Toniolo and Linder, Equation (10-)

Percentage Accurate: 34.8% → 83.1%

Time: 24.2s

Alternatives: 12

Speedup: 2.0×

• 34.5% of points produce a very large (infinite) output. You may want to add a precondition.

• could not determine a ground truth

  1. t = 4.94066e-324
  2. l = -2
  3. k = 0.0

Specification

Math

\[\begin{array}{l} \\ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) - 1\right)} \end{array} \]

FPCore

(FPCore (t l k)
 :precision binary64
 (/
  2.0
  (*
   (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
   (- (+ 1.0 (pow (/ k t) 2.0)) 1.0))))

C

double code(double t, double l, double k) {
	return 2.0 / ((((pow(t, 3.0) / (l * l)) * sin(k)) * tan(k)) * ((1.0 + pow((k / t), 2.0)) - 1.0));
}

Fortran

real(8) function code(t, l, k)
    real(8), intent (in) :: t
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    code = 2.0d0 / (((((t ** 3.0d0) / (l * l)) * sin(k)) * tan(k)) * ((1.0d0 + ((k / t) ** 2.0d0)) - 1.0d0))
end function

Java

public static double code(double t, double l, double k) {
	return 2.0 / ((((Math.pow(t, 3.0) / (l * l)) * Math.sin(k)) * Math.tan(k)) * ((1.0 + Math.pow((k / t), 2.0)) - 1.0));
}

Python

def code(t, l, k):
	return 2.0 / ((((math.pow(t, 3.0) / (l * l)) * math.sin(k)) * math.tan(k)) * ((1.0 + math.pow((k / t), 2.0)) - 1.0))

Julia

function code(t, l, k)
	return Float64(2.0 / Float64(Float64(Float64(Float64((t ^ 3.0) / Float64(l * l)) * sin(k)) * tan(k)) * Float64(Float64(1.0 + (Float64(k / t) ^ 2.0)) - 1.0)))
end

MATLAB

function tmp = code(t, l, k)
	tmp = 2.0 / (((((t ^ 3.0) / (l * l)) * sin(k)) * tan(k)) * ((1.0 + ((k / t) ^ 2.0)) - 1.0));
end

Wolfram

code[t_, l_, k_] := N[(2.0 / N[(N[(N[(N[(N[Power[t, 3.0], $MachinePrecision] / N[(l * l), $MachinePrecision]), $MachinePrecision] * N[Sin[k], $MachinePrecision]), $MachinePrecision] * N[Tan[k], $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 + N[Power[N[(k / t), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 34.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{2}{\left(\left(\frac{{t}^{3}}{\ell \cdot \ell} \cdot \sin k\right) \cdot \tan k\right) \cdot \left(\left(1 + {\left(\frac{k}{t}\right)}^{2}\right) - 1\right)} \end{array} \]

FPCore

(FPCore (t l k)
 :precision binary64
 (/
  2.0
  (*
   (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
   (- (+ 1.0 (pow (/ k t) 2.0)) 1.0))))

C

double code(double t, double l, double k) {
	return 2.0 / ((((pow(t, 3.0) / (l * l)) * sin(k)) * tan(k)) * ((1.0 + pow((k / t), 2.0)) - 1.0));
}

Fortran

real(8) function code(t, l, k)
    real(8), intent (in) :: t
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    code = 2.0d0 / (((((t ** 3.0d0) / (l * l)) * sin(k)) * tan(k)) * ((1.0d0 + ((k / t) ** 2.0d0)) - 1.0d0))
end function

Java

public static double code(double t, double l, double k) {
	return 2.0 / ((((Math.pow(t, 3.0) / (l * l)) * Math.sin(k)) * Math.tan(k)) * ((1.0 + Math.pow((k / t), 2.0)) - 1.0));
}

Python

def code(t, l, k):
	return 2.0 / ((((math.pow(t, 3.0) / (l * l)) * math.sin(k)) * math.tan(k)) * ((1.0 + math.pow((k / t), 2.0)) - 1.0))

Julia

function code(t, l, k)
	return Float64(2.0 / Float64(Float64(Float64(Float64((t ^ 3.0) / Float64(l * l)) * sin(k)) * tan(k)) * Float64(Float64(1.0 + (Float64(k / t) ^ 2.0)) - 1.0)))
end

MATLAB

function tmp = code(t, l, k)
	tmp = 2.0 / (((((t ^ 3.0) / (l * l)) * sin(k)) * tan(k)) * ((1.0 + ((k / t) ^ 2.0)) - 1.0));
end

Wolfram

code[t_, l_, k_] := N[(2.0 / N[(N[(N[(N[(N[Power[t, 3.0], $MachinePrecision] / N[(l * l), $MachinePrecision]), $MachinePrecision] * N[Sin[k], $MachinePrecision]), $MachinePrecision] * N[Tan[k], $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 + N[Power[N[(k / t), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 83.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;\ell \cdot \ell \leq 5 \cdot 10^{-318}:\\ \;\;\;\;{\left(\frac{\ell \cdot \sqrt{2}}{{k}^{2}} \cdot \sqrt{\frac{1}{t_m}}\right)}^{2}\\ \mathbf{elif}\;\ell \cdot \ell \leq 2 \cdot 10^{+51}:\\ \;\;\;\;\frac{-2}{{k}^{2} \cdot t_m} \cdot \left(\frac{\cos k}{{\sin k}^{2}} \cdot \frac{{\ell}^{2}}{-1}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{{\left(\frac{k}{\frac{\ell}{\sin k}} \cdot \sqrt{\frac{t_m}{\cos k}}\right)}^{2}}\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (*
  t_s
  (if (<= (* l l) 5e-318)
    (pow (* (/ (* l (sqrt 2.0)) (pow k 2.0)) (sqrt (/ 1.0 t_m))) 2.0)
    (if (<= (* l l) 2e+51)
      (*
       (/ -2.0 (* (pow k 2.0) t_m))
       (* (/ (cos k) (pow (sin k) 2.0)) (/ (pow l 2.0) -1.0)))
      (/ 2.0 (pow (* (/ k (/ l (sin k))) (sqrt (/ t_m (cos k)))) 2.0))))))

C

t_m = fabs(t);
t_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k) {
	double tmp;
	if ((l * l) <= 5e-318) {
		tmp = pow((((l * sqrt(2.0)) / pow(k, 2.0)) * sqrt((1.0 / t_m))), 2.0);
	} else if ((l * l) <= 2e+51) {
		tmp = (-2.0 / (pow(k, 2.0) * t_m)) * ((cos(k) / pow(sin(k), 2.0)) * (pow(l, 2.0) / -1.0));
	} else {
		tmp = 2.0 / pow(((k / (l / sin(k))) * sqrt((t_m / cos(k)))), 2.0);
	}
	return t_s * tmp;
}

Fortran

t_m = abs(t)
t_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((l * l) <= 5d-318) then
        tmp = (((l * sqrt(2.0d0)) / (k ** 2.0d0)) * sqrt((1.0d0 / t_m))) ** 2.0d0
    else if ((l * l) <= 2d+51) then
        tmp = ((-2.0d0) / ((k ** 2.0d0) * t_m)) * ((cos(k) / (sin(k) ** 2.0d0)) * ((l ** 2.0d0) / (-1.0d0)))
    else
        tmp = 2.0d0 / (((k / (l / sin(k))) * sqrt((t_m / cos(k)))) ** 2.0d0)
    end if
    code = t_s * tmp
end function

