Toniolo and Linder, Equation (2)

Percentage Accurate: 83.5% → 98.3%

Time: 18.1s

Alternatives: 12

Speedup: 1.3×

Specification

Math

\[\begin{array}{l} \\ \sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right) \end{array} \]

FPCore

(FPCore (t l Om Omc)
 :precision binary64
 (asin
  (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

C

double code(double t, double l, double Om, double Omc) {
	return asin(sqrt(((1.0 - pow((Om / Omc), 2.0)) / (1.0 + (2.0 * pow((t / l), 2.0))))));
}

Fortran

real(8) function code(t, l, om, omc)
    real(8), intent (in) :: t
    real(8), intent (in) :: l
    real(8), intent (in) :: om
    real(8), intent (in) :: omc
    code = asin(sqrt(((1.0d0 - ((om / omc) ** 2.0d0)) / (1.0d0 + (2.0d0 * ((t / l) ** 2.0d0))))))
end function

Java

public static double code(double t, double l, double Om, double Omc) {
	return Math.asin(Math.sqrt(((1.0 - Math.pow((Om / Omc), 2.0)) / (1.0 + (2.0 * Math.pow((t / l), 2.0))))));
}

Python

def code(t, l, Om, Omc):
	return math.asin(math.sqrt(((1.0 - math.pow((Om / Omc), 2.0)) / (1.0 + (2.0 * math.pow((t / l), 2.0))))))

Julia

function code(t, l, Om, Omc)
	return asin(sqrt(Float64(Float64(1.0 - (Float64(Om / Omc) ^ 2.0)) / Float64(1.0 + Float64(2.0 * (Float64(t / l) ^ 2.0))))))
end

MATLAB

function tmp = code(t, l, Om, Omc)
	tmp = asin(sqrt(((1.0 - ((Om / Omc) ^ 2.0)) / (1.0 + (2.0 * ((t / l) ^ 2.0))))));
end

Wolfram

code[t_, l_, Om_, Omc_] := N[ArcSin[N[Sqrt[N[(N[(1.0 - N[Power[N[(Om / Omc), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(2.0 * N[Power[N[(t / l), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]

Initial Program: 83.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right) \end{array} \]

FPCore

(FPCore (t l Om Omc)
 :precision binary64
 (asin
  (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))

C

double code(double t, double l, double Om, double Omc) {
	return asin(sqrt(((1.0 - pow((Om / Omc), 2.0)) / (1.0 + (2.0 * pow((t / l), 2.0))))));
}

Fortran

real(8) function code(t, l, om, omc)
    real(8), intent (in) :: t
    real(8), intent (in) :: l
    real(8), intent (in) :: om
    real(8), intent (in) :: omc
    code = asin(sqrt(((1.0d0 - ((om / omc) ** 2.0d0)) / (1.0d0 + (2.0d0 * ((t / l) ** 2.0d0))))))
end function

Java

public static double code(double t, double l, double Om, double Omc) {
	return Math.asin(Math.sqrt(((1.0 - Math.pow((Om / Omc), 2.0)) / (1.0 + (2.0 * Math.pow((t / l), 2.0))))));
}

Python

def code(t, l, Om, Omc):
	return math.asin(math.sqrt(((1.0 - math.pow((Om / Omc), 2.0)) / (1.0 + (2.0 * math.pow((t / l), 2.0))))))

Julia

function code(t, l, Om, Omc)
	return asin(sqrt(Float64(Float64(1.0 - (Float64(Om / Omc) ^ 2.0)) / Float64(1.0 + Float64(2.0 * (Float64(t / l) ^ 2.0))))))
end

MATLAB

function tmp = code(t, l, Om, Omc)
	tmp = asin(sqrt(((1.0 - ((Om / Omc) ^ 2.0)) / (1.0 + (2.0 * ((t / l) ^ 2.0))))));
end

Wolfram

code[t_, l_, Om_, Omc_] := N[ArcSin[N[Sqrt[N[(N[(1.0 - N[Power[N[(Om / Omc), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(2.0 * N[Power[N[(t / l), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]

Alternative 1: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;{\left(\frac{t}{\ell}\right)}^{2} \leq 10^{+271}:\\ \;\;\;\;\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot \frac{\frac{t}{\ell}}{\frac{\ell}{t}}}}\right)\\ \mathbf{else}:\\ \;\;\;\;\sin^{-1} \left(\frac{1}{\mathsf{hypot}\left(1, \frac{t}{\ell \cdot \sqrt{0.5}}\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (t l Om Omc)
 :precision binary64
 (if (<= (pow (/ t l) 2.0) 1e+271)
   (asin
    (sqrt
     (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (/ (/ t l) (/ l t)))))))
   (asin (/ 1.0 (hypot 1.0 (/ t (* l (sqrt 0.5))))))))

C

double code(double t, double l, double Om, double Omc) {
	double tmp;
	if (pow((t / l), 2.0) <= 1e+271) {
		tmp = asin(sqrt(((1.0 - pow((Om / Omc), 2.0)) / (1.0 + (2.0 * ((t / l) / (l / t)))))));
	} else {
		tmp = asin((1.0 / hypot(1.0, (t / (l * sqrt(0.5))))));
	}
	return tmp;
}

