Toniolo and Linder, Equation (2)

Percentage Accurate: 83.9% → 98.5%

Time: 18.6s

Alternatives: 16

Speedup: 1.9×

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: 83.9% 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: 98.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ \begin{array}{l} t_1 := 1 - \frac{\frac{Om}{Omc}}{\frac{Omc}{Om}}\\ \mathbf{if}\;\frac{t_m}{\ell} \leq -1 \cdot 10^{+159}:\\ \;\;\;\;\sin^{-1} \left(\sqrt{t_1} \cdot \left(\ell \cdot \frac{-\sqrt{0.5}}{t_m}\right)\right)\\ \mathbf{elif}\;\frac{t_m}{\ell} \leq 2 \cdot 10^{+70}:\\ \;\;\;\;\sin^{-1} \left(\sqrt{\frac{t_1}{1 + 2 \cdot \frac{\frac{t_m}{\ell}}{\frac{\ell}{t_m}}}}\right)\\ \mathbf{else}:\\ \;\;\;\;\sin^{-1} \left(\frac{\ell \cdot \sqrt{0.5}}{t_m}\right)\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
(FPCore (t_m l Om Omc)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ (/ Om Omc) (/ Omc Om)))))
   (if (<= (/ t_m l) -1e+159)
     (asin (* (sqrt t_1) (* l (/ (- (sqrt 0.5)) t_m))))
     (if (<= (/ t_m l) 2e+70)
       (asin (sqrt (/ t_1 (+ 1.0 (* 2.0 (/ (/ t_m l) (/ l t_m)))))))
       (asin (/ (* l (sqrt 0.5)) t_m))))))

C

t_m = fabs(t);
double code(double t_m, double l, double Om, double Omc) {
	double t_1 = 1.0 - ((Om / Omc) / (Omc / Om));
	double tmp;
	if ((t_m / l) <= -1e+159) {
		tmp = asin((sqrt(t_1) * (l * (-sqrt(0.5) / t_m))));
	} else if ((t_m / l) <= 2e+70) {
		tmp = asin(sqrt((t_1 / (1.0 + (2.0 * ((t_m / l) / (l / t_m)))))));
	} else {
		tmp = asin(((l * sqrt(0.5)) / t_m));
	}
	return tmp;
}

Fortran

t_m = abs(t)
real(8) function code(t_m, l, om, omc)
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: om
    real(8), intent (in) :: omc
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 - ((om / omc) / (omc / om))
    if ((t_m / l) <= (-1d+159)) then
        tmp = asin((sqrt(t_1) * (l * (-sqrt(0.5d0) / t_m))))
    else if ((t_m / l) <= 2d+70) then
        tmp = asin(sqrt((t_1 / (1.0d0 + (2.0d0 * ((t_m / l) / (l / t_m)))))))
    else
        tmp = asin(((l * sqrt(0.5d0)) / t_m))
    end if
    code = tmp
end function

Java

t_m = Math.abs(t);
public static double code(double t_m, double l, double Om, double Omc) {
	double t_1 = 1.0 - ((Om / Omc) / (Omc / Om));
	double tmp;
	if ((t_m / l) <= -1e+159) {
		tmp = Math.asin((Math.sqrt(t_1) * (l * (-Math.sqrt(0.5) / t_m))));
	} else if ((t_m / l) <= 2e+70) {
		tmp = Math.asin(Math.sqrt((t_1 / (1.0 + (2.0 * ((t_m / l) / (l / t_m)))))));
	} else {
		tmp = Math.asin(((l * Math.sqrt(0.5)) / t_m));
	}
	return tmp;
}

Python

t_m = math.fabs(t)
def code(t_m, l, Om, Omc):
	t_1 = 1.0 - ((Om / Omc) / (Omc / Om))
	tmp = 0
	if (t_m / l) <= -1e+159:
		tmp = math.asin((math.sqrt(t_1) * (l * (-math.sqrt(0.5) / t_m))))
	elif (t_m / l) <= 2e+70:
		tmp = math.asin(math.sqrt((t_1 / (1.0 + (2.0 * ((t_m / l) / (l / t_m)))))))
	else:
		tmp = math.asin(((l * math.sqrt(0.5)) / t_m))
	return tmp

