Toniolo and Linder, Equation (13)

Percentage Accurate: 49.9% → 52.6%

Time: 26.8s

Alternatives: 19

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: 49.9% 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: 52.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-215} \lor \neg \left(t \leq 1.45 \cdot 10^{+90}\right):\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(\left(t - \ell \cdot \left(2 \cdot \frac{\ell}{Om}\right)\right) + n \cdot \left({\left(\frac{\ell}{Om}\right)}^{2} \cdot \left(U* - U\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left|t - {\ell}^{2} \cdot \frac{2}{Om}\right|} \cdot \sqrt{2 \cdot \left|n \cdot U\right|}\\ \end{array} \end{array} \]

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (if (or (<= t -2.7e-215) (not (<= t 1.45e+90)))
   (sqrt
    (*
     (* 2.0 n)
     (*
      U
      (+ (- t (* l (* 2.0 (/ l Om)))) (* n (* (pow (/ l Om) 2.0) (- U* U)))))))
   (*
    (sqrt (fabs (- t (* (pow l 2.0) (/ 2.0 Om)))))
    (sqrt (* 2.0 (fabs (* n U)))))))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	double tmp;
	if ((t <= -2.7e-215) || !(t <= 1.45e+90)) {
		tmp = sqrt(((2.0 * n) * (U * ((t - (l * (2.0 * (l / Om)))) + (n * (pow((l / Om), 2.0) * (U_42_ - U)))))));
	} else {
		tmp = sqrt(fabs((t - (pow(l, 2.0) * (2.0 / Om))))) * sqrt((2.0 * fabs((n * U))));
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((t <= (-2.7d-215)) .or. (.not. (t <= 1.45d+90))) then
        tmp = sqrt(((2.0d0 * n) * (u * ((t - (l * (2.0d0 * (l / om)))) + (n * (((l / om) ** 2.0d0) * (u_42 - u)))))))
    else
        tmp = sqrt(abs((t - ((l ** 2.0d0) * (2.0d0 / om))))) * sqrt((2.0d0 * abs((n * u))))
    end if
    code = tmp
end function

Java

public static double code(double n, double U, double t, double l, double Om, double U_42_) {
	double tmp;
	if ((t <= -2.7e-215) || !(t <= 1.45e+90)) {
		tmp = Math.sqrt(((2.0 * n) * (U * ((t - (l * (2.0 * (l / Om)))) + (n * (Math.pow((l / Om), 2.0) * (U_42_ - U)))))));
	} else {
		tmp = Math.sqrt(Math.abs((t - (Math.pow(l, 2.0) * (2.0 / Om))))) * Math.sqrt((2.0 * Math.abs((n * U))));
	}
	return tmp;
}

Python

def code(n, U, t, l, Om, U_42_):
	tmp = 0
	if (t <= -2.7e-215) or not (t <= 1.45e+90):
		tmp = math.sqrt(((2.0 * n) * (U * ((t - (l * (2.0 * (l / Om)))) + (n * (math.pow((l / Om), 2.0) * (U_42_ - U)))))))
	else:
		tmp = math.sqrt(math.fabs((t - (math.pow(l, 2.0) * (2.0 / Om))))) * math.sqrt((2.0 * math.fabs((n * U))))
	return tmp

Julia

function code(n, U, t, l, Om, U_42_)
	tmp = 0.0
	if ((t <= -2.7e-215) || !(t <= 1.45e+90))
		tmp = sqrt(Float64(Float64(2.0 * n) * Float64(U * Float64(Float64(t - Float64(l * Float64(2.0 * Float64(l / Om)))) + Float64(n * Float64((Float64(l / Om) ^ 2.0) * Float64(U_42_ - U)))))));
	else
		tmp = Float64(sqrt(abs(Float64(t - Float64((l ^ 2.0) * Float64(2.0 / Om))))) * sqrt(Float64(2.0 * abs(Float64(n * U)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(n, U, t, l, Om, U_42_)
	tmp = 0.0;
	if ((t <= -2.7e-215) || ~((t <= 1.45e+90)))
		tmp = sqrt(((2.0 * n) * (U * ((t - (l * (2.0 * (l / Om)))) + (n * (((l / Om) ^ 2.0) * (U_42_ - U)))))));
	else
		tmp = sqrt(abs((t - ((l ^ 2.0) * (2.0 / Om))))) * sqrt((2.0 * abs((n * U))));
	end
	tmp_2 = tmp;
end

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := If[Or[LessEqual[t, -2.7e-215], N[Not[LessEqual[t, 1.45e+90]], $MachinePrecision]], N[Sqrt[N[(N[(2.0 * n), $MachinePrecision] * N[(U * N[(N[(t - N[(l * N[(2.0 * N[(l / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(n * N[(N[Power[N[(l / Om), $MachinePrecision], 2.0], $MachinePrecision] * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(N[Sqrt[N[Abs[N[(t - N[(N[Power[l, 2.0], $MachinePrecision] * N[(2.0 / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(2.0 * N[Abs[N[(n * U), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 2: 61.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\\ t_2 := \left(2 \cdot n\right) \cdot U\\ t_3 := \sqrt{t_2 \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) + t_1\right)}\\ \mathbf{if}\;t_3 \leq 5 \cdot 10^{-131}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(t \cdot U\right)}\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;\sqrt{t_2 \cdot \left(\left(t - 2 \cdot \left(\ell \cdot \frac{\ell}{Om}\right)\right) + t_1\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left|-4 \cdot \frac{U \cdot \left(n \cdot {\ell}^{2}\right)}{Om}\right|}\\ \end{array} \end{array} \]

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (let* ((t_1 (* (* n (pow (/ l Om) 2.0)) (- U* U)))
        (t_2 (* (* 2.0 n) U))
        (t_3 (sqrt (* t_2 (+ (- t (* 2.0 (/ (* l l) Om))) t_1)))))
   (if (<= t_3 5e-131)
     (sqrt (* (* 2.0 n) (* t U)))
     (if (<= t_3 INFINITY)
       (sqrt (* t_2 (+ (- t (* 2.0 (* l (/ l Om)))) t_1)))
       (sqrt (fabs (* -4.0 (/ (* U (* n (pow l 2.0))) Om))))))))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	double t_1 = (n * pow((l / Om), 2.0)) * (U_42_ - U);
	double t_2 = (2.0 * n) * U;
	double t_3 = sqrt((t_2 * ((t - (2.0 * ((l * l) / Om))) + t_1)));
	double tmp;
	if (t_3 <= 5e-131) {
		tmp = sqrt(((2.0 * n) * (t * U)));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = sqrt((t_2 * ((t - (2.0 * (l * (l / Om)))) + t_1)));
	} else {
		tmp = sqrt(fabs((-4.0 * ((U * (n * pow(l, 2.0))) / Om))));
	}
	return tmp;
}

Java

public static double code(double n, double U, double t, double l, double Om, double U_42_) {
	double t_1 = (n * Math.pow((l / Om), 2.0)) * (U_42_ - U);
	double t_2 = (2.0 * n) * U;
	double t_3 = Math.sqrt((t_2 * ((t - (2.0 * ((l * l) / Om))) + t_1)));
	double tmp;
	if (t_3 <= 5e-131) {
		tmp = Math.sqrt(((2.0 * n) * (t * U)));
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = Math.sqrt((t_2 * ((t - (2.0 * (l * (l / Om)))) + t_1)));
	} else {
		tmp = Math.sqrt(Math.abs((-4.0 * ((U * (n * Math.pow(l, 2.0))) / Om))));
	}
	return tmp;
}

