Toniolo and Linder, Equation (10-)

Percentage Accurate: 34.4% → 92.8%

Time: 24.5s

Alternatives: 9

Speedup: 2.0×

• 35.0% 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: 34.4% 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: 92.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} k_m = \left|k\right| \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;k_m \leq 1.55:\\ \;\;\;\;2 \cdot {\left(\frac{\ell}{\sqrt{t_m}} \cdot \frac{\sqrt{\cos k_m \cdot {k_m}^{-2}}}{\sin k_m}\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\cos k_m \cdot {\left(\frac{\ell}{k_m}\right)}^{2}}{t_m \cdot {\sin k_m}^{2}}\\ \end{array} \end{array} \]

FPCore

k_m = (fabs.f64 k)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k_m)
 :precision binary64
 (*
  t_s
  (if (<= k_m 1.55)
    (*
     2.0
     (pow
      (* (/ l (sqrt t_m)) (/ (sqrt (* (cos k_m) (pow k_m -2.0))) (sin k_m)))
      2.0))
    (*
     2.0
     (/ (* (cos k_m) (pow (/ l k_m) 2.0)) (* t_m (pow (sin k_m) 2.0)))))))

C

k_m = fabs(k);
t_m = fabs(t);
t_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k_m) {
	double tmp;
	if (k_m <= 1.55) {
		tmp = 2.0 * pow(((l / sqrt(t_m)) * (sqrt((cos(k_m) * pow(k_m, -2.0))) / sin(k_m))), 2.0);
	} else {
		tmp = 2.0 * ((cos(k_m) * pow((l / k_m), 2.0)) / (t_m * pow(sin(k_m), 2.0)));
	}
	return t_s * tmp;
}

Fortran

k_m = abs(k)
t_m = abs(t)
t_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k_m
    real(8) :: tmp
    if (k_m <= 1.55d0) then
        tmp = 2.0d0 * (((l / sqrt(t_m)) * (sqrt((cos(k_m) * (k_m ** (-2.0d0)))) / sin(k_m))) ** 2.0d0)
    else
        tmp = 2.0d0 * ((cos(k_m) * ((l / k_m) ** 2.0d0)) / (t_m * (sin(k_m) ** 2.0d0)))
    end if
    code = t_s * tmp
end function

Java

k_m = Math.abs(k);
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_m) {
	double tmp;
	if (k_m <= 1.55) {
		tmp = 2.0 * Math.pow(((l / Math.sqrt(t_m)) * (Math.sqrt((Math.cos(k_m) * Math.pow(k_m, -2.0))) / Math.sin(k_m))), 2.0);
	} else {
		tmp = 2.0 * ((Math.cos(k_m) * Math.pow((l / k_m), 2.0)) / (t_m * Math.pow(Math.sin(k_m), 2.0)));
	}
	return t_s * tmp;
}

Python

k_m = math.fabs(k)
t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k_m):
	tmp = 0
	if k_m <= 1.55:
		tmp = 2.0 * math.pow(((l / math.sqrt(t_m)) * (math.sqrt((math.cos(k_m) * math.pow(k_m, -2.0))) / math.sin(k_m))), 2.0)
	else:
		tmp = 2.0 * ((math.cos(k_m) * math.pow((l / k_m), 2.0)) / (t_m * math.pow(math.sin(k_m), 2.0)))
	return t_s * tmp

Julia

k_m = abs(k)
t_m = abs(t)
t_s = copysign(1.0, t)
function code(t_s, t_m, l, k_m)
	tmp = 0.0
	if (k_m <= 1.55)
		tmp = Float64(2.0 * (Float64(Float64(l / sqrt(t_m)) * Float64(sqrt(Float64(cos(k_m) * (k_m ^ -2.0))) / sin(k_m))) ^ 2.0));
	else
		tmp = Float64(2.0 * Float64(Float64(cos(k_m) * (Float64(l / k_m) ^ 2.0)) / Float64(t_m * (sin(k_m) ^ 2.0))));
	end
	return Float64(t_s * tmp)
end

