Toniolo and Linder, Equation (13)

Percentage Accurate: 50.7% → 64.2%

Time: 33.5s

Alternatives: 22

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)} \end{array} \]

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (sqrt
  (*
   (* (* 2.0 n) U)
   (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	return sqrt((((2.0 * n) * U) * ((t - (2.0 * ((l * l) / Om))) - ((n * pow((l / Om), 2.0)) * (U - U_42_)))));
}

Fortran

real(8) function code(n, u, t, l, om, u_42)
    real(8), intent (in) :: n
    real(8), intent (in) :: u
    real(8), intent (in) :: t
    real(8), intent (in) :: l
    real(8), intent (in) :: om
    real(8), intent (in) :: u_42
    code = sqrt((((2.0d0 * n) * u) * ((t - (2.0d0 * ((l * l) / om))) - ((n * ((l / om) ** 2.0d0)) * (u - u_42)))))
end function

Java

public static double code(double n, double U, double t, double l, double Om, double U_42_) {
	return Math.sqrt((((2.0 * n) * U) * ((t - (2.0 * ((l * l) / Om))) - ((n * Math.pow((l / Om), 2.0)) * (U - U_42_)))));
}

Python

def code(n, U, t, l, Om, U_42_):
	return math.sqrt((((2.0 * n) * U) * ((t - (2.0 * ((l * l) / Om))) - ((n * math.pow((l / Om), 2.0)) * (U - U_42_)))))

Julia

function code(n, U, t, l, Om, U_42_)
	return sqrt(Float64(Float64(Float64(2.0 * n) * U) * Float64(Float64(t - Float64(2.0 * Float64(Float64(l * l) / Om))) - Float64(Float64(n * (Float64(l / Om) ^ 2.0)) * Float64(U - U_42_)))))
end

MATLAB

function tmp = code(n, U, t, l, Om, U_42_)
	tmp = sqrt((((2.0 * n) * U) * ((t - (2.0 * ((l * l) / Om))) - ((n * ((l / Om) ^ 2.0)) * (U - U_42_)))));
end

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := N[Sqrt[N[(N[(N[(2.0 * n), $MachinePrecision] * U), $MachinePrecision] * N[(N[(t - N[(2.0 * N[(N[(l * l), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(n * N[Power[N[(l / Om), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(U - U$42$), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Initial Program: 50.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) - \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U - U*\right)\right)} \end{array} \]

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (sqrt
  (*
   (* (* 2.0 n) U)
   (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	return sqrt((((2.0 * n) * U) * ((t - (2.0 * ((l * l) / Om))) - ((n * pow((l / Om), 2.0)) * (U - U_42_)))));
}

Fortran

real(8) function code(n, u, t, l, om, u_42)
    real(8), intent (in) :: n
    real(8), intent (in) :: u
    real(8), intent (in) :: t
    real(8), intent (in) :: l
    real(8), intent (in) :: om
    real(8), intent (in) :: u_42
    code = sqrt((((2.0d0 * n) * u) * ((t - (2.0d0 * ((l * l) / om))) - ((n * ((l / om) ** 2.0d0)) * (u - u_42)))))
end function

Java

public static double code(double n, double U, double t, double l, double Om, double U_42_) {
	return Math.sqrt((((2.0 * n) * U) * ((t - (2.0 * ((l * l) / Om))) - ((n * Math.pow((l / Om), 2.0)) * (U - U_42_)))));
}

Python

def code(n, U, t, l, Om, U_42_):
	return math.sqrt((((2.0 * n) * U) * ((t - (2.0 * ((l * l) / Om))) - ((n * math.pow((l / Om), 2.0)) * (U - U_42_)))))

Julia

function code(n, U, t, l, Om, U_42_)
	return sqrt(Float64(Float64(Float64(2.0 * n) * U) * Float64(Float64(t - Float64(2.0 * Float64(Float64(l * l) / Om))) - Float64(Float64(n * (Float64(l / Om) ^ 2.0)) * Float64(U - U_42_)))))
end

MATLAB

function tmp = code(n, U, t, l, Om, U_42_)
	tmp = sqrt((((2.0 * n) * U) * ((t - (2.0 * ((l * l) / Om))) - ((n * ((l / Om) ^ 2.0)) * (U - U_42_)))));
end

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := N[Sqrt[N[(N[(N[(2.0 * n), $MachinePrecision] * U), $MachinePrecision] * N[(N[(t - N[(2.0 * N[(N[(l * l), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(n * N[Power[N[(l / Om), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(U - U$42$), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Alternative 1: 64.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} t_1 := \left(n \cdot U\right) \cdot \left(\frac{n}{{Om}^{2}} \cdot \left(U* - U\right) - \frac{2}{Om}\right)\\ t_2 := \left(n \cdot {\left(\frac{l_m}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\\ t_3 := \left(2 \cdot n\right) \cdot U\\ t_4 := t_3 \cdot \left(\left(t - 2 \cdot \frac{l_m \cdot l_m}{Om}\right) + t_2\right)\\ \mathbf{if}\;t_4 \leq 2 \cdot 10^{-293}:\\ \;\;\;\;\sqrt{2 \cdot n} \cdot \sqrt{-2 \cdot \frac{U \cdot {l_m}^{2}}{Om} + U \cdot t}\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+299}:\\ \;\;\;\;\sqrt{t_3 \cdot \left(\left(t - 2 \cdot \left(l_m \cdot \frac{l_m}{Om}\right)\right) + t_2\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{t_1} \cdot \sqrt[3]{\sqrt{t_1}}\right) \cdot \left(l_m \cdot \sqrt{2}\right)\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (let* ((t_1 (* (* n U) (- (* (/ n (pow Om 2.0)) (- U* U)) (/ 2.0 Om))))
        (t_2 (* (* n (pow (/ l_m Om) 2.0)) (- U* U)))
        (t_3 (* (* 2.0 n) U))
        (t_4 (* t_3 (+ (- t (* 2.0 (/ (* l_m l_m) Om))) t_2))))
   (if (<= t_4 2e-293)
     (*
      (sqrt (* 2.0 n))
      (sqrt (+ (* -2.0 (/ (* U (pow l_m 2.0)) Om)) (* U t))))
     (if (<= t_4 2e+299)
       (sqrt (* t_3 (+ (- t (* 2.0 (* l_m (/ l_m Om)))) t_2)))
       (* (* (cbrt t_1) (cbrt (sqrt t_1))) (* l_m (sqrt 2.0)))))))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double t_1 = (n * U) * (((n / pow(Om, 2.0)) * (U_42_ - U)) - (2.0 / Om));
	double t_2 = (n * pow((l_m / Om), 2.0)) * (U_42_ - U);
	double t_3 = (2.0 * n) * U;
	double t_4 = t_3 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_2);
	double tmp;
	if (t_4 <= 2e-293) {
		tmp = sqrt((2.0 * n)) * sqrt(((-2.0 * ((U * pow(l_m, 2.0)) / Om)) + (U * t)));
	} else if (t_4 <= 2e+299) {
		tmp = sqrt((t_3 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_2)));
	} else {
		tmp = (cbrt(t_1) * cbrt(sqrt(t_1))) * (l_m * sqrt(2.0));
	}
	return tmp;
}

Java

l_m = Math.abs(l);
public static double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double t_1 = (n * U) * (((n / Math.pow(Om, 2.0)) * (U_42_ - U)) - (2.0 / Om));
	double t_2 = (n * Math.pow((l_m / Om), 2.0)) * (U_42_ - U);
	double t_3 = (2.0 * n) * U;
	double t_4 = t_3 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_2);
	double tmp;
	if (t_4 <= 2e-293) {
		tmp = Math.sqrt((2.0 * n)) * Math.sqrt(((-2.0 * ((U * Math.pow(l_m, 2.0)) / Om)) + (U * t)));
	} else if (t_4 <= 2e+299) {
		tmp = Math.sqrt((t_3 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_2)));
	} else {
		tmp = (Math.cbrt(t_1) * Math.cbrt(Math.sqrt(t_1))) * (l_m * Math.sqrt(2.0));
	}
	return tmp;
}

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	t_1 = Float64(Float64(n * U) * Float64(Float64(Float64(n / (Om ^ 2.0)) * Float64(U_42_ - U)) - Float64(2.0 / Om)))
	t_2 = Float64(Float64(n * (Float64(l_m / Om) ^ 2.0)) * Float64(U_42_ - U))
	t_3 = Float64(Float64(2.0 * n) * U)
	t_4 = Float64(t_3 * Float64(Float64(t - Float64(2.0 * Float64(Float64(l_m * l_m) / Om))) + t_2))
	tmp = 0.0
	if (t_4 <= 2e-293)
		tmp = Float64(sqrt(Float64(2.0 * n)) * sqrt(Float64(Float64(-2.0 * Float64(Float64(U * (l_m ^ 2.0)) / Om)) + Float64(U * t))));
	elseif (t_4 <= 2e+299)
		tmp = sqrt(Float64(t_3 * Float64(Float64(t - Float64(2.0 * Float64(l_m * Float64(l_m / Om)))) + t_2)));
	else
		tmp = Float64(Float64(cbrt(t_1) * cbrt(sqrt(t_1))) * Float64(l_m * sqrt(2.0)));
	end
	return tmp
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := Block[{t$95$1 = N[(N[(n * U), $MachinePrecision] * N[(N[(N[(n / N[Power[Om, 2.0], $MachinePrecision]), $MachinePrecision] * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision] - N[(2.0 / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(n * N[Power[N[(l$95$m / Om), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(2.0 * n), $MachinePrecision] * U), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 * N[(N[(t - N[(2.0 * N[(N[(l$95$m * l$95$m), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, 2e-293], N[(N[Sqrt[N[(2.0 * n), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(N[(-2.0 * N[(N[(U * N[Power[l$95$m, 2.0], $MachinePrecision]), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision] + N[(U * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 2e+299], N[Sqrt[N[(t$95$3 * N[(N[(t - N[(2.0 * N[(l$95$m * N[(l$95$m / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(N[(N[Power[t$95$1, 1/3], $MachinePrecision] * N[Power[N[Sqrt[t$95$1], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision] * N[(l$95$m * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

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

Alternative 2: 64.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} t_1 := \left(n \cdot {\left(\frac{l_m}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\\ t_2 := \left(2 \cdot n\right) \cdot U\\ t_3 := t_2 \cdot \left(\left(t - 2 \cdot \frac{l_m \cdot l_m}{Om}\right) + t_1\right)\\ \mathbf{if}\;t_3 \leq 2 \cdot 10^{-293}:\\ \;\;\;\;\sqrt{2 \cdot n} \cdot \sqrt{-2 \cdot \frac{U \cdot {l_m}^{2}}{Om} + U \cdot t}\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+299}:\\ \;\;\;\;\sqrt{t_2 \cdot \left(\left(t - 2 \cdot \left(l_m \cdot \frac{l_m}{Om}\right)\right) + t_1\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(l_m \cdot \sqrt{2}\right) \cdot {\left(\sqrt[3]{\sqrt{\left(n \cdot U\right) \cdot \left(\frac{n}{{Om}^{2}} \cdot \left(U* - U\right) - \frac{2}{Om}\right)}}\right)}^{3}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (let* ((t_1 (* (* n (pow (/ l_m Om) 2.0)) (- U* U)))
        (t_2 (* (* 2.0 n) U))
        (t_3 (* t_2 (+ (- t (* 2.0 (/ (* l_m l_m) Om))) t_1))))
   (if (<= t_3 2e-293)
     (*
      (sqrt (* 2.0 n))
      (sqrt (+ (* -2.0 (/ (* U (pow l_m 2.0)) Om)) (* U t))))
     (if (<= t_3 2e+299)
       (sqrt (* t_2 (+ (- t (* 2.0 (* l_m (/ l_m Om)))) t_1)))
       (*
        (* l_m (sqrt 2.0))
        (pow
         (cbrt
          (sqrt (* (* n U) (- (* (/ n (pow Om 2.0)) (- U* U)) (/ 2.0 Om)))))
         3.0))))))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double t_1 = (n * pow((l_m / Om), 2.0)) * (U_42_ - U);
	double t_2 = (2.0 * n) * U;
	double t_3 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_1);
	double tmp;
	if (t_3 <= 2e-293) {
		tmp = sqrt((2.0 * n)) * sqrt(((-2.0 * ((U * pow(l_m, 2.0)) / Om)) + (U * t)));
	} else if (t_3 <= 2e+299) {
		tmp = sqrt((t_2 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_1)));
	} else {
		tmp = (l_m * sqrt(2.0)) * pow(cbrt(sqrt(((n * U) * (((n / pow(Om, 2.0)) * (U_42_ - U)) - (2.0 / Om))))), 3.0);
	}
	return tmp;
}

Java

l_m = Math.abs(l);
public static double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double t_1 = (n * Math.pow((l_m / Om), 2.0)) * (U_42_ - U);
	double t_2 = (2.0 * n) * U;
	double t_3 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_1);
	double tmp;
	if (t_3 <= 2e-293) {
		tmp = Math.sqrt((2.0 * n)) * Math.sqrt(((-2.0 * ((U * Math.pow(l_m, 2.0)) / Om)) + (U * t)));
	} else if (t_3 <= 2e+299) {
		tmp = Math.sqrt((t_2 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_1)));
	} else {
		tmp = (l_m * Math.sqrt(2.0)) * Math.pow(Math.cbrt(Math.sqrt(((n * U) * (((n / Math.pow(Om, 2.0)) * (U_42_ - U)) - (2.0 / Om))))), 3.0);
	}
	return tmp;
}

