\frac{h \cdot {\left(\frac{M_m}{d_m} \cdot \frac{D_m}{2}\right)}^{2}}{{\left(\sqrt[3]{\ell}\right)}^{2}}}{\sqrt[3]{\ell}}}\right) \end{array} \]

FPCore

M_m = (fabs.f64 M)
D_m = (fabs.f64 D)
d_m = (fabs.f64 d)
w0_m = (fabs.f64 w0)
w0_s = (copysign.f64 1 w0)
NOTE: w0_m, M_m, D_m, h, l, and d_m should be sorted in increasing order before calling this function.
(FPCore (w0_s w0_m M_m D_m h l d_m)
 :precision binary64
 (*
  w0_s
  (*
   w0_m
   (sqrt
    (-
     1.0
     (/
      (/ (* h (pow (* (/ M_m d_m) (/ D_m 2.0)) 2.0)) (pow (cbrt l) 2.0))
      (cbrt l)))))))

C

M_m = fabs(M);
D_m = fabs(D);
d_m = fabs(d);
w0_m = fabs(w0);
w0_s = copysign(1.0, w0);
assert(w0_m < M_m && M_m < D_m && D_m < h && h < l && l < d_m);
double code(double w0_s, double w0_m, double M_m, double D_m, double h, double l, double d_m) {
	return w0_s * (w0_m * sqrt((1.0 - (((h * pow(((M_m / d_m) * (D_m / 2.0)), 2.0)) / pow(cbrt(l), 2.0)) / cbrt(l)))));
}

Java

M_m = Math.abs(M);
D_m = Math.abs(D);
d_m = Math.abs(d);
w0_m = Math.abs(w0);
w0_s = Math.copySign(1.0, w0);
assert w0_m < M_m && M_m < D_m && D_m < h && h < l && l < d_m;
public static double code(double w0_s, double w0_m, double M_m, double D_m, double h, double l, double d_m) {
	return w0_s * (w0_m * Math.sqrt((1.0 - (((h * Math.pow(((M_m / d_m) * (D_m / 2.0)), 2.0)) / Math.pow(Math.cbrt(l), 2.0)) / Math.cbrt(l)))));
}

Julia

M_m = abs(M)
D_m = abs(D)
d_m = abs(d)
w0_m = abs(w0)
w0_s = copysign(1.0, w0)
w0_m, M_m, D_m, h, l, d_m = sort([w0_m, M_m, D_m, h, l, d_m])
function code(w0_s, w0_m, M_m, D_m, h, l, d_m)
	return Float64(w0_s * Float64(w0_m * sqrt(Float64(1.0 - Float64(Float64(Float64(h * (Float64(Float64(M_m / d_m) * Float64(D_m / 2.0)) ^ 2.0)) / (cbrt(l) ^ 2.0)) / cbrt(l))))))
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
D_m = N[Abs[D], $MachinePrecision]
d_m = N[Abs[d], $MachinePrecision]
w0_m = N[Abs[w0], $MachinePrecision]
w0_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[w0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: w0_m, M_m, D_m, h, l, and d_m should be sorted in increasing order before calling this function.
code[w0$95$s_, w0$95$m_, M$95$m_, D$95$m_, h_, l_, d$95$m_] := N[(w0$95$s * N[(w0$95$m * N[Sqrt[N[(1.0 - N[(N[(N[(h * N[Power[N[(N[(M$95$m / d$95$m), $MachinePrecision] * N[(D$95$m / 2.0), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[Power[N[Power[l, 1/3], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[Power[l, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 3: 72.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ D_m = \left|D\right| \\ d_m = \left|d\right| \\ w0_m = \left|w0\right| \\ w0_s = \mathsf{copysign}\left(1, w0\right) \\ [w0_m, M_m, D_m, h, l, d_m] = \mathsf{sort}([w0_m, M_m, D_m, h, l, d_m])\\ \\ w0_s \cdot \begin{array}{l} \mathbf{if}\;M_m \leq 5.6 \cdot 10^{-6}:\\ \;\;\;\;w0_m\\ \mathbf{elif}\;M_m \leq 8.6 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{log1p}\left(\mathsf{expm1}\left(w0_m\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-0.125 \cdot \left({\left(\frac{D_m}{d_m}\right)}^{2} \cdot \frac{{M_m}^{2} \cdot \left(w0_m \cdot h\right)}{\ell}\right)\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
D_m = (fabs.f64 D)
d_m = (fabs.f64 d)
w0_m = (fabs.f64 w0)
w0_s = (copysign.f64 1 w0)
NOTE: w0_m, M_m, D_m, h, l, and d_m should be sorted in increasing order before calling this function.
(FPCore (w0_s w0_m M_m D_m h l d_m)
 :precision binary64
 (*
  w0_s
  (if (<= M_m 5.6e-6)
    w0_m
    (if (<= M_m 8.6e+80)
      (log1p (expm1 w0_m))
      (*
       -0.125
       (* (pow (/ D_m d_m) 2.0) (/ (* (pow M_m 2.0) (* w0_m h)) l)))))))