MATLAB

k_m = abs(k);
t_m = abs(t);
t_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, t_m, l, k_m)
	tmp = 0.0;
	if (k_m <= 1.55)
		tmp = 2.0 * (((l / sqrt(t_m)) * (sqrt((cos(k_m) * (k_m ^ -2.0))) / sin(k_m))) ^ 2.0);
	else
		tmp = 2.0 * ((cos(k_m) * ((l / k_m) ^ 2.0)) / (t_m * (sin(k_m) ^ 2.0)));
	end
	tmp_2 = t_s * tmp;
end

Wolfram

k_m = N[Abs[k], $MachinePrecision]
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$95$m_] := N[(t$95$s * If[LessEqual[k$95$m, 1.55], N[(2.0 * N[Power[N[(N[(l / N[Sqrt[t$95$m], $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[N[(N[Cos[k$95$m], $MachinePrecision] * N[Power[k$95$m, -2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[Sin[k$95$m], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[Cos[k$95$m], $MachinePrecision] * N[Power[N[(l / k$95$m), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[(t$95$m * N[Power[N[Sin[k$95$m], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 2: 92.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} k_m = \left|k\right| \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;\ell \cdot \ell \leq 0:\\ \;\;\;\;{\left(\frac{\ell}{\sqrt{t_m}} \cdot \left({k_m}^{-2} \cdot \sqrt{2}\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\cos k_m \cdot {\left(\frac{\ell}{k_m}\right)}^{2}}{t_m \cdot {\sin k_m}^{2}}\\ \end{array} \end{array} \]

FPCore

k_m = (fabs.f64 k)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k_m)
 :precision binary64
 (*
  t_s
  (if (<= (* l l) 0.0)
    (pow (* (/ l (sqrt t_m)) (* (pow k_m -2.0) (sqrt 2.0))) 2.0)
    (*
     2.0
     (/ (* (cos k_m) (pow (/ l k_m) 2.0)) (* t_m (pow (sin k_m) 2.0)))))))

C

k_m = fabs(k);
t_m = fabs(t);
t_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k_m) {
	double tmp;
	if ((l * l) <= 0.0) {
		tmp = pow(((l / sqrt(t_m)) * (pow(k_m, -2.0) * sqrt(2.0))), 2.0);
	} else {
		tmp = 2.0 * ((cos(k_m) * pow((l / k_m), 2.0)) / (t_m * pow(sin(k_m), 2.0)));
	}
	return t_s * tmp;
}

Fortran

k_m = abs(k)
t_m = abs(t)
t_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k_m
    real(8) :: tmp
    if ((l * l) <= 0.0d0) then
        tmp = ((l / sqrt(t_m)) * ((k_m ** (-2.0d0)) * sqrt(2.0d0))) ** 2.0d0
    else
        tmp = 2.0d0 * ((cos(k_m) * ((l / k_m) ** 2.0d0)) / (t_m * (sin(k_m) ** 2.0d0)))
    end if
    code = t_s * tmp
end function

Java

k_m = Math.abs(k);
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_m) {
	double tmp;
	if ((l * l) <= 0.0) {
		tmp = Math.pow(((l / Math.sqrt(t_m)) * (Math.pow(k_m, -2.0) * Math.sqrt(2.0))), 2.0);
	} else {
		tmp = 2.0 * ((Math.cos(k_m) * Math.pow((l / k_m), 2.0)) / (t_m * Math.pow(Math.sin(k_m), 2.0)));
	}
	return t_s * tmp;
}

Python

k_m = math.fabs(k)
t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k_m):
	tmp = 0
	if (l * l) <= 0.0:
		tmp = math.pow(((l / math.sqrt(t_m)) * (math.pow(k_m, -2.0) * math.sqrt(2.0))), 2.0)
	else:
		tmp = 2.0 * ((math.cos(k_m) * math.pow((l / k_m), 2.0)) / (t_m * math.pow(math.sin(k_m), 2.0)))
	return t_s * tmp

