Henrywood and Agarwal, Equation (9a)

Percentage Accurate: 81.3% → 87.6%

Time: 18.0s

Alternatives: 9

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: 81.3% 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

\[\begin{array}{l} M_m = \left|M\right| \\ D_m = \left|D\right| \\ d_m = \left|d\right| \\ w0_m = \left|w0\right| \\ w0_s = \mathsf{copysign}\left(1, w0\right) \\ [w0_m, M_m, D_m, h, l, d_m] = \mathsf{sort}([w0_m, M_m, D_m, h, l, d_m])\\ \\ \begin{array}{l} t_0 := -2 \cdot \log d_m\\ t_1 := \frac{M_m \cdot D_m}{2 \cdot d_m}\\ w0_s \cdot \begin{array}{l} \mathbf{if}\;t_1 \leq 2 \cdot 10^{+118}:\\ \;\;\;\;w0_m \cdot \sqrt{1 - h \cdot \frac{{\left(0.5 \cdot \left(D_m \cdot \frac{M_m}{d_m}\right)\right)}^{2}}{\ell}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+244}:\\ \;\;\;\;{\left({w0_m}^{0.3333333333333333} \cdot \left(e^{\log \left(-0.25 \cdot \left(h \cdot \frac{{\left(M_m \cdot D_m\right)}^{2}}{\ell}\right)\right) \cdot 0.16666666666666666} \cdot e^{0.16666666666666666 \cdot t_0}\right)\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;{\left({w0_m}^{0.3333333333333333} \cdot e^{0.16666666666666666 \cdot \left(t_0 + \left(\log \left(-0.25 \cdot \frac{h \cdot {M_m}^{2}}{\ell}\right) + 2 \cdot \log D_m\right)\right)}\right)}^{3}\\ \end{array} \end{array} \end{array} \]

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
 (let* ((t_0 (* -2.0 (log d_m))) (t_1 (/ (* M_m D_m) (* 2.0 d_m))))
   (*
    w0_s
    (if (<= t_1 2e+118)
      (* w0_m (sqrt (- 1.0 (* h (/ (pow (* 0.5 (* D_m (/ M_m d_m))) 2.0) l)))))
      (if (<= t_1 2e+244)
        (pow
         (*
          (pow w0_m 0.3333333333333333)
          (*
           (exp
            (*
             (log (* -0.25 (* h (/ (pow (* M_m D_m) 2.0) l))))
             0.16666666666666666))
           (exp (* 0.16666666666666666 t_0))))
         3.0)
        (pow
         (*
          (pow w0_m 0.3333333333333333)
          (exp
           (*
            0.16666666666666666
            (+
             t_0
             (+
              (log (* -0.25 (/ (* h (pow M_m 2.0)) l)))
              (* 2.0 (log D_m)))))))
         3.0))))))

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 t_0 = -2.0 * log(d_m);
	double t_1 = (M_m * D_m) / (2.0 * d_m);
	double tmp;
	if (t_1 <= 2e+118) {
		tmp = w0_m * sqrt((1.0 - (h * (pow((0.5 * (D_m * (M_m / d_m))), 2.0) / l))));
	} else if (t_1 <= 2e+244) {
		tmp = pow((pow(w0_m, 0.3333333333333333) * (exp((log((-0.25 * (h * (pow((M_m * D_m), 2.0) / l)))) * 0.16666666666666666)) * exp((0.16666666666666666 * t_0)))), 3.0);
	} else {
		tmp = pow((pow(w0_m, 0.3333333333333333) * exp((0.16666666666666666 * (t_0 + (log((-0.25 * ((h * pow(M_m, 2.0)) / l))) + (2.0 * log(D_m))))))), 3.0);
	}
	return w0_s * tmp;
}