Java

t_m = Math.abs(t);
t_s = Math.copySign(1.0, t);
public static double code(double t_s, double t_m, double l, double k) {
	double tmp;
	if ((l * l) <= 5e-318) {
		tmp = Math.pow((((l * Math.sqrt(2.0)) / Math.pow(k, 2.0)) * Math.sqrt((1.0 / t_m))), 2.0);
	} else if ((l * l) <= 2e+51) {
		tmp = (-2.0 / (Math.pow(k, 2.0) * t_m)) * ((Math.cos(k) / Math.pow(Math.sin(k), 2.0)) * (Math.pow(l, 2.0) / -1.0));
	} else {
		tmp = 2.0 / Math.pow(((k / (l / Math.sin(k))) * Math.sqrt((t_m / Math.cos(k)))), 2.0);
	}
	return t_s * tmp;
}

Python

t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k):
	tmp = 0
	if (l * l) <= 5e-318:
		tmp = math.pow((((l * math.sqrt(2.0)) / math.pow(k, 2.0)) * math.sqrt((1.0 / t_m))), 2.0)
	elif (l * l) <= 2e+51:
		tmp = (-2.0 / (math.pow(k, 2.0) * t_m)) * ((math.cos(k) / math.pow(math.sin(k), 2.0)) * (math.pow(l, 2.0) / -1.0))
	else:
		tmp = 2.0 / math.pow(((k / (l / math.sin(k))) * math.sqrt((t_m / math.cos(k)))), 2.0)
	return t_s * tmp

Julia

t_m = abs(t)
t_s = copysign(1.0, t)
function code(t_s, t_m, l, k)
	tmp = 0.0
	if (Float64(l * l) <= 5e-318)
		tmp = Float64(Float64(Float64(l * sqrt(2.0)) / (k ^ 2.0)) * sqrt(Float64(1.0 / t_m))) ^ 2.0;
	elseif (Float64(l * l) <= 2e+51)
		tmp = Float64(Float64(-2.0 / Float64((k ^ 2.0) * t_m)) * Float64(Float64(cos(k) / (sin(k) ^ 2.0)) * Float64((l ^ 2.0) / -1.0)));
	else
		tmp = Float64(2.0 / (Float64(Float64(k / Float64(l / sin(k))) * sqrt(Float64(t_m / cos(k)))) ^ 2.0));
	end
	return Float64(t_s * tmp)
end

MATLAB

t_m = abs(t);
t_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, t_m, l, k)
	tmp = 0.0;
	if ((l * l) <= 5e-318)
		tmp = (((l * sqrt(2.0)) / (k ^ 2.0)) * sqrt((1.0 / t_m))) ^ 2.0;
	elseif ((l * l) <= 2e+51)
		tmp = (-2.0 / ((k ^ 2.0) * t_m)) * ((cos(k) / (sin(k) ^ 2.0)) * ((l ^ 2.0) / -1.0));
	else
		tmp = 2.0 / (((k / (l / sin(k))) * sqrt((t_m / cos(k)))) ^ 2.0);
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
t_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, t$95$m_, l_, k_] := N[(t$95$s * If[LessEqual[N[(l * l), $MachinePrecision], 5e-318], N[Power[N[(N[(N[(l * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision] / N[Power[k, 2.0], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(1.0 / t$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision], If[LessEqual[N[(l * l), $MachinePrecision], 2e+51], N[(N[(-2.0 / N[(N[Power[k, 2.0], $MachinePrecision] * t$95$m), $MachinePrecision]), $MachinePrecision] * N[(N[(N[Cos[k], $MachinePrecision] / N[Power[N[Sin[k], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(N[Power[l, 2.0], $MachinePrecision] / -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[Power[N[(N[(k / N[(l / N[Sin[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(t$95$m / N[Cos[k], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 2: 80.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ \begin{array}{l} t_2 := {\left(\frac{k}{t_m}\right)}^{2}\\ t_s \cdot \begin{array}{l} \mathbf{if}\;\frac{2}{\left(\left(\sin k \cdot \frac{{t_m}^{3}}{\ell \cdot \ell}\right) \cdot \tan k\right) \cdot \left(\left(1 + t_2\right) + -1\right)} \leq 10^{+158}:\\ \;\;\;\;\frac{\frac{2}{t_2}}{\left(\left({t_m}^{2} \cdot \frac{1}{\ell}\right) \cdot \frac{t_m}{\ell}\right) \cdot \left(\sin k \cdot \tan k\right)}\\ \mathbf{else}:\\ \;\;\;\;{\left(\sqrt{\frac{\cos k}{t_m}} \cdot \left(\frac{\ell}{k} \cdot \frac{\sqrt{2}}{\sin k}\right)\right)}^{2}\\ \end{array} \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (let* ((t_2 (pow (/ k t_m) 2.0)))
   (*
    t_s
    (if (<=
         (/
          2.0
          (*
           (* (* (sin k) (/ (pow t_m 3.0) (* l l))) (tan k))
           (+ (+ 1.0 t_2) -1.0)))
         1e+158)
      (/
       (/ 2.0 t_2)
       (* (* (* (pow t_m 2.0) (/ 1.0 l)) (/ t_m l)) (* (sin k) (tan k))))
      (pow
       (* (sqrt (/ (cos k) t_m)) (* (/ l k) (/ (sqrt 2.0) (sin k))))
       2.0)))))

C

t_m = fabs(t);
t_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k) {
	double t_2 = pow((k / t_m), 2.0);
	double tmp;
	if ((2.0 / (((sin(k) * (pow(t_m, 3.0) / (l * l))) * tan(k)) * ((1.0 + t_2) + -1.0))) <= 1e+158) {
		tmp = (2.0 / t_2) / (((pow(t_m, 2.0) * (1.0 / l)) * (t_m / l)) * (sin(k) * tan(k)));
	} else {
		tmp = pow((sqrt((cos(k) / t_m)) * ((l / k) * (sqrt(2.0) / sin(k)))), 2.0);
	}
	return t_s * tmp;
}

Fortran

t_m = abs(t)
t_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8) :: t_2
    real(8) :: tmp
    t_2 = (k / t_m) ** 2.0d0
    if ((2.0d0 / (((sin(k) * ((t_m ** 3.0d0) / (l * l))) * tan(k)) * ((1.0d0 + t_2) + (-1.0d0)))) <= 1d+158) then
        tmp = (2.0d0 / t_2) / ((((t_m ** 2.0d0) * (1.0d0 / l)) * (t_m / l)) * (sin(k) * tan(k)))
    else
        tmp = (sqrt((cos(k) / t_m)) * ((l / k) * (sqrt(2.0d0) / sin(k)))) ** 2.0d0
    end if
    code = t_s * tmp
end function

Java

t_m = Math.abs(t);
t_s = Math.copySign(1.0, t);
public static double code(double t_s, double t_m, double l, double k) {
	double t_2 = Math.pow((k / t_m), 2.0);
	double tmp;
	if ((2.0 / (((Math.sin(k) * (Math.pow(t_m, 3.0) / (l * l))) * Math.tan(k)) * ((1.0 + t_2) + -1.0))) <= 1e+158) {
		tmp = (2.0 / t_2) / (((Math.pow(t_m, 2.0) * (1.0 / l)) * (t_m / l)) * (Math.sin(k) * Math.tan(k)));
	} else {
		tmp = Math.pow((Math.sqrt((Math.cos(k) / t_m)) * ((l / k) * (Math.sqrt(2.0) / Math.sin(k)))), 2.0);
	}
	return t_s * tmp;
}

Python

t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k):
	t_2 = math.pow((k / t_m), 2.0)
	tmp = 0
	if (2.0 / (((math.sin(k) * (math.pow(t_m, 3.0) / (l * l))) * math.tan(k)) * ((1.0 + t_2) + -1.0))) <= 1e+158:
		tmp = (2.0 / t_2) / (((math.pow(t_m, 2.0) * (1.0 / l)) * (t_m / l)) * (math.sin(k) * math.tan(k)))
	else:
		tmp = math.pow((math.sqrt((math.cos(k) / t_m)) * ((l / k) * (math.sqrt(2.0) / math.sin(k)))), 2.0)
	return t_s * tmp