Julia

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

MATLAB

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

Wolfram

k_m = N[Abs[k], $MachinePrecision]
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$95$m_] := N[(t$95$s * If[LessEqual[N[(l * l), $MachinePrecision], 0.0], N[Power[N[(N[(l / N[Sqrt[t$95$m], $MachinePrecision]), $MachinePrecision] * N[(N[Power[k$95$m, -2.0], $MachinePrecision] * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision], N[(2.0 * N[(N[(N[Cos[k$95$m], $MachinePrecision] * N[Power[N[(l / k$95$m), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[(t$95$m * N[Power[N[Sin[k$95$m], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 3: 81.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} k_m = \left|k\right| \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;\ell \leq 7 \cdot 10^{-78}:\\ \;\;\;\;{\left(\frac{\ell}{\sqrt{t_m}} \cdot \left({k_m}^{-2} \cdot \sqrt{2}\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\frac{{\left(\frac{\ell}{k_m}\right)}^{2}}{t_m} \cdot \frac{\cos k_m}{{\sin k_m}^{2}}\right)\\ \end{array} \end{array} \]

FPCore

k_m = (fabs.f64 k)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k_m)
 :precision binary64
 (*
  t_s
  (if (<= l 7e-78)
    (pow (* (/ l (sqrt t_m)) (* (pow k_m -2.0) (sqrt 2.0))) 2.0)
    (*
     2.0
     (* (/ (pow (/ l k_m) 2.0) t_m) (/ (cos k_m) (pow (sin k_m) 2.0)))))))

C

k_m = fabs(k);
t_m = fabs(t);
t_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k_m) {
	double tmp;
	if (l <= 7e-78) {
		tmp = pow(((l / sqrt(t_m)) * (pow(k_m, -2.0) * sqrt(2.0))), 2.0);
	} else {
		tmp = 2.0 * ((pow((l / k_m), 2.0) / t_m) * (cos(k_m) / pow(sin(k_m), 2.0)));
	}
	return t_s * tmp;
}

Fortran

k_m = abs(k)
t_m = abs(t)
t_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k_m
    real(8) :: tmp
    if (l <= 7d-78) then
        tmp = ((l / sqrt(t_m)) * ((k_m ** (-2.0d0)) * sqrt(2.0d0))) ** 2.0d0
    else
        tmp = 2.0d0 * ((((l / k_m) ** 2.0d0) / t_m) * (cos(k_m) / (sin(k_m) ** 2.0d0)))
    end if
    code = t_s * tmp
end function

Java

k_m = Math.abs(k);
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_m) {
	double tmp;
	if (l <= 7e-78) {
		tmp = Math.pow(((l / Math.sqrt(t_m)) * (Math.pow(k_m, -2.0) * Math.sqrt(2.0))), 2.0);
	} else {
		tmp = 2.0 * ((Math.pow((l / k_m), 2.0) / t_m) * (Math.cos(k_m) / Math.pow(Math.sin(k_m), 2.0)));
	}
	return t_s * tmp;
}

Python

k_m = math.fabs(k)
t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k_m):
	tmp = 0
	if l <= 7e-78:
		tmp = math.pow(((l / math.sqrt(t_m)) * (math.pow(k_m, -2.0) * math.sqrt(2.0))), 2.0)
	else:
		tmp = 2.0 * ((math.pow((l / k_m), 2.0) / t_m) * (math.cos(k_m) / math.pow(math.sin(k_m), 2.0)))
	return t_s * tmp

Julia

k_m = abs(k)
t_m = abs(t)
t_s = copysign(1.0, t)
function code(t_s, t_m, l, k_m)
	tmp = 0.0
	if (l <= 7e-78)
		tmp = Float64(Float64(l / sqrt(t_m)) * Float64((k_m ^ -2.0) * sqrt(2.0))) ^ 2.0;
	else
		tmp = Float64(2.0 * Float64(Float64((Float64(l / k_m) ^ 2.0) / t_m) * Float64(cos(k_m) / (sin(k_m) ^ 2.0))));
	end
	return Float64(t_s * tmp)
end