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	t_1 = Float64(Float64(n * (Float64(l_m / Om) ^ 2.0)) * Float64(U_42_ - U))
	t_2 = Float64(Float64(2.0 * n) * U)
	t_3 = Float64(t_2 * Float64(Float64(t - Float64(2.0 * Float64(Float64(l_m * l_m) / Om))) + t_1))
	tmp = 0.0
	if (t_3 <= 2e-293)
		tmp = Float64(sqrt(Float64(2.0 * n)) * sqrt(Float64(Float64(-2.0 * Float64(Float64(U * (l_m ^ 2.0)) / Om)) + Float64(U * t))));
	elseif (t_3 <= 2e+299)
		tmp = sqrt(Float64(t_2 * Float64(Float64(t - Float64(2.0 * Float64(l_m * Float64(l_m / Om)))) + t_1)));
	else
		tmp = Float64(Float64(l_m * sqrt(2.0)) * (cbrt(sqrt(Float64(Float64(n * U) * Float64(Float64(Float64(n / (Om ^ 2.0)) * Float64(U_42_ - U)) - Float64(2.0 / Om))))) ^ 3.0));
	end
	return tmp
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := Block[{t$95$1 = N[(N[(n * N[Power[N[(l$95$m / Om), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 * n), $MachinePrecision] * U), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 * N[(N[(t - N[(2.0 * N[(N[(l$95$m * l$95$m), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, 2e-293], N[(N[Sqrt[N[(2.0 * n), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(N[(-2.0 * N[(N[(U * N[Power[l$95$m, 2.0], $MachinePrecision]), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision] + N[(U * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+299], N[Sqrt[N[(t$95$2 * N[(N[(t - N[(2.0 * N[(l$95$m * N[(l$95$m / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(N[(l$95$m * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision] * N[Power[N[Power[N[Sqrt[N[(N[(n * U), $MachinePrecision] * N[(N[(N[(n / N[Power[Om, 2.0], $MachinePrecision]), $MachinePrecision] * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision] - N[(2.0 / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 3: 63.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} t_1 := \left(n \cdot {\left(\frac{l_m}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\\ t_2 := \left(2 \cdot n\right) \cdot U\\ t_3 := t_2 \cdot \left(\left(t - 2 \cdot \frac{l_m \cdot l_m}{Om}\right) + t_1\right)\\ \mathbf{if}\;t_3 \leq 2 \cdot 10^{-293}:\\ \;\;\;\;\sqrt{2 \cdot n} \cdot \sqrt{-2 \cdot \frac{U \cdot {l_m}^{2}}{Om} + U \cdot t}\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+299}:\\ \;\;\;\;\sqrt{t_2 \cdot \left(\left(t - 2 \cdot \left(l_m \cdot \frac{l_m}{Om}\right)\right) + t_1\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(l_m \cdot \sqrt{2}\right) \cdot \sqrt{U \cdot \left(n \cdot \left(\frac{n}{\frac{{Om}^{2}}{U*}} - \frac{2}{Om}\right)\right)}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (let* ((t_1 (* (* n (pow (/ l_m Om) 2.0)) (- U* U)))
        (t_2 (* (* 2.0 n) U))
        (t_3 (* t_2 (+ (- t (* 2.0 (/ (* l_m l_m) Om))) t_1))))
   (if (<= t_3 2e-293)
     (*
      (sqrt (* 2.0 n))
      (sqrt (+ (* -2.0 (/ (* U (pow l_m 2.0)) Om)) (* U t))))
     (if (<= t_3 2e+299)
       (sqrt (* t_2 (+ (- t (* 2.0 (* l_m (/ l_m Om)))) t_1)))
       (*
        (* l_m (sqrt 2.0))
        (sqrt (* U (* n (- (/ n (/ (pow Om 2.0) U*)) (/ 2.0 Om))))))))))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double t_1 = (n * pow((l_m / Om), 2.0)) * (U_42_ - U);
	double t_2 = (2.0 * n) * U;
	double t_3 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_1);
	double tmp;
	if (t_3 <= 2e-293) {
		tmp = sqrt((2.0 * n)) * sqrt(((-2.0 * ((U * pow(l_m, 2.0)) / Om)) + (U * t)));
	} else if (t_3 <= 2e+299) {
		tmp = sqrt((t_2 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_1)));
	} else {
		tmp = (l_m * sqrt(2.0)) * sqrt((U * (n * ((n / (pow(Om, 2.0) / U_42_)) - (2.0 / Om)))));
	}
	return tmp;
}

Fortran

l_m = abs(l)
real(8) function code(n, u, t, l_m, om, u_42)
    real(8), intent (in) :: n
    real(8), intent (in) :: u
    real(8), intent (in) :: t
    real(8), intent (in) :: l_m
    real(8), intent (in) :: om
    real(8), intent (in) :: u_42
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (n * ((l_m / om) ** 2.0d0)) * (u_42 - u)
    t_2 = (2.0d0 * n) * u
    t_3 = t_2 * ((t - (2.0d0 * ((l_m * l_m) / om))) + t_1)
    if (t_3 <= 2d-293) then
        tmp = sqrt((2.0d0 * n)) * sqrt((((-2.0d0) * ((u * (l_m ** 2.0d0)) / om)) + (u * t)))
    else if (t_3 <= 2d+299) then
        tmp = sqrt((t_2 * ((t - (2.0d0 * (l_m * (l_m / om)))) + t_1)))
    else
        tmp = (l_m * sqrt(2.0d0)) * sqrt((u * (n * ((n / ((om ** 2.0d0) / u_42)) - (2.0d0 / om)))))
    end if
    code = tmp
end function

Java

l_m = Math.abs(l);
public static double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double t_1 = (n * Math.pow((l_m / Om), 2.0)) * (U_42_ - U);
	double t_2 = (2.0 * n) * U;
	double t_3 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_1);
	double tmp;
	if (t_3 <= 2e-293) {
		tmp = Math.sqrt((2.0 * n)) * Math.sqrt(((-2.0 * ((U * Math.pow(l_m, 2.0)) / Om)) + (U * t)));
	} else if (t_3 <= 2e+299) {
		tmp = Math.sqrt((t_2 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_1)));
	} else {
		tmp = (l_m * Math.sqrt(2.0)) * Math.sqrt((U * (n * ((n / (Math.pow(Om, 2.0) / U_42_)) - (2.0 / Om)))));
	}
	return tmp;
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	t_1 = (n * math.pow((l_m / Om), 2.0)) * (U_42_ - U)
	t_2 = (2.0 * n) * U
	t_3 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_1)
	tmp = 0
	if t_3 <= 2e-293:
		tmp = math.sqrt((2.0 * n)) * math.sqrt(((-2.0 * ((U * math.pow(l_m, 2.0)) / Om)) + (U * t)))
	elif t_3 <= 2e+299:
		tmp = math.sqrt((t_2 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_1)))
	else:
		tmp = (l_m * math.sqrt(2.0)) * math.sqrt((U * (n * ((n / (math.pow(Om, 2.0) / U_42_)) - (2.0 / Om)))))
	return tmp

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	t_1 = Float64(Float64(n * (Float64(l_m / Om) ^ 2.0)) * Float64(U_42_ - U))
	t_2 = Float64(Float64(2.0 * n) * U)
	t_3 = Float64(t_2 * Float64(Float64(t - Float64(2.0 * Float64(Float64(l_m * l_m) / Om))) + t_1))
	tmp = 0.0
	if (t_3 <= 2e-293)
		tmp = Float64(sqrt(Float64(2.0 * n)) * sqrt(Float64(Float64(-2.0 * Float64(Float64(U * (l_m ^ 2.0)) / Om)) + Float64(U * t))));
	elseif (t_3 <= 2e+299)
		tmp = sqrt(Float64(t_2 * Float64(Float64(t - Float64(2.0 * Float64(l_m * Float64(l_m / Om)))) + t_1)));
	else
		tmp = Float64(Float64(l_m * sqrt(2.0)) * sqrt(Float64(U * Float64(n * Float64(Float64(n / Float64((Om ^ 2.0) / U_42_)) - Float64(2.0 / Om))))));
	end
	return tmp
end

MATLAB

l_m = abs(l);
function tmp_2 = code(n, U, t, l_m, Om, U_42_)
	t_1 = (n * ((l_m / Om) ^ 2.0)) * (U_42_ - U);
	t_2 = (2.0 * n) * U;
	t_3 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_1);
	tmp = 0.0;
	if (t_3 <= 2e-293)
		tmp = sqrt((2.0 * n)) * sqrt(((-2.0 * ((U * (l_m ^ 2.0)) / Om)) + (U * t)));
	elseif (t_3 <= 2e+299)
		tmp = sqrt((t_2 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_1)));
	else
		tmp = (l_m * sqrt(2.0)) * sqrt((U * (n * ((n / ((Om ^ 2.0) / U_42_)) - (2.0 / Om)))));
	end
	tmp_2 = tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := Block[{t$95$1 = N[(N[(n * N[Power[N[(l$95$m / Om), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 * n), $MachinePrecision] * U), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 * N[(N[(t - N[(2.0 * N[(N[(l$95$m * l$95$m), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, 2e-293], N[(N[Sqrt[N[(2.0 * n), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(N[(-2.0 * N[(N[(U * N[Power[l$95$m, 2.0], $MachinePrecision]), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision] + N[(U * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+299], N[Sqrt[N[(t$95$2 * N[(N[(t - N[(2.0 * N[(l$95$m * N[(l$95$m / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(N[(l$95$m * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(U * N[(n * N[(N[(n / N[(N[Power[Om, 2.0], $MachinePrecision] / U$42$), $MachinePrecision]), $MachinePrecision] - N[(2.0 / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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1. Add Preprocessing

Alternative 4: 64.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} t_1 := \left(n \cdot {\left(\frac{l_m}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\\ t_2 := \left(2 \cdot n\right) \cdot U\\ t_3 := t_2 \cdot \left(\left(t - 2 \cdot \frac{l_m \cdot l_m}{Om}\right) + t_1\right)\\ \mathbf{if}\;t_3 \leq 2 \cdot 10^{-293}:\\ \;\;\;\;\sqrt{2 \cdot n} \cdot \sqrt{-2 \cdot \frac{U \cdot {l_m}^{2}}{Om} + U \cdot t}\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+299}:\\ \;\;\;\;\sqrt{t_2 \cdot \left(\left(t - 2 \cdot \left(l_m \cdot \frac{l_m}{Om}\right)\right) + t_1\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(l_m \cdot \sqrt{2}\right) \cdot \sqrt{\left(n \cdot U\right) \cdot \left(\frac{n \cdot U*}{{Om}^{2}} - \frac{2}{Om}\right)}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (let* ((t_1 (* (* n (pow (/ l_m Om) 2.0)) (- U* U)))
        (t_2 (* (* 2.0 n) U))
        (t_3 (* t_2 (+ (- t (* 2.0 (/ (* l_m l_m) Om))) t_1))))
   (if (<= t_3 2e-293)
     (*
      (sqrt (* 2.0 n))
      (sqrt (+ (* -2.0 (/ (* U (pow l_m 2.0)) Om)) (* U t))))
     (if (<= t_3 2e+299)
       (sqrt (* t_2 (+ (- t (* 2.0 (* l_m (/ l_m Om)))) t_1)))
       (*
        (* l_m (sqrt 2.0))
        (sqrt (* (* n U) (- (/ (* n U*) (pow Om 2.0)) (/ 2.0 Om)))))))))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double t_1 = (n * pow((l_m / Om), 2.0)) * (U_42_ - U);
	double t_2 = (2.0 * n) * U;
	double t_3 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_1);
	double tmp;
	if (t_3 <= 2e-293) {
		tmp = sqrt((2.0 * n)) * sqrt(((-2.0 * ((U * pow(l_m, 2.0)) / Om)) + (U * t)));
	} else if (t_3 <= 2e+299) {
		tmp = sqrt((t_2 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_1)));
	} else {
		tmp = (l_m * sqrt(2.0)) * sqrt(((n * U) * (((n * U_42_) / pow(Om, 2.0)) - (2.0 / Om))));
	}
	return tmp;
}

Fortran

l_m = abs(l)
real(8) function code(n, u, t, l_m, om, u_42)
    real(8), intent (in) :: n
    real(8), intent (in) :: u
    real(8), intent (in) :: t
    real(8), intent (in) :: l_m
    real(8), intent (in) :: om
    real(8), intent (in) :: u_42
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (n * ((l_m / om) ** 2.0d0)) * (u_42 - u)
    t_2 = (2.0d0 * n) * u
    t_3 = t_2 * ((t - (2.0d0 * ((l_m * l_m) / om))) + t_1)
    if (t_3 <= 2d-293) then
        tmp = sqrt((2.0d0 * n)) * sqrt((((-2.0d0) * ((u * (l_m ** 2.0d0)) / om)) + (u * t)))
    else if (t_3 <= 2d+299) then
        tmp = sqrt((t_2 * ((t - (2.0d0 * (l_m * (l_m / om)))) + t_1)))
    else
        tmp = (l_m * sqrt(2.0d0)) * sqrt(((n * u) * (((n * u_42) / (om ** 2.0d0)) - (2.0d0 / om))))
    end if
    code = tmp
end function

Java

l_m = Math.abs(l);
public static double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double t_1 = (n * Math.pow((l_m / Om), 2.0)) * (U_42_ - U);
	double t_2 = (2.0 * n) * U;
	double t_3 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_1);
	double tmp;
	if (t_3 <= 2e-293) {
		tmp = Math.sqrt((2.0 * n)) * Math.sqrt(((-2.0 * ((U * Math.pow(l_m, 2.0)) / Om)) + (U * t)));
	} else if (t_3 <= 2e+299) {
		tmp = Math.sqrt((t_2 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_1)));
	} else {
		tmp = (l_m * Math.sqrt(2.0)) * Math.sqrt(((n * U) * (((n * U_42_) / Math.pow(Om, 2.0)) - (2.0 / Om))));
	}
	return tmp;
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	t_1 = (n * math.pow((l_m / Om), 2.0)) * (U_42_ - U)
	t_2 = (2.0 * n) * U
	t_3 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_1)
	tmp = 0
	if t_3 <= 2e-293:
		tmp = math.sqrt((2.0 * n)) * math.sqrt(((-2.0 * ((U * math.pow(l_m, 2.0)) / Om)) + (U * t)))
	elif t_3 <= 2e+299:
		tmp = math.sqrt((t_2 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_1)))
	else:
		tmp = (l_m * math.sqrt(2.0)) * math.sqrt(((n * U) * (((n * U_42_) / math.pow(Om, 2.0)) - (2.0 / Om))))
	return tmp