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
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-2.0d0) * log(d_m_1)
    t_1 = (m_m * d_m) / (2.0d0 * d_m_1)
    if (t_1 <= 2d+118) then
        tmp = w0_m * sqrt((1.0d0 - (h * (((0.5d0 * (d_m * (m_m / d_m_1))) ** 2.0d0) / l))))
    else if (t_1 <= 2d+244) then
        tmp = ((w0_m ** 0.3333333333333333d0) * (exp((log(((-0.25d0) * (h * (((m_m * d_m) ** 2.0d0) / l)))) * 0.16666666666666666d0)) * exp((0.16666666666666666d0 * t_0)))) ** 3.0d0
    else
        tmp = ((w0_m ** 0.3333333333333333d0) * exp((0.16666666666666666d0 * (t_0 + (log(((-0.25d0) * ((h * (m_m ** 2.0d0)) / l))) + (2.0d0 * log(d_m))))))) ** 3.0d0
    end if
    code = w0_s * tmp
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) {
	double t_0 = -2.0 * Math.log(d_m);
	double t_1 = (M_m * D_m) / (2.0 * d_m);
	double tmp;
	if (t_1 <= 2e+118) {
		tmp = w0_m * Math.sqrt((1.0 - (h * (Math.pow((0.5 * (D_m * (M_m / d_m))), 2.0) / l))));
	} else if (t_1 <= 2e+244) {
		tmp = Math.pow((Math.pow(w0_m, 0.3333333333333333) * (Math.exp((Math.log((-0.25 * (h * (Math.pow((M_m * D_m), 2.0) / l)))) * 0.16666666666666666)) * Math.exp((0.16666666666666666 * t_0)))), 3.0);
	} else {
		tmp = Math.pow((Math.pow(w0_m, 0.3333333333333333) * Math.exp((0.16666666666666666 * (t_0 + (Math.log((-0.25 * ((h * Math.pow(M_m, 2.0)) / l))) + (2.0 * Math.log(D_m))))))), 3.0);
	}
	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):
	t_0 = -2.0 * math.log(d_m)
	t_1 = (M_m * D_m) / (2.0 * d_m)
	tmp = 0
	if t_1 <= 2e+118:
		tmp = w0_m * math.sqrt((1.0 - (h * (math.pow((0.5 * (D_m * (M_m / d_m))), 2.0) / l))))
	elif t_1 <= 2e+244:
		tmp = math.pow((math.pow(w0_m, 0.3333333333333333) * (math.exp((math.log((-0.25 * (h * (math.pow((M_m * D_m), 2.0) / l)))) * 0.16666666666666666)) * math.exp((0.16666666666666666 * t_0)))), 3.0)
	else:
		tmp = math.pow((math.pow(w0_m, 0.3333333333333333) * math.exp((0.16666666666666666 * (t_0 + (math.log((-0.25 * ((h * math.pow(M_m, 2.0)) / l))) + (2.0 * math.log(D_m))))))), 3.0)
	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)
	t_0 = Float64(-2.0 * log(d_m))
	t_1 = Float64(Float64(M_m * D_m) / Float64(2.0 * d_m))
	tmp = 0.0
	if (t_1 <= 2e+118)
		tmp = Float64(w0_m * sqrt(Float64(1.0 - Float64(h * Float64((Float64(0.5 * Float64(D_m * Float64(M_m / d_m))) ^ 2.0) / l)))));
	elseif (t_1 <= 2e+244)
		tmp = Float64((w0_m ^ 0.3333333333333333) * Float64(exp(Float64(log(Float64(-0.25 * Float64(h * Float64((Float64(M_m * D_m) ^ 2.0) / l)))) * 0.16666666666666666)) * exp(Float64(0.16666666666666666 * t_0)))) ^ 3.0;
	else
		tmp = Float64((w0_m ^ 0.3333333333333333) * exp(Float64(0.16666666666666666 * Float64(t_0 + Float64(log(Float64(-0.25 * Float64(Float64(h * (M_m ^ 2.0)) / l))) + Float64(2.0 * log(D_m))))))) ^ 3.0;
	end
	return Float64(w0_s * tmp)
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_2 = code(w0_s, w0_m, M_m, D_m, h, l, d_m)
	t_0 = -2.0 * log(d_m);
	t_1 = (M_m * D_m) / (2.0 * d_m);
	tmp = 0.0;
	if (t_1 <= 2e+118)
		tmp = w0_m * sqrt((1.0 - (h * (((0.5 * (D_m * (M_m / d_m))) ^ 2.0) / l))));
	elseif (t_1 <= 2e+244)
		tmp = ((w0_m ^ 0.3333333333333333) * (exp((log((-0.25 * (h * (((M_m * D_m) ^ 2.0) / l)))) * 0.16666666666666666)) * exp((0.16666666666666666 * t_0)))) ^ 3.0;
	else
		tmp = ((w0_m ^ 0.3333333333333333) * exp((0.16666666666666666 * (t_0 + (log((-0.25 * ((h * (M_m ^ 2.0)) / l))) + (2.0 * log(D_m))))))) ^ 3.0;
	end
	tmp_2 = 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_] := Block[{t$95$0 = N[(-2.0 * N[Log[d$95$m], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(M$95$m * D$95$m), $MachinePrecision] / N[(2.0 * d$95$m), $MachinePrecision]), $MachinePrecision]}, N[(w0$95$s * If[LessEqual[t$95$1, 2e+118], N[(w0$95$m * N[Sqrt[N[(1.0 - N[(h * N[(N[Power[N[(0.5 * N[(D$95$m * N[(M$95$m / d$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+244], N[Power[N[(N[Power[w0$95$m, 0.3333333333333333], $MachinePrecision] * N[(N[Exp[N[(N[Log[N[(-0.25 * N[(h * N[(N[Power[N[(M$95$m * D$95$m), $MachinePrecision], 2.0], $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 0.16666666666666666), $MachinePrecision]], $MachinePrecision] * N[Exp[N[(0.16666666666666666 * t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], N[Power[N[(N[Power[w0$95$m, 0.3333333333333333], $MachinePrecision] * N[Exp[N[(0.16666666666666666 * N[(t$95$0 + 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]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]]]), $MachinePrecision]]]

