Toniolo and Linder, Equation (10+)

Percentage Accurate: 54.7% → 87.8%

Time: 23.0s

Alternatives: 14

Speedup: 2.0×

• 27.6% of points produce a very large (infinite) output. You may want to add a precondition.

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: 54.7% 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: 87.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ \begin{array}{l} t_2 := t_m \cdot {\sin k}^{2}\\ t_3 := \frac{2}{{\left(\frac{\frac{t_m}{\sqrt[3]{\ell}}}{\sqrt[3]{\ell}} \cdot \left(\sqrt[3]{\tan k \cdot \left(2 + {\left(\frac{k}{t_m}\right)}^{2}\right)} \cdot \sqrt[3]{\sin k}\right)\right)}^{3}}\\ t_4 := \mathsf{hypot}\left(1, \mathsf{hypot}\left(1, \frac{k}{t_m}\right)\right)\\ t_s \cdot \begin{array}{l} \mathbf{if}\;t_m \leq 10^{-177}:\\ \;\;\;\;\ell \cdot \left(2 \cdot \frac{\ell \cdot \cos k}{{k}^{2} \cdot t_2}\right)\\ \mathbf{elif}\;t_m \leq 1.14 \cdot 10^{-97}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_m \leq 7.5 \cdot 10^{-51}:\\ \;\;\;\;\ell \cdot \left(2 \cdot \left(\frac{\ell}{{k}^{2}} \cdot \frac{\cos k}{t_2}\right)\right)\\ \mathbf{elif}\;t_m \leq 1.48 \cdot 10^{+94}:\\ \;\;\;\;\frac{\ell \cdot \frac{2}{\tan k \cdot \left(\sin k \cdot {t_m}^{3}\right)}}{t_4} \cdot \frac{\ell}{t_4}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (let* ((t_2 (* t_m (pow (sin k) 2.0)))
        (t_3
         (/
          2.0
          (pow
           (*
            (/ (/ t_m (cbrt l)) (cbrt l))
            (* (cbrt (* (tan k) (+ 2.0 (pow (/ k t_m) 2.0)))) (cbrt (sin k))))
           3.0)))
        (t_4 (hypot 1.0 (hypot 1.0 (/ k t_m)))))
   (*
    t_s
    (if (<= t_m 1e-177)
      (* l (* 2.0 (/ (* l (cos k)) (* (pow k 2.0) t_2))))
      (if (<= t_m 1.14e-97)
        t_3
        (if (<= t_m 7.5e-51)
          (* l (* 2.0 (* (/ l (pow k 2.0)) (/ (cos k) t_2))))
          (if (<= t_m 1.48e+94)
            (*
             (/ (* l (/ 2.0 (* (tan k) (* (sin k) (pow t_m 3.0))))) t_4)
             (/ l t_4))
            t_3)))))))

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 = t_m * pow(sin(k), 2.0);
	double t_3 = 2.0 / pow((((t_m / cbrt(l)) / cbrt(l)) * (cbrt((tan(k) * (2.0 + pow((k / t_m), 2.0)))) * cbrt(sin(k)))), 3.0);
	double t_4 = hypot(1.0, hypot(1.0, (k / t_m)));
	double tmp;
	if (t_m <= 1e-177) {
		tmp = l * (2.0 * ((l * cos(k)) / (pow(k, 2.0) * t_2)));
	} else if (t_m <= 1.14e-97) {
		tmp = t_3;
	} else if (t_m <= 7.5e-51) {
		tmp = l * (2.0 * ((l / pow(k, 2.0)) * (cos(k) / t_2)));
	} else if (t_m <= 1.48e+94) {
		tmp = ((l * (2.0 / (tan(k) * (sin(k) * pow(t_m, 3.0))))) / t_4) * (l / t_4);
	} else {
		tmp = t_3;
	}
	return t_s * tmp;
}

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 = t_m * Math.pow(Math.sin(k), 2.0);
	double t_3 = 2.0 / Math.pow((((t_m / Math.cbrt(l)) / Math.cbrt(l)) * (Math.cbrt((Math.tan(k) * (2.0 + Math.pow((k / t_m), 2.0)))) * Math.cbrt(Math.sin(k)))), 3.0);
	double t_4 = Math.hypot(1.0, Math.hypot(1.0, (k / t_m)));
	double tmp;
	if (t_m <= 1e-177) {
		tmp = l * (2.0 * ((l * Math.cos(k)) / (Math.pow(k, 2.0) * t_2)));
	} else if (t_m <= 1.14e-97) {
		tmp = t_3;
	} else if (t_m <= 7.5e-51) {
		tmp = l * (2.0 * ((l / Math.pow(k, 2.0)) * (Math.cos(k) / t_2)));
	} else if (t_m <= 1.48e+94) {
		tmp = ((l * (2.0 / (Math.tan(k) * (Math.sin(k) * Math.pow(t_m, 3.0))))) / t_4) * (l / t_4);
	} else {
		tmp = t_3;
	}
	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(t_m * (sin(k) ^ 2.0))
	t_3 = Float64(2.0 / (Float64(Float64(Float64(t_m / cbrt(l)) / cbrt(l)) * Float64(cbrt(Float64(tan(k) * Float64(2.0 + (Float64(k / t_m) ^ 2.0)))) * cbrt(sin(k)))) ^ 3.0))
	t_4 = hypot(1.0, hypot(1.0, Float64(k / t_m)))
	tmp = 0.0
	if (t_m <= 1e-177)
		tmp = Float64(l * Float64(2.0 * Float64(Float64(l * cos(k)) / Float64((k ^ 2.0) * t_2))));
	elseif (t_m <= 1.14e-97)
		tmp = t_3;
	elseif (t_m <= 7.5e-51)
		tmp = Float64(l * Float64(2.0 * Float64(Float64(l / (k ^ 2.0)) * Float64(cos(k) / t_2))));
	elseif (t_m <= 1.48e+94)
		tmp = Float64(Float64(Float64(l * Float64(2.0 / Float64(tan(k) * Float64(sin(k) * (t_m ^ 3.0))))) / t_4) * Float64(l / t_4));
	else
		tmp = t_3;
	end
	return Float64(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[(t$95$m * N[Power[N[Sin[k], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 / N[Power[N[(N[(N[(t$95$m / N[Power[l, 1/3], $MachinePrecision]), $MachinePrecision] / N[Power[l, 1/3], $MachinePrecision]), $MachinePrecision] * N[(N[Power[N[(N[Tan[k], $MachinePrecision] * N[(2.0 + N[Power[N[(k / t$95$m), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] * N[Power[N[Sin[k], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[Sqrt[1.0 ^ 2 + N[Sqrt[1.0 ^ 2 + N[(k / t$95$m), $MachinePrecision] ^ 2], $MachinePrecision] ^ 2], $MachinePrecision]}, N[(t$95$s * If[LessEqual[t$95$m, 1e-177], N[(l * N[(2.0 * N[(N[(l * N[Cos[k], $MachinePrecision]), $MachinePrecision] / N[(N[Power[k, 2.0], $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$m, 1.14e-97], t$95$3, If[LessEqual[t$95$m, 7.5e-51], N[(l * N[(2.0 * N[(N[(l / N[Power[k, 2.0], $MachinePrecision]), $MachinePrecision] * N[(N[Cos[k], $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$m, 1.48e+94], N[(N[(N[(l * N[(2.0 / N[(N[Tan[k], $MachinePrecision] * N[(N[Sin[k], $MachinePrecision] * N[Power[t$95$m, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision] * N[(l / t$95$4), $MachinePrecision]), $MachinePrecision], t$95$3]]]]), $MachinePrecision]]]]