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	t_1 = Float64(Float64(n * (Float64(l_m / Om) ^ 2.0)) * Float64(U_42_ - U))
	t_2 = Float64(Float64(2.0 * n) * U)
	t_3 = Float64(t_2 * Float64(Float64(t - Float64(2.0 * Float64(Float64(l_m * l_m) / Om))) + t_1))
	tmp = 0.0
	if (t_3 <= 2e-293)
		tmp = Float64(sqrt(Float64(2.0 * n)) * sqrt(Float64(Float64(-2.0 * Float64(Float64(U * (l_m ^ 2.0)) / Om)) + Float64(U * t))));
	elseif (t_3 <= 2e+299)
		tmp = sqrt(Float64(t_2 * Float64(Float64(t - Float64(2.0 * Float64(l_m * Float64(l_m / Om)))) + t_1)));
	else
		tmp = Float64(Float64(l_m * sqrt(2.0)) * sqrt(Float64(Float64(n * U) * Float64(Float64(Float64(n * U_42_) / (Om ^ 2.0)) - Float64(2.0 / Om)))));
	end
	return tmp
end

MATLAB

l_m = abs(l);
function tmp_2 = code(n, U, t, l_m, Om, U_42_)
	t_1 = (n * ((l_m / Om) ^ 2.0)) * (U_42_ - U);
	t_2 = (2.0 * n) * U;
	t_3 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_1);
	tmp = 0.0;
	if (t_3 <= 2e-293)
		tmp = sqrt((2.0 * n)) * sqrt(((-2.0 * ((U * (l_m ^ 2.0)) / Om)) + (U * t)));
	elseif (t_3 <= 2e+299)
		tmp = sqrt((t_2 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_1)));
	else
		tmp = (l_m * sqrt(2.0)) * sqrt(((n * U) * (((n * U_42_) / (Om ^ 2.0)) - (2.0 / Om))));
	end
	tmp_2 = tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := Block[{t$95$1 = N[(N[(n * N[Power[N[(l$95$m / Om), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 * n), $MachinePrecision] * U), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 * N[(N[(t - N[(2.0 * N[(N[(l$95$m * l$95$m), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, 2e-293], N[(N[Sqrt[N[(2.0 * n), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(N[(-2.0 * N[(N[(U * N[Power[l$95$m, 2.0], $MachinePrecision]), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision] + N[(U * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+299], N[Sqrt[N[(t$95$2 * N[(N[(t - N[(2.0 * N[(l$95$m * N[(l$95$m / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(N[(l$95$m * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(N[(n * U), $MachinePrecision] * N[(N[(N[(n * U$42$), $MachinePrecision] / N[Power[Om, 2.0], $MachinePrecision]), $MachinePrecision] - N[(2.0 / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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1. Add Preprocessing

Alternative 5: 60.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} t_1 := \left(n \cdot {\left(\frac{l_m}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\\ t_2 := \left(2 \cdot n\right) \cdot U\\ t_3 := t_2 \cdot \left(\left(t - 2 \cdot \frac{l_m \cdot l_m}{Om}\right) + t_1\right)\\ \mathbf{if}\;t_3 \leq 2 \cdot 10^{-293}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(-2 \cdot \frac{U \cdot {l_m}^{2}}{Om} + U \cdot t\right)}\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;\sqrt{t_2 \cdot \left(\left(t - 2 \cdot \left(l_m \cdot \frac{l_m}{Om}\right)\right) + t_1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{l_m}{\frac{Om}{n \cdot \sqrt{2}}} \cdot \left(-\sqrt{U \cdot U*}\right)\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (let* ((t_1 (* (* n (pow (/ l_m Om) 2.0)) (- U* U)))
        (t_2 (* (* 2.0 n) U))
        (t_3 (* t_2 (+ (- t (* 2.0 (/ (* l_m l_m) Om))) t_1))))
   (if (<= t_3 2e-293)
     (sqrt (* (* 2.0 n) (+ (* -2.0 (/ (* U (pow l_m 2.0)) Om)) (* U t))))
     (if (<= t_3 INFINITY)
       (sqrt (* t_2 (+ (- t (* 2.0 (* l_m (/ l_m Om)))) t_1)))
       (* (/ l_m (/ Om (* n (sqrt 2.0)))) (- (sqrt (* U U*))))))))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double t_1 = (n * pow((l_m / Om), 2.0)) * (U_42_ - U);
	double t_2 = (2.0 * n) * U;
	double t_3 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_1);
	double tmp;
	if (t_3 <= 2e-293) {
		tmp = sqrt(((2.0 * n) * ((-2.0 * ((U * pow(l_m, 2.0)) / Om)) + (U * t))));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = sqrt((t_2 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_1)));
	} else {
		tmp = (l_m / (Om / (n * sqrt(2.0)))) * -sqrt((U * U_42_));
	}
	return tmp;
}

Java

l_m = Math.abs(l);
public static double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double t_1 = (n * Math.pow((l_m / Om), 2.0)) * (U_42_ - U);
	double t_2 = (2.0 * n) * U;
	double t_3 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_1);
	double tmp;
	if (t_3 <= 2e-293) {
		tmp = Math.sqrt(((2.0 * n) * ((-2.0 * ((U * Math.pow(l_m, 2.0)) / Om)) + (U * t))));
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = Math.sqrt((t_2 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_1)));
	} else {
		tmp = (l_m / (Om / (n * Math.sqrt(2.0)))) * -Math.sqrt((U * U_42_));
	}
	return tmp;
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	t_1 = (n * math.pow((l_m / Om), 2.0)) * (U_42_ - U)
	t_2 = (2.0 * n) * U
	t_3 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_1)
	tmp = 0
	if t_3 <= 2e-293:
		tmp = math.sqrt(((2.0 * n) * ((-2.0 * ((U * math.pow(l_m, 2.0)) / Om)) + (U * t))))
	elif t_3 <= math.inf:
		tmp = math.sqrt((t_2 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_1)))
	else:
		tmp = (l_m / (Om / (n * math.sqrt(2.0)))) * -math.sqrt((U * U_42_))
	return tmp

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	t_1 = Float64(Float64(n * (Float64(l_m / Om) ^ 2.0)) * Float64(U_42_ - U))
	t_2 = Float64(Float64(2.0 * n) * U)
	t_3 = Float64(t_2 * Float64(Float64(t - Float64(2.0 * Float64(Float64(l_m * l_m) / Om))) + t_1))
	tmp = 0.0
	if (t_3 <= 2e-293)
		tmp = sqrt(Float64(Float64(2.0 * n) * Float64(Float64(-2.0 * Float64(Float64(U * (l_m ^ 2.0)) / Om)) + Float64(U * t))));
	elseif (t_3 <= Inf)
		tmp = sqrt(Float64(t_2 * Float64(Float64(t - Float64(2.0 * Float64(l_m * Float64(l_m / Om)))) + t_1)));
	else
		tmp = Float64(Float64(l_m / Float64(Om / Float64(n * sqrt(2.0)))) * Float64(-sqrt(Float64(U * U_42_))));
	end
	return tmp
end

MATLAB

l_m = abs(l);
function tmp_2 = code(n, U, t, l_m, Om, U_42_)
	t_1 = (n * ((l_m / Om) ^ 2.0)) * (U_42_ - U);
	t_2 = (2.0 * n) * U;
	t_3 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_1);
	tmp = 0.0;
	if (t_3 <= 2e-293)
		tmp = sqrt(((2.0 * n) * ((-2.0 * ((U * (l_m ^ 2.0)) / Om)) + (U * t))));
	elseif (t_3 <= Inf)
		tmp = sqrt((t_2 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_1)));
	else
		tmp = (l_m / (Om / (n * sqrt(2.0)))) * -sqrt((U * U_42_));
	end
	tmp_2 = tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := Block[{t$95$1 = N[(N[(n * N[Power[N[(l$95$m / Om), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 * n), $MachinePrecision] * U), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 * N[(N[(t - N[(2.0 * N[(N[(l$95$m * l$95$m), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, 2e-293], N[Sqrt[N[(N[(2.0 * n), $MachinePrecision] * N[(N[(-2.0 * N[(N[(U * N[Power[l$95$m, 2.0], $MachinePrecision]), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision] + N[(U * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[Sqrt[N[(t$95$2 * N[(N[(t - N[(2.0 * N[(l$95$m * N[(l$95$m / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(N[(l$95$m / N[(Om / N[(n * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-N[Sqrt[N[(U * U$42$), $MachinePrecision]], $MachinePrecision])), $MachinePrecision]]]]]]

Derivation

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

Alternative 6: 60.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} t_1 := \left(n \cdot {\left(\frac{l_m}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\\ t_2 := \left(2 \cdot n\right) \cdot U\\ t_3 := t_2 \cdot \left(\left(t - 2 \cdot \frac{l_m \cdot l_m}{Om}\right) + t_1\right)\\ \mathbf{if}\;t_3 \leq 2 \cdot 10^{-293}:\\ \;\;\;\;\sqrt{2 \cdot n} \cdot \sqrt{U \cdot \left(t + -2 \cdot \frac{{l_m}^{2}}{Om}\right)}\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;\sqrt{t_2 \cdot \left(\left(t - 2 \cdot \left(l_m \cdot \frac{l_m}{Om}\right)\right) + t_1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{l_m}{\frac{Om}{n \cdot \sqrt{2}}} \cdot \left(-\sqrt{U \cdot U*}\right)\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (let* ((t_1 (* (* n (pow (/ l_m Om) 2.0)) (- U* U)))
        (t_2 (* (* 2.0 n) U))
        (t_3 (* t_2 (+ (- t (* 2.0 (/ (* l_m l_m) Om))) t_1))))
   (if (<= t_3 2e-293)
     (* (sqrt (* 2.0 n)) (sqrt (* U (+ t (* -2.0 (/ (pow l_m 2.0) Om))))))
     (if (<= t_3 INFINITY)
       (sqrt (* t_2 (+ (- t (* 2.0 (* l_m (/ l_m Om)))) t_1)))
       (* (/ l_m (/ Om (* n (sqrt 2.0)))) (- (sqrt (* U U*))))))))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double t_1 = (n * pow((l_m / Om), 2.0)) * (U_42_ - U);
	double t_2 = (2.0 * n) * U;
	double t_3 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_1);
	double tmp;
	if (t_3 <= 2e-293) {
		tmp = sqrt((2.0 * n)) * sqrt((U * (t + (-2.0 * (pow(l_m, 2.0) / Om)))));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = sqrt((t_2 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_1)));
	} else {
		tmp = (l_m / (Om / (n * sqrt(2.0)))) * -sqrt((U * U_42_));
	}
	return tmp;
}

Java

l_m = Math.abs(l);
public static double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double t_1 = (n * Math.pow((l_m / Om), 2.0)) * (U_42_ - U);
	double t_2 = (2.0 * n) * U;
	double t_3 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_1);
	double tmp;
	if (t_3 <= 2e-293) {
		tmp = Math.sqrt((2.0 * n)) * Math.sqrt((U * (t + (-2.0 * (Math.pow(l_m, 2.0) / Om)))));
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = Math.sqrt((t_2 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_1)));
	} else {
		tmp = (l_m / (Om / (n * Math.sqrt(2.0)))) * -Math.sqrt((U * U_42_));
	}
	return tmp;
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	t_1 = (n * math.pow((l_m / Om), 2.0)) * (U_42_ - U)
	t_2 = (2.0 * n) * U
	t_3 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_1)
	tmp = 0
	if t_3 <= 2e-293:
		tmp = math.sqrt((2.0 * n)) * math.sqrt((U * (t + (-2.0 * (math.pow(l_m, 2.0) / Om)))))
	elif t_3 <= math.inf:
		tmp = math.sqrt((t_2 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_1)))
	else:
		tmp = (l_m / (Om / (n * math.sqrt(2.0)))) * -math.sqrt((U * U_42_))
	return tmp

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	t_1 = Float64(Float64(n * (Float64(l_m / Om) ^ 2.0)) * Float64(U_42_ - U))
	t_2 = Float64(Float64(2.0 * n) * U)
	t_3 = Float64(t_2 * Float64(Float64(t - Float64(2.0 * Float64(Float64(l_m * l_m) / Om))) + t_1))
	tmp = 0.0
	if (t_3 <= 2e-293)
		tmp = Float64(sqrt(Float64(2.0 * n)) * sqrt(Float64(U * Float64(t + Float64(-2.0 * Float64((l_m ^ 2.0) / Om))))));
	elseif (t_3 <= Inf)
		tmp = sqrt(Float64(t_2 * Float64(Float64(t - Float64(2.0 * Float64(l_m * Float64(l_m / Om)))) + t_1)));
	else
		tmp = Float64(Float64(l_m / Float64(Om / Float64(n * sqrt(2.0)))) * Float64(-sqrt(Float64(U * U_42_))));
	end
	return tmp
end

MATLAB

l_m = abs(l);
function tmp_2 = code(n, U, t, l_m, Om, U_42_)
	t_1 = (n * ((l_m / Om) ^ 2.0)) * (U_42_ - U);
	t_2 = (2.0 * n) * U;
	t_3 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_1);
	tmp = 0.0;
	if (t_3 <= 2e-293)
		tmp = sqrt((2.0 * n)) * sqrt((U * (t + (-2.0 * ((l_m ^ 2.0) / Om)))));
	elseif (t_3 <= Inf)
		tmp = sqrt((t_2 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_1)));
	else
		tmp = (l_m / (Om / (n * sqrt(2.0)))) * -sqrt((U * U_42_));
	end
	tmp_2 = tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := Block[{t$95$1 = N[(N[(n * N[Power[N[(l$95$m / Om), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 * n), $MachinePrecision] * U), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 * N[(N[(t - N[(2.0 * N[(N[(l$95$m * l$95$m), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, 2e-293], N[(N[Sqrt[N[(2.0 * n), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(U * N[(t + N[(-2.0 * N[(N[Power[l$95$m, 2.0], $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[Sqrt[N[(t$95$2 * N[(N[(t - N[(2.0 * N[(l$95$m * N[(l$95$m / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(N[(l$95$m / N[(Om / N[(n * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-N[Sqrt[N[(U * U$42$), $MachinePrecision]], $MachinePrecision])), $MachinePrecision]]]]]]