Julia

t_m = abs(t)
t_s = copysign(1.0, t)
function code(t_s, t_m, l, k)
	t_2 = Float64(k / t_m) ^ 2.0
	tmp = 0.0
	if (Float64(2.0 / Float64(Float64(Float64(sin(k) * Float64((t_m ^ 3.0) / Float64(l * l))) * tan(k)) * Float64(Float64(1.0 + t_2) + -1.0))) <= 1e+158)
		tmp = Float64(Float64(2.0 / t_2) / Float64(Float64(Float64((t_m ^ 2.0) * Float64(1.0 / l)) * Float64(t_m / l)) * Float64(sin(k) * tan(k))));
	else
		tmp = Float64(sqrt(Float64(cos(k) / t_m)) * Float64(Float64(l / k) * Float64(sqrt(2.0) / sin(k)))) ^ 2.0;
	end
	return Float64(t_s * tmp)
end

MATLAB

t_m = abs(t);
t_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, t_m, l, k)
	t_2 = (k / t_m) ^ 2.0;
	tmp = 0.0;
	if ((2.0 / (((sin(k) * ((t_m ^ 3.0) / (l * l))) * tan(k)) * ((1.0 + t_2) + -1.0))) <= 1e+158)
		tmp = (2.0 / t_2) / ((((t_m ^ 2.0) * (1.0 / l)) * (t_m / l)) * (sin(k) * tan(k)));
	else
		tmp = (sqrt((cos(k) / t_m)) * ((l / k) * (sqrt(2.0) / sin(k)))) ^ 2.0;
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
t_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, t$95$m_, l_, k_] := Block[{t$95$2 = N[Power[N[(k / t$95$m), $MachinePrecision], 2.0], $MachinePrecision]}, N[(t$95$s * If[LessEqual[N[(2.0 / N[(N[(N[(N[Sin[k], $MachinePrecision] * N[(N[Power[t$95$m, 3.0], $MachinePrecision] / N[(l * l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Tan[k], $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 + t$95$2), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1e+158], N[(N[(2.0 / t$95$2), $MachinePrecision] / N[(N[(N[(N[Power[t$95$m, 2.0], $MachinePrecision] * N[(1.0 / l), $MachinePrecision]), $MachinePrecision] * N[(t$95$m / l), $MachinePrecision]), $MachinePrecision] * N[(N[Sin[k], $MachinePrecision] * N[Tan[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[(N[Sqrt[N[(N[Cos[k], $MachinePrecision] / t$95$m), $MachinePrecision]], $MachinePrecision] * N[(N[(l / k), $MachinePrecision] * N[(N[Sqrt[2.0], $MachinePrecision] / N[Sin[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]]), $MachinePrecision]]

Derivation

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

Alternative 3: 80.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ \begin{array}{l} t_2 := {\left(\frac{k}{t_m}\right)}^{2}\\ t_s \cdot \begin{array}{l} \mathbf{if}\;\frac{2}{\left(\left(\sin k \cdot \frac{{t_m}^{3}}{\ell \cdot \ell}\right) \cdot \tan k\right) \cdot \left(\left(1 + t_2\right) + -1\right)} \leq 10^{+158}:\\ \;\;\;\;\frac{\frac{2}{t_2}}{\left(\left({t_m}^{2} \cdot \frac{1}{\ell}\right) \cdot \frac{t_m}{\ell}\right) \cdot \left(\sin k \cdot \tan k\right)}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\ell}{k} \cdot \frac{\sqrt{\frac{\cos k}{t_m}}}{\frac{\sin k}{\sqrt{2}}}\right)}^{2}\\ \end{array} \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (let* ((t_2 (pow (/ k t_m) 2.0)))
   (*
    t_s
    (if (<=
         (/
          2.0
          (*
           (* (* (sin k) (/ (pow t_m 3.0) (* l l))) (tan k))
           (+ (+ 1.0 t_2) -1.0)))
         1e+158)
      (/
       (/ 2.0 t_2)
       (* (* (* (pow t_m 2.0) (/ 1.0 l)) (/ t_m l)) (* (sin k) (tan k))))
      (pow
       (* (/ l k) (/ (sqrt (/ (cos k) t_m)) (/ (sin k) (sqrt 2.0))))
       2.0)))))

C

t_m = fabs(t);
t_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k) {
	double t_2 = pow((k / t_m), 2.0);
	double tmp;
	if ((2.0 / (((sin(k) * (pow(t_m, 3.0) / (l * l))) * tan(k)) * ((1.0 + t_2) + -1.0))) <= 1e+158) {
		tmp = (2.0 / t_2) / (((pow(t_m, 2.0) * (1.0 / l)) * (t_m / l)) * (sin(k) * tan(k)));
	} else {
		tmp = pow(((l / k) * (sqrt((cos(k) / t_m)) / (sin(k) / sqrt(2.0)))), 2.0);
	}
	return t_s * tmp;
}

Fortran

t_m = abs(t)
t_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8) :: t_2
    real(8) :: tmp
    t_2 = (k / t_m) ** 2.0d0
    if ((2.0d0 / (((sin(k) * ((t_m ** 3.0d0) / (l * l))) * tan(k)) * ((1.0d0 + t_2) + (-1.0d0)))) <= 1d+158) then
        tmp = (2.0d0 / t_2) / ((((t_m ** 2.0d0) * (1.0d0 / l)) * (t_m / l)) * (sin(k) * tan(k)))
    else
        tmp = ((l / k) * (sqrt((cos(k) / t_m)) / (sin(k) / sqrt(2.0d0)))) ** 2.0d0
    end if
    code = t_s * tmp
end function

Java

t_m = Math.abs(t);
t_s = Math.copySign(1.0, t);
public static double code(double t_s, double t_m, double l, double k) {
	double t_2 = Math.pow((k / t_m), 2.0);
	double tmp;
	if ((2.0 / (((Math.sin(k) * (Math.pow(t_m, 3.0) / (l * l))) * Math.tan(k)) * ((1.0 + t_2) + -1.0))) <= 1e+158) {
		tmp = (2.0 / t_2) / (((Math.pow(t_m, 2.0) * (1.0 / l)) * (t_m / l)) * (Math.sin(k) * Math.tan(k)));
	} else {
		tmp = Math.pow(((l / k) * (Math.sqrt((Math.cos(k) / t_m)) / (Math.sin(k) / Math.sqrt(2.0)))), 2.0);
	}
	return t_s * tmp;
}

Python

t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k):
	t_2 = math.pow((k / t_m), 2.0)
	tmp = 0
	if (2.0 / (((math.sin(k) * (math.pow(t_m, 3.0) / (l * l))) * math.tan(k)) * ((1.0 + t_2) + -1.0))) <= 1e+158:
		tmp = (2.0 / t_2) / (((math.pow(t_m, 2.0) * (1.0 / l)) * (t_m / l)) * (math.sin(k) * math.tan(k)))
	else:
		tmp = math.pow(((l / k) * (math.sqrt((math.cos(k) / t_m)) / (math.sin(k) / math.sqrt(2.0)))), 2.0)
	return t_s * tmp

Julia

t_m = abs(t)
t_s = copysign(1.0, t)
function code(t_s, t_m, l, k)
	t_2 = Float64(k / t_m) ^ 2.0
	tmp = 0.0
	if (Float64(2.0 / Float64(Float64(Float64(sin(k) * Float64((t_m ^ 3.0) / Float64(l * l))) * tan(k)) * Float64(Float64(1.0 + t_2) + -1.0))) <= 1e+158)
		tmp = Float64(Float64(2.0 / t_2) / Float64(Float64(Float64((t_m ^ 2.0) * Float64(1.0 / l)) * Float64(t_m / l)) * Float64(sin(k) * tan(k))));
	else
		tmp = Float64(Float64(l / k) * Float64(sqrt(Float64(cos(k) / t_m)) / Float64(sin(k) / sqrt(2.0)))) ^ 2.0;
	end
	return Float64(t_s * tmp)
end