Derivation

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

Alternative 2: 87.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ \begin{array}{l} t_2 := \mathsf{hypot}\left(1, \mathsf{hypot}\left(1, \frac{k}{t_m}\right)\right)\\ t_s \cdot \begin{array}{l} \mathbf{if}\;t_m \leq 7 \cdot 10^{-51}:\\ \;\;\;\;\ell \cdot \left(2 \cdot \left(\frac{\ell}{{k}^{2}} \cdot \frac{\cos k}{t_m \cdot {\sin k}^{2}}\right)\right)\\ \mathbf{elif}\;t_m \leq 1.48 \cdot 10^{+94}:\\ \;\;\;\;\frac{\ell \cdot \frac{2}{\tan k \cdot \left(\sin k \cdot {t_m}^{3}\right)}}{t_2} \cdot \frac{\ell}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\left(\tan k \cdot \left(2 + {\left(\frac{k}{t_m}\right)}^{2}\right)\right) \cdot {\left(\frac{\frac{t_m}{\sqrt[3]{\ell}}}{\sqrt[3]{\ell}} \cdot \sqrt[3]{\sin k}\right)}^{3}}\\ \end{array} \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (let* ((t_2 (hypot 1.0 (hypot 1.0 (/ k t_m)))))
   (*
    t_s
    (if (<= t_m 7e-51)
      (* l (* 2.0 (* (/ l (pow k 2.0)) (/ (cos k) (* t_m (pow (sin k) 2.0))))))
      (if (<= t_m 1.48e+94)
        (*
         (/ (* l (/ 2.0 (* (tan k) (* (sin k) (pow t_m 3.0))))) t_2)
         (/ l t_2))
        (/
         2.0
         (*
          (* (tan k) (+ 2.0 (pow (/ k t_m) 2.0)))
          (pow (* (/ (/ t_m (cbrt l)) (cbrt l)) (cbrt (sin k))) 3.0))))))))

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 = hypot(1.0, hypot(1.0, (k / t_m)));
	double tmp;
	if (t_m <= 7e-51) {
		tmp = l * (2.0 * ((l / pow(k, 2.0)) * (cos(k) / (t_m * pow(sin(k), 2.0)))));
	} else if (t_m <= 1.48e+94) {
		tmp = ((l * (2.0 / (tan(k) * (sin(k) * pow(t_m, 3.0))))) / t_2) * (l / t_2);
	} else {
		tmp = 2.0 / ((tan(k) * (2.0 + pow((k / t_m), 2.0))) * pow((((t_m / cbrt(l)) / cbrt(l)) * cbrt(sin(k))), 3.0));
	}
	return t_s * tmp;
}

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.hypot(1.0, Math.hypot(1.0, (k / t_m)));
	double tmp;
	if (t_m <= 7e-51) {
		tmp = l * (2.0 * ((l / Math.pow(k, 2.0)) * (Math.cos(k) / (t_m * Math.pow(Math.sin(k), 2.0)))));
	} else if (t_m <= 1.48e+94) {
		tmp = ((l * (2.0 / (Math.tan(k) * (Math.sin(k) * Math.pow(t_m, 3.0))))) / t_2) * (l / t_2);
	} else {
		tmp = 2.0 / ((Math.tan(k) * (2.0 + Math.pow((k / t_m), 2.0))) * Math.pow((((t_m / Math.cbrt(l)) / Math.cbrt(l)) * Math.cbrt(Math.sin(k))), 3.0));
	}
	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 = hypot(1.0, hypot(1.0, Float64(k / t_m)))
	tmp = 0.0
	if (t_m <= 7e-51)
		tmp = Float64(l * Float64(2.0 * Float64(Float64(l / (k ^ 2.0)) * Float64(cos(k) / Float64(t_m * (sin(k) ^ 2.0))))));
	elseif (t_m <= 1.48e+94)
		tmp = Float64(Float64(Float64(l * Float64(2.0 / Float64(tan(k) * Float64(sin(k) * (t_m ^ 3.0))))) / t_2) * Float64(l / t_2));
	else
		tmp = Float64(2.0 / Float64(Float64(tan(k) * Float64(2.0 + (Float64(k / t_m) ^ 2.0))) * (Float64(Float64(Float64(t_m / cbrt(l)) / cbrt(l)) * cbrt(sin(k))) ^ 3.0)));
	end
	return Float64(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[Sqrt[1.0 ^ 2 + N[Sqrt[1.0 ^ 2 + N[(k / t$95$m), $MachinePrecision] ^ 2], $MachinePrecision] ^ 2], $MachinePrecision]}, N[(t$95$s * If[LessEqual[t$95$m, 7e-51], N[(l * N[(2.0 * N[(N[(l / N[Power[k, 2.0], $MachinePrecision]), $MachinePrecision] * N[(N[Cos[k], $MachinePrecision] / N[(t$95$m * N[Power[N[Sin[k], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$m, 1.48e+94], N[(N[(N[(l * N[(2.0 / N[(N[Tan[k], $MachinePrecision] * N[(N[Sin[k], $MachinePrecision] * N[Power[t$95$m, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision] * N[(l / t$95$2), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[(N[(N[Tan[k], $MachinePrecision] * N[(2.0 + N[Power[N[(k / t$95$m), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Power[N[(N[(N[(t$95$m / N[Power[l, 1/3], $MachinePrecision]), $MachinePrecision] / N[Power[l, 1/3], $MachinePrecision]), $MachinePrecision] * N[Power[N[Sin[k], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