MATLAB

k_m = abs(k);
t_m = abs(t);
t_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, t_m, l, k_m)
	tmp = 0.0;
	if (l <= 7e-78)
		tmp = ((l / sqrt(t_m)) * ((k_m ^ -2.0) * sqrt(2.0))) ^ 2.0;
	else
		tmp = 2.0 * ((((l / k_m) ^ 2.0) / t_m) * (cos(k_m) / (sin(k_m) ^ 2.0)));
	end
	tmp_2 = t_s * tmp;
end

Wolfram

k_m = N[Abs[k], $MachinePrecision]
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$95$m_] := N[(t$95$s * If[LessEqual[l, 7e-78], N[Power[N[(N[(l / N[Sqrt[t$95$m], $MachinePrecision]), $MachinePrecision] * N[(N[Power[k$95$m, -2.0], $MachinePrecision] * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision], N[(2.0 * N[(N[(N[Power[N[(l / k$95$m), $MachinePrecision], 2.0], $MachinePrecision] / t$95$m), $MachinePrecision] * N[(N[Cos[k$95$m], $MachinePrecision] / N[Power[N[Sin[k$95$m], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 4: 71.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} k_m = \left|k\right| \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;k_m \leq 9.6 \cdot 10^{+82}:\\ \;\;\;\;{\left(\frac{\ell}{\sqrt{t_m}} \cdot \left({k_m}^{-2} \cdot \sqrt{2}\right)\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{\ell}^{2}}{{k_m}^{2}}}{t_m} \cdot -0.3333333333333333\\ \end{array} \end{array} \]

FPCore

k_m = (fabs.f64 k)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k_m)
 :precision binary64
 (*
  t_s
  (if (<= k_m 9.6e+82)
    (pow (* (/ l (sqrt t_m)) (* (pow k_m -2.0) (sqrt 2.0))) 2.0)
    (* (/ (/ (pow l 2.0) (pow k_m 2.0)) t_m) -0.3333333333333333))))

C

k_m = fabs(k);
t_m = fabs(t);
t_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k_m) {
	double tmp;
	if (k_m <= 9.6e+82) {
		tmp = pow(((l / sqrt(t_m)) * (pow(k_m, -2.0) * sqrt(2.0))), 2.0);
	} else {
		tmp = ((pow(l, 2.0) / pow(k_m, 2.0)) / t_m) * -0.3333333333333333;
	}
	return t_s * tmp;
}

Fortran

k_m = abs(k)
t_m = abs(t)
t_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k_m
    real(8) :: tmp
    if (k_m <= 9.6d+82) then
        tmp = ((l / sqrt(t_m)) * ((k_m ** (-2.0d0)) * sqrt(2.0d0))) ** 2.0d0
    else
        tmp = (((l ** 2.0d0) / (k_m ** 2.0d0)) / t_m) * (-0.3333333333333333d0)
    end if
    code = t_s * tmp
end function

Java

k_m = Math.abs(k);
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_m) {
	double tmp;
	if (k_m <= 9.6e+82) {
		tmp = Math.pow(((l / Math.sqrt(t_m)) * (Math.pow(k_m, -2.0) * Math.sqrt(2.0))), 2.0);
	} else {
		tmp = ((Math.pow(l, 2.0) / Math.pow(k_m, 2.0)) / t_m) * -0.3333333333333333;
	}
	return t_s * tmp;
}

Python

k_m = math.fabs(k)
t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k_m):
	tmp = 0
	if k_m <= 9.6e+82:
		tmp = math.pow(((l / math.sqrt(t_m)) * (math.pow(k_m, -2.0) * math.sqrt(2.0))), 2.0)
	else:
		tmp = ((math.pow(l, 2.0) / math.pow(k_m, 2.0)) / t_m) * -0.3333333333333333
	return t_s * tmp

