Toniolo and Linder, Equation (13)

Percentage Accurate: 50.8% → 62.2%

Time: 27.6s

Alternatives: 15

Speedup: 1.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 50.8% 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: 62.2% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(n, U, t, l, Om, U_42_)
	t_1 = Float64(Float64(U_42_ - U) * Float64(n * (Float64(l / Om) ^ 2.0)))
	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 = Float64(sqrt(Float64(2.0 * n)) * sqrt(Float64(U * Float64(t - Float64(Float64(l / Om) * Float64(2.0 * l))))));
	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(Float64(Float64(U * -2.0) * Float64(Float64(Float64(2.0 / Om) + Float64(Float64(U - U_42_) / Float64((Om ^ 2.0) / n))) * Float64(n * (l ^ 2.0)))));
	end
	return tmp
end

MATLAB

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

Wolfram

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

Derivation

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

Alternative 2: 62.6% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(n, U, t, l, Om, U_42_)
	t_1 = Float64(Float64(U_42_ - U) * Float64(n * (Float64(l / Om) ^ 2.0)))
	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 <= 0.0)
		tmp = Float64(sqrt(Float64(2.0 * n)) * sqrt(Float64(U * Float64(t - Float64(Float64(l / Om) * Float64(2.0 * l))))));
	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(Float64(Float64(U * U_42_) * (Float64(Float64(n * sqrt(2.0)) * Float64(l / Om)) ^ 2.0)));
	end
	return tmp
end

MATLAB

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

Wolfram

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

Derivation

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

Alternative 3: 62.8% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(n, U, t, l, Om, U_42_)
	t_1 = Float64(Float64(U_42_ - U) * Float64(n * (Float64(l / Om) ^ 2.0)))
	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 <= 0.0)
		tmp = Float64(sqrt(Float64(2.0 * n)) * sqrt(Float64(U * Float64(t - Float64(Float64(l / Om) * Float64(2.0 * l))))));
	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(Float64(U_42_ / Float64((Float64(Float64(Om / l) / Float64(n * sqrt(2.0))) ^ 2.0) / U)));
	end
	return tmp
end

MATLAB

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

Wolfram

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

Derivation

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

Alternative 4: 62.3% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(n, U, t, l, Om, U_42_)
	t_1 = Float64(Float64(U_42_ - U) * Float64(n * (Float64(l / Om) ^ 2.0)))
	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 = Float64(sqrt(Float64(2.0 * n)) * sqrt(Float64(U * Float64(t - Float64(Float64(l / Om) * Float64(2.0 * l))))));
	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(Float64(-2.0 * Float64(Float64(U * (l ^ 2.0)) * Float64(n * Float64(Float64(2.0 / Om) + Float64(Float64(U - U_42_) * Float64(n / (Om ^ 2.0))))))));
	end
	return tmp
end

MATLAB

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

Wolfram

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

Derivation

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

Alternative 5: 62.2% accurate, 0.5× speedup

Math

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

FPCore

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

Python

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

Julia

function code(n, U, t, l, Om, U_42_)
	t_1 = Float64(Float64(U_42_ - U) * Float64(n * (Float64(l / Om) ^ 2.0)))
	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 = Float64(sqrt(Float64(2.0 * n)) * sqrt(Float64(U * Float64(t - Float64(Float64(l / Om) * Float64(2.0 * l))))));
	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(Float64(Float64(U * Float64(Float64(2.0 * n) / Float64(Om / Float64(n * Float64(U_42_ * (l ^ 2.0)))))) / Om));
	end
	return tmp
end