MATLAB

t_m = abs(t);
t_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, t_m, l, k)
	t_2 = (k / t_m) ^ 2.0;
	tmp = 0.0;
	if ((2.0 / (((sin(k) * ((t_m ^ 3.0) / (l * l))) * tan(k)) * ((1.0 + t_2) + -1.0))) <= 1e+158)
		tmp = (2.0 / t_2) / ((((t_m ^ 2.0) * (1.0 / l)) * (t_m / l)) * (sin(k) * tan(k)));
	else
		tmp = ((l / k) * (sqrt((cos(k) / t_m)) / (sin(k) / sqrt(2.0)))) ^ 2.0;
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
t_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, t$95$m_, l_, k_] := Block[{t$95$2 = N[Power[N[(k / t$95$m), $MachinePrecision], 2.0], $MachinePrecision]}, N[(t$95$s * If[LessEqual[N[(2.0 / N[(N[(N[(N[Sin[k], $MachinePrecision] * N[(N[Power[t$95$m, 3.0], $MachinePrecision] / N[(l * l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Tan[k], $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 + t$95$2), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1e+158], N[(N[(2.0 / t$95$2), $MachinePrecision] / N[(N[(N[(N[Power[t$95$m, 2.0], $MachinePrecision] * N[(1.0 / l), $MachinePrecision]), $MachinePrecision] * N[(t$95$m / l), $MachinePrecision]), $MachinePrecision] * N[(N[Sin[k], $MachinePrecision] * N[Tan[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[(N[(l / k), $MachinePrecision] * N[(N[Sqrt[N[(N[Cos[k], $MachinePrecision] / t$95$m), $MachinePrecision]], $MachinePrecision] / N[(N[Sin[k], $MachinePrecision] / N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]]), $MachinePrecision]]

Derivation

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

Alternative 4: 79.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ \begin{array}{l} t_2 := {\left(\frac{k}{t_m}\right)}^{2}\\ t_s \cdot \begin{array}{l} \mathbf{if}\;\left(\left(\sin k \cdot \frac{{t_m}^{3}}{\ell \cdot \ell}\right) \cdot \tan k\right) \cdot \left(\left(1 + t_2\right) + -1\right) \leq 5 \cdot 10^{+158}:\\ \;\;\;\;\frac{\frac{2}{t_2}}{\left(\left({t_m}^{2} \cdot \frac{1}{\ell}\right) \cdot \frac{t_m}{\ell}\right) \cdot \left(\sin k \cdot \tan k\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{{\left(\frac{k}{\frac{\ell}{\sin k}} \cdot \sqrt{\frac{t_m}{\cos k}}\right)}^{2}}\\ \end{array} \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (let* ((t_2 (pow (/ k t_m) 2.0)))
   (*
    t_s
    (if (<=
         (*
          (* (* (sin k) (/ (pow t_m 3.0) (* l l))) (tan k))
          (+ (+ 1.0 t_2) -1.0))
         5e+158)
      (/
       (/ 2.0 t_2)
       (* (* (* (pow t_m 2.0) (/ 1.0 l)) (/ t_m l)) (* (sin k) (tan k))))
      (/ 2.0 (pow (* (/ k (/ l (sin k))) (sqrt (/ t_m (cos k)))) 2.0))))))

C

t_m = fabs(t);
t_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k) {
	double t_2 = pow((k / t_m), 2.0);
	double tmp;
	if ((((sin(k) * (pow(t_m, 3.0) / (l * l))) * tan(k)) * ((1.0 + t_2) + -1.0)) <= 5e+158) {
		tmp = (2.0 / t_2) / (((pow(t_m, 2.0) * (1.0 / l)) * (t_m / l)) * (sin(k) * tan(k)));
	} else {
		tmp = 2.0 / pow(((k / (l / sin(k))) * sqrt((t_m / cos(k)))), 2.0);
	}
	return t_s * tmp;
}

Fortran

t_m = abs(t)
t_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8) :: t_2
    real(8) :: tmp
    t_2 = (k / t_m) ** 2.0d0
    if ((((sin(k) * ((t_m ** 3.0d0) / (l * l))) * tan(k)) * ((1.0d0 + t_2) + (-1.0d0))) <= 5d+158) then
        tmp = (2.0d0 / t_2) / ((((t_m ** 2.0d0) * (1.0d0 / l)) * (t_m / l)) * (sin(k) * tan(k)))
    else
        tmp = 2.0d0 / (((k / (l / sin(k))) * sqrt((t_m / cos(k)))) ** 2.0d0)
    end if
    code = t_s * tmp
end function

Java

t_m = Math.abs(t);
t_s = Math.copySign(1.0, t);
public static double code(double t_s, double t_m, double l, double k) {
	double t_2 = Math.pow((k / t_m), 2.0);
	double tmp;
	if ((((Math.sin(k) * (Math.pow(t_m, 3.0) / (l * l))) * Math.tan(k)) * ((1.0 + t_2) + -1.0)) <= 5e+158) {
		tmp = (2.0 / t_2) / (((Math.pow(t_m, 2.0) * (1.0 / l)) * (t_m / l)) * (Math.sin(k) * Math.tan(k)));
	} else {
		tmp = 2.0 / Math.pow(((k / (l / Math.sin(k))) * Math.sqrt((t_m / Math.cos(k)))), 2.0);
	}
	return t_s * tmp;
}

Python

t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k):
	t_2 = math.pow((k / t_m), 2.0)
	tmp = 0
	if (((math.sin(k) * (math.pow(t_m, 3.0) / (l * l))) * math.tan(k)) * ((1.0 + t_2) + -1.0)) <= 5e+158:
		tmp = (2.0 / t_2) / (((math.pow(t_m, 2.0) * (1.0 / l)) * (t_m / l)) * (math.sin(k) * math.tan(k)))
	else:
		tmp = 2.0 / math.pow(((k / (l / math.sin(k))) * math.sqrt((t_m / math.cos(k)))), 2.0)
	return t_s * tmp

Julia

t_m = abs(t)
t_s = copysign(1.0, t)
function code(t_s, t_m, l, k)
	t_2 = Float64(k / t_m) ^ 2.0
	tmp = 0.0
	if (Float64(Float64(Float64(sin(k) * Float64((t_m ^ 3.0) / Float64(l * l))) * tan(k)) * Float64(Float64(1.0 + t_2) + -1.0)) <= 5e+158)
		tmp = Float64(Float64(2.0 / t_2) / Float64(Float64(Float64((t_m ^ 2.0) * Float64(1.0 / l)) * Float64(t_m / l)) * Float64(sin(k) * tan(k))));
	else
		tmp = Float64(2.0 / (Float64(Float64(k / Float64(l / sin(k))) * sqrt(Float64(t_m / cos(k)))) ^ 2.0));
	end
	return Float64(t_s * tmp)
end