Python

def code(n, U, t, l, Om, U_42_):
	t_1 = (n * math.pow((l / Om), 2.0)) * (U_42_ - U)
	t_2 = (2.0 * n) * U
	t_3 = math.sqrt((t_2 * ((t - (2.0 * ((l * l) / Om))) + t_1)))
	tmp = 0
	if t_3 <= 5e-131:
		tmp = math.sqrt(((2.0 * n) * (t * U)))
	elif t_3 <= math.inf:
		tmp = math.sqrt((t_2 * ((t - (2.0 * (l * (l / Om)))) + t_1)))
	else:
		tmp = math.sqrt(math.fabs((-4.0 * ((U * (n * math.pow(l, 2.0))) / Om))))
	return tmp

Julia

function code(n, U, t, l, Om, U_42_)
	t_1 = Float64(Float64(n * (Float64(l / Om) ^ 2.0)) * Float64(U_42_ - U))
	t_2 = Float64(Float64(2.0 * n) * U)
	t_3 = sqrt(Float64(t_2 * Float64(Float64(t - Float64(2.0 * Float64(Float64(l * l) / Om))) + t_1)))
	tmp = 0.0
	if (t_3 <= 5e-131)
		tmp = sqrt(Float64(Float64(2.0 * n) * Float64(t * U)));
	elseif (t_3 <= Inf)
		tmp = sqrt(Float64(t_2 * Float64(Float64(t - Float64(2.0 * Float64(l * Float64(l / Om)))) + t_1)));
	else
		tmp = sqrt(abs(Float64(-4.0 * Float64(Float64(U * Float64(n * (l ^ 2.0))) / Om))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(n, U, t, l, Om, U_42_)
	t_1 = (n * ((l / Om) ^ 2.0)) * (U_42_ - U);
	t_2 = (2.0 * n) * U;
	t_3 = sqrt((t_2 * ((t - (2.0 * ((l * l) / Om))) + t_1)));
	tmp = 0.0;
	if (t_3 <= 5e-131)
		tmp = sqrt(((2.0 * n) * (t * U)));
	elseif (t_3 <= Inf)
		tmp = sqrt((t_2 * ((t - (2.0 * (l * (l / Om)))) + t_1)));
	else
		tmp = sqrt(abs((-4.0 * ((U * (n * (l ^ 2.0))) / Om))));
	end
	tmp_2 = tmp;
end

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := Block[{t$95$1 = N[(N[(n * N[Power[N[(l / 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[Sqrt[N[(t$95$2 * N[(N[(t - N[(2.0 * N[(N[(l * l), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$3, 5e-131], N[Sqrt[N[(N[(2.0 * n), $MachinePrecision] * N[(t * U), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[Sqrt[N[(t$95$2 * N[(N[(t - N[(2.0 * N[(l * N[(l / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Sqrt[N[Abs[N[(-4.0 * N[(N[(U * N[(n * N[Power[l, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]]]]]]

Derivation

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

Alternative 3: 61.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\\ t_2 := \left(2 \cdot n\right) \cdot U\\ t_3 := \sqrt{t_2 \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) + t_1\right)}\\ \mathbf{if}\;t_3 \leq 5 \cdot 10^{-131}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(t \cdot U\right)}\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;\sqrt{t_2 \cdot \left(\left(t - 2 \cdot \left(\ell \cdot \frac{\ell}{Om}\right)\right) + t_1\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left|-4 \cdot \frac{n \cdot \left(U \cdot {\ell}^{2}\right)}{Om}\right|}\\ \end{array} \end{array} \]

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (let* ((t_1 (* (* n (pow (/ l Om) 2.0)) (- U* U)))
        (t_2 (* (* 2.0 n) U))
        (t_3 (sqrt (* t_2 (+ (- t (* 2.0 (/ (* l l) Om))) t_1)))))
   (if (<= t_3 5e-131)
     (sqrt (* (* 2.0 n) (* t U)))
     (if (<= t_3 INFINITY)
       (sqrt (* t_2 (+ (- t (* 2.0 (* l (/ l Om)))) t_1)))
       (sqrt (fabs (* -4.0 (/ (* n (* U (pow l 2.0))) Om))))))))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	double t_1 = (n * pow((l / Om), 2.0)) * (U_42_ - U);
	double t_2 = (2.0 * n) * U;
	double t_3 = sqrt((t_2 * ((t - (2.0 * ((l * l) / Om))) + t_1)));
	double tmp;
	if (t_3 <= 5e-131) {
		tmp = sqrt(((2.0 * n) * (t * U)));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = sqrt((t_2 * ((t - (2.0 * (l * (l / Om)))) + t_1)));
	} else {
		tmp = sqrt(fabs((-4.0 * ((n * (U * pow(l, 2.0))) / Om))));
	}
	return tmp;
}

Java

public static double code(double n, double U, double t, double l, double Om, double U_42_) {
	double t_1 = (n * Math.pow((l / Om), 2.0)) * (U_42_ - U);
	double t_2 = (2.0 * n) * U;
	double t_3 = Math.sqrt((t_2 * ((t - (2.0 * ((l * l) / Om))) + t_1)));
	double tmp;
	if (t_3 <= 5e-131) {
		tmp = Math.sqrt(((2.0 * n) * (t * U)));
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = Math.sqrt((t_2 * ((t - (2.0 * (l * (l / Om)))) + t_1)));
	} else {
		tmp = Math.sqrt(Math.abs((-4.0 * ((n * (U * Math.pow(l, 2.0))) / Om))));
	}
	return tmp;
}

Python

def code(n, U, t, l, Om, U_42_):
	t_1 = (n * math.pow((l / Om), 2.0)) * (U_42_ - U)
	t_2 = (2.0 * n) * U
	t_3 = math.sqrt((t_2 * ((t - (2.0 * ((l * l) / Om))) + t_1)))
	tmp = 0
	if t_3 <= 5e-131:
		tmp = math.sqrt(((2.0 * n) * (t * U)))
	elif t_3 <= math.inf:
		tmp = math.sqrt((t_2 * ((t - (2.0 * (l * (l / Om)))) + t_1)))
	else:
		tmp = math.sqrt(math.fabs((-4.0 * ((n * (U * math.pow(l, 2.0))) / Om))))
	return tmp

Julia

function code(n, U, t, l, Om, U_42_)
	t_1 = Float64(Float64(n * (Float64(l / Om) ^ 2.0)) * Float64(U_42_ - U))
	t_2 = Float64(Float64(2.0 * n) * U)
	t_3 = sqrt(Float64(t_2 * Float64(Float64(t - Float64(2.0 * Float64(Float64(l * l) / Om))) + t_1)))
	tmp = 0.0
	if (t_3 <= 5e-131)
		tmp = sqrt(Float64(Float64(2.0 * n) * Float64(t * U)));
	elseif (t_3 <= Inf)
		tmp = sqrt(Float64(t_2 * Float64(Float64(t - Float64(2.0 * Float64(l * Float64(l / Om)))) + t_1)));
	else
		tmp = sqrt(abs(Float64(-4.0 * Float64(Float64(n * Float64(U * (l ^ 2.0))) / Om))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(n, U, t, l, Om, U_42_)
	t_1 = (n * ((l / Om) ^ 2.0)) * (U_42_ - U);
	t_2 = (2.0 * n) * U;
	t_3 = sqrt((t_2 * ((t - (2.0 * ((l * l) / Om))) + t_1)));
	tmp = 0.0;
	if (t_3 <= 5e-131)
		tmp = sqrt(((2.0 * n) * (t * U)));
	elseif (t_3 <= Inf)
		tmp = sqrt((t_2 * ((t - (2.0 * (l * (l / Om)))) + t_1)));
	else
		tmp = sqrt(abs((-4.0 * ((n * (U * (l ^ 2.0))) / Om))));
	end
	tmp_2 = tmp;
end