MATLAB

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

Wolfram

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

Derivation

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

Alternative 6: 54.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - 2 \cdot \left(\ell \cdot \frac{\ell}{Om}\right)\\ t_2 := {\left(\left(n \cdot \left(2 \cdot U\right)\right) \cdot \left(t + -2 \cdot \frac{{\ell}^{2}}{Om}\right)\right)}^{0.5}\\ t_3 := \sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(t_1 + \left(n \cdot \left(U* - U\right)\right) \cdot \left(\frac{\ell}{Om} \cdot \frac{\ell}{Om}\right)\right)}\\ \mathbf{if}\;n \leq -2.45 \cdot 10^{+153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;n \leq -1.5 \cdot 10^{-111}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;n \leq -4.9 \cdot 10^{-282}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t_1\right)}\\ \mathbf{elif}\;n \leq 1.6 \cdot 10^{-296}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;n \leq 1.02 \cdot 10^{+142}:\\ \;\;\;\;\sqrt{2 \cdot n} \cdot \sqrt{U \cdot \left(t - \frac{\ell}{Om} \cdot \left(2 \cdot \ell\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (let* ((t_1 (- t (* 2.0 (* l (/ l Om)))))
        (t_2 (pow (* (* n (* 2.0 U)) (+ t (* -2.0 (/ (pow l 2.0) Om)))) 0.5))
        (t_3
         (sqrt
          (*
           (* (* 2.0 n) U)
           (+ t_1 (* (* n (- U* U)) (* (/ l Om) (/ l Om))))))))
   (if (<= n -2.45e+153)
     t_2
     (if (<= n -1.5e-111)
       t_3
       (if (<= n -4.9e-282)
         (sqrt (* (* 2.0 n) (* U t_1)))
         (if (<= n 1.6e-296)
           t_3
           (if (<= n 1.02e+142)
             (* (sqrt (* 2.0 n)) (sqrt (* U (- t (* (/ l Om) (* 2.0 l))))))
             t_2)))))))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	double t_1 = t - (2.0 * (l * (l / Om)));
	double t_2 = pow(((n * (2.0 * U)) * (t + (-2.0 * (pow(l, 2.0) / Om)))), 0.5);
	double t_3 = sqrt((((2.0 * n) * U) * (t_1 + ((n * (U_42_ - U)) * ((l / Om) * (l / Om))))));
	double tmp;
	if (n <= -2.45e+153) {
		tmp = t_2;
	} else if (n <= -1.5e-111) {
		tmp = t_3;
	} else if (n <= -4.9e-282) {
		tmp = sqrt(((2.0 * n) * (U * t_1)));
	} else if (n <= 1.6e-296) {
		tmp = t_3;
	} else if (n <= 1.02e+142) {
		tmp = sqrt((2.0 * n)) * sqrt((U * (t - ((l / Om) * (2.0 * l)))));
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t - (2.0d0 * (l * (l / om)))
    t_2 = ((n * (2.0d0 * u)) * (t + ((-2.0d0) * ((l ** 2.0d0) / om)))) ** 0.5d0
    t_3 = sqrt((((2.0d0 * n) * u) * (t_1 + ((n * (u_42 - u)) * ((l / om) * (l / om))))))
    if (n <= (-2.45d+153)) then
        tmp = t_2
    else if (n <= (-1.5d-111)) then
        tmp = t_3
    else if (n <= (-4.9d-282)) then
        tmp = sqrt(((2.0d0 * n) * (u * t_1)))
    else if (n <= 1.6d-296) then
        tmp = t_3
    else if (n <= 1.02d+142) then
        tmp = sqrt((2.0d0 * n)) * sqrt((u * (t - ((l / om) * (2.0d0 * l)))))
    else
        tmp = t_2
    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 - (2.0 * (l * (l / Om)));
	double t_2 = Math.pow(((n * (2.0 * U)) * (t + (-2.0 * (Math.pow(l, 2.0) / Om)))), 0.5);
	double t_3 = Math.sqrt((((2.0 * n) * U) * (t_1 + ((n * (U_42_ - U)) * ((l / Om) * (l / Om))))));
	double tmp;
	if (n <= -2.45e+153) {
		tmp = t_2;
	} else if (n <= -1.5e-111) {
		tmp = t_3;
	} else if (n <= -4.9e-282) {
		tmp = Math.sqrt(((2.0 * n) * (U * t_1)));
	} else if (n <= 1.6e-296) {
		tmp = t_3;
	} else if (n <= 1.02e+142) {
		tmp = Math.sqrt((2.0 * n)) * Math.sqrt((U * (t - ((l / Om) * (2.0 * l)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(n, U, t, l, Om, U_42_):
	t_1 = t - (2.0 * (l * (l / Om)))
	t_2 = math.pow(((n * (2.0 * U)) * (t + (-2.0 * (math.pow(l, 2.0) / Om)))), 0.5)
	t_3 = math.sqrt((((2.0 * n) * U) * (t_1 + ((n * (U_42_ - U)) * ((l / Om) * (l / Om))))))
	tmp = 0
	if n <= -2.45e+153:
		tmp = t_2
	elif n <= -1.5e-111:
		tmp = t_3
	elif n <= -4.9e-282:
		tmp = math.sqrt(((2.0 * n) * (U * t_1)))
	elif n <= 1.6e-296:
		tmp = t_3
	elif n <= 1.02e+142:
		tmp = math.sqrt((2.0 * n)) * math.sqrt((U * (t - ((l / Om) * (2.0 * l)))))
	else:
		tmp = t_2
	return tmp