Derivation

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

Alternative 7: 60.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} t_1 := \left(n \cdot {\left(\frac{l_m}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\\ t_2 := \left(2 \cdot n\right) \cdot U\\ t_3 := t_2 \cdot \left(\left(t - 2 \cdot \frac{l_m \cdot l_m}{Om}\right) + t_1\right)\\ \mathbf{if}\;t_3 \leq 2 \cdot 10^{-293}:\\ \;\;\;\;\sqrt{2 \cdot n} \cdot \sqrt{-2 \cdot \frac{U \cdot {l_m}^{2}}{Om} + U \cdot t}\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;\sqrt{t_2 \cdot \left(\left(t - 2 \cdot \left(l_m \cdot \frac{l_m}{Om}\right)\right) + t_1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{l_m}{\frac{Om}{n \cdot \sqrt{2}}} \cdot \left(-\sqrt{U \cdot U*}\right)\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (let* ((t_1 (* (* n (pow (/ l_m Om) 2.0)) (- U* U)))
        (t_2 (* (* 2.0 n) U))
        (t_3 (* t_2 (+ (- t (* 2.0 (/ (* l_m l_m) Om))) t_1))))
   (if (<= t_3 2e-293)
     (*
      (sqrt (* 2.0 n))
      (sqrt (+ (* -2.0 (/ (* U (pow l_m 2.0)) Om)) (* U t))))
     (if (<= t_3 INFINITY)
       (sqrt (* t_2 (+ (- t (* 2.0 (* l_m (/ l_m Om)))) t_1)))
       (* (/ l_m (/ Om (* n (sqrt 2.0)))) (- (sqrt (* U U*))))))))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double t_1 = (n * pow((l_m / Om), 2.0)) * (U_42_ - U);
	double t_2 = (2.0 * n) * U;
	double t_3 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_1);
	double tmp;
	if (t_3 <= 2e-293) {
		tmp = sqrt((2.0 * n)) * sqrt(((-2.0 * ((U * pow(l_m, 2.0)) / Om)) + (U * t)));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = sqrt((t_2 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_1)));
	} else {
		tmp = (l_m / (Om / (n * sqrt(2.0)))) * -sqrt((U * U_42_));
	}
	return tmp;
}

Java

l_m = Math.abs(l);
public static double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double t_1 = (n * Math.pow((l_m / Om), 2.0)) * (U_42_ - U);
	double t_2 = (2.0 * n) * U;
	double t_3 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_1);
	double tmp;
	if (t_3 <= 2e-293) {
		tmp = Math.sqrt((2.0 * n)) * Math.sqrt(((-2.0 * ((U * Math.pow(l_m, 2.0)) / Om)) + (U * t)));
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = Math.sqrt((t_2 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_1)));
	} else {
		tmp = (l_m / (Om / (n * Math.sqrt(2.0)))) * -Math.sqrt((U * U_42_));
	}
	return tmp;
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	t_1 = (n * math.pow((l_m / Om), 2.0)) * (U_42_ - U)
	t_2 = (2.0 * n) * U
	t_3 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_1)
	tmp = 0
	if t_3 <= 2e-293:
		tmp = math.sqrt((2.0 * n)) * math.sqrt(((-2.0 * ((U * math.pow(l_m, 2.0)) / Om)) + (U * t)))
	elif t_3 <= math.inf:
		tmp = math.sqrt((t_2 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_1)))
	else:
		tmp = (l_m / (Om / (n * math.sqrt(2.0)))) * -math.sqrt((U * U_42_))
	return tmp

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	t_1 = Float64(Float64(n * (Float64(l_m / Om) ^ 2.0)) * Float64(U_42_ - U))
	t_2 = Float64(Float64(2.0 * n) * U)
	t_3 = Float64(t_2 * Float64(Float64(t - Float64(2.0 * Float64(Float64(l_m * l_m) / Om))) + t_1))
	tmp = 0.0
	if (t_3 <= 2e-293)
		tmp = Float64(sqrt(Float64(2.0 * n)) * sqrt(Float64(Float64(-2.0 * Float64(Float64(U * (l_m ^ 2.0)) / Om)) + Float64(U * t))));
	elseif (t_3 <= Inf)
		tmp = sqrt(Float64(t_2 * Float64(Float64(t - Float64(2.0 * Float64(l_m * Float64(l_m / Om)))) + t_1)));
	else
		tmp = Float64(Float64(l_m / Float64(Om / Float64(n * sqrt(2.0)))) * Float64(-sqrt(Float64(U * U_42_))));
	end
	return tmp
end

MATLAB

l_m = abs(l);
function tmp_2 = code(n, U, t, l_m, Om, U_42_)
	t_1 = (n * ((l_m / Om) ^ 2.0)) * (U_42_ - U);
	t_2 = (2.0 * n) * U;
	t_3 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_1);
	tmp = 0.0;
	if (t_3 <= 2e-293)
		tmp = sqrt((2.0 * n)) * sqrt(((-2.0 * ((U * (l_m ^ 2.0)) / Om)) + (U * t)));
	elseif (t_3 <= Inf)
		tmp = sqrt((t_2 * ((t - (2.0 * (l_m * (l_m / Om)))) + t_1)));
	else
		tmp = (l_m / (Om / (n * sqrt(2.0)))) * -sqrt((U * U_42_));
	end
	tmp_2 = tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := Block[{t$95$1 = N[(N[(n * N[Power[N[(l$95$m / Om), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 * n), $MachinePrecision] * U), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 * N[(N[(t - N[(2.0 * N[(N[(l$95$m * l$95$m), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, 2e-293], N[(N[Sqrt[N[(2.0 * n), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(N[(-2.0 * N[(N[(U * N[Power[l$95$m, 2.0], $MachinePrecision]), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision] + N[(U * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[Sqrt[N[(t$95$2 * N[(N[(t - N[(2.0 * N[(l$95$m * N[(l$95$m / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(N[(l$95$m / N[(Om / N[(n * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * (-N[Sqrt[N[(U * U$42$), $MachinePrecision]], $MachinePrecision])), $MachinePrecision]]]]]]

Derivation

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

Alternative 8: 52.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} t_1 := l_m \cdot \sqrt{2}\\ \mathbf{if}\;l_m \leq 3.7 \cdot 10^{+149}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(\left(t - \frac{2 \cdot \left(l_m \cdot l_m\right)}{Om}\right) + n \cdot \left({\left(\frac{l_m}{Om}\right)}^{2} \cdot \left(U* - U\right)\right)\right)\right)}\\ \mathbf{elif}\;l_m \leq 1.2 \cdot 10^{+187}:\\ \;\;\;\;\sqrt{2 \cdot \left(t \cdot \left(n \cdot U\right)\right)}\\ \mathbf{elif}\;l_m \leq 3.6 \cdot 10^{+197}:\\ \;\;\;\;t_1 \cdot \sqrt{-2 \cdot \frac{n \cdot U}{Om}}\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \sqrt{-2 \cdot \frac{U}{\frac{Om}{n}}}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (let* ((t_1 (* l_m (sqrt 2.0))))
   (if (<= l_m 3.7e+149)
     (sqrt
      (*
       (* 2.0 n)
       (*
        U
        (+
         (- t (/ (* 2.0 (* l_m l_m)) Om))
         (* n (* (pow (/ l_m Om) 2.0) (- U* U)))))))
     (if (<= l_m 1.2e+187)
       (sqrt (* 2.0 (* t (* n U))))
       (if (<= l_m 3.6e+197)
         (* t_1 (sqrt (* -2.0 (/ (* n U) Om))))
         (* t_1 (sqrt (* -2.0 (/ U (/ Om n))))))))))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double t_1 = l_m * sqrt(2.0);
	double tmp;
	if (l_m <= 3.7e+149) {
		tmp = sqrt(((2.0 * n) * (U * ((t - ((2.0 * (l_m * l_m)) / Om)) + (n * (pow((l_m / Om), 2.0) * (U_42_ - U)))))));
	} else if (l_m <= 1.2e+187) {
		tmp = sqrt((2.0 * (t * (n * U))));
	} else if (l_m <= 3.6e+197) {
		tmp = t_1 * sqrt((-2.0 * ((n * U) / Om)));
	} else {
		tmp = t_1 * sqrt((-2.0 * (U / (Om / n))));
	}
	return tmp;
}

Fortran

l_m = abs(l)
real(8) function code(n, u, t, l_m, om, u_42)
    real(8), intent (in) :: n
    real(8), intent (in) :: u
    real(8), intent (in) :: t
    real(8), intent (in) :: l_m
    real(8), intent (in) :: om
    real(8), intent (in) :: u_42
    real(8) :: t_1
    real(8) :: tmp
    t_1 = l_m * sqrt(2.0d0)
    if (l_m <= 3.7d+149) then
        tmp = sqrt(((2.0d0 * n) * (u * ((t - ((2.0d0 * (l_m * l_m)) / om)) + (n * (((l_m / om) ** 2.0d0) * (u_42 - u)))))))
    else if (l_m <= 1.2d+187) then
        tmp = sqrt((2.0d0 * (t * (n * u))))
    else if (l_m <= 3.6d+197) then
        tmp = t_1 * sqrt(((-2.0d0) * ((n * u) / om)))
    else
        tmp = t_1 * sqrt(((-2.0d0) * (u / (om / n))))
    end if
    code = tmp
end function

Java

l_m = Math.abs(l);
public static double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double t_1 = l_m * Math.sqrt(2.0);
	double tmp;
	if (l_m <= 3.7e+149) {
		tmp = Math.sqrt(((2.0 * n) * (U * ((t - ((2.0 * (l_m * l_m)) / Om)) + (n * (Math.pow((l_m / Om), 2.0) * (U_42_ - U)))))));
	} else if (l_m <= 1.2e+187) {
		tmp = Math.sqrt((2.0 * (t * (n * U))));
	} else if (l_m <= 3.6e+197) {
		tmp = t_1 * Math.sqrt((-2.0 * ((n * U) / Om)));
	} else {
		tmp = t_1 * Math.sqrt((-2.0 * (U / (Om / n))));
	}
	return tmp;
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	t_1 = l_m * math.sqrt(2.0)
	tmp = 0
	if l_m <= 3.7e+149:
		tmp = math.sqrt(((2.0 * n) * (U * ((t - ((2.0 * (l_m * l_m)) / Om)) + (n * (math.pow((l_m / Om), 2.0) * (U_42_ - U)))))))
	elif l_m <= 1.2e+187:
		tmp = math.sqrt((2.0 * (t * (n * U))))
	elif l_m <= 3.6e+197:
		tmp = t_1 * math.sqrt((-2.0 * ((n * U) / Om)))
	else:
		tmp = t_1 * math.sqrt((-2.0 * (U / (Om / n))))
	return tmp

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	t_1 = Float64(l_m * sqrt(2.0))
	tmp = 0.0
	if (l_m <= 3.7e+149)
		tmp = sqrt(Float64(Float64(2.0 * n) * Float64(U * Float64(Float64(t - Float64(Float64(2.0 * Float64(l_m * l_m)) / Om)) + Float64(n * Float64((Float64(l_m / Om) ^ 2.0) * Float64(U_42_ - U)))))));
	elseif (l_m <= 1.2e+187)
		tmp = sqrt(Float64(2.0 * Float64(t * Float64(n * U))));
	elseif (l_m <= 3.6e+197)
		tmp = Float64(t_1 * sqrt(Float64(-2.0 * Float64(Float64(n * U) / Om))));
	else
		tmp = Float64(t_1 * sqrt(Float64(-2.0 * Float64(U / Float64(Om / n)))));
	end
	return tmp
end

MATLAB

l_m = abs(l);
function tmp_2 = code(n, U, t, l_m, Om, U_42_)
	t_1 = l_m * sqrt(2.0);
	tmp = 0.0;
	if (l_m <= 3.7e+149)
		tmp = sqrt(((2.0 * n) * (U * ((t - ((2.0 * (l_m * l_m)) / Om)) + (n * (((l_m / Om) ^ 2.0) * (U_42_ - U)))))));
	elseif (l_m <= 1.2e+187)
		tmp = sqrt((2.0 * (t * (n * U))));
	elseif (l_m <= 3.6e+197)
		tmp = t_1 * sqrt((-2.0 * ((n * U) / Om)));
	else
		tmp = t_1 * sqrt((-2.0 * (U / (Om / n))));
	end
	tmp_2 = tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := Block[{t$95$1 = N[(l$95$m * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[l$95$m, 3.7e+149], N[Sqrt[N[(N[(2.0 * n), $MachinePrecision] * N[(U * N[(N[(t - N[(N[(2.0 * N[(l$95$m * l$95$m), $MachinePrecision]), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision] + N[(n * N[(N[Power[N[(l$95$m / Om), $MachinePrecision], 2.0], $MachinePrecision] * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[l$95$m, 1.2e+187], N[Sqrt[N[(2.0 * N[(t * N[(n * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[l$95$m, 3.6e+197], N[(t$95$1 * N[Sqrt[N[(-2.0 * N[(N[(n * U), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[Sqrt[N[(-2.0 * N[(U / N[(Om / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 9: 40.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} \mathbf{if}\;l_m \leq 1.6 \cdot 10^{+19}:\\ \;\;\;\;\sqrt{2} \cdot {\left(n \cdot \left(U \cdot t\right)\right)}^{0.5}\\ \mathbf{elif}\;l_m \leq 8.4 \cdot 10^{+48}:\\ \;\;\;\;\sqrt{\frac{U \cdot -4}{\frac{Om}{n \cdot {l_m}^{2}}}}\\ \mathbf{elif}\;l_m \leq 9.5 \cdot 10^{+146}:\\ \;\;\;\;\sqrt{U \cdot U*} \cdot \left(\frac{l_m}{Om} \cdot \left(n \cdot \sqrt{2}\right)\right)\\ \mathbf{elif}\;l_m \leq 1.2 \cdot 10^{+187}:\\ \;\;\;\;\sqrt{\left|2 \cdot \left(t \cdot \left(n \cdot U\right)\right)\right|}\\ \mathbf{else}:\\ \;\;\;\;\left(l_m \cdot \sqrt{2}\right) \cdot \sqrt{-2 \cdot \frac{n \cdot U}{Om}}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (if (<= l_m 1.6e+19)
   (* (sqrt 2.0) (pow (* n (* U t)) 0.5))
   (if (<= l_m 8.4e+48)
     (sqrt (/ (* U -4.0) (/ Om (* n (pow l_m 2.0)))))
     (if (<= l_m 9.5e+146)
       (* (sqrt (* U U*)) (* (/ l_m Om) (* n (sqrt 2.0))))
       (if (<= l_m 1.2e+187)
         (sqrt (fabs (* 2.0 (* t (* n U)))))
         (* (* l_m (sqrt 2.0)) (sqrt (* -2.0 (/ (* n U) Om)))))))))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if (l_m <= 1.6e+19) {
		tmp = sqrt(2.0) * pow((n * (U * t)), 0.5);
	} else if (l_m <= 8.4e+48) {
		tmp = sqrt(((U * -4.0) / (Om / (n * pow(l_m, 2.0)))));
	} else if (l_m <= 9.5e+146) {
		tmp = sqrt((U * U_42_)) * ((l_m / Om) * (n * sqrt(2.0)));
	} else if (l_m <= 1.2e+187) {
		tmp = sqrt(fabs((2.0 * (t * (n * U)))));
	} else {
		tmp = (l_m * sqrt(2.0)) * sqrt((-2.0 * ((n * U) / Om)));
	}
	return tmp;
}