Derivation

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

Alternative 2: 87.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ D_m = \left|D\right| \\ d_m = \left|d\right| \\ w0_m = \left|w0\right| \\ w0_s = \mathsf{copysign}\left(1, w0\right) \\ [w0_m, M_m, D_m, h, l, d_m] = \mathsf{sort}([w0_m, M_m, D_m, h, l, d_m])\\ \\ w0_s \cdot \begin{array}{l} \mathbf{if}\;{\left(\frac{M_m \cdot D_m}{2 \cdot d_m}\right)}^{2} \leq 5 \cdot 10^{+236}:\\ \;\;\;\;w0_m \cdot \sqrt{1 - h \cdot \frac{{\left(0.5 \cdot \left(D_m \cdot \frac{M_m}{d_m}\right)\right)}^{2}}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;{\left({w0_m}^{0.3333333333333333} \cdot e^{0.16666666666666666 \cdot \left(-2 \cdot \log d_m + \left(\log \left(-0.25 \cdot \frac{h \cdot {M_m}^{2}}{\ell}\right) + 2 \cdot \log D_m\right)\right)}\right)}^{3}\\ \end{array} \end{array} \]

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 (<= (pow (/ (* M_m D_m) (* 2.0 d_m)) 2.0) 5e+236)
    (* w0_m (sqrt (- 1.0 (* h (/ (pow (* 0.5 (* D_m (/ M_m d_m))) 2.0) l)))))
    (pow
     (*
      (pow w0_m 0.3333333333333333)
      (exp
       (*
        0.16666666666666666
        (+
         (* -2.0 (log d_m))
         (+ (log (* -0.25 (/ (* h (pow M_m 2.0)) l))) (* 2.0 (log D_m)))))))
     3.0))))