Julia

function code(n, U, t, l, Om, U_42_)
	t_1 = Float64(t - Float64(2.0 * Float64(l * Float64(l / Om))))
	t_2 = Float64(Float64(n * Float64(2.0 * U)) * Float64(t + Float64(-2.0 * Float64((l ^ 2.0) / Om)))) ^ 0.5
	t_3 = sqrt(Float64(Float64(Float64(2.0 * n) * U) * Float64(t_1 + Float64(Float64(n * Float64(U_42_ - U)) * Float64(Float64(l / Om) * Float64(l / Om))))))
	tmp = 0.0
	if (n <= -2.45e+153)
		tmp = t_2;
	elseif (n <= -1.5e-111)
		tmp = t_3;
	elseif (n <= -4.9e-282)
		tmp = sqrt(Float64(Float64(2.0 * n) * Float64(U * t_1)));
	elseif (n <= 1.6e-296)
		tmp = t_3;
	elseif (n <= 1.02e+142)
		tmp = Float64(sqrt(Float64(2.0 * n)) * sqrt(Float64(U * Float64(t - Float64(Float64(l / Om) * Float64(2.0 * l))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(n, U, t, l, Om, U_42_)
	t_1 = t - (2.0 * (l * (l / Om)));
	t_2 = ((n * (2.0 * U)) * (t + (-2.0 * ((l ^ 2.0) / Om)))) ^ 0.5;
	t_3 = sqrt((((2.0 * n) * U) * (t_1 + ((n * (U_42_ - U)) * ((l / Om) * (l / Om))))));
	tmp = 0.0;
	if (n <= -2.45e+153)
		tmp = t_2;
	elseif (n <= -1.5e-111)
		tmp = t_3;
	elseif (n <= -4.9e-282)
		tmp = sqrt(((2.0 * n) * (U * t_1)));
	elseif (n <= 1.6e-296)
		tmp = t_3;
	elseif (n <= 1.02e+142)
		tmp = sqrt((2.0 * n)) * sqrt((U * (t - ((l / Om) * (2.0 * l)))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := Block[{t$95$1 = N[(t - N[(2.0 * N[(l * N[(l / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Power[N[(N[(n * N[(2.0 * U), $MachinePrecision]), $MachinePrecision] * N[(t + N[(-2.0 * N[(N[Power[l, 2.0], $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]}, Block[{t$95$3 = N[Sqrt[N[(N[(N[(2.0 * n), $MachinePrecision] * U), $MachinePrecision] * N[(t$95$1 + N[(N[(n * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision] * N[(N[(l / Om), $MachinePrecision] * N[(l / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[n, -2.45e+153], t$95$2, If[LessEqual[n, -1.5e-111], t$95$3, If[LessEqual[n, -4.9e-282], N[Sqrt[N[(N[(2.0 * n), $MachinePrecision] * N[(U * t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[n, 1.6e-296], t$95$3, If[LessEqual[n, 1.02e+142], N[(N[Sqrt[N[(2.0 * n), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(U * N[(t - N[(N[(l / Om), $MachinePrecision] * N[(2.0 * l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