Fortran

l_m = abs(l)
real(8) function code(n, u, t, l_m, om, u_42)
    real(8), intent (in) :: n
    real(8), intent (in) :: u
    real(8), intent (in) :: t
    real(8), intent (in) :: l_m
    real(8), intent (in) :: om
    real(8), intent (in) :: u_42
    real(8) :: tmp
    if (l_m <= 1.6d+19) then
        tmp = sqrt(2.0d0) * ((n * (u * t)) ** 0.5d0)
    else if (l_m <= 8.4d+48) then
        tmp = sqrt(((u * (-4.0d0)) / (om / (n * (l_m ** 2.0d0)))))
    else if (l_m <= 9.5d+146) then
        tmp = sqrt((u * u_42)) * ((l_m / om) * (n * sqrt(2.0d0)))
    else if (l_m <= 1.2d+187) then
        tmp = sqrt(abs((2.0d0 * (t * (n * u)))))
    else
        tmp = (l_m * sqrt(2.0d0)) * sqrt(((-2.0d0) * ((n * u) / om)))
    end if
    code = tmp
end function

Java

l_m = Math.abs(l);
public static double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if (l_m <= 1.6e+19) {
		tmp = Math.sqrt(2.0) * Math.pow((n * (U * t)), 0.5);
	} else if (l_m <= 8.4e+48) {
		tmp = Math.sqrt(((U * -4.0) / (Om / (n * Math.pow(l_m, 2.0)))));
	} else if (l_m <= 9.5e+146) {
		tmp = Math.sqrt((U * U_42_)) * ((l_m / Om) * (n * Math.sqrt(2.0)));
	} else if (l_m <= 1.2e+187) {
		tmp = Math.sqrt(Math.abs((2.0 * (t * (n * U)))));
	} else {
		tmp = (l_m * Math.sqrt(2.0)) * Math.sqrt((-2.0 * ((n * U) / Om)));
	}
	return tmp;
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	tmp = 0
	if l_m <= 1.6e+19:
		tmp = math.sqrt(2.0) * math.pow((n * (U * t)), 0.5)
	elif l_m <= 8.4e+48:
		tmp = math.sqrt(((U * -4.0) / (Om / (n * math.pow(l_m, 2.0)))))
	elif l_m <= 9.5e+146:
		tmp = math.sqrt((U * U_42_)) * ((l_m / Om) * (n * math.sqrt(2.0)))
	elif l_m <= 1.2e+187:
		tmp = math.sqrt(math.fabs((2.0 * (t * (n * U)))))
	else:
		tmp = (l_m * math.sqrt(2.0)) * math.sqrt((-2.0 * ((n * U) / Om)))
	return tmp

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0
	if (l_m <= 1.6e+19)
		tmp = Float64(sqrt(2.0) * (Float64(n * Float64(U * t)) ^ 0.5));
	elseif (l_m <= 8.4e+48)
		tmp = sqrt(Float64(Float64(U * -4.0) / Float64(Om / Float64(n * (l_m ^ 2.0)))));
	elseif (l_m <= 9.5e+146)
		tmp = Float64(sqrt(Float64(U * U_42_)) * Float64(Float64(l_m / Om) * Float64(n * sqrt(2.0))));
	elseif (l_m <= 1.2e+187)
		tmp = sqrt(abs(Float64(2.0 * Float64(t * Float64(n * U)))));
	else
		tmp = Float64(Float64(l_m * sqrt(2.0)) * sqrt(Float64(-2.0 * Float64(Float64(n * U) / Om))));
	end
	return tmp
end

MATLAB

l_m = abs(l);
function tmp_2 = code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0;
	if (l_m <= 1.6e+19)
		tmp = sqrt(2.0) * ((n * (U * t)) ^ 0.5);
	elseif (l_m <= 8.4e+48)
		tmp = sqrt(((U * -4.0) / (Om / (n * (l_m ^ 2.0)))));
	elseif (l_m <= 9.5e+146)
		tmp = sqrt((U * U_42_)) * ((l_m / Om) * (n * sqrt(2.0)));
	elseif (l_m <= 1.2e+187)
		tmp = sqrt(abs((2.0 * (t * (n * U)))));
	else
		tmp = (l_m * sqrt(2.0)) * sqrt((-2.0 * ((n * U) / Om)));
	end
	tmp_2 = tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := If[LessEqual[l$95$m, 1.6e+19], N[(N[Sqrt[2.0], $MachinePrecision] * N[Power[N[(n * N[(U * t), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision], If[LessEqual[l$95$m, 8.4e+48], N[Sqrt[N[(N[(U * -4.0), $MachinePrecision] / N[(Om / N[(n * N[Power[l$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[l$95$m, 9.5e+146], N[(N[Sqrt[N[(U * U$42$), $MachinePrecision]], $MachinePrecision] * N[(N[(l$95$m / Om), $MachinePrecision] * N[(n * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[l$95$m, 1.2e+187], N[Sqrt[N[Abs[N[(2.0 * N[(t * N[(n * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision], N[(N[(l$95$m * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(-2.0 * N[(N[(n * U), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 10: 41.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} \mathbf{if}\;l_m \leq 1.4 \cdot 10^{+20}:\\ \;\;\;\;\sqrt{2} \cdot {\left(n \cdot \left(U \cdot t\right)\right)}^{0.5}\\ \mathbf{elif}\;l_m \leq 2.2 \cdot 10^{+49}:\\ \;\;\;\;\sqrt{\frac{U \cdot -4}{\frac{Om}{n \cdot {l_m}^{2}}}}\\ \mathbf{elif}\;l_m \leq 9.5 \cdot 10^{+146}:\\ \;\;\;\;\frac{l_m \cdot \sqrt{U \cdot U*}}{\frac{Om}{n \cdot \sqrt{2}}}\\ \mathbf{elif}\;l_m \leq 2.5 \cdot 10^{+187}:\\ \;\;\;\;\sqrt{\left|2 \cdot \left(t \cdot \left(n \cdot U\right)\right)\right|}\\ \mathbf{else}:\\ \;\;\;\;\left(l_m \cdot \sqrt{2}\right) \cdot \sqrt{-2 \cdot \frac{n \cdot U}{Om}}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (if (<= l_m 1.4e+20)
   (* (sqrt 2.0) (pow (* n (* U t)) 0.5))
   (if (<= l_m 2.2e+49)
     (sqrt (/ (* U -4.0) (/ Om (* n (pow l_m 2.0)))))
     (if (<= l_m 9.5e+146)
       (/ (* l_m (sqrt (* U U*))) (/ Om (* n (sqrt 2.0))))
       (if (<= l_m 2.5e+187)
         (sqrt (fabs (* 2.0 (* t (* n U)))))
         (* (* l_m (sqrt 2.0)) (sqrt (* -2.0 (/ (* n U) Om)))))))))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if (l_m <= 1.4e+20) {
		tmp = sqrt(2.0) * pow((n * (U * t)), 0.5);
	} else if (l_m <= 2.2e+49) {
		tmp = sqrt(((U * -4.0) / (Om / (n * pow(l_m, 2.0)))));
	} else if (l_m <= 9.5e+146) {
		tmp = (l_m * sqrt((U * U_42_))) / (Om / (n * sqrt(2.0)));
	} else if (l_m <= 2.5e+187) {
		tmp = sqrt(fabs((2.0 * (t * (n * U)))));
	} else {
		tmp = (l_m * sqrt(2.0)) * sqrt((-2.0 * ((n * U) / Om)));
	}
	return tmp;
}

Fortran

l_m = abs(l)
real(8) function code(n, u, t, l_m, om, u_42)
    real(8), intent (in) :: n
    real(8), intent (in) :: u
    real(8), intent (in) :: t
    real(8), intent (in) :: l_m
    real(8), intent (in) :: om
    real(8), intent (in) :: u_42
    real(8) :: tmp
    if (l_m <= 1.4d+20) then
        tmp = sqrt(2.0d0) * ((n * (u * t)) ** 0.5d0)
    else if (l_m <= 2.2d+49) then
        tmp = sqrt(((u * (-4.0d0)) / (om / (n * (l_m ** 2.0d0)))))
    else if (l_m <= 9.5d+146) then
        tmp = (l_m * sqrt((u * u_42))) / (om / (n * sqrt(2.0d0)))
    else if (l_m <= 2.5d+187) then
        tmp = sqrt(abs((2.0d0 * (t * (n * u)))))
    else
        tmp = (l_m * sqrt(2.0d0)) * sqrt(((-2.0d0) * ((n * u) / om)))
    end if
    code = tmp
end function

Java

l_m = Math.abs(l);
public static double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if (l_m <= 1.4e+20) {
		tmp = Math.sqrt(2.0) * Math.pow((n * (U * t)), 0.5);
	} else if (l_m <= 2.2e+49) {
		tmp = Math.sqrt(((U * -4.0) / (Om / (n * Math.pow(l_m, 2.0)))));
	} else if (l_m <= 9.5e+146) {
		tmp = (l_m * Math.sqrt((U * U_42_))) / (Om / (n * Math.sqrt(2.0)));
	} else if (l_m <= 2.5e+187) {
		tmp = Math.sqrt(Math.abs((2.0 * (t * (n * U)))));
	} else {
		tmp = (l_m * Math.sqrt(2.0)) * Math.sqrt((-2.0 * ((n * U) / Om)));
	}
	return tmp;
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	tmp = 0
	if l_m <= 1.4e+20:
		tmp = math.sqrt(2.0) * math.pow((n * (U * t)), 0.5)
	elif l_m <= 2.2e+49:
		tmp = math.sqrt(((U * -4.0) / (Om / (n * math.pow(l_m, 2.0)))))
	elif l_m <= 9.5e+146:
		tmp = (l_m * math.sqrt((U * U_42_))) / (Om / (n * math.sqrt(2.0)))
	elif l_m <= 2.5e+187:
		tmp = math.sqrt(math.fabs((2.0 * (t * (n * U)))))
	else:
		tmp = (l_m * math.sqrt(2.0)) * math.sqrt((-2.0 * ((n * U) / Om)))
	return tmp

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0
	if (l_m <= 1.4e+20)
		tmp = Float64(sqrt(2.0) * (Float64(n * Float64(U * t)) ^ 0.5));
	elseif (l_m <= 2.2e+49)
		tmp = sqrt(Float64(Float64(U * -4.0) / Float64(Om / Float64(n * (l_m ^ 2.0)))));
	elseif (l_m <= 9.5e+146)
		tmp = Float64(Float64(l_m * sqrt(Float64(U * U_42_))) / Float64(Om / Float64(n * sqrt(2.0))));
	elseif (l_m <= 2.5e+187)
		tmp = sqrt(abs(Float64(2.0 * Float64(t * Float64(n * U)))));
	else
		tmp = Float64(Float64(l_m * sqrt(2.0)) * sqrt(Float64(-2.0 * Float64(Float64(n * U) / Om))));
	end
	return tmp
end

MATLAB

l_m = abs(l);
function tmp_2 = code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0;
	if (l_m <= 1.4e+20)
		tmp = sqrt(2.0) * ((n * (U * t)) ^ 0.5);
	elseif (l_m <= 2.2e+49)
		tmp = sqrt(((U * -4.0) / (Om / (n * (l_m ^ 2.0)))));
	elseif (l_m <= 9.5e+146)
		tmp = (l_m * sqrt((U * U_42_))) / (Om / (n * sqrt(2.0)));
	elseif (l_m <= 2.5e+187)
		tmp = sqrt(abs((2.0 * (t * (n * U)))));
	else
		tmp = (l_m * sqrt(2.0)) * sqrt((-2.0 * ((n * U) / Om)));
	end
	tmp_2 = tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := If[LessEqual[l$95$m, 1.4e+20], N[(N[Sqrt[2.0], $MachinePrecision] * N[Power[N[(n * N[(U * t), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision], If[LessEqual[l$95$m, 2.2e+49], N[Sqrt[N[(N[(U * -4.0), $MachinePrecision] / N[(Om / N[(n * N[Power[l$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[l$95$m, 9.5e+146], N[(N[(l$95$m * N[Sqrt[N[(U * U$42$), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(Om / N[(n * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[l$95$m, 2.5e+187], N[Sqrt[N[Abs[N[(2.0 * N[(t * N[(n * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision], N[(N[(l$95$m * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(-2.0 * N[(N[(n * U), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 11: 42.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} \mathbf{if}\;l_m \leq 1.02 \cdot 10^{+20}:\\ \;\;\;\;\sqrt{2} \cdot {\left(n \cdot \left(U \cdot t\right)\right)}^{0.5}\\ \mathbf{elif}\;l_m \leq 1.6 \cdot 10^{+147}:\\ \;\;\;\;\sqrt{\frac{U \cdot -4}{\frac{Om}{n \cdot {l_m}^{2}}}}\\ \mathbf{elif}\;l_m \leq 3.2 \cdot 10^{+196}:\\ \;\;\;\;\sqrt{\left|2 \cdot \left(t \cdot \left(n \cdot U\right)\right)\right|}\\ \mathbf{else}:\\ \;\;\;\;\left(l_m \cdot \sqrt{2}\right) \cdot \sqrt{-2 \cdot \frac{U}{\frac{Om}{n}}}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (if (<= l_m 1.02e+20)
   (* (sqrt 2.0) (pow (* n (* U t)) 0.5))
   (if (<= l_m 1.6e+147)
     (sqrt (/ (* U -4.0) (/ Om (* n (pow l_m 2.0)))))
     (if (<= l_m 3.2e+196)
       (sqrt (fabs (* 2.0 (* t (* n U)))))
       (* (* l_m (sqrt 2.0)) (sqrt (* -2.0 (/ U (/ Om n)))))))))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if (l_m <= 1.02e+20) {
		tmp = sqrt(2.0) * pow((n * (U * t)), 0.5);
	} else if (l_m <= 1.6e+147) {
		tmp = sqrt(((U * -4.0) / (Om / (n * pow(l_m, 2.0)))));
	} else if (l_m <= 3.2e+196) {
		tmp = sqrt(fabs((2.0 * (t * (n * U)))));
	} else {
		tmp = (l_m * sqrt(2.0)) * sqrt((-2.0 * (U / (Om / n))));
	}
	return tmp;
}