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 (pow(((M_m * D_m) / (2.0 * d_m)), 2.0) <= 5e+236) {
		tmp = w0_m * sqrt((1.0 - (h * (pow((0.5 * (D_m * (M_m / d_m))), 2.0) / l))));
	} else {
		tmp = pow((pow(w0_m, 0.3333333333333333) * exp((0.16666666666666666 * ((-2.0 * log(d_m)) + (log((-0.25 * ((h * pow(M_m, 2.0)) / l))) + (2.0 * log(D_m))))))), 3.0);
	}
	return w0_s * tmp;
}

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
    real(8) :: tmp
    if ((((m_m * d_m) / (2.0d0 * d_m_1)) ** 2.0d0) <= 5d+236) then
        tmp = w0_m * sqrt((1.0d0 - (h * (((0.5d0 * (d_m * (m_m / d_m_1))) ** 2.0d0) / l))))
    else
        tmp = ((w0_m ** 0.3333333333333333d0) * exp((0.16666666666666666d0 * (((-2.0d0) * log(d_m_1)) + (log(((-0.25d0) * ((h * (m_m ** 2.0d0)) / l))) + (2.0d0 * log(d_m))))))) ** 3.0d0
    end if
    code = w0_s * tmp
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) {
	double tmp;
	if (Math.pow(((M_m * D_m) / (2.0 * d_m)), 2.0) <= 5e+236) {
		tmp = w0_m * Math.sqrt((1.0 - (h * (Math.pow((0.5 * (D_m * (M_m / d_m))), 2.0) / l))));
	} else {
		tmp = Math.pow((Math.pow(w0_m, 0.3333333333333333) * Math.exp((0.16666666666666666 * ((-2.0 * Math.log(d_m)) + (Math.log((-0.25 * ((h * Math.pow(M_m, 2.0)) / l))) + (2.0 * Math.log(D_m))))))), 3.0);
	}
	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 math.pow(((M_m * D_m) / (2.0 * d_m)), 2.0) <= 5e+236:
		tmp = w0_m * math.sqrt((1.0 - (h * (math.pow((0.5 * (D_m * (M_m / d_m))), 2.0) / l))))
	else:
		tmp = math.pow((math.pow(w0_m, 0.3333333333333333) * math.exp((0.16666666666666666 * ((-2.0 * math.log(d_m)) + (math.log((-0.25 * ((h * math.pow(M_m, 2.0)) / l))) + (2.0 * math.log(D_m))))))), 3.0)
	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)) ^ 2.0) <= 5e+236)
		tmp = Float64(w0_m * sqrt(Float64(1.0 - Float64(h * Float64((Float64(0.5 * Float64(D_m * Float64(M_m / d_m))) ^ 2.0) / l)))));
	else
		tmp = Float64((w0_m ^ 0.3333333333333333) * exp(Float64(0.16666666666666666 * Float64(Float64(-2.0 * log(d_m)) + Float64(log(Float64(-0.25 * Float64(Float64(h * (M_m ^ 2.0)) / l))) + Float64(2.0 * log(D_m))))))) ^ 3.0;
	end
	return Float64(w0_s * tmp)
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_2 = code(w0_s, w0_m, M_m, D_m, h, l, d_m)
	tmp = 0.0;
	if ((((M_m * D_m) / (2.0 * d_m)) ^ 2.0) <= 5e+236)
		tmp = w0_m * sqrt((1.0 - (h * (((0.5 * (D_m * (M_m / d_m))) ^ 2.0) / l))));
	else
		tmp = ((w0_m ^ 0.3333333333333333) * exp((0.16666666666666666 * ((-2.0 * log(d_m)) + (log((-0.25 * ((h * (M_m ^ 2.0)) / l))) + (2.0 * log(D_m))))))) ^ 3.0;
	end
	tmp_2 = 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[Power[N[(N[(M$95$m * D$95$m), $MachinePrecision] / N[(2.0 * d$95$m), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision], 5e+236], N[(w0$95$m * N[Sqrt[N[(1.0 - N[(h * N[(N[Power[N[(0.5 * N[(D$95$m * N[(M$95$m / d$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Power[N[(N[Power[w0$95$m, 0.3333333333333333], $MachinePrecision] * N[Exp[N[(0.16666666666666666 * N[(N[(-2.0 * N[Log[d$95$m], $MachinePrecision]), $MachinePrecision] + 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]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 3: 87.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ D_m = \left|D\right| \\ d_m = \left|d\right| \\ w0_m = \left|w0\right| \\ w0_s = \mathsf{copysign}\left(1, w0\right) \\ [w0_m, M_m, D_m, h, l, d_m] = \mathsf{sort}([w0_m, M_m, D_m, h, l, d_m])\\ \\ w0_s \cdot \begin{array}{l} \mathbf{if}\;\ell \leq 4 \cdot 10^{-197}:\\ \;\;\;\;w0_m \cdot \sqrt{1 - h \cdot \frac{{\left(0.5 \cdot \left(D_m \cdot \frac{M_m}{d_m}\right)\right)}^{2}}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;w0_m \cdot \sqrt{1 - h \cdot {\left(\frac{0.5 \cdot \frac{M_m \cdot D_m}{d_m}}{\sqrt{\ell}}\right)}^{2}}\\ \end{array} \end{array} \]