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

Alternative 7: 54.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - 2 \cdot \left(\ell \cdot \frac{\ell}{Om}\right)\\ t_2 := {\left(\left(n \cdot \left(2 \cdot U\right)\right) \cdot \left(t + -2 \cdot \frac{{\ell}^{2}}{Om}\right)\right)}^{0.5}\\ \mathbf{if}\;n \leq -1.4 \cdot 10^{+151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;n \leq -3.9 \cdot 10^{-111}:\\ \;\;\;\;\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(t_1 + \left(n \cdot \left(U* - U\right)\right) \cdot \left(\frac{\ell}{Om} \cdot \frac{\ell}{Om}\right)\right)}\\ \mathbf{elif}\;n \leq -4.5 \cdot 10^{-283}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t_1\right)}\\ \mathbf{elif}\;n \leq 3.5 \cdot 10^{-294}:\\ \;\;\;\;\sqrt{-4 \cdot \frac{U \cdot \left(n \cdot {\ell}^{2}\right)}{Om} + 2 \cdot \left(U \cdot \left(n \cdot t\right)\right)}\\ \mathbf{elif}\;n \leq 7.2 \cdot 10^{+142}:\\ \;\;\;\;\sqrt{2 \cdot n} \cdot \sqrt{U \cdot \left(t - \frac{\ell}{Om} \cdot \left(2 \cdot \ell\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (let* ((t_1 (- t (* 2.0 (* l (/ l Om)))))
        (t_2 (pow (* (* n (* 2.0 U)) (+ t (* -2.0 (/ (pow l 2.0) Om)))) 0.5)))
   (if (<= n -1.4e+151)
     t_2
     (if (<= n -3.9e-111)
       (sqrt
        (* (* (* 2.0 n) U) (+ t_1 (* (* n (- U* U)) (* (/ l Om) (/ l Om))))))
       (if (<= n -4.5e-283)
         (sqrt (* (* 2.0 n) (* U t_1)))
         (if (<= n 3.5e-294)
           (sqrt
            (+ (* -4.0 (/ (* U (* n (pow l 2.0))) Om)) (* 2.0 (* U (* n t)))))
           (if (<= n 7.2e+142)
             (* (sqrt (* 2.0 n)) (sqrt (* U (- t (* (/ l Om) (* 2.0 l))))))
             t_2)))))))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	double t_1 = t - (2.0 * (l * (l / Om)));
	double t_2 = pow(((n * (2.0 * U)) * (t + (-2.0 * (pow(l, 2.0) / Om)))), 0.5);
	double tmp;
	if (n <= -1.4e+151) {
		tmp = t_2;
	} else if (n <= -3.9e-111) {
		tmp = sqrt((((2.0 * n) * U) * (t_1 + ((n * (U_42_ - U)) * ((l / Om) * (l / Om))))));
	} else if (n <= -4.5e-283) {
		tmp = sqrt(((2.0 * n) * (U * t_1)));
	} else if (n <= 3.5e-294) {
		tmp = sqrt(((-4.0 * ((U * (n * pow(l, 2.0))) / Om)) + (2.0 * (U * (n * t)))));
	} else if (n <= 7.2e+142) {
		tmp = sqrt((2.0 * n)) * sqrt((U * (t - ((l / Om) * (2.0 * l)))));
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = t - (2.0d0 * (l * (l / om)))
    t_2 = ((n * (2.0d0 * u)) * (t + ((-2.0d0) * ((l ** 2.0d0) / om)))) ** 0.5d0
    if (n <= (-1.4d+151)) then
        tmp = t_2
    else if (n <= (-3.9d-111)) then
        tmp = sqrt((((2.0d0 * n) * u) * (t_1 + ((n * (u_42 - u)) * ((l / om) * (l / om))))))
    else if (n <= (-4.5d-283)) then
        tmp = sqrt(((2.0d0 * n) * (u * t_1)))
    else if (n <= 3.5d-294) then
        tmp = sqrt((((-4.0d0) * ((u * (n * (l ** 2.0d0))) / om)) + (2.0d0 * (u * (n * t)))))
    else if (n <= 7.2d+142) then
        tmp = sqrt((2.0d0 * n)) * sqrt((u * (t - ((l / om) * (2.0d0 * l)))))
    else
        tmp = t_2
    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 - (2.0 * (l * (l / Om)));
	double t_2 = Math.pow(((n * (2.0 * U)) * (t + (-2.0 * (Math.pow(l, 2.0) / Om)))), 0.5);
	double tmp;
	if (n <= -1.4e+151) {
		tmp = t_2;
	} else if (n <= -3.9e-111) {
		tmp = Math.sqrt((((2.0 * n) * U) * (t_1 + ((n * (U_42_ - U)) * ((l / Om) * (l / Om))))));
	} else if (n <= -4.5e-283) {
		tmp = Math.sqrt(((2.0 * n) * (U * t_1)));
	} else if (n <= 3.5e-294) {
		tmp = Math.sqrt(((-4.0 * ((U * (n * Math.pow(l, 2.0))) / Om)) + (2.0 * (U * (n * t)))));
	} else if (n <= 7.2e+142) {
		tmp = Math.sqrt((2.0 * n)) * Math.sqrt((U * (t - ((l / Om) * (2.0 * l)))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(n, U, t, l, Om, U_42_):
	t_1 = t - (2.0 * (l * (l / Om)))
	t_2 = math.pow(((n * (2.0 * U)) * (t + (-2.0 * (math.pow(l, 2.0) / Om)))), 0.5)
	tmp = 0
	if n <= -1.4e+151:
		tmp = t_2
	elif n <= -3.9e-111:
		tmp = math.sqrt((((2.0 * n) * U) * (t_1 + ((n * (U_42_ - U)) * ((l / Om) * (l / Om))))))
	elif n <= -4.5e-283:
		tmp = math.sqrt(((2.0 * n) * (U * t_1)))
	elif n <= 3.5e-294:
		tmp = math.sqrt(((-4.0 * ((U * (n * math.pow(l, 2.0))) / Om)) + (2.0 * (U * (n * t)))))
	elif n <= 7.2e+142:
		tmp = math.sqrt((2.0 * n)) * math.sqrt((U * (t - ((l / Om) * (2.0 * l)))))
	else:
		tmp = t_2
	return tmp