C

M_m = fabs(M);
D_m = fabs(D);
d_m = fabs(d);
w0_m = fabs(w0);
w0_s = copysign(1.0, w0);
assert(w0_m < M_m && M_m < D_m && D_m < h && h < l && l < d_m);
double code(double w0_s, double w0_m, double M_m, double D_m, double h, double l, double d_m) {
	double tmp;
	if (M_m <= 5.6e-6) {
		tmp = w0_m;
	} else if (M_m <= 8.6e+80) {
		tmp = log1p(expm1(w0_m));
	} else {
		tmp = -0.125 * (pow((D_m / d_m), 2.0) * ((pow(M_m, 2.0) * (w0_m * h)) / l));
	}
	return w0_s * tmp;
}

Java

M_m = Math.abs(M);
D_m = Math.abs(D);
d_m = Math.abs(d);
w0_m = Math.abs(w0);
w0_s = Math.copySign(1.0, w0);
assert w0_m < M_m && M_m < D_m && D_m < h && h < l && l < d_m;
public static double code(double w0_s, double w0_m, double M_m, double D_m, double h, double l, double d_m) {
	double tmp;
	if (M_m <= 5.6e-6) {
		tmp = w0_m;
	} else if (M_m <= 8.6e+80) {
		tmp = Math.log1p(Math.expm1(w0_m));
	} else {
		tmp = -0.125 * (Math.pow((D_m / d_m), 2.0) * ((Math.pow(M_m, 2.0) * (w0_m * h)) / l));
	}
	return w0_s * tmp;
}

Python

M_m = math.fabs(M)
D_m = math.fabs(D)
d_m = math.fabs(d)
w0_m = math.fabs(w0)
w0_s = math.copysign(1.0, w0)
[w0_m, M_m, D_m, h, l, d_m] = sort([w0_m, M_m, D_m, h, l, d_m])
def code(w0_s, w0_m, M_m, D_m, h, l, d_m):
	tmp = 0
	if M_m <= 5.6e-6:
		tmp = w0_m
	elif M_m <= 8.6e+80:
		tmp = math.log1p(math.expm1(w0_m))
	else:
		tmp = -0.125 * (math.pow((D_m / d_m), 2.0) * ((math.pow(M_m, 2.0) * (w0_m * h)) / l))
	return w0_s * tmp

Julia

M_m = abs(M)
D_m = abs(D)
d_m = abs(d)
w0_m = abs(w0)
w0_s = copysign(1.0, w0)
w0_m, M_m, D_m, h, l, d_m = sort([w0_m, M_m, D_m, h, l, d_m])
function code(w0_s, w0_m, M_m, D_m, h, l, d_m)
	tmp = 0.0
	if (M_m <= 5.6e-6)
		tmp = w0_m;
	elseif (M_m <= 8.6e+80)
		tmp = log1p(expm1(w0_m));
	else
		tmp = Float64(-0.125 * Float64((Float64(D_m / d_m) ^ 2.0) * Float64(Float64((M_m ^ 2.0) * Float64(w0_m * h)) / l)));
	end
	return Float64(w0_s * tmp)
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
D_m = N[Abs[D], $MachinePrecision]
d_m = N[Abs[d], $MachinePrecision]
w0_m = N[Abs[w0], $MachinePrecision]
w0_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[w0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: w0_m, M_m, D_m, h, l, and d_m should be sorted in increasing order before calling this function.
code[w0$95$s_, w0$95$m_, M$95$m_, D$95$m_, h_, l_, d$95$m_] := N[(w0$95$s * If[LessEqual[M$95$m, 5.6e-6], w0$95$m, If[LessEqual[M$95$m, 8.6e+80], N[Log[1 + N[(Exp[w0$95$m] - 1), $MachinePrecision]], $MachinePrecision], N[(-0.125 * N[(N[Power[N[(D$95$m / d$95$m), $MachinePrecision], 2.0], $MachinePrecision] * N[(N[(N[Power[M$95$m, 2.0], $MachinePrecision] * N[(w0$95$m * h), $MachinePrecision]), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 4: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ D_m = \left|D\right| \\ d_m = \left|d\right| \\ w0_m = \left|w0\right| \\ w0_s = \mathsf{copysign}\left(1, w0\right) \\ [w0_m, M_m, D_m, h, l, d_m] = \mathsf{sort}([w0_m, M_m, D_m, h, l, d_m])\\ \\ w0_s \cdot \left(w0_m \cdot \sqrt{1 - h \cdot \frac{{\left(\frac{M_m}{d_m} \cdot \frac{D_m}{2}\right)}^{2}}{\ell}}\right) \end{array} \]