MATLAB

t_m = abs(t);
t_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, t_m, l, k)
	t_2 = (k / t_m) ^ 2.0;
	tmp = 0.0;
	if ((((sin(k) * ((t_m ^ 3.0) / (l * l))) * tan(k)) * ((1.0 + t_2) + -1.0)) <= 5e+158)
		tmp = (2.0 / t_2) / ((((t_m ^ 2.0) * (1.0 / l)) * (t_m / l)) * (sin(k) * tan(k)));
	else
		tmp = 2.0 / (((k / (l / sin(k))) * sqrt((t_m / cos(k)))) ^ 2.0);
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
t_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, t$95$m_, l_, k_] := Block[{t$95$2 = N[Power[N[(k / t$95$m), $MachinePrecision], 2.0], $MachinePrecision]}, N[(t$95$s * If[LessEqual[N[(N[(N[(N[Sin[k], $MachinePrecision] * N[(N[Power[t$95$m, 3.0], $MachinePrecision] / N[(l * l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Tan[k], $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 + t$95$2), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], 5e+158], N[(N[(2.0 / t$95$2), $MachinePrecision] / N[(N[(N[(N[Power[t$95$m, 2.0], $MachinePrecision] * N[(1.0 / l), $MachinePrecision]), $MachinePrecision] * N[(t$95$m / l), $MachinePrecision]), $MachinePrecision] * N[(N[Sin[k], $MachinePrecision] * N[Tan[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[Power[N[(N[(k / N[(l / N[Sin[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(t$95$m / N[Cos[k], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

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

Alternative 5: 79.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ \begin{array}{l} t_2 := {\left(\frac{k}{t_m}\right)}^{2}\\ t_s \cdot \begin{array}{l} \mathbf{if}\;\left(\left(\sin k \cdot \frac{{t_m}^{3}}{\ell \cdot \ell}\right) \cdot \tan k\right) \cdot \left(\left(1 + t_2\right) + -1\right) \leq 5 \cdot 10^{+158}:\\ \;\;\;\;\frac{\frac{2}{t_2}}{\left(\sin k \cdot \tan k\right) \cdot \left(\frac{t_m}{\ell} \cdot \frac{{t_m}^{2}}{\ell}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{{\left(\frac{k}{\frac{\ell}{\sin k}} \cdot \sqrt{\frac{t_m}{\cos k}}\right)}^{2}}\\ \end{array} \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (let* ((t_2 (pow (/ k t_m) 2.0)))
   (*
    t_s
    (if (<=
         (*
          (* (* (sin k) (/ (pow t_m 3.0) (* l l))) (tan k))
          (+ (+ 1.0 t_2) -1.0))
         5e+158)
      (/ (/ 2.0 t_2) (* (* (sin k) (tan k)) (* (/ t_m l) (/ (pow t_m 2.0) l))))
      (/ 2.0 (pow (* (/ k (/ l (sin k))) (sqrt (/ t_m (cos k)))) 2.0))))))

C

t_m = fabs(t);
t_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k) {
	double t_2 = pow((k / t_m), 2.0);
	double tmp;
	if ((((sin(k) * (pow(t_m, 3.0) / (l * l))) * tan(k)) * ((1.0 + t_2) + -1.0)) <= 5e+158) {
		tmp = (2.0 / t_2) / ((sin(k) * tan(k)) * ((t_m / l) * (pow(t_m, 2.0) / l)));
	} else {
		tmp = 2.0 / pow(((k / (l / sin(k))) * sqrt((t_m / cos(k)))), 2.0);
	}
	return t_s * tmp;
}

Fortran

t_m = abs(t)
t_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8) :: t_2
    real(8) :: tmp
    t_2 = (k / t_m) ** 2.0d0
    if ((((sin(k) * ((t_m ** 3.0d0) / (l * l))) * tan(k)) * ((1.0d0 + t_2) + (-1.0d0))) <= 5d+158) then
        tmp = (2.0d0 / t_2) / ((sin(k) * tan(k)) * ((t_m / l) * ((t_m ** 2.0d0) / l)))
    else
        tmp = 2.0d0 / (((k / (l / sin(k))) * sqrt((t_m / cos(k)))) ** 2.0d0)
    end if
    code = t_s * tmp
end function

Java

t_m = Math.abs(t);
t_s = Math.copySign(1.0, t);
public static double code(double t_s, double t_m, double l, double k) {
	double t_2 = Math.pow((k / t_m), 2.0);
	double tmp;
	if ((((Math.sin(k) * (Math.pow(t_m, 3.0) / (l * l))) * Math.tan(k)) * ((1.0 + t_2) + -1.0)) <= 5e+158) {
		tmp = (2.0 / t_2) / ((Math.sin(k) * Math.tan(k)) * ((t_m / l) * (Math.pow(t_m, 2.0) / l)));
	} else {
		tmp = 2.0 / Math.pow(((k / (l / Math.sin(k))) * Math.sqrt((t_m / Math.cos(k)))), 2.0);
	}
	return t_s * tmp;
}

Python

t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k):
	t_2 = math.pow((k / t_m), 2.0)
	tmp = 0
	if (((math.sin(k) * (math.pow(t_m, 3.0) / (l * l))) * math.tan(k)) * ((1.0 + t_2) + -1.0)) <= 5e+158:
		tmp = (2.0 / t_2) / ((math.sin(k) * math.tan(k)) * ((t_m / l) * (math.pow(t_m, 2.0) / l)))
	else:
		tmp = 2.0 / math.pow(((k / (l / math.sin(k))) * math.sqrt((t_m / math.cos(k)))), 2.0)
	return t_s * tmp

Julia

t_m = abs(t)
t_s = copysign(1.0, t)
function code(t_s, t_m, l, k)
	t_2 = Float64(k / t_m) ^ 2.0
	tmp = 0.0
	if (Float64(Float64(Float64(sin(k) * Float64((t_m ^ 3.0) / Float64(l * l))) * tan(k)) * Float64(Float64(1.0 + t_2) + -1.0)) <= 5e+158)
		tmp = Float64(Float64(2.0 / t_2) / Float64(Float64(sin(k) * tan(k)) * Float64(Float64(t_m / l) * Float64((t_m ^ 2.0) / l))));
	else
		tmp = Float64(2.0 / (Float64(Float64(k / Float64(l / sin(k))) * sqrt(Float64(t_m / cos(k)))) ^ 2.0));
	end
	return Float64(t_s * tmp)
end

MATLAB

t_m = abs(t);
t_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, t_m, l, k)
	t_2 = (k / t_m) ^ 2.0;
	tmp = 0.0;
	if ((((sin(k) * ((t_m ^ 3.0) / (l * l))) * tan(k)) * ((1.0 + t_2) + -1.0)) <= 5e+158)
		tmp = (2.0 / t_2) / ((sin(k) * tan(k)) * ((t_m / l) * ((t_m ^ 2.0) / l)));
	else
		tmp = 2.0 / (((k / (l / sin(k))) * sqrt((t_m / cos(k)))) ^ 2.0);
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
t_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, t$95$m_, l_, k_] := Block[{t$95$2 = N[Power[N[(k / t$95$m), $MachinePrecision], 2.0], $MachinePrecision]}, N[(t$95$s * If[LessEqual[N[(N[(N[(N[Sin[k], $MachinePrecision] * N[(N[Power[t$95$m, 3.0], $MachinePrecision] / N[(l * l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Tan[k], $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 + t$95$2), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], 5e+158], N[(N[(2.0 / t$95$2), $MachinePrecision] / N[(N[(N[Sin[k], $MachinePrecision] * N[Tan[k], $MachinePrecision]), $MachinePrecision] * N[(N[(t$95$m / l), $MachinePrecision] * N[(N[Power[t$95$m, 2.0], $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[Power[N[(N[(k / N[(l / N[Sin[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(t$95$m / N[Cos[k], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