Julia

function code(n, U, t, l, Om, U_42_)
	t_1 = Float64(t - Float64(2.0 * Float64(l * Float64(l / Om))))
	t_2 = Float64(Float64(n * Float64(2.0 * U)) * Float64(t + Float64(-2.0 * Float64((l ^ 2.0) / Om)))) ^ 0.5
	tmp = 0.0
	if (n <= -1.4e+151)
		tmp = t_2;
	elseif (n <= -3.9e-111)
		tmp = sqrt(Float64(Float64(Float64(2.0 * n) * U) * Float64(t_1 + Float64(Float64(n * Float64(U_42_ - U)) * Float64(Float64(l / Om) * Float64(l / Om))))));
	elseif (n <= -4.5e-283)
		tmp = sqrt(Float64(Float64(2.0 * n) * Float64(U * t_1)));
	elseif (n <= 3.5e-294)
		tmp = sqrt(Float64(Float64(-4.0 * Float64(Float64(U * Float64(n * (l ^ 2.0))) / Om)) + Float64(2.0 * Float64(U * Float64(n * t)))));
	elseif (n <= 7.2e+142)
		tmp = Float64(sqrt(Float64(2.0 * n)) * sqrt(Float64(U * Float64(t - Float64(Float64(l / Om) * Float64(2.0 * l))))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(n, U, t, l, Om, U_42_)
	t_1 = t - (2.0 * (l * (l / Om)));
	t_2 = ((n * (2.0 * U)) * (t + (-2.0 * ((l ^ 2.0) / Om)))) ^ 0.5;
	tmp = 0.0;
	if (n <= -1.4e+151)
		tmp = t_2;
	elseif (n <= -3.9e-111)
		tmp = sqrt((((2.0 * n) * U) * (t_1 + ((n * (U_42_ - U)) * ((l / Om) * (l / Om))))));
	elseif (n <= -4.5e-283)
		tmp = sqrt(((2.0 * n) * (U * t_1)));
	elseif (n <= 3.5e-294)
		tmp = sqrt(((-4.0 * ((U * (n * (l ^ 2.0))) / Om)) + (2.0 * (U * (n * t)))));
	elseif (n <= 7.2e+142)
		tmp = sqrt((2.0 * n)) * sqrt((U * (t - ((l / Om) * (2.0 * l)))));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := Block[{t$95$1 = N[(t - N[(2.0 * N[(l * N[(l / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Power[N[(N[(n * N[(2.0 * U), $MachinePrecision]), $MachinePrecision] * N[(t + N[(-2.0 * N[(N[Power[l, 2.0], $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]}, If[LessEqual[n, -1.4e+151], t$95$2, If[LessEqual[n, -3.9e-111], N[Sqrt[N[(N[(N[(2.0 * n), $MachinePrecision] * U), $MachinePrecision] * N[(t$95$1 + N[(N[(n * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision] * N[(N[(l / Om), $MachinePrecision] * N[(l / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[n, -4.5e-283], N[Sqrt[N[(N[(2.0 * n), $MachinePrecision] * N[(U * t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[n, 3.5e-294], N[Sqrt[N[(N[(-4.0 * N[(N[(U * N[(n * N[Power[l, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(U * N[(n * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[n, 7.2e+142], N[(N[Sqrt[N[(2.0 * n), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(U * N[(t - N[(N[(l / Om), $MachinePrecision] * N[(2.0 * l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