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 (<= l 4e-197)
    (* w0_m (sqrt (- 1.0 (* h (/ (pow (* 0.5 (* D_m (/ M_m d_m))) 2.0) l)))))
    (*
     w0_m
     (sqrt
      (- 1.0 (* h (pow (/ (* 0.5 (/ (* M_m D_m) d_m)) (sqrt l)) 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 (l <= 4e-197) {
		tmp = w0_m * sqrt((1.0 - (h * (pow((0.5 * (D_m * (M_m / d_m))), 2.0) / l))));
	} else {
		tmp = w0_m * sqrt((1.0 - (h * pow(((0.5 * ((M_m * D_m) / d_m)) / sqrt(l)), 2.0))));
	}
	return w0_s * tmp;
}

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
    real(8) :: tmp
    if (l <= 4d-197) then
        tmp = w0_m * sqrt((1.0d0 - (h * (((0.5d0 * (d_m * (m_m / d_m_1))) ** 2.0d0) / l))))
    else
        tmp = w0_m * sqrt((1.0d0 - (h * (((0.5d0 * ((m_m * d_m) / d_m_1)) / sqrt(l)) ** 2.0d0))))
    end if
    code = w0_s * tmp
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) {
	double tmp;
	if (l <= 4e-197) {
		tmp = w0_m * Math.sqrt((1.0 - (h * (Math.pow((0.5 * (D_m * (M_m / d_m))), 2.0) / l))));
	} else {
		tmp = w0_m * Math.sqrt((1.0 - (h * Math.pow(((0.5 * ((M_m * D_m) / d_m)) / Math.sqrt(l)), 2.0))));
	}
	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 l <= 4e-197:
		tmp = w0_m * math.sqrt((1.0 - (h * (math.pow((0.5 * (D_m * (M_m / d_m))), 2.0) / l))))
	else:
		tmp = w0_m * math.sqrt((1.0 - (h * math.pow(((0.5 * ((M_m * D_m) / d_m)) / math.sqrt(l)), 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 (l <= 4e-197)
		tmp = Float64(w0_m * sqrt(Float64(1.0 - Float64(h * Float64((Float64(0.5 * Float64(D_m * Float64(M_m / d_m))) ^ 2.0) / l)))));
	else
		tmp = Float64(w0_m * sqrt(Float64(1.0 - Float64(h * (Float64(Float64(0.5 * Float64(Float64(M_m * D_m) / d_m)) / sqrt(l)) ^ 2.0)))));
	end
	return Float64(w0_s * tmp)
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_2 = code(w0_s, w0_m, M_m, D_m, h, l, d_m)
	tmp = 0.0;
	if (l <= 4e-197)
		tmp = w0_m * sqrt((1.0 - (h * (((0.5 * (D_m * (M_m / d_m))) ^ 2.0) / l))));
	else
		tmp = w0_m * sqrt((1.0 - (h * (((0.5 * ((M_m * D_m) / d_m)) / sqrt(l)) ^ 2.0))));
	end
	tmp_2 = 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[l, 4e-197], N[(w0$95$m * N[Sqrt[N[(1.0 - N[(h * N[(N[Power[N[(0.5 * N[(D$95$m * N[(M$95$m / d$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(w0$95$m * N[Sqrt[N[(1.0 - N[(h * N[Power[N[(N[(0.5 * N[(N[(M$95$m * D$95$m), $MachinePrecision] / d$95$m), $MachinePrecision]), $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 4: 86.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ D_m = \left|D\right| \\ d_m = \left|d\right| \\ w0_m = \left|w0\right| \\ w0_s = \mathsf{copysign}\left(1, w0\right) \\ [w0_m, M_m, D_m, h, l, d_m] = \mathsf{sort}([w0_m, M_m, D_m, h, l, d_m])\\ \\ w0_s \cdot \left(w0_m \cdot \sqrt{1 - h \cdot \frac{{\left(0.5 \cdot \left(D_m \cdot \frac{M_m}{d_m}\right)\right)}^{2}}{\ell}}\right) \end{array} \]