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := Block[{t$95$1 = N[(N[(n * N[Power[N[(l / 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[Sqrt[N[(t$95$2 * N[(N[(t - N[(2.0 * N[(N[(l * l), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$3, 5e-131], N[Sqrt[N[(N[(2.0 * n), $MachinePrecision] * N[(t * U), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[Sqrt[N[(t$95$2 * N[(N[(t - N[(2.0 * N[(l * N[(l / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Sqrt[N[Abs[N[(-4.0 * N[(N[(n * N[(U * N[Power[l, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]]]]]]

Derivation

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

Alternative 4: 60.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(n \cdot {\left(\frac{\ell}{Om}\right)}^{2}\right) \cdot \left(U* - U\right)\\ t_2 := \left(2 \cdot n\right) \cdot U\\ t_3 := \sqrt{t_2 \cdot \left(\left(t - 2 \cdot \frac{\ell \cdot \ell}{Om}\right) + t_1\right)}\\ \mathbf{if}\;t_3 \leq 5 \cdot 10^{-131}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(t \cdot U\right)}\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;\sqrt{t_2 \cdot \left(\left(t - 2 \cdot \left(\ell \cdot \frac{\ell}{Om}\right)\right) + t_1\right)}\\ \mathbf{else}:\\ \;\;\;\;{\left(\left(t - {\ell}^{2} \cdot \frac{2}{Om}\right) \cdot t_2\right)}^{0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (let* ((t_1 (* (* n (pow (/ l Om) 2.0)) (- U* U)))
        (t_2 (* (* 2.0 n) U))
        (t_3 (sqrt (* t_2 (+ (- t (* 2.0 (/ (* l l) Om))) t_1)))))
   (if (<= t_3 5e-131)
     (sqrt (* (* 2.0 n) (* t U)))
     (if (<= t_3 INFINITY)
       (sqrt (* t_2 (+ (- t (* 2.0 (* l (/ l Om)))) t_1)))
       (pow (* (- t (* (pow l 2.0) (/ 2.0 Om))) t_2) 0.5)))))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	double t_1 = (n * pow((l / Om), 2.0)) * (U_42_ - U);
	double t_2 = (2.0 * n) * U;
	double t_3 = sqrt((t_2 * ((t - (2.0 * ((l * l) / Om))) + t_1)));
	double tmp;
	if (t_3 <= 5e-131) {
		tmp = sqrt(((2.0 * n) * (t * U)));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = sqrt((t_2 * ((t - (2.0 * (l * (l / Om)))) + t_1)));
	} else {
		tmp = pow(((t - (pow(l, 2.0) * (2.0 / Om))) * t_2), 0.5);
	}
	return tmp;
}

Java

public static double code(double n, double U, double t, double l, double Om, double U_42_) {
	double t_1 = (n * Math.pow((l / Om), 2.0)) * (U_42_ - U);
	double t_2 = (2.0 * n) * U;
	double t_3 = Math.sqrt((t_2 * ((t - (2.0 * ((l * l) / Om))) + t_1)));
	double tmp;
	if (t_3 <= 5e-131) {
		tmp = Math.sqrt(((2.0 * n) * (t * U)));
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = Math.sqrt((t_2 * ((t - (2.0 * (l * (l / Om)))) + t_1)));
	} else {
		tmp = Math.pow(((t - (Math.pow(l, 2.0) * (2.0 / Om))) * t_2), 0.5);
	}
	return tmp;
}

Python

def code(n, U, t, l, Om, U_42_):
	t_1 = (n * math.pow((l / Om), 2.0)) * (U_42_ - U)
	t_2 = (2.0 * n) * U
	t_3 = math.sqrt((t_2 * ((t - (2.0 * ((l * l) / Om))) + t_1)))
	tmp = 0
	if t_3 <= 5e-131:
		tmp = math.sqrt(((2.0 * n) * (t * U)))
	elif t_3 <= math.inf:
		tmp = math.sqrt((t_2 * ((t - (2.0 * (l * (l / Om)))) + t_1)))
	else:
		tmp = math.pow(((t - (math.pow(l, 2.0) * (2.0 / Om))) * t_2), 0.5)
	return tmp

Julia

function code(n, U, t, l, Om, U_42_)
	t_1 = Float64(Float64(n * (Float64(l / Om) ^ 2.0)) * Float64(U_42_ - U))
	t_2 = Float64(Float64(2.0 * n) * U)
	t_3 = sqrt(Float64(t_2 * Float64(Float64(t - Float64(2.0 * Float64(Float64(l * l) / Om))) + t_1)))
	tmp = 0.0
	if (t_3 <= 5e-131)
		tmp = sqrt(Float64(Float64(2.0 * n) * Float64(t * U)));
	elseif (t_3 <= Inf)
		tmp = sqrt(Float64(t_2 * Float64(Float64(t - Float64(2.0 * Float64(l * Float64(l / Om)))) + t_1)));
	else
		tmp = Float64(Float64(t - Float64((l ^ 2.0) * Float64(2.0 / Om))) * t_2) ^ 0.5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(n, U, t, l, Om, U_42_)
	t_1 = (n * ((l / Om) ^ 2.0)) * (U_42_ - U);
	t_2 = (2.0 * n) * U;
	t_3 = sqrt((t_2 * ((t - (2.0 * ((l * l) / Om))) + t_1)));
	tmp = 0.0;
	if (t_3 <= 5e-131)
		tmp = sqrt(((2.0 * n) * (t * U)));
	elseif (t_3 <= Inf)
		tmp = sqrt((t_2 * ((t - (2.0 * (l * (l / Om)))) + t_1)));
	else
		tmp = ((t - ((l ^ 2.0) * (2.0 / Om))) * t_2) ^ 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := Block[{t$95$1 = N[(N[(n * N[Power[N[(l / 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[Sqrt[N[(t$95$2 * N[(N[(t - N[(2.0 * N[(N[(l * l), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$3, 5e-131], N[Sqrt[N[(N[(2.0 * n), $MachinePrecision] * N[(t * U), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[Sqrt[N[(t$95$2 * N[(N[(t - N[(2.0 * N[(l * N[(l / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Power[N[(N[(t - N[(N[Power[l, 2.0], $MachinePrecision] * N[(2.0 / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision], 0.5], $MachinePrecision]]]]]]

Derivation

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

Alternative 5: 62.3% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (let* ((t_1 (* (* n (pow (/ l Om) 2.0)) (- U* U)))
        (t_2 (* (* 2.0 n) U))
        (t_3 (* t_2 (+ (- t (* 2.0 (/ (* l l) Om))) t_1))))
   (if (<= t_3 0.0)
     (sqrt (fabs (* 2.0 (* U (* n (- (* 2.0 (/ (pow l 2.0) Om)) t))))))
     (if (<= t_3 INFINITY)
       (sqrt (* t_2 (+ (- t (* 2.0 (* l (/ l Om)))) t_1)))
       (sqrt (fabs (* -4.0 (/ (* n (* U (pow l 2.0))) Om))))))))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	double t_1 = (n * pow((l / Om), 2.0)) * (U_42_ - U);
	double t_2 = (2.0 * n) * U;
	double t_3 = t_2 * ((t - (2.0 * ((l * l) / Om))) + t_1);
	double tmp;
	if (t_3 <= 0.0) {
		tmp = sqrt(fabs((2.0 * (U * (n * ((2.0 * (pow(l, 2.0) / Om)) - t))))));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = sqrt((t_2 * ((t - (2.0 * (l * (l / Om)))) + t_1)));
	} else {
		tmp = sqrt(fabs((-4.0 * ((n * (U * pow(l, 2.0))) / Om))));
	}
	return tmp;
}