Julia

k_m = abs(k)
t_m = abs(t)
t_s = copysign(1.0, t)
function code(t_s, t_m, l, k_m)
	tmp = 0.0
	if (k_m <= 9.6e+82)
		tmp = Float64(Float64(l / sqrt(t_m)) * Float64((k_m ^ -2.0) * sqrt(2.0))) ^ 2.0;
	else
		tmp = Float64(Float64(Float64((l ^ 2.0) / (k_m ^ 2.0)) / t_m) * -0.3333333333333333);
	end
	return Float64(t_s * tmp)
end

MATLAB

k_m = abs(k);
t_m = abs(t);
t_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, t_m, l, k_m)
	tmp = 0.0;
	if (k_m <= 9.6e+82)
		tmp = ((l / sqrt(t_m)) * ((k_m ^ -2.0) * sqrt(2.0))) ^ 2.0;
	else
		tmp = (((l ^ 2.0) / (k_m ^ 2.0)) / t_m) * -0.3333333333333333;
	end
	tmp_2 = t_s * tmp;
end

Wolfram

k_m = N[Abs[k], $MachinePrecision]
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$95$m_] := N[(t$95$s * If[LessEqual[k$95$m, 9.6e+82], N[Power[N[(N[(l / N[Sqrt[t$95$m], $MachinePrecision]), $MachinePrecision] * N[(N[Power[k$95$m, -2.0], $MachinePrecision] * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision], N[(N[(N[(N[Power[l, 2.0], $MachinePrecision] / N[Power[k$95$m, 2.0], $MachinePrecision]), $MachinePrecision] / t$95$m), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 5: 71.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} k_m = \left|k\right| \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;k_m \leq 9.6 \cdot 10^{+82}:\\ \;\;\;\;2 \cdot {\left(\frac{\ell}{\sqrt{t_m} \cdot {k_m}^{2}}\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{\ell}^{2}}{{k_m}^{2}}}{t_m} \cdot -0.3333333333333333\\ \end{array} \end{array} \]

FPCore

k_m = (fabs.f64 k)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k_m)
 :precision binary64
 (*
  t_s
  (if (<= k_m 9.6e+82)
    (* 2.0 (pow (/ l (* (sqrt t_m) (pow k_m 2.0))) 2.0))
    (* (/ (/ (pow l 2.0) (pow k_m 2.0)) t_m) -0.3333333333333333))))

C

k_m = fabs(k);
t_m = fabs(t);
t_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k_m) {
	double tmp;
	if (k_m <= 9.6e+82) {
		tmp = 2.0 * pow((l / (sqrt(t_m) * pow(k_m, 2.0))), 2.0);
	} else {
		tmp = ((pow(l, 2.0) / pow(k_m, 2.0)) / t_m) * -0.3333333333333333;
	}
	return t_s * tmp;
}

Fortran

k_m = abs(k)
t_m = abs(t)
t_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k_m
    real(8) :: tmp
    if (k_m <= 9.6d+82) then
        tmp = 2.0d0 * ((l / (sqrt(t_m) * (k_m ** 2.0d0))) ** 2.0d0)
    else
        tmp = (((l ** 2.0d0) / (k_m ** 2.0d0)) / t_m) * (-0.3333333333333333d0)
    end if
    code = t_s * tmp
end function

Java

k_m = Math.abs(k);
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_m) {
	double tmp;
	if (k_m <= 9.6e+82) {
		tmp = 2.0 * Math.pow((l / (Math.sqrt(t_m) * Math.pow(k_m, 2.0))), 2.0);
	} else {
		tmp = ((Math.pow(l, 2.0) / Math.pow(k_m, 2.0)) / t_m) * -0.3333333333333333;
	}
	return t_s * tmp;
}

Python

k_m = math.fabs(k)
t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k_m):
	tmp = 0
	if k_m <= 9.6e+82:
		tmp = 2.0 * math.pow((l / (math.sqrt(t_m) * math.pow(k_m, 2.0))), 2.0)
	else:
		tmp = ((math.pow(l, 2.0) / math.pow(k_m, 2.0)) / t_m) * -0.3333333333333333
	return t_s * tmp