Julia

t_m = abs(t)
function code(t_m, l, Om, Omc)
	t_1 = Float64(1.0 - Float64(Float64(Om / Omc) / Float64(Omc / Om)))
	tmp = 0.0
	if (Float64(t_m / l) <= -1e+159)
		tmp = asin(Float64(sqrt(t_1) * Float64(l * Float64(Float64(-sqrt(0.5)) / t_m))));
	elseif (Float64(t_m / l) <= 2e+70)
		tmp = asin(sqrt(Float64(t_1 / Float64(1.0 + Float64(2.0 * Float64(Float64(t_m / l) / Float64(l / t_m)))))));
	else
		tmp = asin(Float64(Float64(l * sqrt(0.5)) / t_m));
	end
	return tmp
end

MATLAB

t_m = abs(t);
function tmp_2 = code(t_m, l, Om, Omc)
	t_1 = 1.0 - ((Om / Omc) / (Omc / Om));
	tmp = 0.0;
	if ((t_m / l) <= -1e+159)
		tmp = asin((sqrt(t_1) * (l * (-sqrt(0.5) / t_m))));
	elseif ((t_m / l) <= 2e+70)
		tmp = asin(sqrt((t_1 / (1.0 + (2.0 * ((t_m / l) / (l / t_m)))))));
	else
		tmp = asin(((l * sqrt(0.5)) / t_m));
	end
	tmp_2 = tmp;
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
code[t$95$m_, l_, Om_, Omc_] := Block[{t$95$1 = N[(1.0 - N[(N[(Om / Omc), $MachinePrecision] / N[(Omc / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$m / l), $MachinePrecision], -1e+159], N[ArcSin[N[(N[Sqrt[t$95$1], $MachinePrecision] * N[(l * N[((-N[Sqrt[0.5], $MachinePrecision]) / t$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[N[(t$95$m / l), $MachinePrecision], 2e+70], N[ArcSin[N[Sqrt[N[(t$95$1 / N[(1.0 + N[(2.0 * N[(N[(t$95$m / l), $MachinePrecision] / N[(l / t$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision], N[ArcSin[N[(N[(l * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] / t$95$m), $MachinePrecision]], $MachinePrecision]]]]

Derivation

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1. Add Preprocessing

Alternative 2: 98.4% accurate, 0.8× speedup

Math

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

FPCore

t_m = (fabs.f64 t)
(FPCore (t_m l Om Omc)
 :precision binary64
 (asin
  (/
   (sqrt (- 1.0 (pow (/ Om Omc) 2.0)))
   (hypot 1.0 (/ (sqrt 2.0) (/ l t_m))))))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

t_m = N[Abs[t], $MachinePrecision]
code[t$95$m_, 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[Sqrt[2.0], $MachinePrecision] / N[(l / t$95$m), $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

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

Alternative 3: 98.4% accurate, 0.8× speedup

Math

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

FPCore

t_m = (fabs.f64 t)
(FPCore (t_m l Om Omc)
 :precision binary64
 (asin
  (/
   (sqrt (- 1.0 (pow (/ Om Omc) 2.0)))
   (hypot 1.0 (* (sqrt 2.0) (/ t_m l))))))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

t_m = N[Abs[t], $MachinePrecision]
code[t$95$m_, 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[Sqrt[2.0], $MachinePrecision] * N[(t$95$m / l), $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 4: 97.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ \mathsf{expm1}\left(\mathsf{log1p}\left(\sin^{-1} \left(\frac{1}{\mathsf{hypot}\left(1, \frac{\sqrt{2}}{\frac{\ell}{t_m}}\right)}\right)\right)\right) \end{array} \]

FPCore

t_m = (fabs.f64 t)
(FPCore (t_m l Om Omc)
 :precision binary64
 (expm1 (log1p (asin (/ 1.0 (hypot 1.0 (/ (sqrt 2.0) (/ l t_m))))))))

