Toniolo and Linder, Equation (13)

Percentage Accurate: 48.9% → 65.3%

Time: 24.9s

Alternatives: 14

Speedup: 1.1×

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: 48.9% 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: 65.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} t_1 := \sqrt[3]{\left(\frac{n}{{Om}^{2}} \cdot \left(U* - U\right) - \frac{2}{Om}\right) \cdot \left(n \cdot U\right)}\\ t_2 := {\left(\frac{l_m}{Om}\right)}^{2}\\ t_3 := \left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \frac{l_m \cdot l_m}{Om}\right) + \left(n \cdot t_2\right) \cdot \left(U* - U\right)\right)\\ \mathbf{if}\;t_3 \leq 0:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t - \mathsf{fma}\left(2, l_m \cdot \frac{l_m}{Om}, n \cdot \left(t_2 \cdot \left(U - U*\right)\right)\right)\right)\right)}\\ \mathbf{elif}\;t_3 \leq 4 \cdot 10^{+302}:\\ \;\;\;\;\sqrt{t_3}\\ \mathbf{else}:\\ \;\;\;\;\left({\left({t_1}^{2}\right)}^{0.5} \cdot {t_1}^{0.5}\right) \cdot \left(l_m \cdot \sqrt{2}\right)\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (let* ((t_1 (cbrt (* (- (* (/ n (pow Om 2.0)) (- U* U)) (/ 2.0 Om)) (* n U))))
        (t_2 (pow (/ l_m Om) 2.0))
        (t_3
         (*
          (* (* 2.0 n) U)
          (+ (- t (* 2.0 (/ (* l_m l_m) Om))) (* (* n t_2) (- U* U))))))
   (if (<= t_3 0.0)
     (sqrt
      (*
       (* 2.0 n)
       (* U (- t (fma 2.0 (* l_m (/ l_m Om)) (* n (* t_2 (- U U*))))))))
     (if (<= t_3 4e+302)
       (sqrt t_3)
       (* (* (pow (pow t_1 2.0) 0.5) (pow t_1 0.5)) (* 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 = cbrt(((((n / pow(Om, 2.0)) * (U_42_ - U)) - (2.0 / Om)) * (n * U)));
	double t_2 = pow((l_m / Om), 2.0);
	double t_3 = ((2.0 * n) * U) * ((t - (2.0 * ((l_m * l_m) / Om))) + ((n * t_2) * (U_42_ - U)));
	double tmp;
	if (t_3 <= 0.0) {
		tmp = sqrt(((2.0 * n) * (U * (t - fma(2.0, (l_m * (l_m / Om)), (n * (t_2 * (U - U_42_))))))));
	} else if (t_3 <= 4e+302) {
		tmp = sqrt(t_3);
	} else {
		tmp = (pow(pow(t_1, 2.0), 0.5) * pow(t_1, 0.5)) * (l_m * sqrt(2.0));
	}
	return tmp;
}