Julia

k_m = abs(k)
t_m = abs(t)
t_s = copysign(1.0, t)
function code(t_s, t_m, l, k_m)
	tmp = 0.0
	if (k_m <= 9.6e+82)
		tmp = Float64(2.0 * (Float64(l / Float64(sqrt(t_m) * (k_m ^ 2.0))) ^ 2.0));
	else
		tmp = Float64(Float64(Float64((l ^ 2.0) / (k_m ^ 2.0)) / t_m) * -0.3333333333333333);
	end
	return Float64(t_s * tmp)
end

MATLAB

k_m = abs(k);
t_m = abs(t);
t_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, t_m, l, k_m)
	tmp = 0.0;
	if (k_m <= 9.6e+82)
		tmp = 2.0 * ((l / (sqrt(t_m) * (k_m ^ 2.0))) ^ 2.0);
	else
		tmp = (((l ^ 2.0) / (k_m ^ 2.0)) / t_m) * -0.3333333333333333;
	end
	tmp_2 = t_s * tmp;
end

Wolfram

k_m = N[Abs[k], $MachinePrecision]
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$95$m_] := N[(t$95$s * If[LessEqual[k$95$m, 9.6e+82], N[(2.0 * N[Power[N[(l / N[(N[Sqrt[t$95$m], $MachinePrecision] * N[Power[k$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[Power[l, 2.0], $MachinePrecision] / N[Power[k$95$m, 2.0], $MachinePrecision]), $MachinePrecision] / t$95$m), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 6: 61.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} k_m = \left|k\right| \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;k_m \leq 1.9 \cdot 10^{+78}:\\ \;\;\;\;2 \cdot \frac{{\ell}^{2}}{t_m \cdot {k_m}^{4}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{\ell}^{2}}{{k_m}^{2}}}{t_m} \cdot -0.3333333333333333\\ \end{array} \end{array} \]

FPCore

k_m = (fabs.f64 k)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k_m)
 :precision binary64
 (*
  t_s
  (if (<= k_m 1.9e+78)
    (* 2.0 (/ (pow l 2.0) (* t_m (pow k_m 4.0))))
    (* (/ (/ (pow l 2.0) (pow k_m 2.0)) t_m) -0.3333333333333333))))

C

k_m = fabs(k);
t_m = fabs(t);
t_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k_m) {
	double tmp;
	if (k_m <= 1.9e+78) {
		tmp = 2.0 * (pow(l, 2.0) / (t_m * pow(k_m, 4.0)));
	} else {
		tmp = ((pow(l, 2.0) / pow(k_m, 2.0)) / t_m) * -0.3333333333333333;
	}
	return t_s * tmp;
}

Fortran

k_m = abs(k)
t_m = abs(t)
t_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k_m
    real(8) :: tmp
    if (k_m <= 1.9d+78) then
        tmp = 2.0d0 * ((l ** 2.0d0) / (t_m * (k_m ** 4.0d0)))
    else
        tmp = (((l ** 2.0d0) / (k_m ** 2.0d0)) / t_m) * (-0.3333333333333333d0)
    end if
    code = t_s * tmp
end function

Java

k_m = Math.abs(k);
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_m) {
	double tmp;
	if (k_m <= 1.9e+78) {
		tmp = 2.0 * (Math.pow(l, 2.0) / (t_m * Math.pow(k_m, 4.0)));
	} else {
		tmp = ((Math.pow(l, 2.0) / Math.pow(k_m, 2.0)) / t_m) * -0.3333333333333333;
	}
	return t_s * tmp;
}

Python

k_m = math.fabs(k)
t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k_m):
	tmp = 0
	if k_m <= 1.9e+78:
		tmp = 2.0 * (math.pow(l, 2.0) / (t_m * math.pow(k_m, 4.0)))
	else:
		tmp = ((math.pow(l, 2.0) / math.pow(k_m, 2.0)) / t_m) * -0.3333333333333333
	return t_s * tmp