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

Alternative 6: 79.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ \begin{array}{l} t_2 := {\left(\frac{k}{t_m}\right)}^{2}\\ t_s \cdot \begin{array}{l} \mathbf{if}\;\left(\left(\sin k \cdot \frac{{t_m}^{3}}{\ell \cdot \ell}\right) \cdot \tan k\right) \cdot \left(\left(1 + t_2\right) + -1\right) \leq 5 \cdot 10^{+116}:\\ \;\;\;\;\frac{\frac{2}{\sin k \cdot \left(\frac{{t_m}^{3}}{\ell} \cdot \frac{\tan k}{\ell}\right)}}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{{\left(\frac{k}{\frac{\ell}{\sin k}} \cdot \sqrt{\frac{t_m}{\cos k}}\right)}^{2}}\\ \end{array} \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (let* ((t_2 (pow (/ k t_m) 2.0)))
   (*
    t_s
    (if (<=
         (*
          (* (* (sin k) (/ (pow t_m 3.0) (* l l))) (tan k))
          (+ (+ 1.0 t_2) -1.0))
         5e+116)
      (/ (/ 2.0 (* (sin k) (* (/ (pow t_m 3.0) l) (/ (tan k) l)))) t_2)
      (/ 2.0 (pow (* (/ k (/ l (sin k))) (sqrt (/ t_m (cos k)))) 2.0))))))

C

t_m = fabs(t);
t_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k) {
	double t_2 = pow((k / t_m), 2.0);
	double tmp;
	if ((((sin(k) * (pow(t_m, 3.0) / (l * l))) * tan(k)) * ((1.0 + t_2) + -1.0)) <= 5e+116) {
		tmp = (2.0 / (sin(k) * ((pow(t_m, 3.0) / l) * (tan(k) / l)))) / t_2;
	} else {
		tmp = 2.0 / pow(((k / (l / sin(k))) * sqrt((t_m / cos(k)))), 2.0);
	}
	return t_s * tmp;
}

Fortran

t_m = abs(t)
t_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8) :: t_2
    real(8) :: tmp
    t_2 = (k / t_m) ** 2.0d0
    if ((((sin(k) * ((t_m ** 3.0d0) / (l * l))) * tan(k)) * ((1.0d0 + t_2) + (-1.0d0))) <= 5d+116) then
        tmp = (2.0d0 / (sin(k) * (((t_m ** 3.0d0) / l) * (tan(k) / l)))) / t_2
    else
        tmp = 2.0d0 / (((k / (l / sin(k))) * sqrt((t_m / cos(k)))) ** 2.0d0)
    end if
    code = t_s * tmp
end function

Java

t_m = Math.abs(t);
t_s = Math.copySign(1.0, t);
public static double code(double t_s, double t_m, double l, double k) {
	double t_2 = Math.pow((k / t_m), 2.0);
	double tmp;
	if ((((Math.sin(k) * (Math.pow(t_m, 3.0) / (l * l))) * Math.tan(k)) * ((1.0 + t_2) + -1.0)) <= 5e+116) {
		tmp = (2.0 / (Math.sin(k) * ((Math.pow(t_m, 3.0) / l) * (Math.tan(k) / l)))) / t_2;
	} else {
		tmp = 2.0 / Math.pow(((k / (l / Math.sin(k))) * Math.sqrt((t_m / Math.cos(k)))), 2.0);
	}
	return t_s * tmp;
}

Python

t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k):
	t_2 = math.pow((k / t_m), 2.0)
	tmp = 0
	if (((math.sin(k) * (math.pow(t_m, 3.0) / (l * l))) * math.tan(k)) * ((1.0 + t_2) + -1.0)) <= 5e+116:
		tmp = (2.0 / (math.sin(k) * ((math.pow(t_m, 3.0) / l) * (math.tan(k) / l)))) / t_2
	else:
		tmp = 2.0 / math.pow(((k / (l / math.sin(k))) * math.sqrt((t_m / math.cos(k)))), 2.0)
	return t_s * tmp

Julia

t_m = abs(t)
t_s = copysign(1.0, t)
function code(t_s, t_m, l, k)
	t_2 = Float64(k / t_m) ^ 2.0
	tmp = 0.0
	if (Float64(Float64(Float64(sin(k) * Float64((t_m ^ 3.0) / Float64(l * l))) * tan(k)) * Float64(Float64(1.0 + t_2) + -1.0)) <= 5e+116)
		tmp = Float64(Float64(2.0 / Float64(sin(k) * Float64(Float64((t_m ^ 3.0) / l) * Float64(tan(k) / l)))) / t_2);
	else
		tmp = Float64(2.0 / (Float64(Float64(k / Float64(l / sin(k))) * sqrt(Float64(t_m / cos(k)))) ^ 2.0));
	end
	return Float64(t_s * tmp)
end

MATLAB

t_m = abs(t);
t_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, t_m, l, k)
	t_2 = (k / t_m) ^ 2.0;
	tmp = 0.0;
	if ((((sin(k) * ((t_m ^ 3.0) / (l * l))) * tan(k)) * ((1.0 + t_2) + -1.0)) <= 5e+116)
		tmp = (2.0 / (sin(k) * (((t_m ^ 3.0) / l) * (tan(k) / l)))) / t_2;
	else
		tmp = 2.0 / (((k / (l / sin(k))) * sqrt((t_m / cos(k)))) ^ 2.0);
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
t_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, t$95$m_, l_, k_] := Block[{t$95$2 = N[Power[N[(k / t$95$m), $MachinePrecision], 2.0], $MachinePrecision]}, N[(t$95$s * If[LessEqual[N[(N[(N[(N[Sin[k], $MachinePrecision] * N[(N[Power[t$95$m, 3.0], $MachinePrecision] / N[(l * l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Tan[k], $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 + t$95$2), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], 5e+116], N[(N[(2.0 / N[(N[Sin[k], $MachinePrecision] * N[(N[(N[Power[t$95$m, 3.0], $MachinePrecision] / l), $MachinePrecision] * N[(N[Tan[k], $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], N[(2.0 / N[Power[N[(N[(k / N[(l / N[Sin[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(t$95$m / N[Cos[k], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

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

Alternative 7: 81.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;\ell \cdot \ell \leq 2 \cdot 10^{-108}:\\ \;\;\;\;{\left(\frac{\ell \cdot \sqrt{2}}{{k}^{2}} \cdot \sqrt{\frac{1}{t_m}}\right)}^{2}\\ \mathbf{elif}\;\ell \cdot \ell \leq 2 \cdot 10^{+51}:\\ \;\;\;\;2 \cdot \frac{\cos k \cdot {\ell}^{2}}{{k}^{2} \cdot \left(t_m \cdot {\sin k}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{{\left(\frac{k}{\frac{\ell}{\sin k}} \cdot \sqrt{\frac{t_m}{\cos k}}\right)}^{2}}\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (*
  t_s
  (if (<= (* l l) 2e-108)
    (pow (* (/ (* l (sqrt 2.0)) (pow k 2.0)) (sqrt (/ 1.0 t_m))) 2.0)
    (if (<= (* l l) 2e+51)
      (*
       2.0
       (/ (* (cos k) (pow l 2.0)) (* (pow k 2.0) (* t_m (pow (sin k) 2.0)))))
      (/ 2.0 (pow (* (/ k (/ l (sin k))) (sqrt (/ t_m (cos k)))) 2.0))))))

C

t_m = fabs(t);
t_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k) {
	double tmp;
	if ((l * l) <= 2e-108) {
		tmp = pow((((l * sqrt(2.0)) / pow(k, 2.0)) * sqrt((1.0 / t_m))), 2.0);
	} else if ((l * l) <= 2e+51) {
		tmp = 2.0 * ((cos(k) * pow(l, 2.0)) / (pow(k, 2.0) * (t_m * pow(sin(k), 2.0))));
	} else {
		tmp = 2.0 / pow(((k / (l / sin(k))) * sqrt((t_m / cos(k)))), 2.0);
	}
	return t_s * tmp;
}