C

t_m = fabs(t);
double code(double t_m, double l, double Om, double Omc) {
	return expm1(log1p(asin((1.0 / hypot(1.0, (sqrt(2.0) / (l / t_m)))))));
}

Java

t_m = Math.abs(t);
public static double code(double t_m, double l, double Om, double Omc) {
	return Math.expm1(Math.log1p(Math.asin((1.0 / Math.hypot(1.0, (Math.sqrt(2.0) / (l / t_m)))))));
}

Python

t_m = math.fabs(t)
def code(t_m, l, Om, Omc):
	return math.expm1(math.log1p(math.asin((1.0 / math.hypot(1.0, (math.sqrt(2.0) / (l / t_m)))))))

Julia

t_m = abs(t)
function code(t_m, l, Om, Omc)
	return expm1(log1p(asin(Float64(1.0 / hypot(1.0, Float64(sqrt(2.0) / Float64(l / t_m)))))))
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
code[t$95$m_, l_, Om_, Omc_] := N[(Exp[N[Log[1 + N[ArcSin[N[(1.0 / N[Sqrt[1.0 ^ 2 + N[(N[Sqrt[2.0], $MachinePrecision] / N[(l / t$95$m), $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]] - 1), $MachinePrecision]

Derivation

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

Alternative 5: 98.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ \begin{array}{l} t_1 := 1 - \frac{\frac{Om}{Omc}}{\frac{Omc}{Om}}\\ \mathbf{if}\;\frac{t_m}{\ell} \leq -2 \cdot 10^{+58}:\\ \;\;\;\;\sin^{-1} \left(\sqrt{t_1} \cdot \left(\frac{\ell}{t_m} \cdot \left(-\sqrt{0.5}\right)\right)\right)\\ \mathbf{elif}\;\frac{t_m}{\ell} \leq 2 \cdot 10^{+70}:\\ \;\;\;\;\sin^{-1} \left(\sqrt{\frac{t_1}{1 + 2 \cdot \frac{\frac{t_m}{\ell}}{\frac{\ell}{t_m}}}}\right)\\ \mathbf{else}:\\ \;\;\;\;\sin^{-1} \left(\frac{\ell \cdot \sqrt{0.5}}{t_m}\right)\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
(FPCore (t_m l Om Omc)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ (/ Om Omc) (/ Omc Om)))))
   (if (<= (/ t_m l) -2e+58)
     (asin (* (sqrt t_1) (* (/ l t_m) (- (sqrt 0.5)))))
     (if (<= (/ t_m l) 2e+70)
       (asin (sqrt (/ t_1 (+ 1.0 (* 2.0 (/ (/ t_m l) (/ l t_m)))))))
       (asin (/ (* l (sqrt 0.5)) t_m))))))

C

t_m = fabs(t);
double code(double t_m, double l, double Om, double Omc) {
	double t_1 = 1.0 - ((Om / Omc) / (Omc / Om));
	double tmp;
	if ((t_m / l) <= -2e+58) {
		tmp = asin((sqrt(t_1) * ((l / t_m) * -sqrt(0.5))));
	} else if ((t_m / l) <= 2e+70) {
		tmp = asin(sqrt((t_1 / (1.0 + (2.0 * ((t_m / l) / (l / t_m)))))));
	} else {
		tmp = asin(((l * sqrt(0.5)) / t_m));
	}
	return tmp;
}

Fortran

t_m = abs(t)
real(8) function code(t_m, l, om, omc)
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: om
    real(8), intent (in) :: omc
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 - ((om / omc) / (omc / om))
    if ((t_m / l) <= (-2d+58)) then
        tmp = asin((sqrt(t_1) * ((l / t_m) * -sqrt(0.5d0))))
    else if ((t_m / l) <= 2d+70) then
        tmp = asin(sqrt((t_1 / (1.0d0 + (2.0d0 * ((t_m / l) / (l / t_m)))))))
    else
        tmp = asin(((l * sqrt(0.5d0)) / t_m))
    end if
    code = tmp
end function