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 (* 0.5 (* D_m (/ M_m d_m))) 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((0.5 * (D_m * (M_m / d_m))), 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 * (((0.5d0 * (d_m * (m_m / d_m_1))) ** 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((0.5 * (D_m * (M_m / d_m))), 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((0.5 * (D_m * (M_m / d_m))), 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(0.5 * Float64(D_m * Float64(M_m / d_m))) ^ 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 * (((0.5 * (D_m * (M_m / d_m))) ^ 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[(0.5 * N[(D$95$m * N[(M$95$m / d$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 5: 80.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ D_m = \left|D\right| \\ d_m = \left|d\right| \\ w0_m = \left|w0\right| \\ w0_s = \mathsf{copysign}\left(1, w0\right) \\ [w0_m, M_m, D_m, h, l, d_m] = \mathsf{sort}([w0_m, M_m, D_m, h, l, d_m])\\ \\ w0_s \cdot \left(w0_m \cdot \mathsf{fma}\left(h \cdot \frac{{\left(M_m \cdot \frac{D_m}{d_m}\right)}^{2}}{\ell}, -0.125, 1\right)\right) \end{array} \]

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 (fma (* h (/ (pow (* M_m (/ D_m d_m)) 2.0) l)) -0.125 1.0))))

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) {
	return w0_s * (w0_m * fma((h * (pow((M_m * (D_m / d_m)), 2.0) / l)), -0.125, 1.0));
}

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 * fma(Float64(h * Float64((Float64(M_m * Float64(D_m / d_m)) ^ 2.0) / l)), -0.125, 1.0)))
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[(N[(h * N[(N[Power[N[(M$95$m * N[(D$95$m / d$95$m), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision] * -0.125 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 6: 75.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ D_m = \left|D\right| \\ d_m = \left|d\right| \\ w0_m = \left|w0\right| \\ w0_s = \mathsf{copysign}\left(1, w0\right) \\ [w0_m, M_m, D_m, h, l, d_m] = \mathsf{sort}([w0_m, M_m, D_m, h, l, d_m])\\ \\ \begin{array}{l} t_0 := M_m \cdot \frac{D_m}{d_m}\\ w0_s \cdot \begin{array}{l} \mathbf{if}\;D_m \leq 1.35 \cdot 10^{+159}:\\ \;\;\;\;w0_m\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.125, \left(t_0 \cdot t_0\right) \cdot \frac{w0_m \cdot h}{\ell}, w0_m\right)\\ \end{array} \end{array} \end{array} \]