FPCore

M_m = (fabs.f64 M)
D_m = (fabs.f64 D)
d_m = (fabs.f64 d)
w0_m = (fabs.f64 w0)
w0_s = (copysign.f64 1 w0)
NOTE: w0_m, M_m, D_m, h, l, and d_m should be sorted in increasing order before calling this function.
(FPCore (w0_s w0_m M_m D_m h l d_m)
 :precision binary64
 (*
  w0_s
  (* w0_m (sqrt (- 1.0 (* h (/ (pow (* (/ M_m d_m) (/ D_m 2.0)) 2.0) l)))))))

C

M_m = fabs(M);
D_m = fabs(D);
d_m = fabs(d);
w0_m = fabs(w0);
w0_s = copysign(1.0, w0);
assert(w0_m < M_m && M_m < D_m && D_m < h && h < l && l < d_m);
double code(double w0_s, double w0_m, double M_m, double D_m, double h, double l, double d_m) {
	return w0_s * (w0_m * sqrt((1.0 - (h * (pow(((M_m / d_m) * (D_m / 2.0)), 2.0) / l)))));
}

Fortran

M_m = abs(M)
D_m = abs(D)
d_m = abs(d)
w0_m = abs(w0)
w0_s = copysign(1.0d0, w0)
NOTE: w0_m, M_m, D_m, h, l, and d_m should be sorted in increasing order before calling this function.
real(8) function code(w0_s, w0_m, m_m, d_m, h, l, d_m_1)
    real(8), intent (in) :: w0_s
    real(8), intent (in) :: w0_m
    real(8), intent (in) :: m_m
    real(8), intent (in) :: d_m
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: d_m_1
    code = w0_s * (w0_m * sqrt((1.0d0 - (h * ((((m_m / d_m_1) * (d_m / 2.0d0)) ** 2.0d0) / l)))))
end function

Java

M_m = Math.abs(M);
D_m = Math.abs(D);
d_m = Math.abs(d);
w0_m = Math.abs(w0);
w0_s = Math.copySign(1.0, w0);
assert w0_m < M_m && M_m < D_m && D_m < h && h < l && l < d_m;
public static double code(double w0_s, double w0_m, double M_m, double D_m, double h, double l, double d_m) {
	return w0_s * (w0_m * Math.sqrt((1.0 - (h * (Math.pow(((M_m / d_m) * (D_m / 2.0)), 2.0) / l)))));
}

Python

M_m = math.fabs(M)
D_m = math.fabs(D)
d_m = math.fabs(d)
w0_m = math.fabs(w0)
w0_s = math.copysign(1.0, w0)
[w0_m, M_m, D_m, h, l, d_m] = sort([w0_m, M_m, D_m, h, l, d_m])
def code(w0_s, w0_m, M_m, D_m, h, l, d_m):
	return w0_s * (w0_m * math.sqrt((1.0 - (h * (math.pow(((M_m / d_m) * (D_m / 2.0)), 2.0) / l)))))

Julia

M_m = abs(M)
D_m = abs(D)
d_m = abs(d)
w0_m = abs(w0)
w0_s = copysign(1.0, w0)
w0_m, M_m, D_m, h, l, d_m = sort([w0_m, M_m, D_m, h, l, d_m])
function code(w0_s, w0_m, M_m, D_m, h, l, d_m)
	return Float64(w0_s * Float64(w0_m * sqrt(Float64(1.0 - Float64(h * Float64((Float64(Float64(M_m / d_m) * Float64(D_m / 2.0)) ^ 2.0) / l))))))
end