Java

public static double code(double t, double l, double Om, double Omc) {
	double tmp;
	if (Math.pow((t / l), 2.0) <= 1e+271) {
		tmp = Math.asin(Math.sqrt(((1.0 - Math.pow((Om / Omc), 2.0)) / (1.0 + (2.0 * ((t / l) / (l / t)))))));
	} else {
		tmp = Math.asin((1.0 / Math.hypot(1.0, (t / (l * Math.sqrt(0.5))))));
	}
	return tmp;
}

Python

def code(t, l, Om, Omc):
	tmp = 0
	if math.pow((t / l), 2.0) <= 1e+271:
		tmp = math.asin(math.sqrt(((1.0 - math.pow((Om / Omc), 2.0)) / (1.0 + (2.0 * ((t / l) / (l / t)))))))
	else:
		tmp = math.asin((1.0 / math.hypot(1.0, (t / (l * math.sqrt(0.5))))))
	return tmp

Julia

function code(t, l, Om, Omc)
	tmp = 0.0
	if ((Float64(t / l) ^ 2.0) <= 1e+271)
		tmp = asin(sqrt(Float64(Float64(1.0 - (Float64(Om / Omc) ^ 2.0)) / Float64(1.0 + Float64(2.0 * Float64(Float64(t / l) / Float64(l / t)))))));
	else
		tmp = asin(Float64(1.0 / hypot(1.0, Float64(t / Float64(l * sqrt(0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(t, l, Om, Omc)
	tmp = 0.0;
	if (((t / l) ^ 2.0) <= 1e+271)
		tmp = asin(sqrt(((1.0 - ((Om / Omc) ^ 2.0)) / (1.0 + (2.0 * ((t / l) / (l / t)))))));
	else
		tmp = asin((1.0 / hypot(1.0, (t / (l * sqrt(0.5))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[t_, l_, Om_, Omc_] := If[LessEqual[N[Power[N[(t / l), $MachinePrecision], 2.0], $MachinePrecision], 1e+271], N[ArcSin[N[Sqrt[N[(N[(1.0 - N[Power[N[(Om / Omc), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(2.0 * N[(N[(t / l), $MachinePrecision] / N[(l / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision], N[ArcSin[N[(1.0 / N[Sqrt[1.0 ^ 2 + N[(t / N[(l * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 2: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \sin^{-1} \left(\frac{\sqrt{1 - {\left(\frac{Om}{Omc}\right)}^{2}}}{\mathsf{hypot}\left(1, \frac{\frac{t}{{2}^{-0.5}}}{\ell}\right)}\right) \end{array} \]

FPCore

(FPCore (t l Om Omc)
 :precision binary64
 (asin
  (/
   (sqrt (- 1.0 (pow (/ Om Omc) 2.0)))
   (hypot 1.0 (/ (/ t (pow 2.0 -0.5)) l)))))

C

double code(double t, double l, double Om, double Omc) {
	return asin((sqrt((1.0 - pow((Om / Omc), 2.0))) / hypot(1.0, ((t / pow(2.0, -0.5)) / l))));
}

Java

public static double code(double t, double l, double Om, double Omc) {
	return Math.asin((Math.sqrt((1.0 - Math.pow((Om / Omc), 2.0))) / Math.hypot(1.0, ((t / Math.pow(2.0, -0.5)) / l))));
}

Python

def code(t, l, Om, Omc):
	return math.asin((math.sqrt((1.0 - math.pow((Om / Omc), 2.0))) / math.hypot(1.0, ((t / math.pow(2.0, -0.5)) / l))))

Julia

function code(t, l, Om, Omc)
	return asin(Float64(sqrt(Float64(1.0 - (Float64(Om / Omc) ^ 2.0))) / hypot(1.0, Float64(Float64(t / (2.0 ^ -0.5)) / l))))
end

MATLAB

function tmp = code(t, l, Om, Omc)
	tmp = asin((sqrt((1.0 - ((Om / Omc) ^ 2.0))) / hypot(1.0, ((t / (2.0 ^ -0.5)) / l))));
end

Wolfram

code[t_, l_, Om_, Omc_] := N[ArcSin[N[(N[Sqrt[N[(1.0 - N[Power[N[(Om / Omc), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[Sqrt[1.0 ^ 2 + N[(N[(t / N[Power[2.0, -0.5], $MachinePrecision]), $MachinePrecision] / l), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 3: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \sin^{-1} \left(\frac{\sqrt{1 - {\left(\frac{Om}{Omc}\right)}^{2}}}{\mathsf{hypot}\left(1, t \cdot \frac{\sqrt{2}}{\ell}\right)}\right) \end{array} \]

FPCore

(FPCore (t l Om Omc)
 :precision binary64
 (asin
  (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (hypot 1.0 (* t (/ (sqrt 2.0) l))))))

C

double code(double t, double l, double Om, double Omc) {
	return asin((sqrt((1.0 - pow((Om / Omc), 2.0))) / hypot(1.0, (t * (sqrt(2.0) / l)))));
}