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

Alternative 3: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;t_m \leq 1.12 \cdot 10^{-138}:\\ \;\;\;\;\ell \cdot \left(2 \cdot \left(\frac{\ell}{{k}^{2}} \cdot \frac{\cos k}{t_m \cdot {\sin k}^{2}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\left(\tan k \cdot \left(2 + {\left(\frac{k}{t_m}\right)}^{2}\right)\right) \cdot {\left(\sqrt[3]{\sin k} \cdot \frac{t_m}{{\left(\sqrt[3]{\ell}\right)}^{2}}\right)}^{3}}\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (*
  t_s
  (if (<= t_m 1.12e-138)
    (* l (* 2.0 (* (/ l (pow k 2.0)) (/ (cos k) (* t_m (pow (sin k) 2.0))))))
    (/
     2.0
     (*
      (* (tan k) (+ 2.0 (pow (/ k t_m) 2.0)))
      (pow (* (cbrt (sin k)) (/ t_m (pow (cbrt l) 2.0))) 3.0))))))

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 (t_m <= 1.12e-138) {
		tmp = l * (2.0 * ((l / pow(k, 2.0)) * (cos(k) / (t_m * pow(sin(k), 2.0)))));
	} else {
		tmp = 2.0 / ((tan(k) * (2.0 + pow((k / t_m), 2.0))) * pow((cbrt(sin(k)) * (t_m / pow(cbrt(l), 2.0))), 3.0));
	}
	return t_s * tmp;
}

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 (t_m <= 1.12e-138) {
		tmp = l * (2.0 * ((l / Math.pow(k, 2.0)) * (Math.cos(k) / (t_m * Math.pow(Math.sin(k), 2.0)))));
	} else {
		tmp = 2.0 / ((Math.tan(k) * (2.0 + Math.pow((k / t_m), 2.0))) * Math.pow((Math.cbrt(Math.sin(k)) * (t_m / Math.pow(Math.cbrt(l), 2.0))), 3.0));
	}
	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 (t_m <= 1.12e-138)
		tmp = Float64(l * Float64(2.0 * Float64(Float64(l / (k ^ 2.0)) * Float64(cos(k) / Float64(t_m * (sin(k) ^ 2.0))))));
	else
		tmp = Float64(2.0 / Float64(Float64(tan(k) * Float64(2.0 + (Float64(k / t_m) ^ 2.0))) * (Float64(cbrt(sin(k)) * Float64(t_m / (cbrt(l) ^ 2.0))) ^ 3.0)));
	end
	return Float64(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[t$95$m, 1.12e-138], N[(l * N[(2.0 * N[(N[(l / N[Power[k, 2.0], $MachinePrecision]), $MachinePrecision] * N[(N[Cos[k], $MachinePrecision] / N[(t$95$m * N[Power[N[Sin[k], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[(N[(N[Tan[k], $MachinePrecision] * N[(2.0 + N[Power[N[(k / t$95$m), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Power[N[(N[Power[N[Sin[k], $MachinePrecision], 1/3], $MachinePrecision] * N[(t$95$m / N[Power[N[Power[l, 1/3], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 4: 84.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ \begin{array}{l} t_2 := 2 + {\left(\frac{k}{t_m}\right)}^{2}\\ t_s \cdot \begin{array}{l} \mathbf{if}\;t_m \leq 5.2 \cdot 10^{-21}:\\ \;\;\;\;\ell \cdot \left(2 \cdot \left(\frac{\ell}{{k}^{2}} \cdot \frac{\cos k}{t_m \cdot {\sin k}^{2}}\right)\right)\\ \mathbf{elif}\;t_m \leq 3.3 \cdot 10^{+101}:\\ \;\;\;\;\ell \cdot \frac{\frac{2 \cdot \frac{\ell}{\sin k}}{\tan k \cdot {t_m}^{3}}}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\left(\tan k \cdot t_2\right) \cdot \left(\sin k \cdot {\left(\frac{t_m}{{\left(\sqrt[3]{\ell}\right)}^{2}}\right)}^{3}\right)}\\ \end{array} \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (let* ((t_2 (+ 2.0 (pow (/ k t_m) 2.0))))
   (*
    t_s
    (if (<= t_m 5.2e-21)
      (* l (* 2.0 (* (/ l (pow k 2.0)) (/ (cos k) (* t_m (pow (sin k) 2.0))))))
      (if (<= t_m 3.3e+101)
        (* l (/ (/ (* 2.0 (/ l (sin k))) (* (tan k) (pow t_m 3.0))) t_2))
        (/
         2.0
         (*
          (* (tan k) t_2)
          (* (sin k) (pow (/ t_m (pow (cbrt l) 2.0)) 3.0)))))))))

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 = 2.0 + pow((k / t_m), 2.0);
	double tmp;
	if (t_m <= 5.2e-21) {
		tmp = l * (2.0 * ((l / pow(k, 2.0)) * (cos(k) / (t_m * pow(sin(k), 2.0)))));
	} else if (t_m <= 3.3e+101) {
		tmp = l * (((2.0 * (l / sin(k))) / (tan(k) * pow(t_m, 3.0))) / t_2);
	} else {
		tmp = 2.0 / ((tan(k) * t_2) * (sin(k) * pow((t_m / pow(cbrt(l), 2.0)), 3.0)));
	}
	return t_s * tmp;
}