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	t_1 = cbrt(Float64(Float64(Float64(Float64(n / (Om ^ 2.0)) * Float64(U_42_ - U)) - Float64(2.0 / Om)) * Float64(n * U)))
	t_2 = Float64(l_m / Om) ^ 2.0
	t_3 = Float64(Float64(Float64(2.0 * n) * U) * Float64(Float64(t - Float64(2.0 * Float64(Float64(l_m * l_m) / Om))) + Float64(Float64(n * t_2) * Float64(U_42_ - U))))
	tmp = 0.0
	if (t_3 <= 0.0)
		tmp = sqrt(Float64(Float64(2.0 * n) * Float64(U * Float64(t - fma(2.0, Float64(l_m * Float64(l_m / Om)), Float64(n * Float64(t_2 * Float64(U - U_42_))))))));
	elseif (t_3 <= 4e+302)
		tmp = sqrt(t_3);
	else
		tmp = Float64(Float64(((t_1 ^ 2.0) ^ 0.5) * (t_1 ^ 0.5)) * 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[Power[N[(N[(N[(N[(n / N[Power[Om, 2.0], $MachinePrecision]), $MachinePrecision] * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision] - N[(2.0 / Om), $MachinePrecision]), $MachinePrecision] * N[(n * U), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]}, Block[{t$95$2 = N[Power[N[(l$95$m / Om), $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(2.0 * n), $MachinePrecision] * U), $MachinePrecision] * N[(N[(t - N[(2.0 * N[(N[(l$95$m * l$95$m), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(n * t$95$2), $MachinePrecision] * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, 0.0], N[Sqrt[N[(N[(2.0 * n), $MachinePrecision] * N[(U * N[(t - N[(2.0 * N[(l$95$m * N[(l$95$m / Om), $MachinePrecision]), $MachinePrecision] + N[(n * N[(t$95$2 * N[(U - U$42$), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[t$95$3, 4e+302], N[Sqrt[t$95$3], $MachinePrecision], N[(N[(N[Power[N[Power[t$95$1, 2.0], $MachinePrecision], 0.5], $MachinePrecision] * N[Power[t$95$1, 0.5], $MachinePrecision]), $MachinePrecision] * N[(l$95$m * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 2: 64.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} t_1 := t - 2 \cdot \left(l_m \cdot \frac{l_m}{Om}\right)\\ t_2 := \left(n \cdot {\left(\frac{l_m}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\\ t_3 := \left(2 \cdot n\right) \cdot U\\ t_4 := t_3 \cdot \left(\left(t - 2 \cdot \frac{l_m \cdot l_m}{Om}\right) + t_2\right)\\ \mathbf{if}\;t_4 \leq 0:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot t_1\right)\right)}\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;\sqrt{t_3 \cdot \left(t_1 + t_2\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(l_m \cdot \sqrt{2}\right) \cdot \sqrt{U \cdot \left(n \cdot \left(\frac{n \cdot U*}{{Om}^{2}} - \frac{2}{Om}\right)\right)}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (let* ((t_1 (- t (* 2.0 (* l_m (/ l_m 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 0.0)
     (sqrt (* 2.0 (* U (* n t_1))))
     (if (<= t_4 INFINITY)
       (sqrt (* t_3 (+ t_1 t_2)))
       (*
        (* l_m (sqrt 2.0))
        (sqrt (* U (* n (- (/ (* 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 = t - (2.0 * (l_m * (l_m / 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 <= 0.0) {
		tmp = sqrt((2.0 * (U * (n * t_1))));
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = sqrt((t_3 * (t_1 + t_2)));
	} else {
		tmp = (l_m * sqrt(2.0)) * sqrt((U * (n * (((n * U_42_) / pow(Om, 2.0)) - (2.0 / Om)))));
	}
	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 = t - (2.0 * (l_m * (l_m / 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 <= 0.0) {
		tmp = Math.sqrt((2.0 * (U * (n * t_1))));
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = Math.sqrt((t_3 * (t_1 + t_2)));
	} else {
		tmp = (l_m * Math.sqrt(2.0)) * Math.sqrt((U * (n * (((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 = t - (2.0 * (l_m * (l_m / Om)))
	t_2 = (n * math.pow((l_m / Om), 2.0)) * (U_42_ - U)
	t_3 = (2.0 * n) * U
	t_4 = t_3 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_2)
	tmp = 0
	if t_4 <= 0.0:
		tmp = math.sqrt((2.0 * (U * (n * t_1))))
	elif t_4 <= math.inf:
		tmp = math.sqrt((t_3 * (t_1 + t_2)))
	else:
		tmp = (l_m * math.sqrt(2.0)) * math.sqrt((U * (n * (((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(t - Float64(2.0 * Float64(l_m * Float64(l_m / 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 <= 0.0)
		tmp = sqrt(Float64(2.0 * Float64(U * Float64(n * t_1))));
	elseif (t_4 <= Inf)
		tmp = sqrt(Float64(t_3 * Float64(t_1 + t_2)));
	else
		tmp = Float64(Float64(l_m * sqrt(2.0)) * sqrt(Float64(U * Float64(n * 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 = t - (2.0 * (l_m * (l_m / Om)));
	t_2 = (n * ((l_m / Om) ^ 2.0)) * (U_42_ - U);
	t_3 = (2.0 * n) * U;
	t_4 = t_3 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_2);
	tmp = 0.0;
	if (t_4 <= 0.0)
		tmp = sqrt((2.0 * (U * (n * t_1))));
	elseif (t_4 <= Inf)
		tmp = sqrt((t_3 * (t_1 + t_2)));
	else
		tmp = (l_m * sqrt(2.0)) * sqrt((U * (n * (((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[(t - N[(2.0 * N[(l$95$m * N[(l$95$m / Om), $MachinePrecision]), $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, 0.0], N[Sqrt[N[(2.0 * N[(U * N[(n * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[t$95$4, Infinity], N[Sqrt[N[(t$95$3 * N[(t$95$1 + t$95$2), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(N[(l$95$m * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(U * N[(n * N[(N[(N[(n * U$42$), $MachinePrecision] / N[Power[Om, 2.0], $MachinePrecision]), $MachinePrecision] - N[(2.0 / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