Java

public static double code(double t, double l, double Om, double Omc) {
	return Math.asin((Math.sqrt((1.0 - Math.pow((Om / Omc), 2.0))) / Math.hypot(1.0, (t * (Math.sqrt(2.0) / l)))));
}

Python

def code(t, l, Om, Omc):
	return math.asin((math.sqrt((1.0 - math.pow((Om / Omc), 2.0))) / math.hypot(1.0, (t * (math.sqrt(2.0) / l)))))

Julia

function code(t, l, Om, Omc)
	return asin(Float64(sqrt(Float64(1.0 - (Float64(Om / Omc) ^ 2.0))) / hypot(1.0, Float64(t * Float64(sqrt(2.0) / l)))))
end

MATLAB

function tmp = code(t, l, Om, Omc)
	tmp = asin((sqrt((1.0 - ((Om / Omc) ^ 2.0))) / hypot(1.0, (t * (sqrt(2.0) / l)))));
end

Wolfram

code[t_, l_, Om_, Omc_] := N[ArcSin[N[(N[Sqrt[N[(1.0 - N[Power[N[(Om / Omc), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[Sqrt[1.0 ^ 2 + N[(t * N[(N[Sqrt[2.0], $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 4: 97.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{Om}{Omc} \leq 5 \cdot 10^{-8}:\\ \;\;\;\;\sin^{-1} \left(\frac{1}{\mathsf{hypot}\left(1, t \cdot \frac{\sqrt{2}}{\ell}\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\sin^{-1} \left(\sqrt{\frac{1 - \frac{Om}{Omc \cdot \frac{Omc}{Om}}}{1 + 2 \cdot \frac{1}{\frac{\ell}{t \cdot \frac{t}{\ell}}}}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (t l Om Omc)
 :precision binary64
 (if (<= (/ Om Omc) 5e-8)
   (asin (/ 1.0 (hypot 1.0 (* t (/ (sqrt 2.0) l)))))
   (asin
    (sqrt
     (/
      (- 1.0 (/ Om (* Omc (/ Omc Om))))
      (+ 1.0 (* 2.0 (/ 1.0 (/ l (* t (/ t l)))))))))))

C

double code(double t, double l, double Om, double Omc) {
	double tmp;
	if ((Om / Omc) <= 5e-8) {
		tmp = asin((1.0 / hypot(1.0, (t * (sqrt(2.0) / l)))));
	} else {
		tmp = asin(sqrt(((1.0 - (Om / (Omc * (Omc / Om)))) / (1.0 + (2.0 * (1.0 / (l / (t * (t / l)))))))));
	}
	return tmp;
}

Java

public static double code(double t, double l, double Om, double Omc) {
	double tmp;
	if ((Om / Omc) <= 5e-8) {
		tmp = Math.asin((1.0 / Math.hypot(1.0, (t * (Math.sqrt(2.0) / l)))));
	} else {
		tmp = Math.asin(Math.sqrt(((1.0 - (Om / (Omc * (Omc / Om)))) / (1.0 + (2.0 * (1.0 / (l / (t * (t / l)))))))));
	}
	return tmp;
}

Python

def code(t, l, Om, Omc):
	tmp = 0
	if (Om / Omc) <= 5e-8:
		tmp = math.asin((1.0 / math.hypot(1.0, (t * (math.sqrt(2.0) / l)))))
	else:
		tmp = math.asin(math.sqrt(((1.0 - (Om / (Omc * (Omc / Om)))) / (1.0 + (2.0 * (1.0 / (l / (t * (t / l)))))))))
	return tmp

Julia

function code(t, l, Om, Omc)
	tmp = 0.0
	if (Float64(Om / Omc) <= 5e-8)
		tmp = asin(Float64(1.0 / hypot(1.0, Float64(t * Float64(sqrt(2.0) / l)))));
	else
		tmp = asin(sqrt(Float64(Float64(1.0 - Float64(Om / Float64(Omc * Float64(Omc / Om)))) / Float64(1.0 + Float64(2.0 * Float64(1.0 / Float64(l / Float64(t * Float64(t / l)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(t, l, Om, Omc)
	tmp = 0.0;
	if ((Om / Omc) <= 5e-8)
		tmp = asin((1.0 / hypot(1.0, (t * (sqrt(2.0) / l)))));
	else
		tmp = asin(sqrt(((1.0 - (Om / (Omc * (Omc / Om)))) / (1.0 + (2.0 * (1.0 / (l / (t * (t / l)))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[t_, l_, Om_, Omc_] := If[LessEqual[N[(Om / Omc), $MachinePrecision], 5e-8], N[ArcSin[N[(1.0 / N[Sqrt[1.0 ^ 2 + N[(t * N[(N[Sqrt[2.0], $MachinePrecision] / l), $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[ArcSin[N[Sqrt[N[(N[(1.0 - N[(Om / N[(Omc * N[(Omc / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(2.0 * N[(1.0 / N[(l / N[(t * N[(t / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 5: 97.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{Om}{Omc} \leq 5 \cdot 10^{-8}:\\ \;\;\;\;\sin^{-1} \left(\frac{1}{\mathsf{hypot}\left(1, \frac{t}{\ell \cdot \sqrt{0.5}}\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\sin^{-1} \left(\sqrt{\frac{1 - \frac{Om}{Omc \cdot \frac{Omc}{Om}}}{1 + 2 \cdot \frac{1}{\frac{\ell}{t \cdot \frac{t}{\ell}}}}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (t l Om Omc)
 :precision binary64
 (if (<= (/ Om Omc) 5e-8)
   (asin (/ 1.0 (hypot 1.0 (/ t (* l (sqrt 0.5))))))
   (asin
    (sqrt
     (/
      (- 1.0 (/ Om (* Omc (/ Omc Om))))
      (+ 1.0 (* 2.0 (/ 1.0 (/ l (* t (/ t l)))))))))))