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 = 2.0 + Math.pow((k / t_m), 2.0);
	double tmp;
	if (t_m <= 5.2e-21) {
		tmp = l * (2.0 * ((l / Math.pow(k, 2.0)) * (Math.cos(k) / (t_m * Math.pow(Math.sin(k), 2.0)))));
	} else if (t_m <= 3.3e+101) {
		tmp = l * (((2.0 * (l / Math.sin(k))) / (Math.tan(k) * Math.pow(t_m, 3.0))) / t_2);
	} else {
		tmp = 2.0 / ((Math.tan(k) * t_2) * (Math.sin(k) * Math.pow((t_m / Math.pow(Math.cbrt(l), 2.0)), 3.0)));
	}
	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(2.0 + (Float64(k / t_m) ^ 2.0))
	tmp = 0.0
	if (t_m <= 5.2e-21)
		tmp = Float64(l * Float64(2.0 * Float64(Float64(l / (k ^ 2.0)) * Float64(cos(k) / Float64(t_m * (sin(k) ^ 2.0))))));
	elseif (t_m <= 3.3e+101)
		tmp = Float64(l * Float64(Float64(Float64(2.0 * Float64(l / sin(k))) / Float64(tan(k) * (t_m ^ 3.0))) / t_2));
	else
		tmp = Float64(2.0 / Float64(Float64(tan(k) * t_2) * Float64(sin(k) * (Float64(t_m / (cbrt(l) ^ 2.0)) ^ 3.0))));
	end
	return Float64(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[(2.0 + N[Power[N[(k / t$95$m), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]}, N[(t$95$s * If[LessEqual[t$95$m, 5.2e-21], N[(l * N[(2.0 * N[(N[(l / N[Power[k, 2.0], $MachinePrecision]), $MachinePrecision] * N[(N[Cos[k], $MachinePrecision] / N[(t$95$m * N[Power[N[Sin[k], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$m, 3.3e+101], N[(l * N[(N[(N[(2.0 * N[(l / N[Sin[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[Tan[k], $MachinePrecision] * N[Power[t$95$m, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[(N[(N[Tan[k], $MachinePrecision] * t$95$2), $MachinePrecision] * N[(N[Sin[k], $MachinePrecision] * N[Power[N[(t$95$m / N[Power[N[Power[l, 1/3], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

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

Alternative 5: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ \begin{array}{l} t_2 := 2 + {\left(\frac{k}{t_m}\right)}^{2}\\ t_s \cdot \begin{array}{l} \mathbf{if}\;t_m \leq 5.2 \cdot 10^{-21}:\\ \;\;\;\;\ell \cdot \left(2 \cdot \left(\frac{\ell}{{k}^{2}} \cdot \frac{\cos k}{t_m \cdot {\sin k}^{2}}\right)\right)\\ \mathbf{elif}\;t_m \leq 2.6 \cdot 10^{+98}:\\ \;\;\;\;\ell \cdot \frac{\frac{2 \cdot \frac{\ell}{\sin k}}{\tan k \cdot {t_m}^{3}}}{t_2}\\ \mathbf{elif}\;t_m \leq 2.8 \cdot 10^{+203}:\\ \;\;\;\;\frac{2}{\left(\tan k \cdot t_2\right) \cdot \left(\sin k \cdot {\left({t_m}^{1.5} \cdot \frac{1}{\ell}\right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{\sqrt[3]{\ell}}{\sqrt{t_m}} \cdot \sqrt[3]{\frac{1}{k}}\right)}^{2}\right)}^{3}\\ \end{array} \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (let* ((t_2 (+ 2.0 (pow (/ k t_m) 2.0))))
   (*
    t_s
    (if (<= t_m 5.2e-21)
      (* l (* 2.0 (* (/ l (pow k 2.0)) (/ (cos k) (* t_m (pow (sin k) 2.0))))))
      (if (<= t_m 2.6e+98)
        (* l (/ (/ (* 2.0 (/ l (sin k))) (* (tan k) (pow t_m 3.0))) t_2))
        (if (<= t_m 2.8e+203)
          (/
           2.0
           (*
            (* (tan k) t_2)
            (* (sin k) (pow (* (pow t_m 1.5) (/ 1.0 l)) 2.0))))
          (pow
           (pow (* (/ (cbrt l) (sqrt t_m)) (cbrt (/ 1.0 k))) 2.0)
           3.0)))))))

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 = 2.0 + pow((k / t_m), 2.0);
	double tmp;
	if (t_m <= 5.2e-21) {
		tmp = l * (2.0 * ((l / pow(k, 2.0)) * (cos(k) / (t_m * pow(sin(k), 2.0)))));
	} else if (t_m <= 2.6e+98) {
		tmp = l * (((2.0 * (l / sin(k))) / (tan(k) * pow(t_m, 3.0))) / t_2);
	} else if (t_m <= 2.8e+203) {
		tmp = 2.0 / ((tan(k) * t_2) * (sin(k) * pow((pow(t_m, 1.5) * (1.0 / l)), 2.0)));
	} else {
		tmp = pow(pow(((cbrt(l) / sqrt(t_m)) * cbrt((1.0 / k))), 2.0), 3.0);
	}
	return t_s * tmp;
}

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 = 2.0 + Math.pow((k / t_m), 2.0);
	double tmp;
	if (t_m <= 5.2e-21) {
		tmp = l * (2.0 * ((l / Math.pow(k, 2.0)) * (Math.cos(k) / (t_m * Math.pow(Math.sin(k), 2.0)))));
	} else if (t_m <= 2.6e+98) {
		tmp = l * (((2.0 * (l / Math.sin(k))) / (Math.tan(k) * Math.pow(t_m, 3.0))) / t_2);
	} else if (t_m <= 2.8e+203) {
		tmp = 2.0 / ((Math.tan(k) * t_2) * (Math.sin(k) * Math.pow((Math.pow(t_m, 1.5) * (1.0 / l)), 2.0)));
	} else {
		tmp = Math.pow(Math.pow(((Math.cbrt(l) / Math.sqrt(t_m)) * Math.cbrt((1.0 / k))), 2.0), 3.0);
	}
	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(2.0 + (Float64(k / t_m) ^ 2.0))
	tmp = 0.0
	if (t_m <= 5.2e-21)
		tmp = Float64(l * Float64(2.0 * Float64(Float64(l / (k ^ 2.0)) * Float64(cos(k) / Float64(t_m * (sin(k) ^ 2.0))))));
	elseif (t_m <= 2.6e+98)
		tmp = Float64(l * Float64(Float64(Float64(2.0 * Float64(l / sin(k))) / Float64(tan(k) * (t_m ^ 3.0))) / t_2));
	elseif (t_m <= 2.8e+203)
		tmp = Float64(2.0 / Float64(Float64(tan(k) * t_2) * Float64(sin(k) * (Float64((t_m ^ 1.5) * Float64(1.0 / l)) ^ 2.0))));
	else
		tmp = (Float64(Float64(cbrt(l) / sqrt(t_m)) * cbrt(Float64(1.0 / k))) ^ 2.0) ^ 3.0;
	end
	return Float64(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[(2.0 + N[Power[N[(k / t$95$m), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]}, N[(t$95$s * If[LessEqual[t$95$m, 5.2e-21], N[(l * N[(2.0 * N[(N[(l / N[Power[k, 2.0], $MachinePrecision]), $MachinePrecision] * N[(N[Cos[k], $MachinePrecision] / N[(t$95$m * N[Power[N[Sin[k], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$m, 2.6e+98], N[(l * N[(N[(N[(2.0 * N[(l / N[Sin[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[Tan[k], $MachinePrecision] * N[Power[t$95$m, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$m, 2.8e+203], N[(2.0 / N[(N[(N[Tan[k], $MachinePrecision] * t$95$2), $MachinePrecision] * N[(N[Sin[k], $MachinePrecision] * N[Power[N[(N[Power[t$95$m, 1.5], $MachinePrecision] * N[(1.0 / l), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[Power[N[(N[(N[Power[l, 1/3], $MachinePrecision] / N[Sqrt[t$95$m], $MachinePrecision]), $MachinePrecision] * N[Power[N[(1.0 / k), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision], 3.0], $MachinePrecision]]]]), $MachinePrecision]]