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

Alternative 3: 64.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} t_1 := l_m \cdot \frac{l_m}{Om}\\ t_2 := \left(2 \cdot n\right) \cdot U\\ t_3 := {\left(\frac{l_m}{Om}\right)}^{2}\\ t_4 := \left(n \cdot t_3\right) \cdot \left(U* - U\right)\\ t_5 := t_2 \cdot \left(\left(t - 2 \cdot \frac{l_m \cdot l_m}{Om}\right) + t_4\right)\\ \mathbf{if}\;t_5 \leq 0:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(t - \mathsf{fma}\left(2, t_1, n \cdot \left(t_3 \cdot \left(U - U*\right)\right)\right)\right)\right)}\\ \mathbf{elif}\;t_5 \leq \infty:\\ \;\;\;\;\sqrt{t_2 \cdot \left(\left(t - 2 \cdot t_1\right) + t_4\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(l_m \cdot \sqrt{2}\right) \cdot \sqrt{U \cdot \left(n \cdot \left(\frac{n \cdot U*}{{Om}^{2}} - \frac{2}{Om}\right)\right)}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (let* ((t_1 (* l_m (/ l_m Om)))
        (t_2 (* (* 2.0 n) U))
        (t_3 (pow (/ l_m Om) 2.0))
        (t_4 (* (* n t_3) (- U* U)))
        (t_5 (* t_2 (+ (- t (* 2.0 (/ (* l_m l_m) Om))) t_4))))
   (if (<= t_5 0.0)
     (sqrt (* (* 2.0 n) (* U (- t (fma 2.0 t_1 (* n (* t_3 (- U U*))))))))
     (if (<= t_5 INFINITY)
       (sqrt (* t_2 (+ (- t (* 2.0 t_1)) t_4)))
       (*
        (* l_m (sqrt 2.0))
        (sqrt (* U (* n (- (/ (* 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 = l_m * (l_m / Om);
	double t_2 = (2.0 * n) * U;
	double t_3 = pow((l_m / Om), 2.0);
	double t_4 = (n * t_3) * (U_42_ - U);
	double t_5 = t_2 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_4);
	double tmp;
	if (t_5 <= 0.0) {
		tmp = sqrt(((2.0 * n) * (U * (t - fma(2.0, t_1, (n * (t_3 * (U - U_42_))))))));
	} else if (t_5 <= ((double) INFINITY)) {
		tmp = sqrt((t_2 * ((t - (2.0 * t_1)) + t_4)));
	} else {
		tmp = (l_m * sqrt(2.0)) * sqrt((U * (n * (((n * U_42_) / 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(l_m * Float64(l_m / Om))
	t_2 = Float64(Float64(2.0 * n) * U)
	t_3 = Float64(l_m / Om) ^ 2.0
	t_4 = Float64(Float64(n * t_3) * Float64(U_42_ - U))
	t_5 = Float64(t_2 * Float64(Float64(t - Float64(2.0 * Float64(Float64(l_m * l_m) / Om))) + t_4))
	tmp = 0.0
	if (t_5 <= 0.0)
		tmp = sqrt(Float64(Float64(2.0 * n) * Float64(U * Float64(t - fma(2.0, t_1, Float64(n * Float64(t_3 * Float64(U - U_42_))))))));
	elseif (t_5 <= Inf)
		tmp = sqrt(Float64(t_2 * Float64(Float64(t - Float64(2.0 * t_1)) + t_4)));
	else
		tmp = Float64(Float64(l_m * sqrt(2.0)) * sqrt(Float64(U * Float64(n * Float64(Float64(Float64(n * U_42_) / (Om ^ 2.0)) - Float64(2.0 / Om))))));
	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[(l$95$m * N[(l$95$m / Om), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 * n), $MachinePrecision] * U), $MachinePrecision]}, Block[{t$95$3 = N[Power[N[(l$95$m / Om), $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$4 = N[(N[(n * t$95$3), $MachinePrecision] * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = 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$4), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, 0.0], N[Sqrt[N[(N[(2.0 * n), $MachinePrecision] * N[(U * N[(t - N[(2.0 * t$95$1 + N[(n * N[(t$95$3 * N[(U - U$42$), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[t$95$5, Infinity], N[Sqrt[N[(t$95$2 * N[(N[(t - N[(2.0 * t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(N[(l$95$m * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(U * N[(n * N[(N[(N[(n * U$42$), $MachinePrecision] / N[Power[Om, 2.0], $MachinePrecision]), $MachinePrecision] - N[(2.0 / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