C

double code(double t, double l, double Om, double Omc) {
	double tmp;
	if ((Om / Omc) <= 5e-8) {
		tmp = asin((1.0 / hypot(1.0, (t / (l * sqrt(0.5))))));
	} else {
		tmp = asin(sqrt(((1.0 - (Om / (Omc * (Omc / Om)))) / (1.0 + (2.0 * (1.0 / (l / (t * (t / l)))))))));
	}
	return tmp;
}

Java

public static double code(double t, double l, double Om, double Omc) {
	double tmp;
	if ((Om / Omc) <= 5e-8) {
		tmp = Math.asin((1.0 / Math.hypot(1.0, (t / (l * Math.sqrt(0.5))))));
	} else {
		tmp = Math.asin(Math.sqrt(((1.0 - (Om / (Omc * (Omc / Om)))) / (1.0 + (2.0 * (1.0 / (l / (t * (t / l)))))))));
	}
	return tmp;
}

Python

def code(t, l, Om, Omc):
	tmp = 0
	if (Om / Omc) <= 5e-8:
		tmp = math.asin((1.0 / math.hypot(1.0, (t / (l * math.sqrt(0.5))))))
	else:
		tmp = math.asin(math.sqrt(((1.0 - (Om / (Omc * (Omc / Om)))) / (1.0 + (2.0 * (1.0 / (l / (t * (t / l)))))))))
	return tmp

Julia

function code(t, l, Om, Omc)
	tmp = 0.0
	if (Float64(Om / Omc) <= 5e-8)
		tmp = asin(Float64(1.0 / hypot(1.0, Float64(t / Float64(l * sqrt(0.5))))));
	else
		tmp = asin(sqrt(Float64(Float64(1.0 - Float64(Om / Float64(Omc * Float64(Omc / Om)))) / Float64(1.0 + Float64(2.0 * Float64(1.0 / Float64(l / Float64(t * Float64(t / l)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(t, l, Om, Omc)
	tmp = 0.0;
	if ((Om / Omc) <= 5e-8)
		tmp = asin((1.0 / hypot(1.0, (t / (l * sqrt(0.5))))));
	else
		tmp = asin(sqrt(((1.0 - (Om / (Omc * (Omc / Om)))) / (1.0 + (2.0 * (1.0 / (l / (t * (t / l)))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[t_, l_, Om_, Omc_] := If[LessEqual[N[(Om / Omc), $MachinePrecision], 5e-8], N[ArcSin[N[(1.0 / N[Sqrt[1.0 ^ 2 + N[(t / N[(l * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[ArcSin[N[Sqrt[N[(N[(1.0 - N[(Om / N[(Omc * N[(Omc / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(2.0 * N[(1.0 / N[(l / N[(t * N[(t / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 6: 79.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sin^{-1} \left(\sqrt{\frac{1 - \frac{Om}{Omc \cdot \frac{Omc}{Om}}}{1 + 2 \cdot \frac{1}{\frac{\ell}{t} \cdot \frac{\ell}{t}}}}\right)\\ \mathbf{if}\;\ell \leq -7.5 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\ell \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\sin^{-1} \left(\frac{\sqrt{0.5} \cdot \left(-\ell\right)}{t}\right)\\ \mathbf{elif}\;\ell \leq 1.95 \cdot 10^{-160}:\\ \;\;\;\;\sin^{-1} \left(\frac{\ell \cdot \sqrt{0.5}}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (t l Om Omc)
 :precision binary64
 (let* ((t_1
         (asin
          (sqrt
           (/
            (- 1.0 (/ Om (* Omc (/ Omc Om))))
            (+ 1.0 (* 2.0 (/ 1.0 (* (/ l t) (/ l t))))))))))
   (if (<= l -7.5e-103)
     t_1
     (if (<= l -5e-310)
       (asin (/ (* (sqrt 0.5) (- l)) t))
       (if (<= l 1.95e-160) (asin (/ (* l (sqrt 0.5)) t)) t_1)))))