Java

t_m = Math.abs(t);
public static double code(double t_m, double l, double Om, double Omc) {
	double t_1 = 1.0 - ((Om / Omc) / (Omc / Om));
	double tmp;
	if ((t_m / l) <= -2e+58) {
		tmp = Math.asin((Math.sqrt(t_1) * ((l / t_m) * -Math.sqrt(0.5))));
	} else if ((t_m / l) <= 2e+70) {
		tmp = Math.asin(Math.sqrt((t_1 / (1.0 + (2.0 * ((t_m / l) / (l / t_m)))))));
	} else {
		tmp = Math.asin(((l * Math.sqrt(0.5)) / t_m));
	}
	return tmp;
}

Python

t_m = math.fabs(t)
def code(t_m, l, Om, Omc):
	t_1 = 1.0 - ((Om / Omc) / (Omc / Om))
	tmp = 0
	if (t_m / l) <= -2e+58:
		tmp = math.asin((math.sqrt(t_1) * ((l / t_m) * -math.sqrt(0.5))))
	elif (t_m / l) <= 2e+70:
		tmp = math.asin(math.sqrt((t_1 / (1.0 + (2.0 * ((t_m / l) / (l / t_m)))))))
	else:
		tmp = math.asin(((l * math.sqrt(0.5)) / t_m))
	return tmp

Julia

t_m = abs(t)
function code(t_m, l, Om, Omc)
	t_1 = Float64(1.0 - Float64(Float64(Om / Omc) / Float64(Omc / Om)))
	tmp = 0.0
	if (Float64(t_m / l) <= -2e+58)
		tmp = asin(Float64(sqrt(t_1) * Float64(Float64(l / t_m) * Float64(-sqrt(0.5)))));
	elseif (Float64(t_m / l) <= 2e+70)
		tmp = asin(sqrt(Float64(t_1 / Float64(1.0 + Float64(2.0 * Float64(Float64(t_m / l) / Float64(l / t_m)))))));
	else
		tmp = asin(Float64(Float64(l * sqrt(0.5)) / t_m));
	end
	return tmp
end

MATLAB

t_m = abs(t);
function tmp_2 = code(t_m, l, Om, Omc)
	t_1 = 1.0 - ((Om / Omc) / (Omc / Om));
	tmp = 0.0;
	if ((t_m / l) <= -2e+58)
		tmp = asin((sqrt(t_1) * ((l / t_m) * -sqrt(0.5))));
	elseif ((t_m / l) <= 2e+70)
		tmp = asin(sqrt((t_1 / (1.0 + (2.0 * ((t_m / l) / (l / t_m)))))));
	else
		tmp = asin(((l * sqrt(0.5)) / t_m));
	end
	tmp_2 = tmp;
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
code[t$95$m_, l_, Om_, Omc_] := Block[{t$95$1 = N[(1.0 - N[(N[(Om / Omc), $MachinePrecision] / N[(Omc / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$m / l), $MachinePrecision], -2e+58], N[ArcSin[N[(N[Sqrt[t$95$1], $MachinePrecision] * N[(N[(l / t$95$m), $MachinePrecision] * (-N[Sqrt[0.5], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[N[(t$95$m / l), $MachinePrecision], 2e+70], N[ArcSin[N[Sqrt[N[(t$95$1 / N[(1.0 + N[(2.0 * N[(N[(t$95$m / l), $MachinePrecision] / N[(l / t$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision], N[ArcSin[N[(N[(l * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] / t$95$m), $MachinePrecision]], $MachinePrecision]]]]

Derivation

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1. Add Preprocessing

Alternative 6: 97.5% accurate, 1.3× speedup

Math

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

FPCore

t_m = (fabs.f64 t)
(FPCore (t_m l Om Omc)
 :precision binary64
 (asin (/ 1.0 (hypot 1.0 (* (sqrt 2.0) (/ t_m l))))))