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

Alternative 4: 63.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} t_1 := t - 2 \cdot \left(l_m \cdot \frac{l_m}{Om}\right)\\ t_2 := \left(n \cdot {\left(\frac{l_m}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\\ t_3 := \left(2 \cdot n\right) \cdot U\\ t_4 := t_3 \cdot \left(\left(t - 2 \cdot \frac{l_m \cdot l_m}{Om}\right) + t_2\right)\\ \mathbf{if}\;t_4 \leq 0:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot t_1\right)\right)}\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;\sqrt{t_3 \cdot \left(t_1 + t_2\right)}\\ \mathbf{else}:\\ \;\;\;\;\left|\left(n \cdot \left(l_m \cdot \sqrt{2}\right)\right) \cdot \frac{\sqrt{U \cdot \left(U* - U\right)}}{Om}\right|\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (let* ((t_1 (- t (* 2.0 (* l_m (/ l_m 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 0.0)
     (sqrt (* 2.0 (* U (* n t_1))))
     (if (<= t_4 INFINITY)
       (sqrt (* t_3 (+ t_1 t_2)))
       (fabs (* (* n (* l_m (sqrt 2.0))) (/ (sqrt (* U (- U* U))) 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 = t - (2.0 * (l_m * (l_m / 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 <= 0.0) {
		tmp = sqrt((2.0 * (U * (n * t_1))));
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = sqrt((t_3 * (t_1 + t_2)));
	} else {
		tmp = fabs(((n * (l_m * sqrt(2.0))) * (sqrt((U * (U_42_ - U))) / Om)));
	}
	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 = t - (2.0 * (l_m * (l_m / 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 <= 0.0) {
		tmp = Math.sqrt((2.0 * (U * (n * t_1))));
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = Math.sqrt((t_3 * (t_1 + t_2)));
	} else {
		tmp = Math.abs(((n * (l_m * Math.sqrt(2.0))) * (Math.sqrt((U * (U_42_ - U))) / Om)));
	}
	return tmp;
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	t_1 = t - (2.0 * (l_m * (l_m / Om)))
	t_2 = (n * math.pow((l_m / Om), 2.0)) * (U_42_ - U)
	t_3 = (2.0 * n) * U
	t_4 = t_3 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_2)
	tmp = 0
	if t_4 <= 0.0:
		tmp = math.sqrt((2.0 * (U * (n * t_1))))
	elif t_4 <= math.inf:
		tmp = math.sqrt((t_3 * (t_1 + t_2)))
	else:
		tmp = math.fabs(((n * (l_m * math.sqrt(2.0))) * (math.sqrt((U * (U_42_ - U))) / Om)))
	return tmp

Julia

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

MATLAB

l_m = abs(l);
function tmp_2 = code(n, U, t, l_m, Om, U_42_)
	t_1 = t - (2.0 * (l_m * (l_m / Om)));
	t_2 = (n * ((l_m / Om) ^ 2.0)) * (U_42_ - U);
	t_3 = (2.0 * n) * U;
	t_4 = t_3 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_2);
	tmp = 0.0;
	if (t_4 <= 0.0)
		tmp = sqrt((2.0 * (U * (n * t_1))));
	elseif (t_4 <= Inf)
		tmp = sqrt((t_3 * (t_1 + t_2)));
	else
		tmp = abs(((n * (l_m * sqrt(2.0))) * (sqrt((U * (U_42_ - U))) / 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[(t - N[(2.0 * N[(l$95$m * N[(l$95$m / Om), $MachinePrecision]), $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, 0.0], N[Sqrt[N[(2.0 * N[(U * N[(n * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[t$95$4, Infinity], N[Sqrt[N[(t$95$3 * N[(t$95$1 + t$95$2), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Abs[N[(N[(n * N[(l$95$m * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[N[(U * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]]]]]

Derivation

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

Alternative 5: 62.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} t_1 := t - 2 \cdot \left(l_m \cdot \frac{l_m}{Om}\right)\\ t_2 := \left(n \cdot {\left(\frac{l_m}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\\ t_3 := \left(2 \cdot n\right) \cdot U\\ t_4 := t_3 \cdot \left(\left(t - 2 \cdot \frac{l_m \cdot l_m}{Om}\right) + t_2\right)\\ \mathbf{if}\;t_4 \leq 0:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot t_1\right)\right)}\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;\sqrt{t_3 \cdot \left(t_1 + t_2\right)}\\ \mathbf{else}:\\ \;\;\;\;{\left(\left(-2 \cdot \frac{U}{\frac{Om}{n}}\right) \cdot \left(2 \cdot {l_m}^{2}\right)\right)}^{0.5}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (let* ((t_1 (- t (* 2.0 (* l_m (/ l_m 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 0.0)
     (sqrt (* 2.0 (* U (* n t_1))))
     (if (<= t_4 INFINITY)
       (sqrt (* t_3 (+ t_1 t_2)))
       (pow (* (* -2.0 (/ U (/ Om n))) (* 2.0 (pow l_m 2.0))) 0.5)))))