C

double code(double t, double l, double Om, double Omc) {
	double t_1 = asin(sqrt(((1.0 - (Om / (Omc * (Omc / Om)))) / (1.0 + (2.0 * (1.0 / ((l / t) * (l / t))))))));
	double tmp;
	if (l <= -7.5e-103) {
		tmp = t_1;
	} else if (l <= -5e-310) {
		tmp = asin(((sqrt(0.5) * -l) / t));
	} else if (l <= 1.95e-160) {
		tmp = asin(((l * sqrt(0.5)) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(t, l, om, omc)
    real(8), intent (in) :: t
    real(8), intent (in) :: l
    real(8), intent (in) :: om
    real(8), intent (in) :: omc
    real(8) :: t_1
    real(8) :: tmp
    t_1 = asin(sqrt(((1.0d0 - (om / (omc * (omc / om)))) / (1.0d0 + (2.0d0 * (1.0d0 / ((l / t) * (l / t))))))))
    if (l <= (-7.5d-103)) then
        tmp = t_1
    else if (l <= (-5d-310)) then
        tmp = asin(((sqrt(0.5d0) * -l) / t))
    else if (l <= 1.95d-160) then
        tmp = asin(((l * sqrt(0.5d0)) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double t, double l, double Om, double Omc) {
	double t_1 = Math.asin(Math.sqrt(((1.0 - (Om / (Omc * (Omc / Om)))) / (1.0 + (2.0 * (1.0 / ((l / t) * (l / t))))))));
	double tmp;
	if (l <= -7.5e-103) {
		tmp = t_1;
	} else if (l <= -5e-310) {
		tmp = Math.asin(((Math.sqrt(0.5) * -l) / t));
	} else if (l <= 1.95e-160) {
		tmp = Math.asin(((l * Math.sqrt(0.5)) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(t, l, Om, Omc):
	t_1 = math.asin(math.sqrt(((1.0 - (Om / (Omc * (Omc / Om)))) / (1.0 + (2.0 * (1.0 / ((l / t) * (l / t))))))))
	tmp = 0
	if l <= -7.5e-103:
		tmp = t_1
	elif l <= -5e-310:
		tmp = math.asin(((math.sqrt(0.5) * -l) / t))
	elif l <= 1.95e-160:
		tmp = math.asin(((l * math.sqrt(0.5)) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(t, l, Om, Omc)
	t_1 = asin(sqrt(Float64(Float64(1.0 - Float64(Om / Float64(Omc * Float64(Omc / Om)))) / Float64(1.0 + Float64(2.0 * Float64(1.0 / Float64(Float64(l / t) * Float64(l / t))))))))
	tmp = 0.0
	if (l <= -7.5e-103)
		tmp = t_1;
	elseif (l <= -5e-310)
		tmp = asin(Float64(Float64(sqrt(0.5) * Float64(-l)) / t));
	elseif (l <= 1.95e-160)
		tmp = asin(Float64(Float64(l * sqrt(0.5)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(t, l, Om, Omc)
	t_1 = asin(sqrt(((1.0 - (Om / (Omc * (Omc / Om)))) / (1.0 + (2.0 * (1.0 / ((l / t) * (l / t))))))));
	tmp = 0.0;
	if (l <= -7.5e-103)
		tmp = t_1;
	elseif (l <= -5e-310)
		tmp = asin(((sqrt(0.5) * -l) / t));
	elseif (l <= 1.95e-160)
		tmp = asin(((l * sqrt(0.5)) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[t_, l_, Om_, Omc_] := Block[{t$95$1 = N[ArcSin[N[Sqrt[N[(N[(1.0 - N[(Om / N[(Omc * N[(Omc / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(2.0 * N[(1.0 / N[(N[(l / t), $MachinePrecision] * N[(l / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]}, If[LessEqual[l, -7.5e-103], t$95$1, If[LessEqual[l, -5e-310], N[ArcSin[N[(N[(N[Sqrt[0.5], $MachinePrecision] * (-l)), $MachinePrecision] / t), $MachinePrecision]], $MachinePrecision], If[LessEqual[l, 1.95e-160], N[ArcSin[N[(N[(l * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]], $MachinePrecision], t$95$1]]]]

Derivation

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

Alternative 7: 79.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sin^{-1} \left(\sqrt{\frac{1 - \frac{Om}{Omc \cdot \frac{Omc}{Om}}}{1 + 2 \cdot \frac{1}{\frac{\ell \cdot \frac{\ell}{t}}{t}}}}\right)\\ \mathbf{if}\;\ell \leq -1.32 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\ell \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\sin^{-1} \left(\frac{\sqrt{0.5} \cdot \left(-\ell\right)}{t}\right)\\ \mathbf{elif}\;\ell \leq 1.3 \cdot 10^{-163}:\\ \;\;\;\;\sin^{-1} \left(\frac{\ell \cdot \sqrt{0.5}}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (t l Om Omc)
 :precision binary64
 (let* ((t_1
         (asin
          (sqrt
           (/
            (- 1.0 (/ Om (* Omc (/ Omc Om))))
            (+ 1.0 (* 2.0 (/ 1.0 (/ (* l (/ l t)) t)))))))))
   (if (<= l -1.32e-107)
     t_1
     (if (<= l -5e-310)
       (asin (/ (* (sqrt 0.5) (- l)) t))
       (if (<= l 1.3e-163) (asin (/ (* l (sqrt 0.5)) t)) t_1)))))