Julia

k_m = abs(k)
t_m = abs(t)
t_s = copysign(1.0, t)
function code(t_s, t_m, l, k_m)
	tmp = 0.0
	if (k_m <= 1.9e+78)
		tmp = Float64(2.0 * Float64((l ^ 2.0) / Float64(t_m * (k_m ^ 4.0))));
	else
		tmp = Float64(Float64(Float64((l ^ 2.0) / (k_m ^ 2.0)) / t_m) * -0.3333333333333333);
	end
	return Float64(t_s * tmp)
end

MATLAB

k_m = abs(k);
t_m = abs(t);
t_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, t_m, l, k_m)
	tmp = 0.0;
	if (k_m <= 1.9e+78)
		tmp = 2.0 * ((l ^ 2.0) / (t_m * (k_m ^ 4.0)));
	else
		tmp = (((l ^ 2.0) / (k_m ^ 2.0)) / t_m) * -0.3333333333333333;
	end
	tmp_2 = t_s * tmp;
end

Wolfram

k_m = N[Abs[k], $MachinePrecision]
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$95$m_] := N[(t$95$s * If[LessEqual[k$95$m, 1.9e+78], N[(2.0 * N[(N[Power[l, 2.0], $MachinePrecision] / N[(t$95$m * N[Power[k$95$m, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[Power[l, 2.0], $MachinePrecision] / N[Power[k$95$m, 2.0], $MachinePrecision]), $MachinePrecision] / t$95$m), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 7: 61.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} k_m = \left|k\right| \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \begin{array}{l} \mathbf{if}\;k_m \leq 1.9 \cdot 10^{+78}:\\ \;\;\;\;\frac{2 \cdot {\ell}^{2}}{t_m \cdot {k_m}^{4}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{\ell}^{2}}{{k_m}^{2}}}{t_m} \cdot -0.3333333333333333\\ \end{array} \end{array} \]

FPCore

k_m = (fabs.f64 k)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k_m)
 :precision binary64
 (*
  t_s
  (if (<= k_m 1.9e+78)
    (/ (* 2.0 (pow l 2.0)) (* t_m (pow k_m 4.0)))
    (* (/ (/ (pow l 2.0) (pow k_m 2.0)) t_m) -0.3333333333333333))))

C

k_m = fabs(k);
t_m = fabs(t);
t_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k_m) {
	double tmp;
	if (k_m <= 1.9e+78) {
		tmp = (2.0 * pow(l, 2.0)) / (t_m * pow(k_m, 4.0));
	} else {
		tmp = ((pow(l, 2.0) / pow(k_m, 2.0)) / t_m) * -0.3333333333333333;
	}
	return t_s * tmp;
}

Fortran

k_m = abs(k)
t_m = abs(t)
t_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k_m
    real(8) :: tmp
    if (k_m <= 1.9d+78) then
        tmp = (2.0d0 * (l ** 2.0d0)) / (t_m * (k_m ** 4.0d0))
    else
        tmp = (((l ** 2.0d0) / (k_m ** 2.0d0)) / t_m) * (-0.3333333333333333d0)
    end if
    code = t_s * tmp
end function

Java

k_m = Math.abs(k);
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_m) {
	double tmp;
	if (k_m <= 1.9e+78) {
		tmp = (2.0 * Math.pow(l, 2.0)) / (t_m * Math.pow(k_m, 4.0));
	} else {
		tmp = ((Math.pow(l, 2.0) / Math.pow(k_m, 2.0)) / t_m) * -0.3333333333333333;
	}
	return t_s * tmp;
}

Python

k_m = math.fabs(k)
t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k_m):
	tmp = 0
	if k_m <= 1.9e+78:
		tmp = (2.0 * math.pow(l, 2.0)) / (t_m * math.pow(k_m, 4.0))
	else:
		tmp = ((math.pow(l, 2.0) / math.pow(k_m, 2.0)) / t_m) * -0.3333333333333333
	return t_s * tmp

Julia

k_m = abs(k)
t_m = abs(t)
t_s = copysign(1.0, t)
function code(t_s, t_m, l, k_m)
	tmp = 0.0
	if (k_m <= 1.9e+78)
		tmp = Float64(Float64(2.0 * (l ^ 2.0)) / Float64(t_m * (k_m ^ 4.0)));
	else
		tmp = Float64(Float64(Float64((l ^ 2.0) / (k_m ^ 2.0)) / t_m) * -0.3333333333333333);
	end
	return Float64(t_s * tmp)
end