Fortran

l_m = abs(l)
real(8) function code(n, u, t, l_m, om, u_42)
    real(8), intent (in) :: n
    real(8), intent (in) :: u
    real(8), intent (in) :: t
    real(8), intent (in) :: l_m
    real(8), intent (in) :: om
    real(8), intent (in) :: u_42
    real(8) :: tmp
    if (l_m <= 1.02d+20) then
        tmp = sqrt(2.0d0) * ((n * (u * t)) ** 0.5d0)
    else if (l_m <= 1.6d+147) then
        tmp = sqrt(((u * (-4.0d0)) / (om / (n * (l_m ** 2.0d0)))))
    else if (l_m <= 3.2d+196) then
        tmp = sqrt(abs((2.0d0 * (t * (n * u)))))
    else
        tmp = (l_m * sqrt(2.0d0)) * sqrt(((-2.0d0) * (u / (om / n))))
    end if
    code = tmp
end function

Java

l_m = Math.abs(l);
public static double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if (l_m <= 1.02e+20) {
		tmp = Math.sqrt(2.0) * Math.pow((n * (U * t)), 0.5);
	} else if (l_m <= 1.6e+147) {
		tmp = Math.sqrt(((U * -4.0) / (Om / (n * Math.pow(l_m, 2.0)))));
	} else if (l_m <= 3.2e+196) {
		tmp = Math.sqrt(Math.abs((2.0 * (t * (n * U)))));
	} else {
		tmp = (l_m * Math.sqrt(2.0)) * Math.sqrt((-2.0 * (U / (Om / n))));
	}
	return tmp;
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	tmp = 0
	if l_m <= 1.02e+20:
		tmp = math.sqrt(2.0) * math.pow((n * (U * t)), 0.5)
	elif l_m <= 1.6e+147:
		tmp = math.sqrt(((U * -4.0) / (Om / (n * math.pow(l_m, 2.0)))))
	elif l_m <= 3.2e+196:
		tmp = math.sqrt(math.fabs((2.0 * (t * (n * U)))))
	else:
		tmp = (l_m * math.sqrt(2.0)) * math.sqrt((-2.0 * (U / (Om / n))))
	return tmp

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0
	if (l_m <= 1.02e+20)
		tmp = Float64(sqrt(2.0) * (Float64(n * Float64(U * t)) ^ 0.5));
	elseif (l_m <= 1.6e+147)
		tmp = sqrt(Float64(Float64(U * -4.0) / Float64(Om / Float64(n * (l_m ^ 2.0)))));
	elseif (l_m <= 3.2e+196)
		tmp = sqrt(abs(Float64(2.0 * Float64(t * Float64(n * U)))));
	else
		tmp = Float64(Float64(l_m * sqrt(2.0)) * sqrt(Float64(-2.0 * Float64(U / Float64(Om / n)))));
	end
	return tmp
end

MATLAB

l_m = abs(l);
function tmp_2 = code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0;
	if (l_m <= 1.02e+20)
		tmp = sqrt(2.0) * ((n * (U * t)) ^ 0.5);
	elseif (l_m <= 1.6e+147)
		tmp = sqrt(((U * -4.0) / (Om / (n * (l_m ^ 2.0)))));
	elseif (l_m <= 3.2e+196)
		tmp = sqrt(abs((2.0 * (t * (n * U)))));
	else
		tmp = (l_m * sqrt(2.0)) * sqrt((-2.0 * (U / (Om / n))));
	end
	tmp_2 = tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := If[LessEqual[l$95$m, 1.02e+20], N[(N[Sqrt[2.0], $MachinePrecision] * N[Power[N[(n * N[(U * t), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision], If[LessEqual[l$95$m, 1.6e+147], N[Sqrt[N[(N[(U * -4.0), $MachinePrecision] / N[(Om / N[(n * N[Power[l$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[l$95$m, 3.2e+196], N[Sqrt[N[Abs[N[(2.0 * N[(t * N[(n * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision], N[(N[(l$95$m * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(-2.0 * N[(U / N[(Om / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 12: 43.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} \mathbf{if}\;l_m \leq 6.9 \cdot 10^{+19}:\\ \;\;\;\;\sqrt{2} \cdot {\left(n \cdot \left(U \cdot t\right)\right)}^{0.5}\\ \mathbf{elif}\;l_m \leq 1.15 \cdot 10^{+147}:\\ \;\;\;\;\sqrt{\frac{U \cdot -4}{\frac{Om}{n \cdot {l_m}^{2}}}}\\ \mathbf{elif}\;l_m \leq 2.95 \cdot 10^{+187}:\\ \;\;\;\;\sqrt{\left|2 \cdot \left(t \cdot \left(n \cdot U\right)\right)\right|}\\ \mathbf{else}:\\ \;\;\;\;\left(l_m \cdot \sqrt{2}\right) \cdot \sqrt{-2 \cdot \frac{n \cdot U}{Om}}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (if (<= l_m 6.9e+19)
   (* (sqrt 2.0) (pow (* n (* U t)) 0.5))
   (if (<= l_m 1.15e+147)
     (sqrt (/ (* U -4.0) (/ Om (* n (pow l_m 2.0)))))
     (if (<= l_m 2.95e+187)
       (sqrt (fabs (* 2.0 (* t (* n U)))))
       (* (* l_m (sqrt 2.0)) (sqrt (* -2.0 (/ (* n U) Om))))))))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if (l_m <= 6.9e+19) {
		tmp = sqrt(2.0) * pow((n * (U * t)), 0.5);
	} else if (l_m <= 1.15e+147) {
		tmp = sqrt(((U * -4.0) / (Om / (n * pow(l_m, 2.0)))));
	} else if (l_m <= 2.95e+187) {
		tmp = sqrt(fabs((2.0 * (t * (n * U)))));
	} else {
		tmp = (l_m * sqrt(2.0)) * sqrt((-2.0 * ((n * U) / Om)));
	}
	return tmp;
}

Fortran

l_m = abs(l)
real(8) function code(n, u, t, l_m, om, u_42)
    real(8), intent (in) :: n
    real(8), intent (in) :: u
    real(8), intent (in) :: t
    real(8), intent (in) :: l_m
    real(8), intent (in) :: om
    real(8), intent (in) :: u_42
    real(8) :: tmp
    if (l_m <= 6.9d+19) then
        tmp = sqrt(2.0d0) * ((n * (u * t)) ** 0.5d0)
    else if (l_m <= 1.15d+147) then
        tmp = sqrt(((u * (-4.0d0)) / (om / (n * (l_m ** 2.0d0)))))
    else if (l_m <= 2.95d+187) then
        tmp = sqrt(abs((2.0d0 * (t * (n * u)))))
    else
        tmp = (l_m * sqrt(2.0d0)) * sqrt(((-2.0d0) * ((n * u) / om)))
    end if
    code = tmp
end function

Java

l_m = Math.abs(l);
public static double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if (l_m <= 6.9e+19) {
		tmp = Math.sqrt(2.0) * Math.pow((n * (U * t)), 0.5);
	} else if (l_m <= 1.15e+147) {
		tmp = Math.sqrt(((U * -4.0) / (Om / (n * Math.pow(l_m, 2.0)))));
	} else if (l_m <= 2.95e+187) {
		tmp = Math.sqrt(Math.abs((2.0 * (t * (n * U)))));
	} else {
		tmp = (l_m * Math.sqrt(2.0)) * Math.sqrt((-2.0 * ((n * U) / Om)));
	}
	return tmp;
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	tmp = 0
	if l_m <= 6.9e+19:
		tmp = math.sqrt(2.0) * math.pow((n * (U * t)), 0.5)
	elif l_m <= 1.15e+147:
		tmp = math.sqrt(((U * -4.0) / (Om / (n * math.pow(l_m, 2.0)))))
	elif l_m <= 2.95e+187:
		tmp = math.sqrt(math.fabs((2.0 * (t * (n * U)))))
	else:
		tmp = (l_m * math.sqrt(2.0)) * math.sqrt((-2.0 * ((n * U) / Om)))
	return tmp

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0
	if (l_m <= 6.9e+19)
		tmp = Float64(sqrt(2.0) * (Float64(n * Float64(U * t)) ^ 0.5));
	elseif (l_m <= 1.15e+147)
		tmp = sqrt(Float64(Float64(U * -4.0) / Float64(Om / Float64(n * (l_m ^ 2.0)))));
	elseif (l_m <= 2.95e+187)
		tmp = sqrt(abs(Float64(2.0 * Float64(t * Float64(n * U)))));
	else
		tmp = Float64(Float64(l_m * sqrt(2.0)) * sqrt(Float64(-2.0 * Float64(Float64(n * U) / Om))));
	end
	return tmp
end

MATLAB

l_m = abs(l);
function tmp_2 = code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0;
	if (l_m <= 6.9e+19)
		tmp = sqrt(2.0) * ((n * (U * t)) ^ 0.5);
	elseif (l_m <= 1.15e+147)
		tmp = sqrt(((U * -4.0) / (Om / (n * (l_m ^ 2.0)))));
	elseif (l_m <= 2.95e+187)
		tmp = sqrt(abs((2.0 * (t * (n * U)))));
	else
		tmp = (l_m * sqrt(2.0)) * sqrt((-2.0 * ((n * U) / Om)));
	end
	tmp_2 = tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := If[LessEqual[l$95$m, 6.9e+19], N[(N[Sqrt[2.0], $MachinePrecision] * N[Power[N[(n * N[(U * t), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision], If[LessEqual[l$95$m, 1.15e+147], N[Sqrt[N[(N[(U * -4.0), $MachinePrecision] / N[(Om / N[(n * N[Power[l$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[l$95$m, 2.95e+187], N[Sqrt[N[Abs[N[(2.0 * N[(t * N[(n * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision], N[(N[(l$95$m * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(-2.0 * N[(N[(n * U), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 13: 40.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} \mathbf{if}\;l_m \leq 1.4 \cdot 10^{+20}:\\ \;\;\;\;\sqrt{2} \cdot {\left(n \cdot \left(U \cdot t\right)\right)}^{0.5}\\ \mathbf{elif}\;l_m \leq 2 \cdot 10^{+147} \lor \neg \left(l_m \leq 1.26 \cdot 10^{+187}\right):\\ \;\;\;\;\sqrt{-4 \cdot \frac{U \cdot \left(n \cdot {l_m}^{2}\right)}{Om}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left|2 \cdot \left(t \cdot \left(n \cdot U\right)\right)\right|}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (if (<= l_m 1.4e+20)
   (* (sqrt 2.0) (pow (* n (* U t)) 0.5))
   (if (or (<= l_m 2e+147) (not (<= l_m 1.26e+187)))
     (sqrt (* -4.0 (/ (* U (* n (pow l_m 2.0))) Om)))
     (sqrt (fabs (* 2.0 (* t (* n U))))))))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if (l_m <= 1.4e+20) {
		tmp = sqrt(2.0) * pow((n * (U * t)), 0.5);
	} else if ((l_m <= 2e+147) || !(l_m <= 1.26e+187)) {
		tmp = sqrt((-4.0 * ((U * (n * pow(l_m, 2.0))) / Om)));
	} else {
		tmp = sqrt(fabs((2.0 * (t * (n * U)))));
	}
	return tmp;
}

Fortran

l_m = abs(l)
real(8) function code(n, u, t, l_m, om, u_42)
    real(8), intent (in) :: n
    real(8), intent (in) :: u
    real(8), intent (in) :: t
    real(8), intent (in) :: l_m
    real(8), intent (in) :: om
    real(8), intent (in) :: u_42
    real(8) :: tmp
    if (l_m <= 1.4d+20) then
        tmp = sqrt(2.0d0) * ((n * (u * t)) ** 0.5d0)
    else if ((l_m <= 2d+147) .or. (.not. (l_m <= 1.26d+187))) then
        tmp = sqrt(((-4.0d0) * ((u * (n * (l_m ** 2.0d0))) / om)))
    else
        tmp = sqrt(abs((2.0d0 * (t * (n * u)))))
    end if
    code = tmp
end function

Java

l_m = Math.abs(l);
public static double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if (l_m <= 1.4e+20) {
		tmp = Math.sqrt(2.0) * Math.pow((n * (U * t)), 0.5);
	} else if ((l_m <= 2e+147) || !(l_m <= 1.26e+187)) {
		tmp = Math.sqrt((-4.0 * ((U * (n * Math.pow(l_m, 2.0))) / Om)));
	} else {
		tmp = Math.sqrt(Math.abs((2.0 * (t * (n * U)))));
	}
	return tmp;
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	tmp = 0
	if l_m <= 1.4e+20:
		tmp = math.sqrt(2.0) * math.pow((n * (U * t)), 0.5)
	elif (l_m <= 2e+147) or not (l_m <= 1.26e+187):
		tmp = math.sqrt((-4.0 * ((U * (n * math.pow(l_m, 2.0))) / Om)))
	else:
		tmp = math.sqrt(math.fabs((2.0 * (t * (n * U)))))
	return tmp

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0
	if (l_m <= 1.4e+20)
		tmp = Float64(sqrt(2.0) * (Float64(n * Float64(U * t)) ^ 0.5));
	elseif ((l_m <= 2e+147) || !(l_m <= 1.26e+187))
		tmp = sqrt(Float64(-4.0 * Float64(Float64(U * Float64(n * (l_m ^ 2.0))) / Om)));
	else
		tmp = sqrt(abs(Float64(2.0 * Float64(t * Float64(n * U)))));
	end
	return tmp
end