C

double code(double t, double l, double Om, double Omc) {
	double t_1 = asin(sqrt(((1.0 - (Om / (Omc * (Omc / Om)))) / (1.0 + (2.0 * (1.0 / ((l * (l / t)) / t)))))));
	double tmp;
	if (l <= -1.32e-107) {
		tmp = t_1;
	} else if (l <= -5e-310) {
		tmp = asin(((sqrt(0.5) * -l) / t));
	} else if (l <= 1.3e-163) {
		tmp = asin(((l * sqrt(0.5)) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(t, l, om, omc)
    real(8), intent (in) :: t
    real(8), intent (in) :: l
    real(8), intent (in) :: om
    real(8), intent (in) :: omc
    real(8) :: t_1
    real(8) :: tmp
    t_1 = asin(sqrt(((1.0d0 - (om / (omc * (omc / om)))) / (1.0d0 + (2.0d0 * (1.0d0 / ((l * (l / t)) / t)))))))
    if (l <= (-1.32d-107)) then
        tmp = t_1
    else if (l <= (-5d-310)) then
        tmp = asin(((sqrt(0.5d0) * -l) / t))
    else if (l <= 1.3d-163) then
        tmp = asin(((l * sqrt(0.5d0)) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double t, double l, double Om, double Omc) {
	double t_1 = Math.asin(Math.sqrt(((1.0 - (Om / (Omc * (Omc / Om)))) / (1.0 + (2.0 * (1.0 / ((l * (l / t)) / t)))))));
	double tmp;
	if (l <= -1.32e-107) {
		tmp = t_1;
	} else if (l <= -5e-310) {
		tmp = Math.asin(((Math.sqrt(0.5) * -l) / t));
	} else if (l <= 1.3e-163) {
		tmp = Math.asin(((l * Math.sqrt(0.5)) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(t, l, Om, Omc):
	t_1 = math.asin(math.sqrt(((1.0 - (Om / (Omc * (Omc / Om)))) / (1.0 + (2.0 * (1.0 / ((l * (l / t)) / t)))))))
	tmp = 0
	if l <= -1.32e-107:
		tmp = t_1
	elif l <= -5e-310:
		tmp = math.asin(((math.sqrt(0.5) * -l) / t))
	elif l <= 1.3e-163:
		tmp = math.asin(((l * math.sqrt(0.5)) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(t, l, Om, Omc)
	t_1 = asin(sqrt(Float64(Float64(1.0 - Float64(Om / Float64(Omc * Float64(Omc / Om)))) / Float64(1.0 + Float64(2.0 * Float64(1.0 / Float64(Float64(l * Float64(l / t)) / t)))))))
	tmp = 0.0
	if (l <= -1.32e-107)
		tmp = t_1;
	elseif (l <= -5e-310)
		tmp = asin(Float64(Float64(sqrt(0.5) * Float64(-l)) / t));
	elseif (l <= 1.3e-163)
		tmp = asin(Float64(Float64(l * sqrt(0.5)) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(t, l, Om, Omc)
	t_1 = asin(sqrt(((1.0 - (Om / (Omc * (Omc / Om)))) / (1.0 + (2.0 * (1.0 / ((l * (l / t)) / t)))))));
	tmp = 0.0;
	if (l <= -1.32e-107)
		tmp = t_1;
	elseif (l <= -5e-310)
		tmp = asin(((sqrt(0.5) * -l) / t));
	elseif (l <= 1.3e-163)
		tmp = asin(((l * sqrt(0.5)) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[t_, l_, Om_, Omc_] := Block[{t$95$1 = N[ArcSin[N[Sqrt[N[(N[(1.0 - N[(Om / N[(Omc * N[(Omc / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(2.0 * N[(1.0 / N[(N[(l * N[(l / t), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]}, If[LessEqual[l, -1.32e-107], t$95$1, If[LessEqual[l, -5e-310], N[ArcSin[N[(N[(N[Sqrt[0.5], $MachinePrecision] * (-l)), $MachinePrecision] / t), $MachinePrecision]], $MachinePrecision], If[LessEqual[l, 1.3e-163], N[ArcSin[N[(N[(l * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]], $MachinePrecision], t$95$1]]]]

Derivation

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

Alternative 8: 57.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{+46}:\\ \;\;\;\;\sin^{-1} \left(\sqrt{1 + \frac{-1}{\frac{Omc}{Om} \cdot \frac{Omc}{Om}}}\right)\\ \mathbf{else}:\\ \;\;\;\;\sin^{-1} \left(\frac{\ell \cdot \sqrt{0.5}}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (t l Om Omc)
 :precision binary64
 (if (<= t 5.2e+46)
   (asin (sqrt (+ 1.0 (/ -1.0 (* (/ Omc Om) (/ Omc Om))))))
   (asin (/ (* l (sqrt 0.5)) t))))

C

double code(double t, double l, double Om, double Omc) {
	double tmp;
	if (t <= 5.2e+46) {
		tmp = asin(sqrt((1.0 + (-1.0 / ((Omc / Om) * (Omc / Om))))));
	} else {
		tmp = asin(((l * sqrt(0.5)) / t));
	}
	return tmp;
}