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

Alternative 8: 55.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {\left(\left(n \cdot \left(2 \cdot U\right)\right) \cdot \left(t + -2 \cdot \frac{{\ell}^{2}}{Om}\right)\right)}^{0.5}\\ \mathbf{if}\;n \leq -7.5 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;n \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot \left(\left(t - 2 \cdot \frac{\ell}{\frac{Om}{\ell}}\right) - {\left(\frac{\ell}{Om}\right)}^{2} \cdot \left(n \cdot \left(U - U*\right)\right)\right)\right)}\\ \mathbf{elif}\;n \leq 1.65 \cdot 10^{-72}:\\ \;\;\;\;\sqrt{2 \cdot n} \cdot \sqrt{U \cdot \left(t - \frac{\ell}{Om} \cdot \left(2 \cdot \ell\right)\right)}\\ \mathbf{elif}\;n \leq 1.25 \cdot 10^{+76}:\\ \;\;\;\;\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(\left(t - 2 \cdot \left(\ell \cdot \frac{\ell}{Om}\right)\right) + \left(n \cdot \left(U* - U\right)\right) \cdot \left(\frac{\ell}{Om} \cdot \frac{\ell}{Om}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (let* ((t_1 (pow (* (* n (* 2.0 U)) (+ t (* -2.0 (/ (pow l 2.0) Om)))) 0.5)))
   (if (<= n -7.5e+152)
     t_1
     (if (<= n -5e-310)
       (sqrt
        (*
         (* 2.0 n)
         (*
          U
          (-
           (- t (* 2.0 (/ l (/ Om l))))
           (* (pow (/ l Om) 2.0) (* n (- U U*)))))))
       (if (<= n 1.65e-72)
         (* (sqrt (* 2.0 n)) (sqrt (* U (- t (* (/ l Om) (* 2.0 l))))))
         (if (<= n 1.25e+76)
           (sqrt
            (*
             (* (* 2.0 n) U)
             (+
              (- t (* 2.0 (* l (/ l Om))))
              (* (* n (- U* U)) (* (/ l Om) (/ l Om))))))
           t_1))))))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	double t_1 = pow(((n * (2.0 * U)) * (t + (-2.0 * (pow(l, 2.0) / Om)))), 0.5);
	double tmp;
	if (n <= -7.5e+152) {
		tmp = t_1;
	} else if (n <= -5e-310) {
		tmp = sqrt(((2.0 * n) * (U * ((t - (2.0 * (l / (Om / l)))) - (pow((l / Om), 2.0) * (n * (U - U_42_)))))));
	} else if (n <= 1.65e-72) {
		tmp = sqrt((2.0 * n)) * sqrt((U * (t - ((l / Om) * (2.0 * l)))));
	} else if (n <= 1.25e+76) {
		tmp = sqrt((((2.0 * n) * U) * ((t - (2.0 * (l * (l / Om)))) + ((n * (U_42_ - U)) * ((l / Om) * (l / Om))))));
	} 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 = ((n * (2.0d0 * u)) * (t + ((-2.0d0) * ((l ** 2.0d0) / om)))) ** 0.5d0
    if (n <= (-7.5d+152)) then
        tmp = t_1
    else if (n <= (-5d-310)) then
        tmp = sqrt(((2.0d0 * n) * (u * ((t - (2.0d0 * (l / (om / l)))) - (((l / om) ** 2.0d0) * (n * (u - u_42)))))))
    else if (n <= 1.65d-72) then
        tmp = sqrt((2.0d0 * n)) * sqrt((u * (t - ((l / om) * (2.0d0 * l)))))
    else if (n <= 1.25d+76) then
        tmp = sqrt((((2.0d0 * n) * u) * ((t - (2.0d0 * (l * (l / om)))) + ((n * (u_42 - u)) * ((l / om) * (l / om))))))
    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.pow(((n * (2.0 * U)) * (t + (-2.0 * (Math.pow(l, 2.0) / Om)))), 0.5);
	double tmp;
	if (n <= -7.5e+152) {
		tmp = t_1;
	} else if (n <= -5e-310) {
		tmp = Math.sqrt(((2.0 * n) * (U * ((t - (2.0 * (l / (Om / l)))) - (Math.pow((l / Om), 2.0) * (n * (U - U_42_)))))));
	} else if (n <= 1.65e-72) {
		tmp = Math.sqrt((2.0 * n)) * Math.sqrt((U * (t - ((l / Om) * (2.0 * l)))));
	} else if (n <= 1.25e+76) {
		tmp = Math.sqrt((((2.0 * n) * U) * ((t - (2.0 * (l * (l / Om)))) + ((n * (U_42_ - U)) * ((l / Om) * (l / Om))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(n, U, t, l, Om, U_42_):
	t_1 = math.pow(((n * (2.0 * U)) * (t + (-2.0 * (math.pow(l, 2.0) / Om)))), 0.5)
	tmp = 0
	if n <= -7.5e+152:
		tmp = t_1
	elif n <= -5e-310:
		tmp = math.sqrt(((2.0 * n) * (U * ((t - (2.0 * (l / (Om / l)))) - (math.pow((l / Om), 2.0) * (n * (U - U_42_)))))))
	elif n <= 1.65e-72:
		tmp = math.sqrt((2.0 * n)) * math.sqrt((U * (t - ((l / Om) * (2.0 * l)))))
	elif n <= 1.25e+76:
		tmp = math.sqrt((((2.0 * n) * U) * ((t - (2.0 * (l * (l / Om)))) + ((n * (U_42_ - U)) * ((l / Om) * (l / Om))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(n, U, t, l, Om, U_42_)
	t_1 = Float64(Float64(n * Float64(2.0 * U)) * Float64(t + Float64(-2.0 * Float64((l ^ 2.0) / Om)))) ^ 0.5
	tmp = 0.0
	if (n <= -7.5e+152)
		tmp = t_1;
	elseif (n <= -5e-310)
		tmp = sqrt(Float64(Float64(2.0 * n) * Float64(U * Float64(Float64(t - Float64(2.0 * Float64(l / Float64(Om / l)))) - Float64((Float64(l / Om) ^ 2.0) * Float64(n * Float64(U - U_42_)))))));
	elseif (n <= 1.65e-72)
		tmp = Float64(sqrt(Float64(2.0 * n)) * sqrt(Float64(U * Float64(t - Float64(Float64(l / Om) * Float64(2.0 * l))))));
	elseif (n <= 1.25e+76)
		tmp = sqrt(Float64(Float64(Float64(2.0 * n) * U) * Float64(Float64(t - Float64(2.0 * Float64(l * Float64(l / Om)))) + Float64(Float64(n * Float64(U_42_ - U)) * Float64(Float64(l / Om) * Float64(l / Om))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(n, U, t, l, Om, U_42_)
	t_1 = ((n * (2.0 * U)) * (t + (-2.0 * ((l ^ 2.0) / Om)))) ^ 0.5;
	tmp = 0.0;
	if (n <= -7.5e+152)
		tmp = t_1;
	elseif (n <= -5e-310)
		tmp = sqrt(((2.0 * n) * (U * ((t - (2.0 * (l / (Om / l)))) - (((l / Om) ^ 2.0) * (n * (U - U_42_)))))));
	elseif (n <= 1.65e-72)
		tmp = sqrt((2.0 * n)) * sqrt((U * (t - ((l / Om) * (2.0 * l)))));
	elseif (n <= 1.25e+76)
		tmp = sqrt((((2.0 * n) * U) * ((t - (2.0 * (l * (l / Om)))) + ((n * (U_42_ - U)) * ((l / Om) * (l / Om))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := Block[{t$95$1 = N[Power[N[(N[(n * N[(2.0 * U), $MachinePrecision]), $MachinePrecision] * N[(t + N[(-2.0 * N[(N[Power[l, 2.0], $MachinePrecision] / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]}, If[LessEqual[n, -7.5e+152], t$95$1, If[LessEqual[n, -5e-310], N[Sqrt[N[(N[(2.0 * n), $MachinePrecision] * N[(U * N[(N[(t - N[(2.0 * N[(l / N[(Om / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[Power[N[(l / Om), $MachinePrecision], 2.0], $MachinePrecision] * N[(n * N[(U - U$42$), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[n, 1.65e-72], N[(N[Sqrt[N[(2.0 * n), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(U * N[(t - N[(N[(l / Om), $MachinePrecision] * N[(2.0 * l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 1.25e+76], N[Sqrt[N[(N[(N[(2.0 * n), $MachinePrecision] * U), $MachinePrecision] * N[(N[(t - N[(2.0 * N[(l * N[(l / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(n * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision] * N[(N[(l / Om), $MachinePrecision] * N[(l / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], t$95$1]]]]]