Fortran

t_m = abs(t)
t_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((l * l) <= 2d-108) then
        tmp = (((l * sqrt(2.0d0)) / (k ** 2.0d0)) * sqrt((1.0d0 / t_m))) ** 2.0d0
    else if ((l * l) <= 2d+51) then
        tmp = 2.0d0 * ((cos(k) * (l ** 2.0d0)) / ((k ** 2.0d0) * (t_m * (sin(k) ** 2.0d0))))
    else
        tmp = 2.0d0 / (((k / (l / sin(k))) * sqrt((t_m / cos(k)))) ** 2.0d0)
    end if
    code = t_s * tmp
end function

Java

t_m = Math.abs(t);
t_s = Math.copySign(1.0, t);
public static double code(double t_s, double t_m, double l, double k) {
	double tmp;
	if ((l * l) <= 2e-108) {
		tmp = Math.pow((((l * Math.sqrt(2.0)) / Math.pow(k, 2.0)) * Math.sqrt((1.0 / t_m))), 2.0);
	} else if ((l * l) <= 2e+51) {
		tmp = 2.0 * ((Math.cos(k) * Math.pow(l, 2.0)) / (Math.pow(k, 2.0) * (t_m * Math.pow(Math.sin(k), 2.0))));
	} else {
		tmp = 2.0 / Math.pow(((k / (l / Math.sin(k))) * Math.sqrt((t_m / Math.cos(k)))), 2.0);
	}
	return t_s * tmp;
}

Python

t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k):
	tmp = 0
	if (l * l) <= 2e-108:
		tmp = math.pow((((l * math.sqrt(2.0)) / math.pow(k, 2.0)) * math.sqrt((1.0 / t_m))), 2.0)
	elif (l * l) <= 2e+51:
		tmp = 2.0 * ((math.cos(k) * math.pow(l, 2.0)) / (math.pow(k, 2.0) * (t_m * math.pow(math.sin(k), 2.0))))
	else:
		tmp = 2.0 / math.pow(((k / (l / math.sin(k))) * math.sqrt((t_m / math.cos(k)))), 2.0)
	return t_s * tmp

Julia

t_m = abs(t)
t_s = copysign(1.0, t)
function code(t_s, t_m, l, k)
	tmp = 0.0
	if (Float64(l * l) <= 2e-108)
		tmp = Float64(Float64(Float64(l * sqrt(2.0)) / (k ^ 2.0)) * sqrt(Float64(1.0 / t_m))) ^ 2.0;
	elseif (Float64(l * l) <= 2e+51)
		tmp = Float64(2.0 * Float64(Float64(cos(k) * (l ^ 2.0)) / Float64((k ^ 2.0) * Float64(t_m * (sin(k) ^ 2.0)))));
	else
		tmp = Float64(2.0 / (Float64(Float64(k / Float64(l / sin(k))) * sqrt(Float64(t_m / cos(k)))) ^ 2.0));
	end
	return Float64(t_s * tmp)
end

MATLAB

t_m = abs(t);
t_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, t_m, l, k)
	tmp = 0.0;
	if ((l * l) <= 2e-108)
		tmp = (((l * sqrt(2.0)) / (k ^ 2.0)) * sqrt((1.0 / t_m))) ^ 2.0;
	elseif ((l * l) <= 2e+51)
		tmp = 2.0 * ((cos(k) * (l ^ 2.0)) / ((k ^ 2.0) * (t_m * (sin(k) ^ 2.0))));
	else
		tmp = 2.0 / (((k / (l / sin(k))) * sqrt((t_m / cos(k)))) ^ 2.0);
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
t_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, t$95$m_, l_, k_] := N[(t$95$s * If[LessEqual[N[(l * l), $MachinePrecision], 2e-108], N[Power[N[(N[(N[(l * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision] / N[Power[k, 2.0], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(1.0 / t$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision], If[LessEqual[N[(l * l), $MachinePrecision], 2e+51], N[(2.0 * N[(N[(N[Cos[k], $MachinePrecision] * N[Power[l, 2.0], $MachinePrecision]), $MachinePrecision] / N[(N[Power[k, 2.0], $MachinePrecision] * N[(t$95$m * N[Power[N[Sin[k], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[Power[N[(N[(k / N[(l / N[Sin[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(t$95$m / N[Cos[k], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 8: 79.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;\ell \cdot \ell \leq 5 \cdot 10^{+14}:\\ \;\;\;\;{\left(\frac{\ell \cdot \sqrt{2}}{{k}^{2}} \cdot \sqrt{\frac{1}{t_m}}\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{{\left(\frac{k}{\frac{\ell}{\sin k}} \cdot \sqrt{\frac{t_m}{\cos k}}\right)}^{2}}\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (*
  t_s
  (if (<= (* l l) 5e+14)
    (pow (* (/ (* l (sqrt 2.0)) (pow k 2.0)) (sqrt (/ 1.0 t_m))) 2.0)
    (/ 2.0 (pow (* (/ k (/ l (sin k))) (sqrt (/ t_m (cos k)))) 2.0)))))

C

t_m = fabs(t);
t_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k) {
	double tmp;
	if ((l * l) <= 5e+14) {
		tmp = pow((((l * sqrt(2.0)) / pow(k, 2.0)) * sqrt((1.0 / t_m))), 2.0);
	} else {
		tmp = 2.0 / pow(((k / (l / sin(k))) * sqrt((t_m / cos(k)))), 2.0);
	}
	return t_s * tmp;
}

Fortran

t_m = abs(t)
t_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    real(8) :: tmp
    if ((l * l) <= 5d+14) then
        tmp = (((l * sqrt(2.0d0)) / (k ** 2.0d0)) * sqrt((1.0d0 / t_m))) ** 2.0d0
    else
        tmp = 2.0d0 / (((k / (l / sin(k))) * sqrt((t_m / cos(k)))) ** 2.0d0)
    end if
    code = t_s * tmp
end function

Java

t_m = Math.abs(t);
t_s = Math.copySign(1.0, t);
public static double code(double t_s, double t_m, double l, double k) {
	double tmp;
	if ((l * l) <= 5e+14) {
		tmp = Math.pow((((l * Math.sqrt(2.0)) / Math.pow(k, 2.0)) * Math.sqrt((1.0 / t_m))), 2.0);
	} else {
		tmp = 2.0 / Math.pow(((k / (l / Math.sin(k))) * Math.sqrt((t_m / Math.cos(k)))), 2.0);
	}
	return t_s * tmp;
}

Python

t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k):
	tmp = 0
	if (l * l) <= 5e+14:
		tmp = math.pow((((l * math.sqrt(2.0)) / math.pow(k, 2.0)) * math.sqrt((1.0 / t_m))), 2.0)
	else:
		tmp = 2.0 / math.pow(((k / (l / math.sin(k))) * math.sqrt((t_m / math.cos(k)))), 2.0)
	return t_s * tmp

Julia

t_m = abs(t)
t_s = copysign(1.0, t)
function code(t_s, t_m, l, k)
	tmp = 0.0
	if (Float64(l * l) <= 5e+14)
		tmp = Float64(Float64(Float64(l * sqrt(2.0)) / (k ^ 2.0)) * sqrt(Float64(1.0 / t_m))) ^ 2.0;
	else
		tmp = Float64(2.0 / (Float64(Float64(k / Float64(l / sin(k))) * sqrt(Float64(t_m / cos(k)))) ^ 2.0));
	end
	return Float64(t_s * tmp)
end

MATLAB

t_m = abs(t);
t_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, t_m, l, k)
	tmp = 0.0;
	if ((l * l) <= 5e+14)
		tmp = (((l * sqrt(2.0)) / (k ^ 2.0)) * sqrt((1.0 / t_m))) ^ 2.0;
	else
		tmp = 2.0 / (((k / (l / sin(k))) * sqrt((t_m / cos(k)))) ^ 2.0);
	end
	tmp_2 = t_s * tmp;
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
t_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, t$95$m_, l_, k_] := N[(t$95$s * If[LessEqual[N[(l * l), $MachinePrecision], 5e+14], N[Power[N[(N[(N[(l * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision] / N[Power[k, 2.0], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(1.0 / t$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision], N[(2.0 / N[Power[N[(N[(k / N[(l / N[Sin[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(t$95$m / N[Cos[k], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 9: 72.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot {\left(\frac{\ell \cdot \sqrt{2}}{{k}^{2}} \cdot \sqrt{\frac{1}{t_m}}\right)}^{2} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (* t_s (pow (* (/ (* l (sqrt 2.0)) (pow k 2.0)) (sqrt (/ 1.0 t_m))) 2.0)))