Java

public static double code(double n, double U, double t, double l, double Om, double U_42_) {
	double t_1 = (n * Math.pow((l / Om), 2.0)) * (U_42_ - U);
	double t_2 = (2.0 * n) * U;
	double t_3 = t_2 * ((t - (2.0 * ((l * l) / Om))) + t_1);
	double tmp;
	if (t_3 <= 0.0) {
		tmp = Math.sqrt(Math.abs((2.0 * (U * (n * ((2.0 * (Math.pow(l, 2.0) / Om)) - t))))));
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = Math.sqrt((t_2 * ((t - (2.0 * (l * (l / Om)))) + t_1)));
	} else {
		tmp = Math.sqrt(Math.abs((-4.0 * ((n * (U * Math.pow(l, 2.0))) / Om))));
	}
	return tmp;
}

Python

def code(n, U, t, l, Om, U_42_):
	t_1 = (n * math.pow((l / Om), 2.0)) * (U_42_ - U)
	t_2 = (2.0 * n) * U
	t_3 = t_2 * ((t - (2.0 * ((l * l) / Om))) + t_1)
	tmp = 0
	if t_3 <= 0.0:
		tmp = math.sqrt(math.fabs((2.0 * (U * (n * ((2.0 * (math.pow(l, 2.0) / Om)) - t))))))
	elif t_3 <= math.inf:
		tmp = math.sqrt((t_2 * ((t - (2.0 * (l * (l / Om)))) + t_1)))
	else:
		tmp = math.sqrt(math.fabs((-4.0 * ((n * (U * math.pow(l, 2.0))) / Om))))
	return tmp

Julia

function code(n, U, t, l, Om, U_42_)
	t_1 = Float64(Float64(n * (Float64(l / 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 * l) / Om))) + t_1))
	tmp = 0.0
	if (t_3 <= 0.0)
		tmp = sqrt(abs(Float64(2.0 * Float64(U * Float64(n * Float64(Float64(2.0 * Float64((l ^ 2.0) / Om)) - t))))));
	elseif (t_3 <= Inf)
		tmp = sqrt(Float64(t_2 * Float64(Float64(t - Float64(2.0 * Float64(l * Float64(l / Om)))) + t_1)));
	else
		tmp = sqrt(abs(Float64(-4.0 * Float64(Float64(n * Float64(U * (l ^ 2.0))) / Om))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(n, U, t, l, Om, U_42_)
	t_1 = (n * ((l / Om) ^ 2.0)) * (U_42_ - U);
	t_2 = (2.0 * n) * U;
	t_3 = t_2 * ((t - (2.0 * ((l * l) / Om))) + t_1);
	tmp = 0.0;
	if (t_3 <= 0.0)
		tmp = sqrt(abs((2.0 * (U * (n * ((2.0 * ((l ^ 2.0) / Om)) - t))))));
	elseif (t_3 <= Inf)
		tmp = sqrt((t_2 * ((t - (2.0 * (l * (l / Om)))) + t_1)));
	else
		tmp = sqrt(abs((-4.0 * ((n * (U * (l ^ 2.0))) / Om))));
	end
	tmp_2 = tmp;
end

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := Block[{t$95$1 = N[(N[(n * N[Power[N[(l / 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 * l), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, 0.0], N[Sqrt[N[Abs[N[(2.0 * N[(U * N[(n * N[(N[(2.0 * N[(N[Power[l, 2.0], $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision] - t), $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 * N[(l / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Sqrt[N[Abs[N[(-4.0 * N[(N[(n * N[(U * N[Power[l, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]]]]]]

Derivation

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

Alternative 6: 53.1% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (sqrt
  (*
   (* 2.0 n)
   (*
    U
    (+ (- t (* l (* 2.0 (/ 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 - (l * (2.0 * (l / Om)))) + (n * (pow((l / Om), 2.0) * (U_42_ - U)))))));
}

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 - (l * (2.0d0 * (l / om)))) + (n * (((l / om) ** 2.0d0) * (u_42 - u)))))))
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 - (l * (2.0 * (l / Om)))) + (n * (Math.pow((l / Om), 2.0) * (U_42_ - U)))))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 7: 38.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt{\left|2 \cdot \left(n \cdot \left(t \cdot U\right)\right)\right|}\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-180}:\\ \;\;\;\;{\left(t \cdot \left(n \cdot \left(2 \cdot U\right)\right)\right)}^{0.5}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-240}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \frac{\left(U \cdot {\ell}^{2}\right) \cdot -2}{Om}}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+89}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot U} \cdot \sqrt{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (let* ((t_1 (sqrt (fabs (* 2.0 (* n (* t U)))))))
   (if (<= t -7.2e+168)
     t_1
     (if (<= t -2.55e-180)
       (pow (* t (* n (* 2.0 U))) 0.5)
       (if (<= t 4.4e-240)
         (sqrt (* (* 2.0 n) (/ (* (* U (pow l 2.0)) -2.0) Om)))
         (if (<= t 9.5e+89) (* (sqrt (* (* 2.0 n) U)) (sqrt t)) t_1))))))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	double t_1 = sqrt(fabs((2.0 * (n * (t * U)))));
	double tmp;
	if (t <= -7.2e+168) {
		tmp = t_1;
	} else if (t <= -2.55e-180) {
		tmp = pow((t * (n * (2.0 * U))), 0.5);
	} else if (t <= 4.4e-240) {
		tmp = sqrt(((2.0 * n) * (((U * pow(l, 2.0)) * -2.0) / Om)));
	} else if (t <= 9.5e+89) {
		tmp = sqrt(((2.0 * n) * U)) * sqrt(t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = sqrt(abs((2.0d0 * (n * (t * u)))))
    if (t <= (-7.2d+168)) then
        tmp = t_1
    else if (t <= (-2.55d-180)) then
        tmp = (t * (n * (2.0d0 * u))) ** 0.5d0
    else if (t <= 4.4d-240) then
        tmp = sqrt(((2.0d0 * n) * (((u * (l ** 2.0d0)) * (-2.0d0)) / om)))
    else if (t <= 9.5d+89) then
        tmp = sqrt(((2.0d0 * n) * u)) * sqrt(t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double n, double U, double t, double l, double Om, double U_42_) {
	double t_1 = Math.sqrt(Math.abs((2.0 * (n * (t * U)))));
	double tmp;
	if (t <= -7.2e+168) {
		tmp = t_1;
	} else if (t <= -2.55e-180) {
		tmp = Math.pow((t * (n * (2.0 * U))), 0.5);
	} else if (t <= 4.4e-240) {
		tmp = Math.sqrt(((2.0 * n) * (((U * Math.pow(l, 2.0)) * -2.0) / Om)));
	} else if (t <= 9.5e+89) {
		tmp = Math.sqrt(((2.0 * n) * U)) * Math.sqrt(t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(n, U, t, l, Om, U_42_):
	t_1 = math.sqrt(math.fabs((2.0 * (n * (t * U)))))
	tmp = 0
	if t <= -7.2e+168:
		tmp = t_1
	elif t <= -2.55e-180:
		tmp = math.pow((t * (n * (2.0 * U))), 0.5)
	elif t <= 4.4e-240:
		tmp = math.sqrt(((2.0 * n) * (((U * math.pow(l, 2.0)) * -2.0) / Om)))
	elif t <= 9.5e+89:
		tmp = math.sqrt(((2.0 * n) * U)) * math.sqrt(t)
	else:
		tmp = t_1
	return tmp