C

l_m = fabs(l);
double code(double n, double U, double t, double l_m, double Om, double U_42_) {
	double t_1 = t - (2.0 * (l_m * (l_m / 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 <= 0.0) {
		tmp = sqrt((2.0 * (U * (n * t_1))));
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = sqrt((t_3 * (t_1 + t_2)));
	} else {
		tmp = pow(((-2.0 * (U / (Om / n))) * (2.0 * pow(l_m, 2.0))), 0.5);
	}
	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 = t - (2.0 * (l_m * (l_m / 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 <= 0.0) {
		tmp = Math.sqrt((2.0 * (U * (n * t_1))));
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = Math.sqrt((t_3 * (t_1 + t_2)));
	} else {
		tmp = Math.pow(((-2.0 * (U / (Om / n))) * (2.0 * Math.pow(l_m, 2.0))), 0.5);
	}
	return tmp;
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	t_1 = t - (2.0 * (l_m * (l_m / Om)))
	t_2 = (n * math.pow((l_m / Om), 2.0)) * (U_42_ - U)
	t_3 = (2.0 * n) * U
	t_4 = t_3 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_2)
	tmp = 0
	if t_4 <= 0.0:
		tmp = math.sqrt((2.0 * (U * (n * t_1))))
	elif t_4 <= math.inf:
		tmp = math.sqrt((t_3 * (t_1 + t_2)))
	else:
		tmp = math.pow(((-2.0 * (U / (Om / n))) * (2.0 * math.pow(l_m, 2.0))), 0.5)
	return tmp

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	t_1 = Float64(t - Float64(2.0 * Float64(l_m * Float64(l_m / 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 <= 0.0)
		tmp = sqrt(Float64(2.0 * Float64(U * Float64(n * t_1))));
	elseif (t_4 <= Inf)
		tmp = sqrt(Float64(t_3 * Float64(t_1 + t_2)));
	else
		tmp = Float64(Float64(-2.0 * Float64(U / Float64(Om / n))) * Float64(2.0 * (l_m ^ 2.0))) ^ 0.5;
	end
	return tmp
end

MATLAB

l_m = abs(l);
function tmp_2 = code(n, U, t, l_m, Om, U_42_)
	t_1 = t - (2.0 * (l_m * (l_m / Om)));
	t_2 = (n * ((l_m / Om) ^ 2.0)) * (U_42_ - U);
	t_3 = (2.0 * n) * U;
	t_4 = t_3 * ((t - (2.0 * ((l_m * l_m) / Om))) + t_2);
	tmp = 0.0;
	if (t_4 <= 0.0)
		tmp = sqrt((2.0 * (U * (n * t_1))));
	elseif (t_4 <= Inf)
		tmp = sqrt((t_3 * (t_1 + t_2)));
	else
		tmp = ((-2.0 * (U / (Om / n))) * (2.0 * (l_m ^ 2.0))) ^ 0.5;
	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[(t - N[(2.0 * N[(l$95$m * N[(l$95$m / Om), $MachinePrecision]), $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, 0.0], N[Sqrt[N[(2.0 * N[(U * N[(n * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[t$95$4, Infinity], N[Sqrt[N[(t$95$3 * N[(t$95$1 + t$95$2), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Power[N[(N[(-2.0 * N[(U / N[(Om / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(2.0 * N[Power[l$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]]]]]]]

Derivation

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

Alternative 6: 52.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} t_1 := l_m \cdot \sqrt{2}\\ \mathbf{if}\;l_m \leq 3.3 \cdot 10^{+157}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(\left(t - \frac{2 \cdot \left(l_m \cdot l_m\right)}{Om}\right) + n \cdot \left({\left(\frac{l_m}{Om}\right)}^{2} \cdot \left(U* - U\right)\right)\right)\right)}\\ \mathbf{elif}\;l_m \leq 2.7 \cdot 10^{+216}:\\ \;\;\;\;t_1 \cdot \sqrt{-2 \cdot \left(n \cdot \frac{U}{Om}\right)}\\ \mathbf{elif}\;l_m \leq 1.4 \cdot 10^{+253}:\\ \;\;\;\;\left(n \cdot t_1\right) \cdot \frac{\sqrt{U \cdot \left(U* - U\right)}}{Om}\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot {\left(\frac{U \cdot -2}{\frac{Om}{n}}\right)}^{0.5}\\ \end{array} \end{array} \]

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 3.3e+157)
     (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 2.7e+216)
       (* t_1 (sqrt (* -2.0 (* n (/ U Om)))))
       (if (<= l_m 1.4e+253)
         (* (* n t_1) (/ (sqrt (* U (- U* U))) Om))
         (* t_1 (pow (/ (* U -2.0) (/ Om n)) 0.5)))))))