Derivation

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

Alternative 6: 85.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ \begin{array}{l} t_2 := 2 + {\left(\frac{k}{t_m}\right)}^{2}\\ t_s \cdot \begin{array}{l} \mathbf{if}\;t_m \leq 5.2 \cdot 10^{-21}:\\ \;\;\;\;\ell \cdot \left(2 \cdot \left(\frac{\ell}{{k}^{2}} \cdot \frac{\cos k}{t_m \cdot {\sin k}^{2}}\right)\right)\\ \mathbf{elif}\;t_m \leq 2.15 \cdot 10^{+101}:\\ \;\;\;\;\ell \cdot \frac{\frac{2 \cdot \frac{\ell}{\sin k}}{\tan k \cdot {t_m}^{3}}}{t_2}\\ \mathbf{elif}\;t_m \leq 1.4 \cdot 10^{+203}:\\ \;\;\;\;\frac{2}{\left(\tan k \cdot t_2\right) \cdot \left(\sin k \cdot {\left(\frac{{t_m}^{1.5}}{\ell}\right)}^{2}\right)}\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{\sqrt[3]{\ell}}{\sqrt{t_m}} \cdot \sqrt[3]{\frac{1}{k}}\right)}^{2}\right)}^{3}\\ \end{array} \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (let* ((t_2 (+ 2.0 (pow (/ k t_m) 2.0))))
   (*
    t_s
    (if (<= t_m 5.2e-21)
      (* l (* 2.0 (* (/ l (pow k 2.0)) (/ (cos k) (* t_m (pow (sin k) 2.0))))))
      (if (<= t_m 2.15e+101)
        (* l (/ (/ (* 2.0 (/ l (sin k))) (* (tan k) (pow t_m 3.0))) t_2))
        (if (<= t_m 1.4e+203)
          (/ 2.0 (* (* (tan k) t_2) (* (sin k) (pow (/ (pow t_m 1.5) l) 2.0))))
          (pow
           (pow (* (/ (cbrt l) (sqrt t_m)) (cbrt (/ 1.0 k))) 2.0)
           3.0)))))))

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 = 2.0 + pow((k / t_m), 2.0);
	double tmp;
	if (t_m <= 5.2e-21) {
		tmp = l * (2.0 * ((l / pow(k, 2.0)) * (cos(k) / (t_m * pow(sin(k), 2.0)))));
	} else if (t_m <= 2.15e+101) {
		tmp = l * (((2.0 * (l / sin(k))) / (tan(k) * pow(t_m, 3.0))) / t_2);
	} else if (t_m <= 1.4e+203) {
		tmp = 2.0 / ((tan(k) * t_2) * (sin(k) * pow((pow(t_m, 1.5) / l), 2.0)));
	} else {
		tmp = pow(pow(((cbrt(l) / sqrt(t_m)) * cbrt((1.0 / k))), 2.0), 3.0);
	}
	return t_s * tmp;
}

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 = 2.0 + Math.pow((k / t_m), 2.0);
	double tmp;
	if (t_m <= 5.2e-21) {
		tmp = l * (2.0 * ((l / Math.pow(k, 2.0)) * (Math.cos(k) / (t_m * Math.pow(Math.sin(k), 2.0)))));
	} else if (t_m <= 2.15e+101) {
		tmp = l * (((2.0 * (l / Math.sin(k))) / (Math.tan(k) * Math.pow(t_m, 3.0))) / t_2);
	} else if (t_m <= 1.4e+203) {
		tmp = 2.0 / ((Math.tan(k) * t_2) * (Math.sin(k) * Math.pow((Math.pow(t_m, 1.5) / l), 2.0)));
	} else {
		tmp = Math.pow(Math.pow(((Math.cbrt(l) / Math.sqrt(t_m)) * Math.cbrt((1.0 / k))), 2.0), 3.0);
	}
	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(2.0 + (Float64(k / t_m) ^ 2.0))
	tmp = 0.0
	if (t_m <= 5.2e-21)
		tmp = Float64(l * Float64(2.0 * Float64(Float64(l / (k ^ 2.0)) * Float64(cos(k) / Float64(t_m * (sin(k) ^ 2.0))))));
	elseif (t_m <= 2.15e+101)
		tmp = Float64(l * Float64(Float64(Float64(2.0 * Float64(l / sin(k))) / Float64(tan(k) * (t_m ^ 3.0))) / t_2));
	elseif (t_m <= 1.4e+203)
		tmp = Float64(2.0 / Float64(Float64(tan(k) * t_2) * Float64(sin(k) * (Float64((t_m ^ 1.5) / l) ^ 2.0))));
	else
		tmp = (Float64(Float64(cbrt(l) / sqrt(t_m)) * cbrt(Float64(1.0 / k))) ^ 2.0) ^ 3.0;
	end
	return Float64(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[(2.0 + N[Power[N[(k / t$95$m), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]}, N[(t$95$s * If[LessEqual[t$95$m, 5.2e-21], N[(l * N[(2.0 * N[(N[(l / N[Power[k, 2.0], $MachinePrecision]), $MachinePrecision] * N[(N[Cos[k], $MachinePrecision] / N[(t$95$m * N[Power[N[Sin[k], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$m, 2.15e+101], N[(l * N[(N[(N[(2.0 * N[(l / N[Sin[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[Tan[k], $MachinePrecision] * N[Power[t$95$m, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$m, 1.4e+203], N[(2.0 / N[(N[(N[Tan[k], $MachinePrecision] * t$95$2), $MachinePrecision] * N[(N[Sin[k], $MachinePrecision] * N[Power[N[(N[Power[t$95$m, 1.5], $MachinePrecision] / l), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[Power[N[(N[(N[Power[l, 1/3], $MachinePrecision] / N[Sqrt[t$95$m], $MachinePrecision]), $MachinePrecision] * N[Power[N[(1.0 / k), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision], 3.0], $MachinePrecision]]]]), $MachinePrecision]]