MATLAB

M_m = abs(M);
D_m = abs(D);
d_m = abs(d);
w0_m = abs(w0);
w0_s = sign(w0) * abs(1.0);
w0_m, M_m, D_m, h, l, d_m = num2cell(sort([w0_m, M_m, D_m, h, l, d_m])){:}
function tmp = code(w0_s, w0_m, M_m, D_m, h, l, d_m)
	tmp = w0_s * (w0_m * sqrt((1.0 - (h * ((((M_m / d_m) * (D_m / 2.0)) ^ 2.0) / l)))));
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
D_m = N[Abs[D], $MachinePrecision]
d_m = N[Abs[d], $MachinePrecision]
w0_m = N[Abs[w0], $MachinePrecision]
w0_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[w0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: w0_m, M_m, D_m, h, l, and d_m should be sorted in increasing order before calling this function.
code[w0$95$s_, w0$95$m_, M$95$m_, D$95$m_, h_, l_, d$95$m_] := N[(w0$95$s * N[(w0$95$m * N[Sqrt[N[(1.0 - N[(h * N[(N[Power[N[(N[(M$95$m / d$95$m), $MachinePrecision] * N[(D$95$m / 2.0), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 5: 71.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ D_m = \left|D\right| \\ d_m = \left|d\right| \\ w0_m = \left|w0\right| \\ w0_s = \mathsf{copysign}\left(1, w0\right) \\ [w0_m, M_m, D_m, h, l, d_m] = \mathsf{sort}([w0_m, M_m, D_m, h, l, d_m])\\ \\ w0_s \cdot \begin{array}{l} \mathbf{if}\;M_m \leq 3.3 \cdot 10^{-6}:\\ \;\;\;\;w0_m\\ \mathbf{else}:\\ \;\;\;\;\mathsf{log1p}\left(\mathsf{expm1}\left(w0_m\right)\right)\\ \end{array} \end{array} \]

FPCore

M_m = (fabs.f64 M)
D_m = (fabs.f64 D)
d_m = (fabs.f64 d)
w0_m = (fabs.f64 w0)
w0_s = (copysign.f64 1 w0)
NOTE: w0_m, M_m, D_m, h, l, and d_m should be sorted in increasing order before calling this function.
(FPCore (w0_s w0_m M_m D_m h l d_m)
 :precision binary64
 (* w0_s (if (<= M_m 3.3e-6) w0_m (log1p (expm1 w0_m)))))

C

M_m = fabs(M);
D_m = fabs(D);
d_m = fabs(d);
w0_m = fabs(w0);
w0_s = copysign(1.0, w0);
assert(w0_m < M_m && M_m < D_m && D_m < h && h < l && l < d_m);
double code(double w0_s, double w0_m, double M_m, double D_m, double h, double l, double d_m) {
	double tmp;
	if (M_m <= 3.3e-6) {
		tmp = w0_m;
	} else {
		tmp = log1p(expm1(w0_m));
	}
	return w0_s * tmp;
}

Java

M_m = Math.abs(M);
D_m = Math.abs(D);
d_m = Math.abs(d);
w0_m = Math.abs(w0);
w0_s = Math.copySign(1.0, w0);
assert w0_m < M_m && M_m < D_m && D_m < h && h < l && l < d_m;
public static double code(double w0_s, double w0_m, double M_m, double D_m, double h, double l, double d_m) {
	double tmp;
	if (M_m <= 3.3e-6) {
		tmp = w0_m;
	} else {
		tmp = Math.log1p(Math.expm1(w0_m));
	}
	return w0_s * tmp;
}

Python

M_m = math.fabs(M)
D_m = math.fabs(D)
d_m = math.fabs(d)
w0_m = math.fabs(w0)
w0_s = math.copysign(1.0, w0)
[w0_m, M_m, D_m, h, l, d_m] = sort([w0_m, M_m, D_m, h, l, d_m])
def code(w0_s, w0_m, M_m, D_m, h, l, d_m):
	tmp = 0
	if M_m <= 3.3e-6:
		tmp = w0_m
	else:
		tmp = math.log1p(math.expm1(w0_m))
	return w0_s * tmp