MATLAB

k_m = abs(k);
t_m = abs(t);
t_s = sign(t) * abs(1.0);
function tmp_2 = code(t_s, t_m, l, k_m)
	tmp = 0.0;
	if (k_m <= 1.9e+78)
		tmp = (2.0 * (l ^ 2.0)) / (t_m * (k_m ^ 4.0));
	else
		tmp = (((l ^ 2.0) / (k_m ^ 2.0)) / t_m) * -0.3333333333333333;
	end
	tmp_2 = t_s * tmp;
end

Wolfram

k_m = N[Abs[k], $MachinePrecision]
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$95$m_] := N[(t$95$s * If[LessEqual[k$95$m, 1.9e+78], N[(N[(2.0 * N[Power[l, 2.0], $MachinePrecision]), $MachinePrecision] / N[(t$95$m * N[Power[k$95$m, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[Power[l, 2.0], $MachinePrecision] / N[Power[k$95$m, 2.0], $MachinePrecision]), $MachinePrecision] / t$95$m), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 8: 61.1% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

k_m = Math.abs(k);
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_m) {
	return t_s * (2.0 * (Math.pow(l, 2.0) / (t_m * Math.pow(k_m, 4.0))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

k_m = N[Abs[k], $MachinePrecision]
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$95$m_] := N[(t$95$s * N[(2.0 * N[(N[Power[l, 2.0], $MachinePrecision] / N[(t$95$m * N[Power[k$95$m, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 9: 29.6% accurate, 4.0× speedup

Math

\[\begin{array}{l} k_m = \left|k\right| \\ t_m = \left|t\right| \\ t_s = \mathsf{copysign}\left(1, t\right) \\ t_s \cdot \left(2 \cdot \frac{{\ell}^{2}}{0}\right) \end{array} \]

FPCore

k_m = (fabs.f64 k)
t_m = (fabs.f64 t)
t_s = (copysign.f64 1 t)
(FPCore (t_s t_m l k_m)
 :precision binary64
 (* t_s (* 2.0 (/ (pow l 2.0) 0.0))))

C

k_m = fabs(k);
t_m = fabs(t);
t_s = copysign(1.0, t);
double code(double t_s, double t_m, double l, double k_m) {
	return t_s * (2.0 * (pow(l, 2.0) / 0.0));
}

Fortran

k_m = abs(k)
t_m = abs(t)
t_s = copysign(1.0d0, t)
real(8) function code(t_s, t_m, l, k_m)
    real(8), intent (in) :: t_s
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: k_m
    code = t_s * (2.0d0 * ((l ** 2.0d0) / 0.0d0))
end function

Java

k_m = Math.abs(k);
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_m) {
	return t_s * (2.0 * (Math.pow(l, 2.0) / 0.0));
}

Python

k_m = math.fabs(k)
t_m = math.fabs(t)
t_s = math.copysign(1.0, t)
def code(t_s, t_m, l, k_m):
	return t_s * (2.0 * (math.pow(l, 2.0) / 0.0))

Julia

k_m = abs(k)
t_m = abs(t)
t_s = copysign(1.0, t)
function code(t_s, t_m, l, k_m)
	return Float64(t_s * Float64(2.0 * Float64((l ^ 2.0) / 0.0)))
end

MATLAB

k_m = abs(k);
t_m = abs(t);
t_s = sign(t) * abs(1.0);
function tmp = code(t_s, t_m, l, k_m)
	tmp = t_s * (2.0 * ((l ^ 2.0) / 0.0));
end

Wolfram

k_m = N[Abs[k], $MachinePrecision]
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$95$m_] := N[(t$95$s * N[(2.0 * N[(N[Power[l, 2.0], $MachinePrecision] / 0.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Reproduce

herbie shell --seed 2023348 
(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))))