MATLAB

l_m = abs(l);
function tmp_2 = code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0;
	if (l_m <= 1.4e+20)
		tmp = sqrt(2.0) * ((n * (U * t)) ^ 0.5);
	elseif ((l_m <= 2e+147) || ~((l_m <= 1.26e+187)))
		tmp = sqrt((-4.0 * ((U * (n * (l_m ^ 2.0))) / Om)));
	else
		tmp = sqrt(abs((2.0 * (t * (n * U)))));
	end
	tmp_2 = tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := If[LessEqual[l$95$m, 1.4e+20], N[(N[Sqrt[2.0], $MachinePrecision] * N[Power[N[(n * N[(U * t), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[l$95$m, 2e+147], N[Not[LessEqual[l$95$m, 1.26e+187]], $MachinePrecision]], N[Sqrt[N[(-4.0 * N[(N[(U * N[(n * N[Power[l$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Sqrt[N[Abs[N[(2.0 * N[(t * N[(n * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]]]

Derivation

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

Alternative 14: 40.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} t_1 := n \cdot {l_m}^{2}\\ \mathbf{if}\;l_m \leq 1.15 \cdot 10^{+20}:\\ \;\;\;\;\sqrt{2} \cdot {\left(n \cdot \left(U \cdot t\right)\right)}^{0.5}\\ \mathbf{elif}\;l_m \leq 2.2 \cdot 10^{+147}:\\ \;\;\;\;\sqrt{\frac{U \cdot -4}{\frac{Om}{t_1}}}\\ \mathbf{elif}\;l_m \leq 2.5 \cdot 10^{+187}:\\ \;\;\;\;\sqrt{\left|2 \cdot \left(t \cdot \left(n \cdot U\right)\right)\right|}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{-4 \cdot \frac{U \cdot t_1}{Om}}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (let* ((t_1 (* n (pow l_m 2.0))))
   (if (<= l_m 1.15e+20)
     (* (sqrt 2.0) (pow (* n (* U t)) 0.5))
     (if (<= l_m 2.2e+147)
       (sqrt (/ (* U -4.0) (/ Om t_1)))
       (if (<= l_m 2.5e+187)
         (sqrt (fabs (* 2.0 (* t (* n U)))))
         (sqrt (* -4.0 (/ (* U t_1) Om))))))))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double t_1 = n * pow(l_m, 2.0);
	double tmp;
	if (l_m <= 1.15e+20) {
		tmp = sqrt(2.0) * pow((n * (U * t)), 0.5);
	} else if (l_m <= 2.2e+147) {
		tmp = sqrt(((U * -4.0) / (Om / t_1)));
	} else if (l_m <= 2.5e+187) {
		tmp = sqrt(fabs((2.0 * (t * (n * U)))));
	} else {
		tmp = sqrt((-4.0 * ((U * t_1) / Om)));
	}
	return tmp;
}

Fortran

l_m = abs(l)
real(8) function code(n, u, t, l_m, om, u_42)
    real(8), intent (in) :: n
    real(8), intent (in) :: u
    real(8), intent (in) :: t
    real(8), intent (in) :: l_m
    real(8), intent (in) :: om
    real(8), intent (in) :: u_42
    real(8) :: t_1
    real(8) :: tmp
    t_1 = n * (l_m ** 2.0d0)
    if (l_m <= 1.15d+20) then
        tmp = sqrt(2.0d0) * ((n * (u * t)) ** 0.5d0)
    else if (l_m <= 2.2d+147) then
        tmp = sqrt(((u * (-4.0d0)) / (om / t_1)))
    else if (l_m <= 2.5d+187) then
        tmp = sqrt(abs((2.0d0 * (t * (n * u)))))
    else
        tmp = sqrt(((-4.0d0) * ((u * t_1) / om)))
    end if
    code = tmp
end function

Java

l_m = Math.abs(l);
public static double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double t_1 = n * Math.pow(l_m, 2.0);
	double tmp;
	if (l_m <= 1.15e+20) {
		tmp = Math.sqrt(2.0) * Math.pow((n * (U * t)), 0.5);
	} else if (l_m <= 2.2e+147) {
		tmp = Math.sqrt(((U * -4.0) / (Om / t_1)));
	} else if (l_m <= 2.5e+187) {
		tmp = Math.sqrt(Math.abs((2.0 * (t * (n * U)))));
	} else {
		tmp = Math.sqrt((-4.0 * ((U * t_1) / Om)));
	}
	return tmp;
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	t_1 = n * math.pow(l_m, 2.0)
	tmp = 0
	if l_m <= 1.15e+20:
		tmp = math.sqrt(2.0) * math.pow((n * (U * t)), 0.5)
	elif l_m <= 2.2e+147:
		tmp = math.sqrt(((U * -4.0) / (Om / t_1)))
	elif l_m <= 2.5e+187:
		tmp = math.sqrt(math.fabs((2.0 * (t * (n * U)))))
	else:
		tmp = math.sqrt((-4.0 * ((U * t_1) / Om)))
	return tmp

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	t_1 = Float64(n * (l_m ^ 2.0))
	tmp = 0.0
	if (l_m <= 1.15e+20)
		tmp = Float64(sqrt(2.0) * (Float64(n * Float64(U * t)) ^ 0.5));
	elseif (l_m <= 2.2e+147)
		tmp = sqrt(Float64(Float64(U * -4.0) / Float64(Om / t_1)));
	elseif (l_m <= 2.5e+187)
		tmp = sqrt(abs(Float64(2.0 * Float64(t * Float64(n * U)))));
	else
		tmp = sqrt(Float64(-4.0 * Float64(Float64(U * t_1) / Om)));
	end
	return tmp
end

MATLAB

l_m = abs(l);
function tmp_2 = code(n, U, t, l_m, Om, U_42_)
	t_1 = n * (l_m ^ 2.0);
	tmp = 0.0;
	if (l_m <= 1.15e+20)
		tmp = sqrt(2.0) * ((n * (U * t)) ^ 0.5);
	elseif (l_m <= 2.2e+147)
		tmp = sqrt(((U * -4.0) / (Om / t_1)));
	elseif (l_m <= 2.5e+187)
		tmp = sqrt(abs((2.0 * (t * (n * U)))));
	else
		tmp = sqrt((-4.0 * ((U * t_1) / Om)));
	end
	tmp_2 = tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := Block[{t$95$1 = N[(n * N[Power[l$95$m, 2.0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[l$95$m, 1.15e+20], N[(N[Sqrt[2.0], $MachinePrecision] * N[Power[N[(n * N[(U * t), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision], If[LessEqual[l$95$m, 2.2e+147], N[Sqrt[N[(N[(U * -4.0), $MachinePrecision] / N[(Om / t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[l$95$m, 2.5e+187], N[Sqrt[N[Abs[N[(2.0 * N[(t * N[(n * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision], N[Sqrt[N[(-4.0 * N[(N[(U * t$95$1), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]]]

Derivation

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

Alternative 15: 47.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} \mathbf{if}\;l_m \leq 1.6 \cdot 10^{+147}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(t - 2 \cdot \frac{{l_m}^{2}}{Om}\right)\right)\right)}\\ \mathbf{elif}\;l_m \leq 1.2 \cdot 10^{+187}:\\ \;\;\;\;\sqrt{\left|2 \cdot \left(t \cdot \left(n \cdot U\right)\right)\right|}\\ \mathbf{else}:\\ \;\;\;\;\left(l_m \cdot \sqrt{2}\right) \cdot \sqrt{-2 \cdot \frac{n \cdot U}{Om}}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (if (<= l_m 1.6e+147)
   (sqrt (* 2.0 (* U (* n (- t (* 2.0 (/ (pow l_m 2.0) Om)))))))
   (if (<= l_m 1.2e+187)
     (sqrt (fabs (* 2.0 (* t (* n U)))))
     (* (* l_m (sqrt 2.0)) (sqrt (* -2.0 (/ (* n U) Om)))))))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if (l_m <= 1.6e+147) {
		tmp = sqrt((2.0 * (U * (n * (t - (2.0 * (pow(l_m, 2.0) / Om)))))));
	} else if (l_m <= 1.2e+187) {
		tmp = sqrt(fabs((2.0 * (t * (n * U)))));
	} else {
		tmp = (l_m * sqrt(2.0)) * sqrt((-2.0 * ((n * U) / Om)));
	}
	return tmp;
}

Fortran

l_m = abs(l)
real(8) function code(n, u, t, l_m, om, u_42)
    real(8), intent (in) :: n
    real(8), intent (in) :: u
    real(8), intent (in) :: t
    real(8), intent (in) :: l_m
    real(8), intent (in) :: om
    real(8), intent (in) :: u_42
    real(8) :: tmp
    if (l_m <= 1.6d+147) then
        tmp = sqrt((2.0d0 * (u * (n * (t - (2.0d0 * ((l_m ** 2.0d0) / om)))))))
    else if (l_m <= 1.2d+187) then
        tmp = sqrt(abs((2.0d0 * (t * (n * u)))))
    else
        tmp = (l_m * sqrt(2.0d0)) * sqrt(((-2.0d0) * ((n * u) / om)))
    end if
    code = tmp
end function

Java

l_m = Math.abs(l);
public static double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if (l_m <= 1.6e+147) {
		tmp = Math.sqrt((2.0 * (U * (n * (t - (2.0 * (Math.pow(l_m, 2.0) / Om)))))));
	} else if (l_m <= 1.2e+187) {
		tmp = Math.sqrt(Math.abs((2.0 * (t * (n * U)))));
	} else {
		tmp = (l_m * Math.sqrt(2.0)) * Math.sqrt((-2.0 * ((n * U) / Om)));
	}
	return tmp;
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	tmp = 0
	if l_m <= 1.6e+147:
		tmp = math.sqrt((2.0 * (U * (n * (t - (2.0 * (math.pow(l_m, 2.0) / Om)))))))
	elif l_m <= 1.2e+187:
		tmp = math.sqrt(math.fabs((2.0 * (t * (n * U)))))
	else:
		tmp = (l_m * math.sqrt(2.0)) * math.sqrt((-2.0 * ((n * U) / Om)))
	return tmp

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0
	if (l_m <= 1.6e+147)
		tmp = sqrt(Float64(2.0 * Float64(U * Float64(n * Float64(t - Float64(2.0 * Float64((l_m ^ 2.0) / Om)))))));
	elseif (l_m <= 1.2e+187)
		tmp = sqrt(abs(Float64(2.0 * Float64(t * Float64(n * U)))));
	else
		tmp = Float64(Float64(l_m * sqrt(2.0)) * sqrt(Float64(-2.0 * Float64(Float64(n * U) / Om))));
	end
	return tmp
end

MATLAB

l_m = abs(l);
function tmp_2 = code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0;
	if (l_m <= 1.6e+147)
		tmp = sqrt((2.0 * (U * (n * (t - (2.0 * ((l_m ^ 2.0) / Om)))))));
	elseif (l_m <= 1.2e+187)
		tmp = sqrt(abs((2.0 * (t * (n * U)))));
	else
		tmp = (l_m * sqrt(2.0)) * sqrt((-2.0 * ((n * U) / Om)));
	end
	tmp_2 = tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := If[LessEqual[l$95$m, 1.6e+147], N[Sqrt[N[(2.0 * N[(U * N[(n * N[(t - N[(2.0 * N[(N[Power[l$95$m, 2.0], $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[l$95$m, 1.2e+187], N[Sqrt[N[Abs[N[(2.0 * N[(t * N[(n * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision], N[(N[(l$95$m * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(-2.0 * N[(N[(n * U), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 16: 40.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} \mathbf{if}\;U \leq 1.8 \cdot 10^{-303} \lor \neg \left(U \leq 1.25 \cdot 10^{-250}\right) \land U \leq 9.2 \cdot 10^{-175}:\\ \;\;\;\;\sqrt{\left|2 \cdot \left(t \cdot \left(n \cdot U\right)\right)\right|}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 \cdot U} \cdot \sqrt{n \cdot t}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (if (or (<= U 1.8e-303) (and (not (<= U 1.25e-250)) (<= U 9.2e-175)))
   (sqrt (fabs (* 2.0 (* t (* n U)))))
   (* (sqrt (* 2.0 U)) (sqrt (* n t)))))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if ((U <= 1.8e-303) || (!(U <= 1.25e-250) && (U <= 9.2e-175))) {
		tmp = sqrt(fabs((2.0 * (t * (n * U)))));
	} else {
		tmp = sqrt((2.0 * U)) * sqrt((n * t));
	}
	return tmp;
}

Fortran

l_m = abs(l)
real(8) function code(n, u, t, l_m, om, u_42)
    real(8), intent (in) :: n
    real(8), intent (in) :: u
    real(8), intent (in) :: t
    real(8), intent (in) :: l_m
    real(8), intent (in) :: om
    real(8), intent (in) :: u_42
    real(8) :: tmp
    if ((u <= 1.8d-303) .or. (.not. (u <= 1.25d-250)) .and. (u <= 9.2d-175)) then
        tmp = sqrt(abs((2.0d0 * (t * (n * u)))))
    else
        tmp = sqrt((2.0d0 * u)) * sqrt((n * t))
    end if
    code = tmp
end function

Java

l_m = Math.abs(l);
public static double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if ((U <= 1.8e-303) || (!(U <= 1.25e-250) && (U <= 9.2e-175))) {
		tmp = Math.sqrt(Math.abs((2.0 * (t * (n * U)))));
	} else {
		tmp = Math.sqrt((2.0 * U)) * Math.sqrt((n * t));
	}
	return tmp;
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	tmp = 0
	if (U <= 1.8e-303) or (not (U <= 1.25e-250) and (U <= 9.2e-175)):
		tmp = math.sqrt(math.fabs((2.0 * (t * (n * U)))))
	else:
		tmp = math.sqrt((2.0 * U)) * math.sqrt((n * t))
	return tmp

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0
	if ((U <= 1.8e-303) || (!(U <= 1.25e-250) && (U <= 9.2e-175)))
		tmp = sqrt(abs(Float64(2.0 * Float64(t * Float64(n * U)))));
	else
		tmp = Float64(sqrt(Float64(2.0 * U)) * sqrt(Float64(n * t)));
	end
	return tmp
end