Derivation

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

Alternative 7: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;t_m \leq 1.05 \cdot 10^{-89}:\\ \;\;\;\;\ell \cdot \left(2 \cdot \left(\frac{\ell}{{k}^{2}} \cdot \frac{\cos k}{t_m \cdot {\sin k}^{2}}\right)\right)\\ \mathbf{elif}\;t_m \leq 1.6 \cdot 10^{+94}:\\ \;\;\;\;\ell \cdot \frac{\frac{2}{{t_m}^{3}} \cdot \frac{\frac{\ell}{\sin k}}{\tan k}}{2 + {\left(\frac{k}{t_m}\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;{\left({\left(\frac{\sqrt[3]{\ell}}{\sqrt{t_m}} \cdot \sqrt[3]{\frac{1}{k}}\right)}^{2}\right)}^{3}\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (*
  t_s
  (if (<= t_m 1.05e-89)
    (* l (* 2.0 (* (/ l (pow k 2.0)) (/ (cos k) (* t_m (pow (sin k) 2.0))))))
    (if (<= t_m 1.6e+94)
      (*
       l
       (/
        (* (/ 2.0 (pow t_m 3.0)) (/ (/ l (sin k)) (tan k)))
        (+ 2.0 (pow (/ k t_m) 2.0))))
      (pow (pow (* (/ (cbrt l) (sqrt t_m)) (cbrt (/ 1.0 k))) 2.0) 3.0)))))

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 (t_m <= 1.05e-89) {
		tmp = l * (2.0 * ((l / pow(k, 2.0)) * (cos(k) / (t_m * pow(sin(k), 2.0)))));
	} else if (t_m <= 1.6e+94) {
		tmp = l * (((2.0 / pow(t_m, 3.0)) * ((l / sin(k)) / tan(k))) / (2.0 + pow((k / t_m), 2.0)));
	} else {
		tmp = pow(pow(((cbrt(l) / sqrt(t_m)) * cbrt((1.0 / k))), 2.0), 3.0);
	}
	return t_s * tmp;
}

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 (t_m <= 1.05e-89) {
		tmp = l * (2.0 * ((l / Math.pow(k, 2.0)) * (Math.cos(k) / (t_m * Math.pow(Math.sin(k), 2.0)))));
	} else if (t_m <= 1.6e+94) {
		tmp = l * (((2.0 / Math.pow(t_m, 3.0)) * ((l / Math.sin(k)) / Math.tan(k))) / (2.0 + Math.pow((k / t_m), 2.0)));
	} else {
		tmp = Math.pow(Math.pow(((Math.cbrt(l) / Math.sqrt(t_m)) * Math.cbrt((1.0 / k))), 2.0), 3.0);
	}
	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 (t_m <= 1.05e-89)
		tmp = Float64(l * Float64(2.0 * Float64(Float64(l / (k ^ 2.0)) * Float64(cos(k) / Float64(t_m * (sin(k) ^ 2.0))))));
	elseif (t_m <= 1.6e+94)
		tmp = Float64(l * Float64(Float64(Float64(2.0 / (t_m ^ 3.0)) * Float64(Float64(l / sin(k)) / tan(k))) / Float64(2.0 + (Float64(k / t_m) ^ 2.0))));
	else
		tmp = (Float64(Float64(cbrt(l) / sqrt(t_m)) * cbrt(Float64(1.0 / k))) ^ 2.0) ^ 3.0;
	end
	return Float64(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[t$95$m, 1.05e-89], N[(l * N[(2.0 * N[(N[(l / N[Power[k, 2.0], $MachinePrecision]), $MachinePrecision] * N[(N[Cos[k], $MachinePrecision] / N[(t$95$m * N[Power[N[Sin[k], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$m, 1.6e+94], N[(l * N[(N[(N[(2.0 / N[Power[t$95$m, 3.0], $MachinePrecision]), $MachinePrecision] * N[(N[(l / N[Sin[k], $MachinePrecision]), $MachinePrecision] / N[Tan[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(2.0 + N[Power[N[(k / t$95$m), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[Power[N[(N[(N[Power[l, 1/3], $MachinePrecision] / N[Sqrt[t$95$m], $MachinePrecision]), $MachinePrecision] * N[Power[N[(1.0 / k), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision], 3.0], $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 8: 69.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;t_m \leq 1.05 \cdot 10^{-89}:\\ \;\;\;\;\ell \cdot \left(2 \cdot \left(\frac{\ell}{{k}^{2}} \cdot \frac{\cos k}{t_m \cdot {\sin k}^{2}}\right)\right)\\ \mathbf{elif}\;t_m \leq 1.6 \cdot 10^{+94}:\\ \;\;\;\;\ell \cdot \frac{\frac{2}{{t_m}^{3}} \cdot \frac{\frac{\ell}{\sin k}}{\tan k}}{2 + {\left(\frac{k}{t_m}\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{{\left(\sqrt[3]{\ell}\right)}^{2}}{t_m} \cdot {k}^{-0.6666666666666666}\right)}^{3}\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (*
  t_s
  (if (<= t_m 1.05e-89)
    (* l (* 2.0 (* (/ l (pow k 2.0)) (/ (cos k) (* t_m (pow (sin k) 2.0))))))
    (if (<= t_m 1.6e+94)
      (*
       l
       (/
        (* (/ 2.0 (pow t_m 3.0)) (/ (/ l (sin k)) (tan k)))
        (+ 2.0 (pow (/ k t_m) 2.0))))
      (pow (* (/ (pow (cbrt l) 2.0) t_m) (pow k -0.6666666666666666)) 3.0)))))