Fortran

real(8) function code(t, l, om, omc)
    real(8), intent (in) :: t
    real(8), intent (in) :: l
    real(8), intent (in) :: om
    real(8), intent (in) :: omc
    real(8) :: tmp
    if (t <= 5.2d+46) then
        tmp = asin(sqrt((1.0d0 + ((-1.0d0) / ((omc / om) * (omc / om))))))
    else
        tmp = asin(((l * sqrt(0.5d0)) / t))
    end if
    code = tmp
end function

Java

public static double code(double t, double l, double Om, double Omc) {
	double tmp;
	if (t <= 5.2e+46) {
		tmp = Math.asin(Math.sqrt((1.0 + (-1.0 / ((Omc / Om) * (Omc / Om))))));
	} else {
		tmp = Math.asin(((l * Math.sqrt(0.5)) / t));
	}
	return tmp;
}

Python

def code(t, l, Om, Omc):
	tmp = 0
	if t <= 5.2e+46:
		tmp = math.asin(math.sqrt((1.0 + (-1.0 / ((Omc / Om) * (Omc / Om))))))
	else:
		tmp = math.asin(((l * math.sqrt(0.5)) / t))
	return tmp

Julia

function code(t, l, Om, Omc)
	tmp = 0.0
	if (t <= 5.2e+46)
		tmp = asin(sqrt(Float64(1.0 + Float64(-1.0 / Float64(Float64(Omc / Om) * Float64(Omc / Om))))));
	else
		tmp = asin(Float64(Float64(l * sqrt(0.5)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(t, l, Om, Omc)
	tmp = 0.0;
	if (t <= 5.2e+46)
		tmp = asin(sqrt((1.0 + (-1.0 / ((Omc / Om) * (Omc / Om))))));
	else
		tmp = asin(((l * sqrt(0.5)) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[t_, l_, Om_, Omc_] := If[LessEqual[t, 5.2e+46], N[ArcSin[N[Sqrt[N[(1.0 + N[(-1.0 / N[(N[(Omc / Om), $MachinePrecision] * N[(Omc / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision], N[ArcSin[N[(N[(l * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]], $MachinePrecision]]

Derivation

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

Alternative 9: 57.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{+46}:\\ \;\;\;\;\sin^{-1} \left(\sqrt{1 - \frac{Om}{Omc \cdot \frac{Omc}{Om}}}\right)\\ \mathbf{else}:\\ \;\;\;\;\sin^{-1} \left(\frac{\ell \cdot \sqrt{0.5}}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (t l Om Omc)
 :precision binary64
 (if (<= t 5.2e+46)
   (asin (sqrt (- 1.0 (/ Om (* Omc (/ Omc Om))))))
   (asin (/ (* l (sqrt 0.5)) t))))

C

double code(double t, double l, double Om, double Omc) {
	double tmp;
	if (t <= 5.2e+46) {
		tmp = asin(sqrt((1.0 - (Om / (Omc * (Omc / Om))))));
	} else {
		tmp = asin(((l * sqrt(0.5)) / t));
	}
	return tmp;
}

Fortran

real(8) function code(t, l, om, omc)
    real(8), intent (in) :: t
    real(8), intent (in) :: l
    real(8), intent (in) :: om
    real(8), intent (in) :: omc
    real(8) :: tmp
    if (t <= 5.2d+46) then
        tmp = asin(sqrt((1.0d0 - (om / (omc * (omc / om))))))
    else
        tmp = asin(((l * sqrt(0.5d0)) / t))
    end if
    code = tmp
end function

Java

public static double code(double t, double l, double Om, double Omc) {
	double tmp;
	if (t <= 5.2e+46) {
		tmp = Math.asin(Math.sqrt((1.0 - (Om / (Omc * (Omc / Om))))));
	} else {
		tmp = Math.asin(((l * Math.sqrt(0.5)) / t));
	}
	return tmp;
}

Python

def code(t, l, Om, Omc):
	tmp = 0
	if t <= 5.2e+46:
		tmp = math.asin(math.sqrt((1.0 - (Om / (Omc * (Omc / Om))))))
	else:
		tmp = math.asin(((l * math.sqrt(0.5)) / t))
	return tmp

Julia

function code(t, l, Om, Omc)
	tmp = 0.0
	if (t <= 5.2e+46)
		tmp = asin(sqrt(Float64(1.0 - Float64(Om / Float64(Omc * Float64(Omc / Om))))));
	else
		tmp = asin(Float64(Float64(l * sqrt(0.5)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(t, l, Om, Omc)
	tmp = 0.0;
	if (t <= 5.2e+46)
		tmp = asin(sqrt((1.0 - (Om / (Omc * (Omc / Om))))));
	else
		tmp = asin(((l * sqrt(0.5)) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[t_, l_, Om_, Omc_] := If[LessEqual[t, 5.2e+46], N[ArcSin[N[Sqrt[N[(1.0 - N[(Om / N[(Omc * N[(Omc / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision], N[ArcSin[N[(N[(l * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]], $MachinePrecision]]

Derivation

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

Alternative 10: 57.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 4.4 \cdot 10^{+46}:\\ \;\;\;\;\sin^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\sin^{-1} \left(\frac{\ell}{t \cdot \sqrt{2}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (t l Om Omc)
 :precision binary64
 (if (<= t 4.4e+46) (asin 1.0) (asin (/ l (* t (sqrt 2.0))))))