Julia

function code(n, U, t, l, Om, U_42_)
	t_1 = sqrt(abs(Float64(2.0 * Float64(n * Float64(t * U)))))
	tmp = 0.0
	if (t <= -7.2e+168)
		tmp = t_1;
	elseif (t <= -2.55e-180)
		tmp = Float64(t * Float64(n * Float64(2.0 * U))) ^ 0.5;
	elseif (t <= 4.4e-240)
		tmp = sqrt(Float64(Float64(2.0 * n) * Float64(Float64(Float64(U * (l ^ 2.0)) * -2.0) / Om)));
	elseif (t <= 9.5e+89)
		tmp = Float64(sqrt(Float64(Float64(2.0 * n) * U)) * sqrt(t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(n, U, t, l, Om, U_42_)
	t_1 = sqrt(abs((2.0 * (n * (t * U)))));
	tmp = 0.0;
	if (t <= -7.2e+168)
		tmp = t_1;
	elseif (t <= -2.55e-180)
		tmp = (t * (n * (2.0 * U))) ^ 0.5;
	elseif (t <= 4.4e-240)
		tmp = sqrt(((2.0 * n) * (((U * (l ^ 2.0)) * -2.0) / Om)));
	elseif (t <= 9.5e+89)
		tmp = sqrt(((2.0 * n) * U)) * sqrt(t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := Block[{t$95$1 = N[Sqrt[N[Abs[N[(2.0 * N[(n * N[(t * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t, -7.2e+168], t$95$1, If[LessEqual[t, -2.55e-180], N[Power[N[(t * N[(n * N[(2.0 * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision], If[LessEqual[t, 4.4e-240], N[Sqrt[N[(N[(2.0 * n), $MachinePrecision] * N[(N[(N[(U * N[Power[l, 2.0], $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[t, 9.5e+89], N[(N[Sqrt[N[(N[(2.0 * n), $MachinePrecision] * U), $MachinePrecision]], $MachinePrecision] * N[Sqrt[t], $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

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

Alternative 8: 45.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - {\ell}^{2} \cdot \frac{2}{Om}\\ \mathbf{if}\;\ell \leq 9.2 \cdot 10^{+54}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t_1\right)}\\ \mathbf{else}:\\ \;\;\;\;{\left(t_1 \cdot \left(\left(2 \cdot n\right) \cdot U\right)\right)}^{0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (let* ((t_1 (- t (* (pow l 2.0) (/ 2.0 Om)))))
   (if (<= l 9.2e+54)
     (sqrt (* (* 2.0 n) (* U t_1)))
     (pow (* t_1 (* (* 2.0 n) U)) 0.5))))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	double t_1 = t - (pow(l, 2.0) * (2.0 / Om));
	double tmp;
	if (l <= 9.2e+54) {
		tmp = sqrt(((2.0 * n) * (U * t_1)));
	} else {
		tmp = pow((t_1 * ((2.0 * n) * U)), 0.5);
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - ((l ** 2.0d0) * (2.0d0 / om))
    if (l <= 9.2d+54) then
        tmp = sqrt(((2.0d0 * n) * (u * t_1)))
    else
        tmp = (t_1 * ((2.0d0 * n) * u)) ** 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double n, double U, double t, double l, double Om, double U_42_) {
	double t_1 = t - (Math.pow(l, 2.0) * (2.0 / Om));
	double tmp;
	if (l <= 9.2e+54) {
		tmp = Math.sqrt(((2.0 * n) * (U * t_1)));
	} else {
		tmp = Math.pow((t_1 * ((2.0 * n) * U)), 0.5);
	}
	return tmp;
}

Python

def code(n, U, t, l, Om, U_42_):
	t_1 = t - (math.pow(l, 2.0) * (2.0 / Om))
	tmp = 0
	if l <= 9.2e+54:
		tmp = math.sqrt(((2.0 * n) * (U * t_1)))
	else:
		tmp = math.pow((t_1 * ((2.0 * n) * U)), 0.5)
	return tmp

Julia

function code(n, U, t, l, Om, U_42_)
	t_1 = Float64(t - Float64((l ^ 2.0) * Float64(2.0 / Om)))
	tmp = 0.0
	if (l <= 9.2e+54)
		tmp = sqrt(Float64(Float64(2.0 * n) * Float64(U * t_1)));
	else
		tmp = Float64(t_1 * Float64(Float64(2.0 * n) * U)) ^ 0.5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(n, U, t, l, Om, U_42_)
	t_1 = t - ((l ^ 2.0) * (2.0 / Om));
	tmp = 0.0;
	if (l <= 9.2e+54)
		tmp = sqrt(((2.0 * n) * (U * t_1)));
	else
		tmp = (t_1 * ((2.0 * n) * U)) ^ 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := Block[{t$95$1 = N[(t - N[(N[Power[l, 2.0], $MachinePrecision] * N[(2.0 / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[l, 9.2e+54], N[Sqrt[N[(N[(2.0 * n), $MachinePrecision] * N[(U * t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Power[N[(t$95$1 * N[(N[(2.0 * n), $MachinePrecision] * U), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]]]

Derivation

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

Alternative 9: 38.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt{\left|2 \cdot \left(n \cdot \left(t \cdot U\right)\right)\right|}\\ \mathbf{if}\;t \leq -4 \cdot 10^{+168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.3 \cdot 10^{-179}:\\ \;\;\;\;{\left(t \cdot \left(n \cdot \left(2 \cdot U\right)\right)\right)}^{0.5}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-240}:\\ \;\;\;\;\sqrt{-4 \cdot \frac{U}{\frac{Om}{n \cdot {\ell}^{2}}}}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+91}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot U} \cdot \sqrt{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (let* ((t_1 (sqrt (fabs (* 2.0 (* n (* t U)))))))
   (if (<= t -4e+168)
     t_1
     (if (<= t -5.3e-179)
       (pow (* t (* n (* 2.0 U))) 0.5)
       (if (<= t 5.6e-240)
         (sqrt (* -4.0 (/ U (/ Om (* n (pow l 2.0))))))
         (if (<= t 2.35e+91) (* (sqrt (* (* 2.0 n) U)) (sqrt t)) t_1))))))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	double t_1 = sqrt(fabs((2.0 * (n * (t * U)))));
	double tmp;
	if (t <= -4e+168) {
		tmp = t_1;
	} else if (t <= -5.3e-179) {
		tmp = pow((t * (n * (2.0 * U))), 0.5);
	} else if (t <= 5.6e-240) {
		tmp = sqrt((-4.0 * (U / (Om / (n * pow(l, 2.0))))));
	} else if (t <= 2.35e+91) {
		tmp = sqrt(((2.0 * n) * U)) * sqrt(t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = sqrt(abs((2.0d0 * (n * (t * u)))))
    if (t <= (-4d+168)) then
        tmp = t_1
    else if (t <= (-5.3d-179)) then
        tmp = (t * (n * (2.0d0 * u))) ** 0.5d0
    else if (t <= 5.6d-240) then
        tmp = sqrt(((-4.0d0) * (u / (om / (n * (l ** 2.0d0))))))
    else if (t <= 2.35d+91) then
        tmp = sqrt(((2.0d0 * n) * u)) * sqrt(t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double n, double U, double t, double l, double Om, double U_42_) {
	double t_1 = Math.sqrt(Math.abs((2.0 * (n * (t * U)))));
	double tmp;
	if (t <= -4e+168) {
		tmp = t_1;
	} else if (t <= -5.3e-179) {
		tmp = Math.pow((t * (n * (2.0 * U))), 0.5);
	} else if (t <= 5.6e-240) {
		tmp = Math.sqrt((-4.0 * (U / (Om / (n * Math.pow(l, 2.0))))));
	} else if (t <= 2.35e+91) {
		tmp = Math.sqrt(((2.0 * n) * U)) * Math.sqrt(t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(n, U, t, l, Om, U_42_):
	t_1 = math.sqrt(math.fabs((2.0 * (n * (t * U)))))
	tmp = 0
	if t <= -4e+168:
		tmp = t_1
	elif t <= -5.3e-179:
		tmp = math.pow((t * (n * (2.0 * U))), 0.5)
	elif t <= 5.6e-240:
		tmp = math.sqrt((-4.0 * (U / (Om / (n * math.pow(l, 2.0))))))
	elif t <= 2.35e+91:
		tmp = math.sqrt(((2.0 * n) * U)) * math.sqrt(t)
	else:
		tmp = t_1
	return tmp