Julia

M_m = abs(M)
D_m = abs(D)
d_m = abs(d)
w0_m = abs(w0)
w0_s = copysign(1.0, w0)
w0_m, M_m, D_m, h, l, d_m = sort([w0_m, M_m, D_m, h, l, d_m])
function code(w0_s, w0_m, M_m, D_m, h, l, d_m)
	tmp = 0.0
	if (M_m <= 3.3e-6)
		tmp = w0_m;
	else
		tmp = log1p(expm1(w0_m));
	end
	return Float64(w0_s * tmp)
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
D_m = N[Abs[D], $MachinePrecision]
d_m = N[Abs[d], $MachinePrecision]
w0_m = N[Abs[w0], $MachinePrecision]
w0_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[w0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: w0_m, M_m, D_m, h, l, and d_m should be sorted in increasing order before calling this function.
code[w0$95$s_, w0$95$m_, M$95$m_, D$95$m_, h_, l_, d$95$m_] := N[(w0$95$s * If[LessEqual[M$95$m, 3.3e-6], w0$95$m, N[Log[1 + N[(Exp[w0$95$m] - 1), $MachinePrecision]], $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 6: 67.9% accurate, 216.0× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ D_m = \left|D\right| \\ d_m = \left|d\right| \\ w0_m = \left|w0\right| \\ w0_s = \mathsf{copysign}\left(1, w0\right) \\ [w0_m, M_m, D_m, h, l, d_m] = \mathsf{sort}([w0_m, M_m, D_m, h, l, d_m])\\ \\ w0_s \cdot w0_m \end{array} \]

FPCore

M_m = (fabs.f64 M)
D_m = (fabs.f64 D)
d_m = (fabs.f64 d)
w0_m = (fabs.f64 w0)
w0_s = (copysign.f64 1 w0)
NOTE: w0_m, M_m, D_m, h, l, and d_m should be sorted in increasing order before calling this function.
(FPCore (w0_s w0_m M_m D_m h l d_m) :precision binary64 (* w0_s w0_m))

C

M_m = fabs(M);
D_m = fabs(D);
d_m = fabs(d);
w0_m = fabs(w0);
w0_s = copysign(1.0, w0);
assert(w0_m < M_m && M_m < D_m && D_m < h && h < l && l < d_m);
double code(double w0_s, double w0_m, double M_m, double D_m, double h, double l, double d_m) {
	return w0_s * w0_m;
}

Fortran

M_m = abs(M)
D_m = abs(D)
d_m = abs(d)
w0_m = abs(w0)
w0_s = copysign(1.0d0, w0)
NOTE: w0_m, M_m, D_m, h, l, and d_m should be sorted in increasing order before calling this function.
real(8) function code(w0_s, w0_m, m_m, d_m, h, l, d_m_1)
    real(8), intent (in) :: w0_s
    real(8), intent (in) :: w0_m
    real(8), intent (in) :: m_m
    real(8), intent (in) :: d_m
    real(8), intent (in) :: h
    real(8), intent (in) :: l
    real(8), intent (in) :: d_m_1
    code = w0_s * w0_m
end function

Java

M_m = Math.abs(M);
D_m = Math.abs(D);
d_m = Math.abs(d);
w0_m = Math.abs(w0);
w0_s = Math.copySign(1.0, w0);
assert w0_m < M_m && M_m < D_m && D_m < h && h < l && l < d_m;
public static double code(double w0_s, double w0_m, double M_m, double D_m, double h, double l, double d_m) {
	return w0_s * w0_m;
}

Python

M_m = math.fabs(M)
D_m = math.fabs(D)
d_m = math.fabs(d)
w0_m = math.fabs(w0)
w0_s = math.copysign(1.0, w0)
[w0_m, M_m, D_m, h, l, d_m] = sort([w0_m, M_m, D_m, h, l, d_m])
def code(w0_s, w0_m, M_m, D_m, h, l, d_m):
	return w0_s * w0_m

Julia

M_m = abs(M)
D_m = abs(D)
d_m = abs(d)
w0_m = abs(w0)
w0_s = copysign(1.0, w0)
w0_m, M_m, D_m, h, l, d_m = sort([w0_m, M_m, D_m, h, l, d_m])
function code(w0_s, w0_m, M_m, D_m, h, l, d_m)
	return Float64(w0_s * w0_m)
end

MATLAB

M_m = abs(M);
D_m = abs(D);
d_m = abs(d);
w0_m = abs(w0);
w0_s = sign(w0) * abs(1.0);
w0_m, M_m, D_m, h, l, d_m = num2cell(sort([w0_m, M_m, D_m, h, l, d_m])){:}
function tmp = code(w0_s, w0_m, M_m, D_m, h, l, d_m)
	tmp = w0_s * w0_m;
end

Wolfram

M_m = N[Abs[M], $MachinePrecision]
D_m = N[Abs[D], $MachinePrecision]
d_m = N[Abs[d], $MachinePrecision]
w0_m = N[Abs[w0], $MachinePrecision]
w0_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[w0]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: w0_m, M_m, D_m, h, l, and d_m should be sorted in increasing order before calling this function.
code[w0$95$s_, w0$95$m_, M$95$m_, D$95$m_, h_, l_, d$95$m_] := N[(w0$95$s * w0$95$m), $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2023350 
(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))))))