C

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

Java

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

Python

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

Julia

t_m = abs(t)
function code(t_m, l, Om, Omc)
	return asin(Float64(1.0 / hypot(1.0, Float64(sqrt(2.0) * Float64(t_m / l)))))
end

MATLAB

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

Wolfram

t_m = N[Abs[t], $MachinePrecision]
code[t$95$m_, l_, Om_, Omc_] := N[ArcSin[N[(1.0 / N[Sqrt[1.0 ^ 2 + N[(N[Sqrt[2.0], $MachinePrecision] * N[(t$95$m / l), $MachinePrecision]), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 7: 98.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ \begin{array}{l} \mathbf{if}\;\frac{t_m}{\ell} \leq -2 \cdot 10^{+78}:\\ \;\;\;\;\sin^{-1} \left(\frac{-\ell}{\sqrt{2} \cdot t_m}\right)\\ \mathbf{elif}\;\frac{t_m}{\ell} \leq 2 \cdot 10^{+70}:\\ \;\;\;\;\sin^{-1} \left(\sqrt{\frac{1 - \frac{\frac{Om}{Omc}}{\frac{Omc}{Om}}}{1 + 2 \cdot \left(\frac{t_m}{\ell} \cdot \frac{t_m}{\ell}\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;\sin^{-1} \left(\frac{\ell \cdot \sqrt{0.5}}{t_m}\right)\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
(FPCore (t_m l Om Omc)
 :precision binary64
 (if (<= (/ t_m l) -2e+78)
   (asin (/ (- l) (* (sqrt 2.0) t_m)))
   (if (<= (/ t_m l) 2e+70)
     (asin
      (sqrt
       (/
        (- 1.0 (/ (/ Om Omc) (/ Omc Om)))
        (+ 1.0 (* 2.0 (* (/ t_m l) (/ t_m l)))))))
     (asin (/ (* l (sqrt 0.5)) t_m)))))

C

t_m = fabs(t);
double code(double t_m, double l, double Om, double Omc) {
	double tmp;
	if ((t_m / l) <= -2e+78) {
		tmp = asin((-l / (sqrt(2.0) * t_m)));
	} else if ((t_m / l) <= 2e+70) {
		tmp = asin(sqrt(((1.0 - ((Om / Omc) / (Omc / Om))) / (1.0 + (2.0 * ((t_m / l) * (t_m / l)))))));
	} else {
		tmp = asin(((l * sqrt(0.5)) / t_m));
	}
	return tmp;
}

Fortran

t_m = abs(t)
real(8) function code(t_m, l, om, omc)
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: om
    real(8), intent (in) :: omc
    real(8) :: tmp
    if ((t_m / l) <= (-2d+78)) then
        tmp = asin((-l / (sqrt(2.0d0) * t_m)))
    else if ((t_m / l) <= 2d+70) then
        tmp = asin(sqrt(((1.0d0 - ((om / omc) / (omc / om))) / (1.0d0 + (2.0d0 * ((t_m / l) * (t_m / l)))))))
    else
        tmp = asin(((l * sqrt(0.5d0)) / t_m))
    end if
    code = tmp
end function

Java

t_m = Math.abs(t);
public static double code(double t_m, double l, double Om, double Omc) {
	double tmp;
	if ((t_m / l) <= -2e+78) {
		tmp = Math.asin((-l / (Math.sqrt(2.0) * t_m)));
	} else if ((t_m / l) <= 2e+70) {
		tmp = Math.asin(Math.sqrt(((1.0 - ((Om / Omc) / (Omc / Om))) / (1.0 + (2.0 * ((t_m / l) * (t_m / l)))))));
	} else {
		tmp = Math.asin(((l * Math.sqrt(0.5)) / t_m));
	}
	return tmp;
}

Python

t_m = math.fabs(t)
def code(t_m, l, Om, Omc):
	tmp = 0
	if (t_m / l) <= -2e+78:
		tmp = math.asin((-l / (math.sqrt(2.0) * t_m)))
	elif (t_m / l) <= 2e+70:
		tmp = math.asin(math.sqrt(((1.0 - ((Om / Omc) / (Omc / Om))) / (1.0 + (2.0 * ((t_m / l) * (t_m / l)))))))
	else:
		tmp = math.asin(((l * math.sqrt(0.5)) / t_m))
	return tmp