Julia

function code(n, U, t, l, Om, U_42_)
	t_1 = sqrt(abs(Float64(2.0 * Float64(n * Float64(t * U)))))
	tmp = 0.0
	if (t <= -4e+168)
		tmp = t_1;
	elseif (t <= -5.3e-179)
		tmp = Float64(t * Float64(n * Float64(2.0 * U))) ^ 0.5;
	elseif (t <= 5.6e-240)
		tmp = sqrt(Float64(-4.0 * Float64(U / Float64(Om / Float64(n * (l ^ 2.0))))));
	elseif (t <= 2.35e+91)
		tmp = Float64(sqrt(Float64(Float64(2.0 * n) * U)) * sqrt(t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(n, U, t, l, Om, U_42_)
	t_1 = sqrt(abs((2.0 * (n * (t * U)))));
	tmp = 0.0;
	if (t <= -4e+168)
		tmp = t_1;
	elseif (t <= -5.3e-179)
		tmp = (t * (n * (2.0 * U))) ^ 0.5;
	elseif (t <= 5.6e-240)
		tmp = sqrt((-4.0 * (U / (Om / (n * (l ^ 2.0))))));
	elseif (t <= 2.35e+91)
		tmp = sqrt(((2.0 * n) * U)) * sqrt(t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := Block[{t$95$1 = N[Sqrt[N[Abs[N[(2.0 * N[(n * N[(t * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t, -4e+168], t$95$1, If[LessEqual[t, -5.3e-179], N[Power[N[(t * N[(n * N[(2.0 * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision], If[LessEqual[t, 5.6e-240], N[Sqrt[N[(-4.0 * N[(U / N[(Om / N[(n * N[Power[l, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[t, 2.35e+91], N[(N[Sqrt[N[(N[(2.0 * n), $MachinePrecision] * U), $MachinePrecision]], $MachinePrecision] * N[Sqrt[t], $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

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

Alternative 10: 44.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.65 \cdot 10^{+193}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(n \cdot \left(t - 2 \cdot \frac{{\ell}^{2}}{Om}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left|2 \cdot \left(n \cdot \left(t \cdot U\right)\right)\right|}\\ \end{array} \end{array} \]

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (if (<= t 1.65e+193)
   (sqrt (* 2.0 (* U (* n (- t (* 2.0 (/ (pow l 2.0) Om)))))))
   (sqrt (fabs (* 2.0 (* n (* t U)))))))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	double tmp;
	if (t <= 1.65e+193) {
		tmp = sqrt((2.0 * (U * (n * (t - (2.0 * (pow(l, 2.0) / Om)))))));
	} else {
		tmp = sqrt(fabs((2.0 * (n * (t * U)))));
	}
	return tmp;
}

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
    real(8) :: tmp
    if (t <= 1.65d+193) then
        tmp = sqrt((2.0d0 * (u * (n * (t - (2.0d0 * ((l ** 2.0d0) / om)))))))
    else
        tmp = sqrt(abs((2.0d0 * (n * (t * u)))))
    end if
    code = tmp
end function

Java

public static double code(double n, double U, double t, double l, double Om, double U_42_) {
	double tmp;
	if (t <= 1.65e+193) {
		tmp = Math.sqrt((2.0 * (U * (n * (t - (2.0 * (Math.pow(l, 2.0) / Om)))))));
	} else {
		tmp = Math.sqrt(Math.abs((2.0 * (n * (t * U)))));
	}
	return tmp;
}

Python

def code(n, U, t, l, Om, U_42_):
	tmp = 0
	if t <= 1.65e+193:
		tmp = math.sqrt((2.0 * (U * (n * (t - (2.0 * (math.pow(l, 2.0) / Om)))))))
	else:
		tmp = math.sqrt(math.fabs((2.0 * (n * (t * U)))))
	return tmp

Julia

function code(n, U, t, l, Om, U_42_)
	tmp = 0.0
	if (t <= 1.65e+193)
		tmp = sqrt(Float64(2.0 * Float64(U * Float64(n * Float64(t - Float64(2.0 * Float64((l ^ 2.0) / Om)))))));
	else
		tmp = sqrt(abs(Float64(2.0 * Float64(n * Float64(t * U)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(n, U, t, l, Om, U_42_)
	tmp = 0.0;
	if (t <= 1.65e+193)
		tmp = sqrt((2.0 * (U * (n * (t - (2.0 * ((l ^ 2.0) / Om)))))));
	else
		tmp = sqrt(abs((2.0 * (n * (t * U)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := If[LessEqual[t, 1.65e+193], N[Sqrt[N[(2.0 * N[(U * N[(n * N[(t - N[(2.0 * N[(N[Power[l, 2.0], $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Sqrt[N[Abs[N[(2.0 * N[(n * N[(t * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]]

Derivation

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

Alternative 11: 43.3% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

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 - ((l ** 2.0d0) * (2.0d0 / om))))))
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 - (Math.pow(l, 2.0) * (2.0 / Om))))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 12: 38.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt{\left|2 \cdot \left(n \cdot \left(t \cdot U\right)\right)\right|}\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-282}:\\ \;\;\;\;{\left(t \cdot \left(n \cdot \left(2 \cdot U\right)\right)\right)}^{0.5}\\ \mathbf{elif}\;t \leq 10^{+95}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot U} \cdot \sqrt{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (let* ((t_1 (sqrt (fabs (* 2.0 (* n (* t U)))))))
   (if (<= t -5.8e+169)
     t_1
     (if (<= t 1.25e-282)
       (pow (* t (* n (* 2.0 U))) 0.5)
       (if (<= t 1e+95) (* (sqrt (* (* 2.0 n) U)) (sqrt t)) t_1)))))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	double t_1 = sqrt(fabs((2.0 * (n * (t * U)))));
	double tmp;
	if (t <= -5.8e+169) {
		tmp = t_1;
	} else if (t <= 1.25e-282) {
		tmp = pow((t * (n * (2.0 * U))), 0.5);
	} else if (t <= 1e+95) {
		tmp = sqrt(((2.0 * n) * U)) * sqrt(t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = sqrt(abs((2.0d0 * (n * (t * u)))))
    if (t <= (-5.8d+169)) then
        tmp = t_1
    else if (t <= 1.25d-282) then
        tmp = (t * (n * (2.0d0 * u))) ** 0.5d0
    else if (t <= 1d+95) then
        tmp = sqrt(((2.0d0 * n) * u)) * sqrt(t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double n, double U, double t, double l, double Om, double U_42_) {
	double t_1 = Math.sqrt(Math.abs((2.0 * (n * (t * U)))));
	double tmp;
	if (t <= -5.8e+169) {
		tmp = t_1;
	} else if (t <= 1.25e-282) {
		tmp = Math.pow((t * (n * (2.0 * U))), 0.5);
	} else if (t <= 1e+95) {
		tmp = Math.sqrt(((2.0 * n) * U)) * Math.sqrt(t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(n, U, t, l, Om, U_42_):
	t_1 = math.sqrt(math.fabs((2.0 * (n * (t * U)))))
	tmp = 0
	if t <= -5.8e+169:
		tmp = t_1
	elif t <= 1.25e-282:
		tmp = math.pow((t * (n * (2.0 * U))), 0.5)
	elif t <= 1e+95:
		tmp = math.sqrt(((2.0 * n) * U)) * math.sqrt(t)
	else:
		tmp = t_1
	return tmp