Derivation

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

Alternative 9: 54.5% accurate, 1.0× speedup

Math

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

FPCore

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

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 / (Om / l)))) - ((U - U_42_) * (n * pow((l / Om), 2.0)))))));
}

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 10: 51.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - 2 \cdot \left(\ell \cdot \frac{\ell}{Om}\right)\\ \mathbf{if}\;U \leq -8.5 \cdot 10^{-221} \lor \neg \left(U \leq 1.9 \cdot 10^{-90}\right):\\ \;\;\;\;\sqrt{\left(\left(2 \cdot n\right) \cdot U\right) \cdot \left(t_1 + \left(n \cdot \left(U* - U\right)\right) \cdot \left(\frac{\ell}{Om} \cdot \frac{\ell}{Om}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left(2 \cdot n\right) \cdot \left(U \cdot t_1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (let* ((t_1 (- t (* 2.0 (* l (/ l Om))))))
   (if (or (<= U -8.5e-221) (not (<= U 1.9e-90)))
     (sqrt
      (* (* (* 2.0 n) U) (+ t_1 (* (* n (- U* U)) (* (/ l Om) (/ l Om))))))
     (sqrt (* (* 2.0 n) (* U t_1))))))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	double t_1 = t - (2.0 * (l * (l / Om)));
	double tmp;
	if ((U <= -8.5e-221) || !(U <= 1.9e-90)) {
		tmp = sqrt((((2.0 * n) * U) * (t_1 + ((n * (U_42_ - U)) * ((l / Om) * (l / Om))))));
	} else {
		tmp = sqrt(((2.0 * n) * (U * 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 = t - (2.0d0 * (l * (l / om)))
    if ((u <= (-8.5d-221)) .or. (.not. (u <= 1.9d-90))) then
        tmp = sqrt((((2.0d0 * n) * u) * (t_1 + ((n * (u_42 - u)) * ((l / om) * (l / om))))))
    else
        tmp = sqrt(((2.0d0 * n) * (u * 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 = t - (2.0 * (l * (l / Om)));
	double tmp;
	if ((U <= -8.5e-221) || !(U <= 1.9e-90)) {
		tmp = Math.sqrt((((2.0 * n) * U) * (t_1 + ((n * (U_42_ - U)) * ((l / Om) * (l / Om))))));
	} else {
		tmp = Math.sqrt(((2.0 * n) * (U * t_1)));
	}
	return tmp;
}

Python

def code(n, U, t, l, Om, U_42_):
	t_1 = t - (2.0 * (l * (l / Om)))
	tmp = 0
	if (U <= -8.5e-221) or not (U <= 1.9e-90):
		tmp = math.sqrt((((2.0 * n) * U) * (t_1 + ((n * (U_42_ - U)) * ((l / Om) * (l / Om))))))
	else:
		tmp = math.sqrt(((2.0 * n) * (U * t_1)))
	return tmp