Julia

t_m = abs(t)
function code(t_m, l, Om, Omc)
	tmp = 0.0
	if (Float64(t_m / l) <= -2e+78)
		tmp = asin(Float64(Float64(-l) / Float64(sqrt(2.0) * t_m)));
	elseif (Float64(t_m / l) <= 2e+70)
		tmp = asin(sqrt(Float64(Float64(1.0 - Float64(Float64(Om / Omc) / Float64(Omc / Om))) / Float64(1.0 + Float64(2.0 * Float64(Float64(t_m / l) * Float64(t_m / l)))))));
	else
		tmp = asin(Float64(Float64(l * sqrt(0.5)) / t_m));
	end
	return tmp
end

MATLAB

t_m = abs(t);
function tmp_2 = code(t_m, l, Om, Omc)
	tmp = 0.0;
	if ((t_m / l) <= -2e+78)
		tmp = asin((-l / (sqrt(2.0) * t_m)));
	elseif ((t_m / l) <= 2e+70)
		tmp = asin(sqrt(((1.0 - ((Om / Omc) / (Omc / Om))) / (1.0 + (2.0 * ((t_m / l) * (t_m / l)))))));
	else
		tmp = asin(((l * sqrt(0.5)) / t_m));
	end
	tmp_2 = tmp;
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
code[t$95$m_, l_, Om_, Omc_] := If[LessEqual[N[(t$95$m / l), $MachinePrecision], -2e+78], N[ArcSin[N[((-l) / N[(N[Sqrt[2.0], $MachinePrecision] * t$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[N[(t$95$m / l), $MachinePrecision], 2e+70], N[ArcSin[N[Sqrt[N[(N[(1.0 - N[(N[(Om / Omc), $MachinePrecision] / N[(Omc / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(2.0 * N[(N[(t$95$m / l), $MachinePrecision] * N[(t$95$m / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision], N[ArcSin[N[(N[(l * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] / t$95$m), $MachinePrecision]], $MachinePrecision]]]

Derivation

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

Alternative 8: 98.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ \begin{array}{l} \mathbf{if}\;\frac{t_m}{\ell} \leq -1 \cdot 10^{+159}:\\ \;\;\;\;\sin^{-1} \left(\frac{-\ell}{\sqrt{2} \cdot t_m}\right)\\ \mathbf{elif}\;\frac{t_m}{\ell} \leq 2 \cdot 10^{+70}:\\ \;\;\;\;\sin^{-1} \left(\sqrt{\frac{1 - \frac{\frac{Om}{Omc}}{\frac{Omc}{Om}}}{1 + 2 \cdot \frac{\frac{t_m}{\ell}}{\frac{\ell}{t_m}}}}\right)\\ \mathbf{else}:\\ \;\;\;\;\sin^{-1} \left(\frac{\ell \cdot \sqrt{0.5}}{t_m}\right)\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
(FPCore (t_m l Om Omc)
 :precision binary64
 (if (<= (/ t_m l) -1e+159)
   (asin (/ (- l) (* (sqrt 2.0) t_m)))
   (if (<= (/ t_m l) 2e+70)
     (asin
      (sqrt
       (/
        (- 1.0 (/ (/ Om Omc) (/ Omc Om)))
        (+ 1.0 (* 2.0 (/ (/ t_m l) (/ l t_m)))))))
     (asin (/ (* l (sqrt 0.5)) t_m)))))

C

t_m = fabs(t);
double code(double t_m, double l, double Om, double Omc) {
	double tmp;
	if ((t_m / l) <= -1e+159) {
		tmp = asin((-l / (sqrt(2.0) * t_m)));
	} else if ((t_m / l) <= 2e+70) {
		tmp = asin(sqrt(((1.0 - ((Om / Omc) / (Omc / Om))) / (1.0 + (2.0 * ((t_m / l) / (l / t_m)))))));
	} else {
		tmp = asin(((l * sqrt(0.5)) / t_m));
	}
	return tmp;
}