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
 (let* ((t_0 (* M_m (/ D_m d_m))))
   (*
    w0_s
    (if (<= D_m 1.35e+159)
      w0_m
      (fma -0.125 (* (* t_0 t_0) (/ (* w0_m h) l)) 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 t_0 = M_m * (D_m / d_m);
	double tmp;
	if (D_m <= 1.35e+159) {
		tmp = w0_m;
	} else {
		tmp = fma(-0.125, ((t_0 * t_0) * ((w0_m * h) / l)), 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)
	t_0 = Float64(M_m * Float64(D_m / d_m))
	tmp = 0.0
	if (D_m <= 1.35e+159)
		tmp = w0_m;
	else
		tmp = fma(-0.125, Float64(Float64(t_0 * t_0) * Float64(Float64(w0_m * h) / l)), 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_] := Block[{t$95$0 = N[(M$95$m * N[(D$95$m / d$95$m), $MachinePrecision]), $MachinePrecision]}, N[(w0$95$s * If[LessEqual[D$95$m, 1.35e+159], w0$95$m, N[(-0.125 * N[(N[(t$95$0 * t$95$0), $MachinePrecision] * N[(N[(w0$95$m * h), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision] + w0$95$m), $MachinePrecision]]), $MachinePrecision]]

Derivation

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

Alternative 7: 72.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ D_m = \left|D\right| \\ d_m = \left|d\right| \\ w0_m = \left|w0\right| \\ w0_s = \mathsf{copysign}\left(1, w0\right) \\ [w0_m, M_m, D_m, h, l, d_m] = \mathsf{sort}([w0_m, M_m, D_m, h, l, d_m])\\ \\ w0_s \cdot \begin{array}{l} \mathbf{if}\;M_m \leq 5.6 \cdot 10^{+44}:\\ \;\;\;\;w0_m\\ \mathbf{else}:\\ \;\;\;\;-0.125 \cdot \left({\left(M_m \cdot \frac{D_m}{d_m}\right)}^{2} \cdot \frac{h}{\frac{\ell}{w0_m}}\right)\\ \end{array} \end{array} \]

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+44)
    w0_m
    (* -0.125 (* (pow (* M_m (/ D_m d_m)) 2.0) (/ h (/ l 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 <= 5.6e+44) {
		tmp = w0_m;
	} else {
		tmp = -0.125 * (pow((M_m * (D_m / d_m)), 2.0) * (h / (l / w0_m)));
	}
	return w0_s * tmp;
}

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
    real(8) :: tmp
    if (m_m <= 5.6d+44) then
        tmp = w0_m
    else
        tmp = (-0.125d0) * (((m_m * (d_m / d_m_1)) ** 2.0d0) * (h / (l / w0_m)))
    end if
    code = w0_s * tmp
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) {
	double tmp;
	if (M_m <= 5.6e+44) {
		tmp = w0_m;
	} else {
		tmp = -0.125 * (Math.pow((M_m * (D_m / d_m)), 2.0) * (h / (l / 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 <= 5.6e+44:
		tmp = w0_m
	else:
		tmp = -0.125 * (math.pow((M_m * (D_m / d_m)), 2.0) * (h / (l / 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 <= 5.6e+44)
		tmp = w0_m;
	else
		tmp = Float64(-0.125 * Float64((Float64(M_m * Float64(D_m / d_m)) ^ 2.0) * Float64(h / Float64(l / w0_m))));
	end
	return Float64(w0_s * tmp)
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_2 = code(w0_s, w0_m, M_m, D_m, h, l, d_m)
	tmp = 0.0;
	if (M_m <= 5.6e+44)
		tmp = w0_m;
	else
		tmp = -0.125 * (((M_m * (D_m / d_m)) ^ 2.0) * (h / (l / w0_m)));
	end
	tmp_2 = 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+44], w0$95$m, N[(-0.125 * N[(N[Power[N[(M$95$m * N[(D$95$m / d$95$m), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision] * N[(h / N[(l / w0$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 8: 72.7% accurate, 10.3× speedup