MATLAB

l_m = abs(l);
function tmp_2 = code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0;
	if ((U <= 1.8e-303) || (~((U <= 1.25e-250)) && (U <= 9.2e-175)))
		tmp = sqrt(abs((2.0 * (t * (n * U)))));
	else
		tmp = sqrt((2.0 * U)) * sqrt((n * t));
	end
	tmp_2 = tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := If[Or[LessEqual[U, 1.8e-303], And[N[Not[LessEqual[U, 1.25e-250]], $MachinePrecision], LessEqual[U, 9.2e-175]]], N[Sqrt[N[Abs[N[(2.0 * N[(t * N[(n * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision], N[(N[Sqrt[N[(2.0 * U), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(n * t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 17: 38.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} \mathbf{if}\;U* \leq 3 \cdot 10^{-142}:\\ \;\;\;\;\sqrt{\left|2 \cdot \left(t \cdot \left(n \cdot U\right)\right)\right|}\\ \mathbf{else}:\\ \;\;\;\;{\left(\left(2 \cdot U\right) \cdot \left(n \cdot t\right)\right)}^{0.5}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (if (<= U* 3e-142)
   (sqrt (fabs (* 2.0 (* t (* n U)))))
   (pow (* (* 2.0 U) (* n t)) 0.5)))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if (U_42_ <= 3e-142) {
		tmp = sqrt(fabs((2.0 * (t * (n * U)))));
	} else {
		tmp = pow(((2.0 * U) * (n * t)), 0.5);
	}
	return tmp;
}

Fortran

l_m = abs(l)
real(8) function code(n, u, t, l_m, om, u_42)
    real(8), intent (in) :: n
    real(8), intent (in) :: u
    real(8), intent (in) :: t
    real(8), intent (in) :: l_m
    real(8), intent (in) :: om
    real(8), intent (in) :: u_42
    real(8) :: tmp
    if (u_42 <= 3d-142) then
        tmp = sqrt(abs((2.0d0 * (t * (n * u)))))
    else
        tmp = ((2.0d0 * u) * (n * t)) ** 0.5d0
    end if
    code = tmp
end function

Java

l_m = Math.abs(l);
public static double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if (U_42_ <= 3e-142) {
		tmp = Math.sqrt(Math.abs((2.0 * (t * (n * U)))));
	} else {
		tmp = Math.pow(((2.0 * U) * (n * t)), 0.5);
	}
	return tmp;
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	tmp = 0
	if U_42_ <= 3e-142:
		tmp = math.sqrt(math.fabs((2.0 * (t * (n * U)))))
	else:
		tmp = math.pow(((2.0 * U) * (n * t)), 0.5)
	return tmp

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0
	if (U_42_ <= 3e-142)
		tmp = sqrt(abs(Float64(2.0 * Float64(t * Float64(n * U)))));
	else
		tmp = Float64(Float64(2.0 * U) * Float64(n * t)) ^ 0.5;
	end
	return tmp
end

MATLAB

l_m = abs(l);
function tmp_2 = code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0;
	if (U_42_ <= 3e-142)
		tmp = sqrt(abs((2.0 * (t * (n * U)))));
	else
		tmp = ((2.0 * U) * (n * t)) ^ 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := If[LessEqual[U$42$, 3e-142], N[Sqrt[N[Abs[N[(2.0 * N[(t * N[(n * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision], N[Power[N[(N[(2.0 * U), $MachinePrecision] * N[(n * t), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]]

Derivation

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

Alternative 18: 39.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} \mathbf{if}\;U* \leq -4.6 \cdot 10^{-279}:\\ \;\;\;\;\sqrt{\left|2 \cdot \left(t \cdot \left(n \cdot U\right)\right)\right|}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left|\left(2 \cdot U\right) \cdot \left(n \cdot t\right)\right|}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (if (<= U* -4.6e-279)
   (sqrt (fabs (* 2.0 (* t (* n U)))))
   (sqrt (fabs (* (* 2.0 U) (* n t))))))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if (U_42_ <= -4.6e-279) {
		tmp = sqrt(fabs((2.0 * (t * (n * U)))));
	} else {
		tmp = sqrt(fabs(((2.0 * U) * (n * t))));
	}
	return tmp;
}

Fortran

l_m = abs(l)
real(8) function code(n, u, t, l_m, om, u_42)
    real(8), intent (in) :: n
    real(8), intent (in) :: u
    real(8), intent (in) :: t
    real(8), intent (in) :: l_m
    real(8), intent (in) :: om
    real(8), intent (in) :: u_42
    real(8) :: tmp
    if (u_42 <= (-4.6d-279)) then
        tmp = sqrt(abs((2.0d0 * (t * (n * u)))))
    else
        tmp = sqrt(abs(((2.0d0 * u) * (n * t))))
    end if
    code = tmp
end function

Java

l_m = Math.abs(l);
public static double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if (U_42_ <= -4.6e-279) {
		tmp = Math.sqrt(Math.abs((2.0 * (t * (n * U)))));
	} else {
		tmp = Math.sqrt(Math.abs(((2.0 * U) * (n * t))));
	}
	return tmp;
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	tmp = 0
	if U_42_ <= -4.6e-279:
		tmp = math.sqrt(math.fabs((2.0 * (t * (n * U)))))
	else:
		tmp = math.sqrt(math.fabs(((2.0 * U) * (n * t))))
	return tmp

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0
	if (U_42_ <= -4.6e-279)
		tmp = sqrt(abs(Float64(2.0 * Float64(t * Float64(n * U)))));
	else
		tmp = sqrt(abs(Float64(Float64(2.0 * U) * Float64(n * t))));
	end
	return tmp
end

MATLAB

l_m = abs(l);
function tmp_2 = code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0;
	if (U_42_ <= -4.6e-279)
		tmp = sqrt(abs((2.0 * (t * (n * U)))));
	else
		tmp = sqrt(abs(((2.0 * U) * (n * t))));
	end
	tmp_2 = tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := If[LessEqual[U$42$, -4.6e-279], N[Sqrt[N[Abs[N[(2.0 * N[(t * N[(n * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision], N[Sqrt[N[Abs[N[(N[(2.0 * U), $MachinePrecision] * N[(n * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]]

Derivation

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

Alternative 19: 38.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} \mathbf{if}\;Om \leq 5.1 \cdot 10^{+87}:\\ \;\;\;\;{\left(\left(2 \cdot U\right) \cdot \left(n \cdot t\right)\right)}^{0.5}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 \cdot \left(t \cdot \left(n \cdot U\right)\right)}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (if (<= Om 5.1e+87)
   (pow (* (* 2.0 U) (* n t)) 0.5)
   (sqrt (* 2.0 (* t (* n U))))))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if (Om <= 5.1e+87) {
		tmp = pow(((2.0 * U) * (n * t)), 0.5);
	} else {
		tmp = sqrt((2.0 * (t * (n * U))));
	}
	return tmp;
}

Fortran

l_m = abs(l)
real(8) function code(n, u, t, l_m, om, u_42)
    real(8), intent (in) :: n
    real(8), intent (in) :: u
    real(8), intent (in) :: t
    real(8), intent (in) :: l_m
    real(8), intent (in) :: om
    real(8), intent (in) :: u_42
    real(8) :: tmp
    if (om <= 5.1d+87) then
        tmp = ((2.0d0 * u) * (n * t)) ** 0.5d0
    else
        tmp = sqrt((2.0d0 * (t * (n * u))))
    end if
    code = tmp
end function

Java

l_m = Math.abs(l);
public static double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if (Om <= 5.1e+87) {
		tmp = Math.pow(((2.0 * U) * (n * t)), 0.5);
	} else {
		tmp = Math.sqrt((2.0 * (t * (n * U))));
	}
	return tmp;
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	tmp = 0
	if Om <= 5.1e+87:
		tmp = math.pow(((2.0 * U) * (n * t)), 0.5)
	else:
		tmp = math.sqrt((2.0 * (t * (n * U))))
	return tmp

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0
	if (Om <= 5.1e+87)
		tmp = Float64(Float64(2.0 * U) * Float64(n * t)) ^ 0.5;
	else
		tmp = sqrt(Float64(2.0 * Float64(t * Float64(n * U))));
	end
	return tmp
end

MATLAB

l_m = abs(l);
function tmp_2 = code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0;
	if (Om <= 5.1e+87)
		tmp = ((2.0 * U) * (n * t)) ^ 0.5;
	else
		tmp = sqrt((2.0 * (t * (n * U))));
	end
	tmp_2 = tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := If[LessEqual[Om, 5.1e+87], N[Power[N[(N[(2.0 * U), $MachinePrecision] * N[(n * t), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision], N[Sqrt[N[(2.0 * N[(t * N[(n * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

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

Alternative 20: 36.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} \mathbf{if}\;Om \leq 2.05 \cdot 10^{+88}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot t\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 \cdot \left(t \cdot \left(n \cdot U\right)\right)}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (if (<= Om 2.05e+88)
   (sqrt (* 2.0 (* U (* n t))))
   (sqrt (* 2.0 (* t (* n U))))))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if (Om <= 2.05e+88) {
		tmp = sqrt((2.0 * (U * (n * t))));
	} else {
		tmp = sqrt((2.0 * (t * (n * U))));
	}
	return tmp;
}

Fortran

l_m = abs(l)
real(8) function code(n, u, t, l_m, om, u_42)
    real(8), intent (in) :: n
    real(8), intent (in) :: u
    real(8), intent (in) :: t
    real(8), intent (in) :: l_m
    real(8), intent (in) :: om
    real(8), intent (in) :: u_42
    real(8) :: tmp
    if (om <= 2.05d+88) then
        tmp = sqrt((2.0d0 * (u * (n * t))))
    else
        tmp = sqrt((2.0d0 * (t * (n * u))))
    end if
    code = tmp
end function

Java

l_m = Math.abs(l);
public static double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if (Om <= 2.05e+88) {
		tmp = Math.sqrt((2.0 * (U * (n * t))));
	} else {
		tmp = Math.sqrt((2.0 * (t * (n * U))));
	}
	return tmp;
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	tmp = 0
	if Om <= 2.05e+88:
		tmp = math.sqrt((2.0 * (U * (n * t))))
	else:
		tmp = math.sqrt((2.0 * (t * (n * U))))
	return tmp

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0
	if (Om <= 2.05e+88)
		tmp = sqrt(Float64(2.0 * Float64(U * Float64(n * t))));
	else
		tmp = sqrt(Float64(2.0 * Float64(t * Float64(n * U))));
	end
	return tmp
end

MATLAB

l_m = abs(l);
function tmp_2 = code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0;
	if (Om <= 2.05e+88)
		tmp = sqrt((2.0 * (U * (n * t))));
	else
		tmp = sqrt((2.0 * (t * (n * U))));
	end
	tmp_2 = tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := If[LessEqual[Om, 2.05e+88], N[Sqrt[N[(2.0 * N[(U * N[(n * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Sqrt[N[(2.0 * N[(t * N[(n * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

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

Alternative 21: 35.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} \mathbf{if}\;U \leq 1.02 \cdot 10^{-216}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot t\right)\right)}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (if (<= U 1.02e-216)
   (sqrt (* (* 2.0 n) (* U t)))
   (sqrt (* 2.0 (* U (* n t))))))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if (U <= 1.02e-216) {
		tmp = sqrt(((2.0 * n) * (U * t)));
	} else {
		tmp = sqrt((2.0 * (U * (n * t))));
	}
	return tmp;
}

Fortran

l_m = abs(l)
real(8) function code(n, u, t, l_m, om, u_42)
    real(8), intent (in) :: n
    real(8), intent (in) :: u
    real(8), intent (in) :: t
    real(8), intent (in) :: l_m
    real(8), intent (in) :: om
    real(8), intent (in) :: u_42
    real(8) :: tmp
    if (u <= 1.02d-216) then
        tmp = sqrt(((2.0d0 * n) * (u * t)))
    else
        tmp = sqrt((2.0d0 * (u * (n * t))))
    end if
    code = tmp
end function

Java

l_m = Math.abs(l);
public static double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double tmp;
	if (U <= 1.02e-216) {
		tmp = Math.sqrt(((2.0 * n) * (U * t)));
	} else {
		tmp = Math.sqrt((2.0 * (U * (n * t))));
	}
	return tmp;
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	tmp = 0
	if U <= 1.02e-216:
		tmp = math.sqrt(((2.0 * n) * (U * t)))
	else:
		tmp = math.sqrt((2.0 * (U * (n * t))))
	return tmp

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0
	if (U <= 1.02e-216)
		tmp = sqrt(Float64(Float64(2.0 * n) * Float64(U * t)));
	else
		tmp = sqrt(Float64(2.0 * Float64(U * Float64(n * t))));
	end
	return tmp
end

MATLAB

l_m = abs(l);
function tmp_2 = code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0;
	if (U <= 1.02e-216)
		tmp = sqrt(((2.0 * n) * (U * t)));
	else
		tmp = sqrt((2.0 * (U * (n * t))));
	end
	tmp_2 = tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := If[LessEqual[U, 1.02e-216], N[Sqrt[N[(N[(2.0 * n), $MachinePrecision] * N[(U * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Sqrt[N[(2.0 * N[(U * N[(n * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

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

Alternative 22: 36.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \sqrt{2 \cdot \left(U \cdot \left(n \cdot t\right)\right)} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*) :precision binary64 (sqrt (* 2.0 (* U (* n t)))))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	return sqrt((2.0 * (U * (n * t))));
}

Fortran

l_m = abs(l)
real(8) function code(n, u, t, l_m, om, u_42)
    real(8), intent (in) :: n
    real(8), intent (in) :: u
    real(8), intent (in) :: t
    real(8), intent (in) :: l_m
    real(8), intent (in) :: om
    real(8), intent (in) :: u_42
    code = sqrt((2.0d0 * (u * (n * t))))
end function

Java

l_m = Math.abs(l);
public static double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	return Math.sqrt((2.0 * (U * (n * t))));
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	return math.sqrt((2.0 * (U * (n * t))))

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	return sqrt(Float64(2.0 * Float64(U * Float64(n * t))))
end

MATLAB

l_m = abs(l);
function tmp = code(n, U, t, l_m, Om, U_42_)
	tmp = sqrt((2.0 * (U * (n * t))));
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := N[Sqrt[N[(2.0 * N[(U * N[(n * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2024003 
(FPCore (n U t l Om U*)
  :name "Toniolo and Linder, Equation (13)"
  :precision binary64
  (sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))