Julia

function code(n, U, t, l, Om, U_42_)
	t_1 = sqrt(abs(Float64(2.0 * Float64(n * Float64(t * U)))))
	tmp = 0.0
	if (t <= -5.8e+169)
		tmp = t_1;
	elseif (t <= 1.25e-282)
		tmp = Float64(t * Float64(n * Float64(2.0 * U))) ^ 0.5;
	elseif (t <= 1e+95)
		tmp = Float64(sqrt(Float64(Float64(2.0 * n) * U)) * sqrt(t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(n, U, t, l, Om, U_42_)
	t_1 = sqrt(abs((2.0 * (n * (t * U)))));
	tmp = 0.0;
	if (t <= -5.8e+169)
		tmp = t_1;
	elseif (t <= 1.25e-282)
		tmp = (t * (n * (2.0 * U))) ^ 0.5;
	elseif (t <= 1e+95)
		tmp = sqrt(((2.0 * n) * U)) * sqrt(t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := Block[{t$95$1 = N[Sqrt[N[Abs[N[(2.0 * N[(n * N[(t * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t, -5.8e+169], t$95$1, If[LessEqual[t, 1.25e-282], N[Power[N[(t * N[(n * N[(2.0 * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision], If[LessEqual[t, 1e+95], N[(N[Sqrt[N[(N[(2.0 * n), $MachinePrecision] * U), $MachinePrecision]], $MachinePrecision] * N[Sqrt[t], $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

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

Alternative 13: 40.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;U \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\sqrt{2 \cdot \left|U \cdot \left(t \cdot n\right)\right|}\\ \mathbf{elif}\;U \leq 4.2 \cdot 10^{-102}:\\ \;\;\;\;\sqrt{2 \cdot U} \cdot \sqrt{t \cdot n}\\ \mathbf{else}:\\ \;\;\;\;{\left(t \cdot \left(n \cdot \left(2 \cdot U\right)\right)\right)}^{0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (if (<= U -5e-310)
   (sqrt (* 2.0 (fabs (* U (* t n)))))
   (if (<= U 4.2e-102)
     (* (sqrt (* 2.0 U)) (sqrt (* t n)))
     (pow (* t (* n (* 2.0 U))) 0.5))))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	double tmp;
	if (U <= -5e-310) {
		tmp = sqrt((2.0 * fabs((U * (t * n)))));
	} else if (U <= 4.2e-102) {
		tmp = sqrt((2.0 * U)) * sqrt((t * n));
	} else {
		tmp = pow((t * (n * (2.0 * U))), 0.5);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (u <= (-5d-310)) then
        tmp = sqrt((2.0d0 * abs((u * (t * n)))))
    else if (u <= 4.2d-102) then
        tmp = sqrt((2.0d0 * u)) * sqrt((t * n))
    else
        tmp = (t * (n * (2.0d0 * u))) ** 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double n, double U, double t, double l, double Om, double U_42_) {
	double tmp;
	if (U <= -5e-310) {
		tmp = Math.sqrt((2.0 * Math.abs((U * (t * n)))));
	} else if (U <= 4.2e-102) {
		tmp = Math.sqrt((2.0 * U)) * Math.sqrt((t * n));
	} else {
		tmp = Math.pow((t * (n * (2.0 * U))), 0.5);
	}
	return tmp;
}

Python

def code(n, U, t, l, Om, U_42_):
	tmp = 0
	if U <= -5e-310:
		tmp = math.sqrt((2.0 * math.fabs((U * (t * n)))))
	elif U <= 4.2e-102:
		tmp = math.sqrt((2.0 * U)) * math.sqrt((t * n))
	else:
		tmp = math.pow((t * (n * (2.0 * U))), 0.5)
	return tmp

Julia

function code(n, U, t, l, Om, U_42_)
	tmp = 0.0
	if (U <= -5e-310)
		tmp = sqrt(Float64(2.0 * abs(Float64(U * Float64(t * n)))));
	elseif (U <= 4.2e-102)
		tmp = Float64(sqrt(Float64(2.0 * U)) * sqrt(Float64(t * n)));
	else
		tmp = Float64(t * Float64(n * Float64(2.0 * U))) ^ 0.5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(n, U, t, l, Om, U_42_)
	tmp = 0.0;
	if (U <= -5e-310)
		tmp = sqrt((2.0 * abs((U * (t * n)))));
	elseif (U <= 4.2e-102)
		tmp = sqrt((2.0 * U)) * sqrt((t * n));
	else
		tmp = (t * (n * (2.0 * U))) ^ 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := If[LessEqual[U, -5e-310], N[Sqrt[N[(2.0 * N[Abs[N[(U * N[(t * n), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[U, 4.2e-102], N[(N[Sqrt[N[(2.0 * U), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(t * n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Power[N[(t * N[(n * N[(2.0 * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]]]

Derivation

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

Alternative 14: 40.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;U \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\sqrt{2 \cdot \left|U \cdot \left(t \cdot n\right)\right|}\\ \mathbf{elif}\;U \leq 5.5 \cdot 10^{-102}:\\ \;\;\;\;\sqrt{t \cdot \left(2 \cdot n\right)} \cdot \sqrt{U}\\ \mathbf{else}:\\ \;\;\;\;{\left(t \cdot \left(n \cdot \left(2 \cdot U\right)\right)\right)}^{0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (if (<= U -5e-310)
   (sqrt (* 2.0 (fabs (* U (* t n)))))
   (if (<= U 5.5e-102)
     (* (sqrt (* t (* 2.0 n))) (sqrt U))
     (pow (* t (* n (* 2.0 U))) 0.5))))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	double tmp;
	if (U <= -5e-310) {
		tmp = sqrt((2.0 * fabs((U * (t * n)))));
	} else if (U <= 5.5e-102) {
		tmp = sqrt((t * (2.0 * n))) * sqrt(U);
	} else {
		tmp = pow((t * (n * (2.0 * U))), 0.5);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (u <= (-5d-310)) then
        tmp = sqrt((2.0d0 * abs((u * (t * n)))))
    else if (u <= 5.5d-102) then
        tmp = sqrt((t * (2.0d0 * n))) * sqrt(u)
    else
        tmp = (t * (n * (2.0d0 * u))) ** 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double n, double U, double t, double l, double Om, double U_42_) {
	double tmp;
	if (U <= -5e-310) {
		tmp = Math.sqrt((2.0 * Math.abs((U * (t * n)))));
	} else if (U <= 5.5e-102) {
		tmp = Math.sqrt((t * (2.0 * n))) * Math.sqrt(U);
	} else {
		tmp = Math.pow((t * (n * (2.0 * U))), 0.5);
	}
	return tmp;
}

Python

def code(n, U, t, l, Om, U_42_):
	tmp = 0
	if U <= -5e-310:
		tmp = math.sqrt((2.0 * math.fabs((U * (t * n)))))
	elif U <= 5.5e-102:
		tmp = math.sqrt((t * (2.0 * n))) * math.sqrt(U)
	else:
		tmp = math.pow((t * (n * (2.0 * U))), 0.5)
	return tmp

Julia

function code(n, U, t, l, Om, U_42_)
	tmp = 0.0
	if (U <= -5e-310)
		tmp = sqrt(Float64(2.0 * abs(Float64(U * Float64(t * n)))));
	elseif (U <= 5.5e-102)
		tmp = Float64(sqrt(Float64(t * Float64(2.0 * n))) * sqrt(U));
	else
		tmp = Float64(t * Float64(n * Float64(2.0 * U))) ^ 0.5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(n, U, t, l, Om, U_42_)
	tmp = 0.0;
	if (U <= -5e-310)
		tmp = sqrt((2.0 * abs((U * (t * n)))));
	elseif (U <= 5.5e-102)
		tmp = sqrt((t * (2.0 * n))) * sqrt(U);
	else
		tmp = (t * (n * (2.0 * U))) ^ 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := If[LessEqual[U, -5e-310], N[Sqrt[N[(2.0 * N[Abs[N[(U * N[(t * n), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[U, 5.5e-102], N[(N[Sqrt[N[(t * N[(2.0 * n), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[U], $MachinePrecision]), $MachinePrecision], N[Power[N[(t * N[(n * N[(2.0 * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]]]