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 (t_m <= 1.05e-89) {
		tmp = l * (2.0 * ((l / pow(k, 2.0)) * (cos(k) / (t_m * pow(sin(k), 2.0)))));
	} else if (t_m <= 1.6e+94) {
		tmp = l * (((2.0 / pow(t_m, 3.0)) * ((l / sin(k)) / tan(k))) / (2.0 + pow((k / t_m), 2.0)));
	} else {
		tmp = pow(((pow(cbrt(l), 2.0) / t_m) * pow(k, -0.6666666666666666)), 3.0);
	}
	return t_s * tmp;
}

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 (t_m <= 1.05e-89) {
		tmp = l * (2.0 * ((l / Math.pow(k, 2.0)) * (Math.cos(k) / (t_m * Math.pow(Math.sin(k), 2.0)))));
	} else if (t_m <= 1.6e+94) {
		tmp = l * (((2.0 / Math.pow(t_m, 3.0)) * ((l / Math.sin(k)) / Math.tan(k))) / (2.0 + Math.pow((k / t_m), 2.0)));
	} else {
		tmp = Math.pow(((Math.pow(Math.cbrt(l), 2.0) / t_m) * Math.pow(k, -0.6666666666666666)), 3.0);
	}
	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 (t_m <= 1.05e-89)
		tmp = Float64(l * Float64(2.0 * Float64(Float64(l / (k ^ 2.0)) * Float64(cos(k) / Float64(t_m * (sin(k) ^ 2.0))))));
	elseif (t_m <= 1.6e+94)
		tmp = Float64(l * Float64(Float64(Float64(2.0 / (t_m ^ 3.0)) * Float64(Float64(l / sin(k)) / tan(k))) / Float64(2.0 + (Float64(k / t_m) ^ 2.0))));
	else
		tmp = Float64(Float64((cbrt(l) ^ 2.0) / t_m) * (k ^ -0.6666666666666666)) ^ 3.0;
	end
	return Float64(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[t$95$m, 1.05e-89], N[(l * N[(2.0 * N[(N[(l / N[Power[k, 2.0], $MachinePrecision]), $MachinePrecision] * N[(N[Cos[k], $MachinePrecision] / N[(t$95$m * N[Power[N[Sin[k], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$m, 1.6e+94], N[(l * N[(N[(N[(2.0 / N[Power[t$95$m, 3.0], $MachinePrecision]), $MachinePrecision] * N[(N[(l / N[Sin[k], $MachinePrecision]), $MachinePrecision] / N[Tan[k], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(2.0 + N[Power[N[(k / t$95$m), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[(N[(N[Power[N[Power[l, 1/3], $MachinePrecision], 2.0], $MachinePrecision] / t$95$m), $MachinePrecision] * N[Power[k, -0.6666666666666666], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 9: 61.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;t_m \leq 29000000000:\\ \;\;\;\;\ell \cdot \left(2 \cdot \left(\frac{\ell}{{k}^{2}} \cdot \frac{\cos k}{t_m \cdot {\sin k}^{2}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{{\left(\sqrt[3]{\ell}\right)}^{2}}{t_m} \cdot {k}^{-0.6666666666666666}\right)}^{3}\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (*
  t_s
  (if (<= t_m 29000000000.0)
    (* l (* 2.0 (* (/ l (pow k 2.0)) (/ (cos k) (* t_m (pow (sin k) 2.0))))))
    (pow (* (/ (pow (cbrt l) 2.0) t_m) (pow k -0.6666666666666666)) 3.0))))

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 (t_m <= 29000000000.0) {
		tmp = l * (2.0 * ((l / pow(k, 2.0)) * (cos(k) / (t_m * pow(sin(k), 2.0)))));
	} else {
		tmp = pow(((pow(cbrt(l), 2.0) / t_m) * pow(k, -0.6666666666666666)), 3.0);
	}
	return t_s * tmp;
}

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 (t_m <= 29000000000.0) {
		tmp = l * (2.0 * ((l / Math.pow(k, 2.0)) * (Math.cos(k) / (t_m * Math.pow(Math.sin(k), 2.0)))));
	} else {
		tmp = Math.pow(((Math.pow(Math.cbrt(l), 2.0) / t_m) * Math.pow(k, -0.6666666666666666)), 3.0);
	}
	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 (t_m <= 29000000000.0)
		tmp = Float64(l * Float64(2.0 * Float64(Float64(l / (k ^ 2.0)) * Float64(cos(k) / Float64(t_m * (sin(k) ^ 2.0))))));
	else
		tmp = Float64(Float64((cbrt(l) ^ 2.0) / t_m) * (k ^ -0.6666666666666666)) ^ 3.0;
	end
	return Float64(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[t$95$m, 29000000000.0], N[(l * N[(2.0 * N[(N[(l / N[Power[k, 2.0], $MachinePrecision]), $MachinePrecision] * N[(N[Cos[k], $MachinePrecision] / N[(t$95$m * N[Power[N[Sin[k], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[(N[(N[Power[N[Power[l, 1/3], $MachinePrecision], 2.0], $MachinePrecision] / t$95$m), $MachinePrecision] * N[Power[k, -0.6666666666666666], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 10: 56.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;t_m \leq 5.2 \cdot 10^{-21}:\\ \;\;\;\;\frac{2}{{\left(\frac{k}{\frac{\ell}{\sin k}} \cdot \sqrt{\frac{t_m}{\cos k}}\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{{\left(\sqrt[3]{\ell}\right)}^{2}}{t_m} \cdot {k}^{-0.6666666666666666}\right)}^{3}\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (*
  t_s
  (if (<= t_m 5.2e-21)
    (/ 2.0 (pow (* (/ k (/ l (sin k))) (sqrt (/ t_m (cos k)))) 2.0))
    (pow (* (/ (pow (cbrt l) 2.0) t_m) (pow k -0.6666666666666666)) 3.0))))

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 (t_m <= 5.2e-21) {
		tmp = 2.0 / pow(((k / (l / sin(k))) * sqrt((t_m / cos(k)))), 2.0);
	} else {
		tmp = pow(((pow(cbrt(l), 2.0) / t_m) * pow(k, -0.6666666666666666)), 3.0);
	}
	return t_s * tmp;
}