C

t_m = fabs(t);
t_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k) {
	return t_s * pow((((l * sqrt(2.0)) / pow(k, 2.0)) * sqrt((1.0 / t_m))), 2.0);
}

Fortran

t_m = abs(t)
t_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    code = t_s * ((((l * sqrt(2.0d0)) / (k ** 2.0d0)) * sqrt((1.0d0 / t_m))) ** 2.0d0)
end function

Java

t_m = Math.abs(t);
t_s = Math.copySign(1.0, t);
public static double code(double t_s, double t_m, double l, double k) {
	return t_s * Math.pow((((l * Math.sqrt(2.0)) / Math.pow(k, 2.0)) * Math.sqrt((1.0 / t_m))), 2.0);
}

Python

t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k):
	return t_s * math.pow((((l * math.sqrt(2.0)) / math.pow(k, 2.0)) * math.sqrt((1.0 / t_m))), 2.0)

Julia

t_m = abs(t)
t_s = copysign(1.0, t)
function code(t_s, t_m, l, k)
	return Float64(t_s * (Float64(Float64(Float64(l * sqrt(2.0)) / (k ^ 2.0)) * sqrt(Float64(1.0 / t_m))) ^ 2.0))
end

MATLAB

t_m = abs(t);
t_s = sign(t) * abs(1.0);
function tmp = code(t_s, t_m, l, k)
	tmp = t_s * ((((l * sqrt(2.0)) / (k ^ 2.0)) * sqrt((1.0 / t_m))) ^ 2.0);
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
t_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, t$95$m_, l_, k_] := N[(t$95$s * N[Power[N[(N[(N[(l * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision] / N[Power[k, 2.0], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(1.0 / t$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 10: 72.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \frac{2}{{\left(\frac{{k}^{2}}{\ell} \cdot \sqrt{t_m}\right)}^{2}} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (* t_s (/ 2.0 (pow (* (/ (pow k 2.0) l) (sqrt t_m)) 2.0))))

C

t_m = fabs(t);
t_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k) {
	return t_s * (2.0 / pow(((pow(k, 2.0) / l) * sqrt(t_m)), 2.0));
}

Fortran

t_m = abs(t)
t_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    code = t_s * (2.0d0 / ((((k ** 2.0d0) / l) * sqrt(t_m)) ** 2.0d0))
end function

Java

t_m = Math.abs(t);
t_s = Math.copySign(1.0, t);
public static double code(double t_s, double t_m, double l, double k) {
	return t_s * (2.0 / Math.pow(((Math.pow(k, 2.0) / l) * Math.sqrt(t_m)), 2.0));
}

Python

t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k):
	return t_s * (2.0 / math.pow(((math.pow(k, 2.0) / l) * math.sqrt(t_m)), 2.0))

Julia

t_m = abs(t)
t_s = copysign(1.0, t)
function code(t_s, t_m, l, k)
	return Float64(t_s * Float64(2.0 / (Float64(Float64((k ^ 2.0) / l) * sqrt(t_m)) ^ 2.0)))
end

MATLAB

t_m = abs(t);
t_s = sign(t) * abs(1.0);
function tmp = code(t_s, t_m, l, k)
	tmp = t_s * (2.0 / ((((k ^ 2.0) / l) * sqrt(t_m)) ^ 2.0));
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
t_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, t$95$m_, l_, k_] := N[(t$95$s * N[(2.0 / N[Power[N[(N[(N[Power[k, 2.0], $MachinePrecision] / l), $MachinePrecision] * N[Sqrt[t$95$m], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 11: 60.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \left(2 \cdot \left(\frac{{\ell}^{2}}{t_m} \cdot {k}^{-4}\right)\right) \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (* t_s (* 2.0 (* (/ (pow l 2.0) t_m) (pow k -4.0)))))

C

t_m = fabs(t);
t_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k) {
	return t_s * (2.0 * ((pow(l, 2.0) / t_m) * pow(k, -4.0)));
}

Fortran

t_m = abs(t)
t_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    code = t_s * (2.0d0 * (((l ** 2.0d0) / t_m) * (k ** (-4.0d0))))
end function

Java

t_m = Math.abs(t);
t_s = Math.copySign(1.0, t);
public static double code(double t_s, double t_m, double l, double k) {
	return t_s * (2.0 * ((Math.pow(l, 2.0) / t_m) * Math.pow(k, -4.0)));
}

Python

t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k):
	return t_s * (2.0 * ((math.pow(l, 2.0) / t_m) * math.pow(k, -4.0)))

Julia

t_m = abs(t)
t_s = copysign(1.0, t)
function code(t_s, t_m, l, k)
	return Float64(t_s * Float64(2.0 * Float64(Float64((l ^ 2.0) / t_m) * (k ^ -4.0))))
end

MATLAB

t_m = abs(t);
t_s = sign(t) * abs(1.0);
function tmp = code(t_s, t_m, l, k)
	tmp = t_s * (2.0 * (((l ^ 2.0) / t_m) * (k ^ -4.0)));
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
t_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, t$95$m_, l_, k_] := N[(t$95$s * N[(2.0 * N[(N[(N[Power[l, 2.0], $MachinePrecision] / t$95$m), $MachinePrecision] * N[Power[k, -4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 12: 61.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \left(2 \cdot \frac{\frac{{\ell}^{2}}{{k}^{4}}}{t_m}\right) \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (* t_s (* 2.0 (/ (/ (pow l 2.0) (pow k 4.0)) t_m))))

C

t_m = fabs(t);
t_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k) {
	return t_s * (2.0 * ((pow(l, 2.0) / pow(k, 4.0)) / t_m));
}

Fortran

t_m = abs(t)
t_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k
    code = t_s * (2.0d0 * (((l ** 2.0d0) / (k ** 4.0d0)) / t_m))
end function

Java

t_m = Math.abs(t);
t_s = Math.copySign(1.0, t);
public static double code(double t_s, double t_m, double l, double k) {
	return t_s * (2.0 * ((Math.pow(l, 2.0) / Math.pow(k, 4.0)) / t_m));
}

Python

t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k):
	return t_s * (2.0 * ((math.pow(l, 2.0) / math.pow(k, 4.0)) / t_m))

Julia

t_m = abs(t)
t_s = copysign(1.0, t)
function code(t_s, t_m, l, k)
	return Float64(t_s * Float64(2.0 * Float64(Float64((l ^ 2.0) / (k ^ 4.0)) / t_m)))
end

MATLAB

t_m = abs(t);
t_s = sign(t) * abs(1.0);
function tmp = code(t_s, t_m, l, k)
	tmp = t_s * (2.0 * (((l ^ 2.0) / (k ^ 4.0)) / t_m));
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
t_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[t$95$s_, t$95$m_, l_, k_] := N[(t$95$s * N[(2.0 * N[(N[(N[Power[l, 2.0], $MachinePrecision] / N[Power[k, 4.0], $MachinePrecision]), $MachinePrecision] / t$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Reproduce

herbie shell --seed 2023364 
(FPCore (t l k)
  :name "Toniolo and Linder, Equation (10-)"
  :precision binary64
  (/ 2.0 (* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (- (+ 1.0 (pow (/ k t) 2.0)) 1.0))))