C

double code(double t, double l, double Om, double Omc) {
	double tmp;
	if (t <= 4.4e+46) {
		tmp = asin(1.0);
	} else {
		tmp = asin((l / (t * sqrt(2.0))));
	}
	return tmp;
}

Fortran

real(8) function code(t, l, om, omc)
    real(8), intent (in) :: t
    real(8), intent (in) :: l
    real(8), intent (in) :: om
    real(8), intent (in) :: omc
    real(8) :: tmp
    if (t <= 4.4d+46) then
        tmp = asin(1.0d0)
    else
        tmp = asin((l / (t * sqrt(2.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double t, double l, double Om, double Omc) {
	double tmp;
	if (t <= 4.4e+46) {
		tmp = Math.asin(1.0);
	} else {
		tmp = Math.asin((l / (t * Math.sqrt(2.0))));
	}
	return tmp;
}

Python

def code(t, l, Om, Omc):
	tmp = 0
	if t <= 4.4e+46:
		tmp = math.asin(1.0)
	else:
		tmp = math.asin((l / (t * math.sqrt(2.0))))
	return tmp

Julia

function code(t, l, Om, Omc)
	tmp = 0.0
	if (t <= 4.4e+46)
		tmp = asin(1.0);
	else
		tmp = asin(Float64(l / Float64(t * sqrt(2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(t, l, Om, Omc)
	tmp = 0.0;
	if (t <= 4.4e+46)
		tmp = asin(1.0);
	else
		tmp = asin((l / (t * sqrt(2.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[t_, l_, Om_, Omc_] := If[LessEqual[t, 4.4e+46], N[ArcSin[1.0], $MachinePrecision], N[ArcSin[N[(l / N[(t * N[Sqrt[2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

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

Alternative 11: 57.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.5 \cdot 10^{+46}:\\ \;\;\;\;\sin^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\sin^{-1} \left(\frac{\ell \cdot \sqrt{0.5}}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (t l Om Omc)
 :precision binary64
 (if (<= t 1.5e+46) (asin 1.0) (asin (/ (* l (sqrt 0.5)) t))))

C

double code(double t, double l, double Om, double Omc) {
	double tmp;
	if (t <= 1.5e+46) {
		tmp = asin(1.0);
	} else {
		tmp = asin(((l * sqrt(0.5)) / t));
	}
	return tmp;
}

Fortran

real(8) function code(t, l, om, omc)
    real(8), intent (in) :: t
    real(8), intent (in) :: l
    real(8), intent (in) :: om
    real(8), intent (in) :: omc
    real(8) :: tmp
    if (t <= 1.5d+46) then
        tmp = asin(1.0d0)
    else
        tmp = asin(((l * sqrt(0.5d0)) / t))
    end if
    code = tmp
end function

Java

public static double code(double t, double l, double Om, double Omc) {
	double tmp;
	if (t <= 1.5e+46) {
		tmp = Math.asin(1.0);
	} else {
		tmp = Math.asin(((l * Math.sqrt(0.5)) / t));
	}
	return tmp;
}

Python

def code(t, l, Om, Omc):
	tmp = 0
	if t <= 1.5e+46:
		tmp = math.asin(1.0)
	else:
		tmp = math.asin(((l * math.sqrt(0.5)) / t))
	return tmp

Julia

function code(t, l, Om, Omc)
	tmp = 0.0
	if (t <= 1.5e+46)
		tmp = asin(1.0);
	else
		tmp = asin(Float64(Float64(l * sqrt(0.5)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(t, l, Om, Omc)
	tmp = 0.0;
	if (t <= 1.5e+46)
		tmp = asin(1.0);
	else
		tmp = asin(((l * sqrt(0.5)) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[t_, l_, Om_, Omc_] := If[LessEqual[t, 1.5e+46], N[ArcSin[1.0], $MachinePrecision], N[ArcSin[N[(N[(l * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]], $MachinePrecision]]

Derivation

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

Alternative 12: 51.6% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \sin^{-1} 1 \end{array} \]

FPCore

(FPCore (t l Om Omc) :precision binary64 (asin 1.0))

C

double code(double t, double l, double Om, double Omc) {
	return asin(1.0);
}

Fortran

real(8) function code(t, l, om, omc)
    real(8), intent (in) :: t
    real(8), intent (in) :: l
    real(8), intent (in) :: om
    real(8), intent (in) :: omc
    code = asin(1.0d0)
end function

Java

public static double code(double t, double l, double Om, double Omc) {
	return Math.asin(1.0);
}

Python

def code(t, l, Om, Omc):
	return math.asin(1.0)

Julia

function code(t, l, Om, Omc)
	return asin(1.0)
end

MATLAB

function tmp = code(t, l, Om, Omc)
	tmp = asin(1.0);
end

Wolfram

code[t_, l_, Om_, Omc_] := N[ArcSin[1.0], $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2023348 
(FPCore (t l Om Omc)
  :name "Toniolo and Linder, Equation (2)"
  :precision binary64
  (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))