Math

\[\begin{array}{l} M_m = \left|M\right| \\ D_m = \left|D\right| \\ d_m = \left|d\right| \\ w0_m = \left|w0\right| \\ w0_s = \mathsf{copysign}\left(1, w0\right) \\ [w0_m, M_m, D_m, h, l, d_m] = \mathsf{sort}([w0_m, M_m, D_m, h, l, d_m])\\ \\ \begin{array}{l} t_0 := M_m \cdot \frac{D_m}{d_m}\\ w0_s \cdot \begin{array}{l} \mathbf{if}\;M_m \leq 5.5 \cdot 10^{+44}:\\ \;\;\;\;w0_m\\ \mathbf{else}:\\ \;\;\;\;-0.125 \cdot \left(\left(t_0 \cdot t_0\right) \cdot \frac{w0_m \cdot h}{\ell}\right)\\ \end{array} \end{array} \end{array} \]

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
 (let* ((t_0 (* M_m (/ D_m d_m))))
   (*
    w0_s
    (if (<= M_m 5.5e+44) w0_m (* -0.125 (* (* t_0 t_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 t_0 = M_m * (D_m / d_m);
	double tmp;
	if (M_m <= 5.5e+44) {
		tmp = w0_m;
	} else {
		tmp = -0.125 * ((t_0 * t_0) * ((w0_m * h) / l));
	}
	return w0_s * tmp;
}

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
    real(8) :: t_0
    real(8) :: tmp
    t_0 = m_m * (d_m / d_m_1)
    if (m_m <= 5.5d+44) then
        tmp = w0_m
    else
        tmp = (-0.125d0) * ((t_0 * t_0) * ((w0_m * h) / l))
    end if
    code = w0_s * tmp
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) {
	double t_0 = M_m * (D_m / d_m);
	double tmp;
	if (M_m <= 5.5e+44) {
		tmp = w0_m;
	} else {
		tmp = -0.125 * ((t_0 * t_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):
	t_0 = M_m * (D_m / d_m)
	tmp = 0
	if M_m <= 5.5e+44:
		tmp = w0_m
	else:
		tmp = -0.125 * ((t_0 * t_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)
	t_0 = Float64(M_m * Float64(D_m / d_m))
	tmp = 0.0
	if (M_m <= 5.5e+44)
		tmp = w0_m;
	else
		tmp = Float64(-0.125 * Float64(Float64(t_0 * t_0) * Float64(Float64(w0_m * h) / l)));
	end
	return Float64(w0_s * tmp)
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_2 = code(w0_s, w0_m, M_m, D_m, h, l, d_m)
	t_0 = M_m * (D_m / d_m);
	tmp = 0.0;
	if (M_m <= 5.5e+44)
		tmp = w0_m;
	else
		tmp = -0.125 * ((t_0 * t_0) * ((w0_m * h) / l));
	end
	tmp_2 = 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_] := Block[{t$95$0 = N[(M$95$m * N[(D$95$m / d$95$m), $MachinePrecision]), $MachinePrecision]}, N[(w0$95$s * If[LessEqual[M$95$m, 5.5e+44], w0$95$m, N[(-0.125 * N[(N[(t$95$0 * t$95$0), $MachinePrecision] * N[(N[(w0$95$m * h), $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

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

Alternative 9: 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 2023364 
(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))))))