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 (t_m <= 5.2e-21) {
		tmp = 2.0 / Math.pow(((k / (l / Math.sin(k))) * Math.sqrt((t_m / Math.cos(k)))), 2.0);
	} else {
		tmp = Math.pow(((Math.pow(Math.cbrt(l), 2.0) / t_m) * Math.pow(k, -0.6666666666666666)), 3.0);
	}
	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 (t_m <= 5.2e-21)
		tmp = Float64(2.0 / (Float64(Float64(k / Float64(l / sin(k))) * sqrt(Float64(t_m / cos(k)))) ^ 2.0));
	else
		tmp = Float64(Float64((cbrt(l) ^ 2.0) / t_m) * (k ^ -0.6666666666666666)) ^ 3.0;
	end
	return Float64(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[t$95$m, 5.2e-21], 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], N[Power[N[(N[(N[Power[N[Power[l, 1/3], $MachinePrecision], 2.0], $MachinePrecision] / t$95$m), $MachinePrecision] * N[Power[k, -0.6666666666666666], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 11: 45.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;t_m \leq 7.8 \cdot 10^{-151}:\\ \;\;\;\;\ell \cdot {\left(\frac{\sqrt[3]{\frac{\ell}{{k}^{2}}}}{t_m}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{{\left(\sqrt[3]{\ell}\right)}^{2}}{t_m} \cdot {k}^{-0.6666666666666666}\right)}^{3}\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (*
  t_s
  (if (<= t_m 7.8e-151)
    (* l (pow (/ (cbrt (/ l (pow k 2.0))) t_m) 3.0))
    (pow (* (/ (pow (cbrt l) 2.0) t_m) (pow k -0.6666666666666666)) 3.0))))

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 (t_m <= 7.8e-151) {
		tmp = l * pow((cbrt((l / pow(k, 2.0))) / t_m), 3.0);
	} else {
		tmp = pow(((pow(cbrt(l), 2.0) / t_m) * pow(k, -0.6666666666666666)), 3.0);
	}
	return t_s * tmp;
}

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 (t_m <= 7.8e-151) {
		tmp = l * Math.pow((Math.cbrt((l / Math.pow(k, 2.0))) / t_m), 3.0);
	} else {
		tmp = Math.pow(((Math.pow(Math.cbrt(l), 2.0) / t_m) * Math.pow(k, -0.6666666666666666)), 3.0);
	}
	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 (t_m <= 7.8e-151)
		tmp = Float64(l * (Float64(cbrt(Float64(l / (k ^ 2.0))) / t_m) ^ 3.0));
	else
		tmp = Float64(Float64((cbrt(l) ^ 2.0) / t_m) * (k ^ -0.6666666666666666)) ^ 3.0;
	end
	return Float64(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[t$95$m, 7.8e-151], N[(l * N[Power[N[(N[Power[N[(l / N[Power[k, 2.0], $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] / t$95$m), $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision], N[Power[N[(N[(N[Power[N[Power[l, 1/3], $MachinePrecision], 2.0], $MachinePrecision] / t$95$m), $MachinePrecision] * N[Power[k, -0.6666666666666666], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 12: 70.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;t_m \leq 7.8 \cdot 10^{-151}:\\ \;\;\;\;\ell \cdot {\left(\frac{\sqrt[3]{\frac{\ell}{{k}^{2}}}}{t_m}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{{\left(k \cdot \frac{{t_m}^{1.5}}{\ell}\right)}^{2}}\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (*
  t_s
  (if (<= t_m 7.8e-151)
    (* l (pow (/ (cbrt (/ l (pow k 2.0))) t_m) 3.0))
    (/ 1.0 (pow (* k (/ (pow t_m 1.5) l)) 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 (t_m <= 7.8e-151) {
		tmp = l * pow((cbrt((l / pow(k, 2.0))) / t_m), 3.0);
	} else {
		tmp = 1.0 / pow((k * (pow(t_m, 1.5) / l)), 2.0);
	}
	return t_s * tmp;
}

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 (t_m <= 7.8e-151) {
		tmp = l * Math.pow((Math.cbrt((l / Math.pow(k, 2.0))) / t_m), 3.0);
	} else {
		tmp = 1.0 / Math.pow((k * (Math.pow(t_m, 1.5) / l)), 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 (t_m <= 7.8e-151)
		tmp = Float64(l * (Float64(cbrt(Float64(l / (k ^ 2.0))) / t_m) ^ 3.0));
	else
		tmp = Float64(1.0 / (Float64(k * Float64((t_m ^ 1.5) / l)) ^ 2.0));
	end
	return Float64(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[t$95$m, 7.8e-151], N[(l * N[Power[N[(N[Power[N[(l / N[Power[k, 2.0], $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] / t$95$m), $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision], N[(1.0 / N[Power[N[(k * N[(N[Power[t$95$m, 1.5], $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 13: 67.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \frac{1}{{\left(k \cdot \frac{{t_m}^{1.5}}{\ell}\right)}^{2}} \end{array} \]

FPCore

t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k)
 :precision binary64
 (* t_s (/ 1.0 (pow (* k (/ (pow t_m 1.5) l)) 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 * (1.0 / pow((k * (pow(t_m, 1.5) / l)), 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 * (1.0d0 / ((k * ((t_m ** 1.5d0) / l)) ** 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 * (1.0 / Math.pow((k * (Math.pow(t_m, 1.5) / l)), 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 * (1.0 / math.pow((k * (math.pow(t_m, 1.5) / l)), 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(1.0 / (Float64(k * Float64((t_m ^ 1.5) / l)) ^ 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 * (1.0 / ((k * ((t_m ^ 1.5) / l)) ^ 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[(1.0 / N[Power[N[(k * N[(N[Power[t$95$m, 1.5], $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 14: 68.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot {\left(\frac{\ell}{k \cdot {t_m}^{1.5}}\right)}^{2} \end{array} \]

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 (* k (pow t_m 1.5))) 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 / (k * pow(t_m, 1.5))), 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 / (k * (t_m ** 1.5d0))) ** 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 / (k * Math.pow(t_m, 1.5))), 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 / (k * math.pow(t_m, 1.5))), 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(l / Float64(k * (t_m ^ 1.5))) ^ 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 / (k * (t_m ^ 1.5))) ^ 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[(l / N[(k * N[Power[t$95$m, 1.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2023350 
(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))))