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 <= 3.3e+157) {
		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 <= 2.7e+216) {
		tmp = t_1 * sqrt((-2.0 * (n * (U / Om))));
	} else if (l_m <= 1.4e+253) {
		tmp = (n * t_1) * (sqrt((U * (U_42_ - U))) / Om);
	} else {
		tmp = t_1 * pow(((U * -2.0) / (Om / n)), 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) :: t_1
    real(8) :: tmp
    t_1 = l_m * sqrt(2.0d0)
    if (l_m <= 3.3d+157) 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 <= 2.7d+216) then
        tmp = t_1 * sqrt(((-2.0d0) * (n * (u / om))))
    else if (l_m <= 1.4d+253) then
        tmp = (n * t_1) * (sqrt((u * (u_42 - u))) / om)
    else
        tmp = t_1 * (((u * (-2.0d0)) / (om / n)) ** 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 t_1 = l_m * Math.sqrt(2.0);
	double tmp;
	if (l_m <= 3.3e+157) {
		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 <= 2.7e+216) {
		tmp = t_1 * Math.sqrt((-2.0 * (n * (U / Om))));
	} else if (l_m <= 1.4e+253) {
		tmp = (n * t_1) * (Math.sqrt((U * (U_42_ - U))) / Om);
	} else {
		tmp = t_1 * Math.pow(((U * -2.0) / (Om / n)), 0.5);
	}
	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 <= 3.3e+157:
		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 <= 2.7e+216:
		tmp = t_1 * math.sqrt((-2.0 * (n * (U / Om))))
	elif l_m <= 1.4e+253:
		tmp = (n * t_1) * (math.sqrt((U * (U_42_ - U))) / Om)
	else:
		tmp = t_1 * math.pow(((U * -2.0) / (Om / n)), 0.5)
	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 <= 3.3e+157)
		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 <= 2.7e+216)
		tmp = Float64(t_1 * sqrt(Float64(-2.0 * Float64(n * Float64(U / Om)))));
	elseif (l_m <= 1.4e+253)
		tmp = Float64(Float64(n * t_1) * Float64(sqrt(Float64(U * Float64(U_42_ - U))) / Om));
	else
		tmp = Float64(t_1 * (Float64(Float64(U * -2.0) / Float64(Om / n)) ^ 0.5));
	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 <= 3.3e+157)
		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 <= 2.7e+216)
		tmp = t_1 * sqrt((-2.0 * (n * (U / Om))));
	elseif (l_m <= 1.4e+253)
		tmp = (n * t_1) * (sqrt((U * (U_42_ - U))) / Om);
	else
		tmp = t_1 * (((U * -2.0) / (Om / n)) ^ 0.5);
	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, 3.3e+157], 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, 2.7e+216], N[(t$95$1 * N[Sqrt[N[(-2.0 * N[(n * N[(U / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[l$95$m, 1.4e+253], N[(N[(n * t$95$1), $MachinePrecision] * N[(N[Sqrt[N[(U * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[Power[N[(N[(U * -2.0), $MachinePrecision] / N[(Om / n), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 7: 49.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} \mathbf{if}\;l_m \leq 2.8 \cdot 10^{+243}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(t - 2 \cdot \left(l_m \cdot \frac{l_m}{Om}\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(l_m \cdot \sqrt{2}\right) \cdot {\left(\frac{U \cdot -2}{\frac{Om}{n}}\right)}^{0.5}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (if (<= l_m 2.8e+243)
   (sqrt (* 2.0 (* U (* n (- t (* 2.0 (* l_m (/ l_m Om))))))))
   (* (* l_m (sqrt 2.0)) (pow (/ (* U -2.0) (/ Om n)) 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 (l_m <= 2.8e+243) {
		tmp = sqrt((2.0 * (U * (n * (t - (2.0 * (l_m * (l_m / Om))))))));
	} else {
		tmp = (l_m * sqrt(2.0)) * pow(((U * -2.0) / (Om / n)), 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 (l_m <= 2.8d+243) then
        tmp = sqrt((2.0d0 * (u * (n * (t - (2.0d0 * (l_m * (l_m / om))))))))
    else
        tmp = (l_m * sqrt(2.0d0)) * (((u * (-2.0d0)) / (om / n)) ** 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 (l_m <= 2.8e+243) {
		tmp = Math.sqrt((2.0 * (U * (n * (t - (2.0 * (l_m * (l_m / Om))))))));
	} else {
		tmp = (l_m * Math.sqrt(2.0)) * Math.pow(((U * -2.0) / (Om / n)), 0.5);
	}
	return tmp;
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	tmp = 0
	if l_m <= 2.8e+243:
		tmp = math.sqrt((2.0 * (U * (n * (t - (2.0 * (l_m * (l_m / Om))))))))
	else:
		tmp = (l_m * math.sqrt(2.0)) * math.pow(((U * -2.0) / (Om / n)), 0.5)
	return tmp