Julia

function code(n, U, t, l, Om, U_42_)
	t_1 = Float64(t - Float64(2.0 * Float64(l * Float64(l / Om))))
	tmp = 0.0
	if ((U <= -8.5e-221) || !(U <= 1.9e-90))
		tmp = sqrt(Float64(Float64(Float64(2.0 * n) * U) * Float64(t_1 + Float64(Float64(n * Float64(U_42_ - U)) * Float64(Float64(l / Om) * Float64(l / Om))))));
	else
		tmp = sqrt(Float64(Float64(2.0 * n) * Float64(U * t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(n, U, t, l, Om, U_42_)
	t_1 = t - (2.0 * (l * (l / Om)));
	tmp = 0.0;
	if ((U <= -8.5e-221) || ~((U <= 1.9e-90)))
		tmp = sqrt((((2.0 * n) * U) * (t_1 + ((n * (U_42_ - U)) * ((l / Om) * (l / Om))))));
	else
		tmp = sqrt(((2.0 * n) * (U * t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := Block[{t$95$1 = N[(t - N[(2.0 * N[(l * N[(l / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[U, -8.5e-221], N[Not[LessEqual[U, 1.9e-90]], $MachinePrecision]], N[Sqrt[N[(N[(N[(2.0 * n), $MachinePrecision] * U), $MachinePrecision] * N[(t$95$1 + N[(N[(n * N[(U$42$ - U), $MachinePrecision]), $MachinePrecision] * N[(N[(l / Om), $MachinePrecision] * N[(l / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Sqrt[N[(N[(2.0 * n), $MachinePrecision] * N[(U * t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]

Derivation

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

Alternative 11: 47.9% accurate, 2.0× speedup

Math

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

FPCore

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

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)))))));
}

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)))))))
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)))))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 12: 37.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 7 \cdot 10^{-87}:\\ \;\;\;\;\sqrt{t \cdot \left(2 \cdot \left(n \cdot U\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;{\left(2 \cdot \left(n \cdot \left(U \cdot t\right)\right)\right)}^{0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (n U t l Om U*)
 :precision binary64
 (if (<= t 7e-87)
   (sqrt (* t (* 2.0 (* n U))))
   (pow (* 2.0 (* n (* U t))) 0.5)))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	double tmp;
	if (t <= 7e-87) {
		tmp = sqrt((t * (2.0 * (n * U))));
	} else {
		tmp = pow((2.0 * (n * (U * t))), 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 (t <= 7d-87) then
        tmp = sqrt((t * (2.0d0 * (n * u))))
    else
        tmp = (2.0d0 * (n * (u * t))) ** 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 (t <= 7e-87) {
		tmp = Math.sqrt((t * (2.0 * (n * U))));
	} else {
		tmp = Math.pow((2.0 * (n * (U * t))), 0.5);
	}
	return tmp;
}

Python

def code(n, U, t, l, Om, U_42_):
	tmp = 0
	if t <= 7e-87:
		tmp = math.sqrt((t * (2.0 * (n * U))))
	else:
		tmp = math.pow((2.0 * (n * (U * t))), 0.5)
	return tmp

Julia

function code(n, U, t, l, Om, U_42_)
	tmp = 0.0
	if (t <= 7e-87)
		tmp = sqrt(Float64(t * Float64(2.0 * Float64(n * U))));
	else
		tmp = Float64(2.0 * Float64(n * Float64(U * t))) ^ 0.5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(n, U, t, l, Om, U_42_)
	tmp = 0.0;
	if (t <= 7e-87)
		tmp = sqrt((t * (2.0 * (n * U))));
	else
		tmp = (2.0 * (n * (U * t))) ^ 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := If[LessEqual[t, 7e-87], N[Sqrt[N[(t * N[(2.0 * N[(n * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Power[N[(2.0 * N[(n * N[(U * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]]

Derivation

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

Alternative 13: 38.4% accurate, 2.1× speedup

Math

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

FPCore

(FPCore (n U t l Om U*) :precision binary64 (pow (* 2.0 (* t (* n U))) 0.5))

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	return pow((2.0 * (t * (n * U))), 0.5);
}

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 = (2.0d0 * (t * (n * u))) ** 0.5d0
end function

Java

public static double code(double n, double U, double t, double l, double Om, double U_42_) {
	return Math.pow((2.0 * (t * (n * U))), 0.5);
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[n_, U_, t_, l_, Om_, U$42$_] := N[Power[N[(2.0 * N[(t * N[(n * U), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]

Derivation

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

Alternative 14: 36.7% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

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 * (n * t))))
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 * (n * t))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[n_, U_, t_, l_, 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 15: 36.3% accurate, 2.1× speedup

Math

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

FPCore

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

C

double code(double n, double U, double t, double l, double Om, double U_42_) {
	return sqrt((t * (2.0 * (n * 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((t * (2.0d0 * (n * u))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Reproduce

herbie shell --seed 2024006 
(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*))))))