Derivation

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

Alternative 15: 37.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;U* \leq 1.2 \cdot 10^{+200}:\\ \;\;\;\;\sqrt{\left|2 \cdot \left(n \cdot \left(t \cdot U\right)\right)\right|}\\ \mathbf{else}:\\ \;\;\;\;{\left(t \cdot \left(n \cdot \left(2 \cdot U\right)\right)\right)}^{0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (if (<= U* 1.2e+200)
   (sqrt (fabs (* 2.0 (* n (* t U)))))
   (pow (* t (* n (* 2.0 U))) 0.5)))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	double tmp;
	if (U_42_ <= 1.2e+200) {
		tmp = sqrt(fabs((2.0 * (n * (t * U)))));
	} else {
		tmp = pow((t * (n * (2.0 * U))), 0.5);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (u_42 <= 1.2d+200) then
        tmp = sqrt(abs((2.0d0 * (n * (t * u)))))
    else
        tmp = (t * (n * (2.0d0 * u))) ** 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double n, double U, double t, double l, double Om, double U_42_) {
	double tmp;
	if (U_42_ <= 1.2e+200) {
		tmp = Math.sqrt(Math.abs((2.0 * (n * (t * U)))));
	} else {
		tmp = Math.pow((t * (n * (2.0 * U))), 0.5);
	}
	return tmp;
}

Python

def code(n, U, t, l, Om, U_42_):
	tmp = 0
	if U_42_ <= 1.2e+200:
		tmp = math.sqrt(math.fabs((2.0 * (n * (t * U)))))
	else:
		tmp = math.pow((t * (n * (2.0 * U))), 0.5)
	return tmp

Julia

function code(n, U, t, l, Om, U_42_)
	tmp = 0.0
	if (U_42_ <= 1.2e+200)
		tmp = sqrt(abs(Float64(2.0 * Float64(n * Float64(t * U)))));
	else
		tmp = Float64(t * Float64(n * Float64(2.0 * U))) ^ 0.5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(n, U, t, l, Om, U_42_)
	tmp = 0.0;
	if (U_42_ <= 1.2e+200)
		tmp = sqrt(abs((2.0 * (n * (t * U)))));
	else
		tmp = (t * (n * (2.0 * U))) ^ 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := If[LessEqual[U$42$, 1.2e+200], N[Sqrt[N[Abs[N[(2.0 * N[(n * N[(t * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision], N[Power[N[(t * N[(n * N[(2.0 * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]]

Derivation

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

Alternative 16: 37.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;U \leq 1.6 \cdot 10^{-115}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(t \cdot U\right)}\\ \mathbf{else}:\\ \;\;\;\;{\left(t \cdot \left(n \cdot \left(2 \cdot U\right)\right)\right)}^{0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (if (<= U 1.6e-115)
   (sqrt (* (* 2.0 n) (* t U)))
   (pow (* t (* n (* 2.0 U))) 0.5)))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	double tmp;
	if (U <= 1.6e-115) {
		tmp = sqrt(((2.0 * n) * (t * U)));
	} else {
		tmp = pow((t * (n * (2.0 * U))), 0.5);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (u <= 1.6d-115) then
        tmp = sqrt(((2.0d0 * n) * (t * u)))
    else
        tmp = (t * (n * (2.0d0 * u))) ** 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double n, double U, double t, double l, double Om, double U_42_) {
	double tmp;
	if (U <= 1.6e-115) {
		tmp = Math.sqrt(((2.0 * n) * (t * U)));
	} else {
		tmp = Math.pow((t * (n * (2.0 * U))), 0.5);
	}
	return tmp;
}

Python

def code(n, U, t, l, Om, U_42_):
	tmp = 0
	if U <= 1.6e-115:
		tmp = math.sqrt(((2.0 * n) * (t * U)))
	else:
		tmp = math.pow((t * (n * (2.0 * U))), 0.5)
	return tmp

Julia

function code(n, U, t, l, Om, U_42_)
	tmp = 0.0
	if (U <= 1.6e-115)
		tmp = sqrt(Float64(Float64(2.0 * n) * Float64(t * U)));
	else
		tmp = Float64(t * Float64(n * Float64(2.0 * U))) ^ 0.5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(n, U, t, l, Om, U_42_)
	tmp = 0.0;
	if (U <= 1.6e-115)
		tmp = sqrt(((2.0 * n) * (t * U)));
	else
		tmp = (t * (n * (2.0 * U))) ^ 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := If[LessEqual[U, 1.6e-115], N[Sqrt[N[(N[(2.0 * n), $MachinePrecision] * N[(t * U), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Power[N[(t * N[(n * N[(2.0 * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]]

Derivation

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

Alternative 17: 36.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;U \leq 2.1 \cdot 10^{-191}:\\ \;\;\;\;\sqrt{2 \cdot \left(U \cdot \left(t \cdot n\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{t \cdot \left(\left(2 \cdot n\right) \cdot U\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (if (<= U 2.1e-191)
   (sqrt (* 2.0 (* U (* t n))))
   (sqrt (* t (* (* 2.0 n) U)))))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	double tmp;
	if (U <= 2.1e-191) {
		tmp = sqrt((2.0 * (U * (t * n))));
	} else {
		tmp = sqrt((t * ((2.0 * n) * U)));
	}
	return tmp;
}

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
    real(8) :: tmp
    if (u <= 2.1d-191) then
        tmp = sqrt((2.0d0 * (u * (t * n))))
    else
        tmp = sqrt((t * ((2.0d0 * n) * u)))
    end if
    code = tmp
end function

Java

public static double code(double n, double U, double t, double l, double Om, double U_42_) {
	double tmp;
	if (U <= 2.1e-191) {
		tmp = Math.sqrt((2.0 * (U * (t * n))));
	} else {
		tmp = Math.sqrt((t * ((2.0 * n) * U)));
	}
	return tmp;
}

Python

def code(n, U, t, l, Om, U_42_):
	tmp = 0
	if U <= 2.1e-191:
		tmp = math.sqrt((2.0 * (U * (t * n))))
	else:
		tmp = math.sqrt((t * ((2.0 * n) * U)))
	return tmp

Julia

function code(n, U, t, l, Om, U_42_)
	tmp = 0.0
	if (U <= 2.1e-191)
		tmp = sqrt(Float64(2.0 * Float64(U * Float64(t * n))));
	else
		tmp = sqrt(Float64(t * Float64(Float64(2.0 * n) * U)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(n, U, t, l, Om, U_42_)
	tmp = 0.0;
	if (U <= 2.1e-191)
		tmp = sqrt((2.0 * (U * (t * n))));
	else
		tmp = sqrt((t * ((2.0 * n) * U)));
	end
	tmp_2 = tmp;
end

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := If[LessEqual[U, 2.1e-191], N[Sqrt[N[(2.0 * N[(U * N[(t * n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Sqrt[N[(t * N[(N[(2.0 * n), $MachinePrecision] * U), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

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

Alternative 18: 36.3% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

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 * (u * (t * n))))
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 * (U * (t * n))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 19: 35.3% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

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) * (t * u)))
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) * (t * U)));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Reproduce

herbie shell --seed 2023348 
(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*))))))