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	tmp = 0.0
	if (l_m <= 2.8e+243)
		tmp = sqrt(Float64(2.0 * Float64(U * Float64(n * Float64(t - Float64(2.0 * Float64(l_m * Float64(l_m / Om))))))));
	else
		tmp = Float64(Float64(l_m * sqrt(2.0)) * (Float64(Float64(U * -2.0) / Float64(Om / n)) ^ 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 (l_m <= 2.8e+243)
		tmp = sqrt((2.0 * (U * (n * (t - (2.0 * (l_m * (l_m / Om))))))));
	else
		tmp = (l_m * sqrt(2.0)) * (((U * -2.0) / (Om / n)) ^ 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[l$95$m, 2.8e+243], N[Sqrt[N[(2.0 * N[(U * N[(n * N[(t - N[(2.0 * N[(l$95$m * N[(l$95$m / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(N[(l$95$m * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision] * N[Power[N[(N[(U * -2.0), $MachinePrecision] / N[(Om / n), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 8: 48.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} \mathbf{if}\;l_m \leq 5 \cdot 10^{+247}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(t - 2 \cdot \left(l_m \cdot \frac{l_m}{Om}\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;l_m \cdot \left(\sqrt{2} \cdot \sqrt{\frac{U \cdot -2}{\frac{Om}{n}}}\right)\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (if (<= l_m 5e+247)
   (sqrt (* 2.0 (* U (* n (- t (* 2.0 (* l_m (/ l_m Om))))))))
   (* l_m (* (sqrt 2.0) (sqrt (/ (* U -2.0) (/ 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 <= 5e+247) {
		tmp = sqrt((2.0 * (U * (n * (t - (2.0 * (l_m * (l_m / Om))))))));
	} else {
		tmp = l_m * (sqrt(2.0) * sqrt(((U * -2.0) / (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 <= 5d+247) then
        tmp = sqrt((2.0d0 * (u * (n * (t - (2.0d0 * (l_m * (l_m / om))))))))
    else
        tmp = l_m * (sqrt(2.0d0) * sqrt(((u * (-2.0d0)) / (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 <= 5e+247) {
		tmp = Math.sqrt((2.0 * (U * (n * (t - (2.0 * (l_m * (l_m / Om))))))));
	} else {
		tmp = l_m * (Math.sqrt(2.0) * Math.sqrt(((U * -2.0) / (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 <= 5e+247:
		tmp = math.sqrt((2.0 * (U * (n * (t - (2.0 * (l_m * (l_m / Om))))))))
	else:
		tmp = l_m * (math.sqrt(2.0) * math.sqrt(((U * -2.0) / (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 <= 5e+247)
		tmp = sqrt(Float64(2.0 * Float64(U * Float64(n * Float64(t - Float64(2.0 * Float64(l_m * Float64(l_m / Om))))))));
	else
		tmp = Float64(l_m * Float64(sqrt(2.0) * sqrt(Float64(Float64(U * -2.0) / 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 <= 5e+247)
		tmp = sqrt((2.0 * (U * (n * (t - (2.0 * (l_m * (l_m / Om))))))));
	else
		tmp = l_m * (sqrt(2.0) * sqrt(((U * -2.0) / (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, 5e+247], N[Sqrt[N[(2.0 * N[(U * N[(n * N[(t - N[(2.0 * N[(l$95$m * N[(l$95$m / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(l$95$m * N[(N[Sqrt[2.0], $MachinePrecision] * N[Sqrt[N[(N[(U * -2.0), $MachinePrecision] / N[(Om / n), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 9: 47.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} \mathbf{if}\;l_m \leq 9 \cdot 10^{+159}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(t - 2 \cdot \left(l_m \cdot \frac{l_m}{Om}\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(l_m \cdot \sqrt{2}\right) \cdot \sqrt{-2 \cdot \left(n \cdot \frac{U}{Om}\right)}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (if (<= l_m 9e+159)
   (sqrt (* 2.0 (* U (* n (- t (* 2.0 (* l_m (/ l_m Om))))))))
   (* (* 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 <= 9e+159) {
		tmp = sqrt((2.0 * (U * (n * (t - (2.0 * (l_m * (l_m / Om))))))));
	} 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 <= 9d+159) then
        tmp = sqrt((2.0d0 * (u * (n * (t - (2.0d0 * (l_m * (l_m / om))))))))
    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 <= 9e+159) {
		tmp = Math.sqrt((2.0 * (U * (n * (t - (2.0 * (l_m * (l_m / Om))))))));
	} 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 <= 9e+159:
		tmp = math.sqrt((2.0 * (U * (n * (t - (2.0 * (l_m * (l_m / Om))))))))
	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 <= 9e+159)
		tmp = sqrt(Float64(2.0 * Float64(U * Float64(n * Float64(t - Float64(2.0 * Float64(l_m * Float64(l_m / Om))))))));
	else
		tmp = Float64(Float64(l_m * sqrt(2.0)) * sqrt(Float64(-2.0 * Float64(n * Float64(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 <= 9e+159)
		tmp = sqrt((2.0 * (U * (n * (t - (2.0 * (l_m * (l_m / Om))))))));
	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, 9e+159], N[Sqrt[N[(2.0 * N[(U * N[(n * N[(t - N[(2.0 * N[(l$95$m * N[(l$95$m / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 47.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ \begin{array}{l} \mathbf{if}\;l_m \leq 1.2 \cdot 10^{+161}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(t - 2 \cdot \left(l_m \cdot \frac{l_m}{Om}\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(l_m \cdot \sqrt{2}\right) \cdot \sqrt{-2 \cdot \frac{n \cdot U}{Om}}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*)
 :precision binary64
 (if (<= l_m 1.2e+161)
   (sqrt (* 2.0 (* U (* n (- t (* 2.0 (* l_m (/ l_m Om))))))))
   (* (* 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 <= 1.2e+161) {
		tmp = sqrt((2.0 * (U * (n * (t - (2.0 * (l_m * (l_m / Om))))))));
	} 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 <= 1.2d+161) then
        tmp = sqrt((2.0d0 * (u * (n * (t - (2.0d0 * (l_m * (l_m / om))))))))
    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 <= 1.2e+161) {
		tmp = Math.sqrt((2.0 * (U * (n * (t - (2.0 * (l_m * (l_m / Om))))))));
	} 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 <= 1.2e+161:
		tmp = math.sqrt((2.0 * (U * (n * (t - (2.0 * (l_m * (l_m / Om))))))))
	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 <= 1.2e+161)
		tmp = sqrt(Float64(2.0 * Float64(U * Float64(n * Float64(t - Float64(2.0 * Float64(l_m * Float64(l_m / Om))))))));
	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 <= 1.2e+161)
		tmp = sqrt((2.0 * (U * (n * (t - (2.0 * (l_m * (l_m / Om))))))));
	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, 1.2e+161], N[Sqrt[N[(2.0 * N[(U * N[(n * N[(t - N[(2.0 * N[(l$95$m * N[(l$95$m / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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: 47.7% accurate, 2.0× speedup

Math

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

FPCore

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

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 - (2.0 * (l_m * (l_m / Om))))))));
}

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 - (2.0d0 * (l_m * (l_m / om))))))))
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 - (2.0 * (l_m * (l_m / Om))))))));
}

Python

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

Julia

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

MATLAB

l_m = abs(l);
function tmp = code(n, U, t, l_m, Om, U_42_)
	tmp = sqrt((2.0 * (U * (n * (t - (2.0 * (l_m * (l_m / Om))))))));
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 * N[(t - N[(2.0 * N[(l$95$m * N[(l$95$m / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

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

Alternative 12: 37.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ {\left(\left(2 \cdot U\right) \cdot \left(n \cdot t\right)\right)}^{0.5} \end{array} \]

FPCore

l_m = (fabs.f64 l)
(FPCore (n U t l_m Om U*) :precision binary64 (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_) {
	return pow(((2.0 * U) * (n * t)), 0.5);
}

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 = ((2.0d0 * u) * (n * t)) ** 0.5d0
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.pow(((2.0 * U) * (n * t)), 0.5);
}

Python

l_m = math.fabs(l)
def code(n, U, t, l_m, Om, U_42_):
	return math.pow(((2.0 * U) * (n * t)), 0.5)

Julia

l_m = abs(l)
function code(n, U, t, l_m, Om, U_42_)
	return Float64(Float64(2.0 * U) * Float64(n * t)) ^ 0.5
end

MATLAB

l_m = abs(l);
function tmp = code(n, U, t, l_m, Om, U_42_)
	tmp = ((2.0 * U) * (n * t)) ^ 0.5;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
code[n_, U_, t_, l$95$m_, Om_, U$42$_] := 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 13: 35.5% 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

Alternative 14: 35.5% accurate, 2.1× speedup

Math

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

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(Float64(2.0 * 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[(N[(2.0 * U), $MachinePrecision] * N[(n * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2023350 
(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*))))))