Fortran

t_m = abs(t)
real(8) function code(t_m, l, om, omc)
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: om
    real(8), intent (in) :: omc
    real(8) :: tmp
    if ((t_m / l) <= (-1d+159)) then
        tmp = asin((-l / (sqrt(2.0d0) * t_m)))
    else if ((t_m / l) <= 2d+70) then
        tmp = asin(sqrt(((1.0d0 - ((om / omc) / (omc / om))) / (1.0d0 + (2.0d0 * ((t_m / l) / (l / t_m)))))))
    else
        tmp = asin(((l * sqrt(0.5d0)) / t_m))
    end if
    code = tmp
end function

Java

t_m = Math.abs(t);
public static double code(double t_m, double l, double Om, double Omc) {
	double tmp;
	if ((t_m / l) <= -1e+159) {
		tmp = Math.asin((-l / (Math.sqrt(2.0) * t_m)));
	} else if ((t_m / l) <= 2e+70) {
		tmp = Math.asin(Math.sqrt(((1.0 - ((Om / Omc) / (Omc / Om))) / (1.0 + (2.0 * ((t_m / l) / (l / t_m)))))));
	} else {
		tmp = Math.asin(((l * Math.sqrt(0.5)) / t_m));
	}
	return tmp;
}

Python

t_m = math.fabs(t)
def code(t_m, l, Om, Omc):
	tmp = 0
	if (t_m / l) <= -1e+159:
		tmp = math.asin((-l / (math.sqrt(2.0) * t_m)))
	elif (t_m / l) <= 2e+70:
		tmp = math.asin(math.sqrt(((1.0 - ((Om / Omc) / (Omc / Om))) / (1.0 + (2.0 * ((t_m / l) / (l / t_m)))))))
	else:
		tmp = math.asin(((l * math.sqrt(0.5)) / t_m))
	return tmp

Julia

t_m = abs(t)
function code(t_m, l, Om, Omc)
	tmp = 0.0
	if (Float64(t_m / l) <= -1e+159)
		tmp = asin(Float64(Float64(-l) / Float64(sqrt(2.0) * t_m)));
	elseif (Float64(t_m / l) <= 2e+70)
		tmp = asin(sqrt(Float64(Float64(1.0 - Float64(Float64(Om / Omc) / Float64(Omc / Om))) / Float64(1.0 + Float64(2.0 * Float64(Float64(t_m / l) / Float64(l / t_m)))))));
	else
		tmp = asin(Float64(Float64(l * sqrt(0.5)) / t_m));
	end
	return tmp
end

MATLAB

t_m = abs(t);
function tmp_2 = code(t_m, l, Om, Omc)
	tmp = 0.0;
	if ((t_m / l) <= -1e+159)
		tmp = asin((-l / (sqrt(2.0) * t_m)));
	elseif ((t_m / l) <= 2e+70)
		tmp = asin(sqrt(((1.0 - ((Om / Omc) / (Omc / Om))) / (1.0 + (2.0 * ((t_m / l) / (l / t_m)))))));
	else
		tmp = asin(((l * sqrt(0.5)) / t_m));
	end
	tmp_2 = tmp;
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
code[t$95$m_, l_, Om_, Omc_] := If[LessEqual[N[(t$95$m / l), $MachinePrecision], -1e+159], N[ArcSin[N[((-l) / N[(N[Sqrt[2.0], $MachinePrecision] * t$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[N[(t$95$m / l), $MachinePrecision], 2e+70], N[ArcSin[N[Sqrt[N[(N[(1.0 - N[(N[(Om / Omc), $MachinePrecision] / N[(Omc / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(2.0 * N[(N[(t$95$m / l), $MachinePrecision] / N[(l / t$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision], N[ArcSin[N[(N[(l * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] / t$95$m), $MachinePrecision]], $MachinePrecision]]]

Derivation

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

Alternative 9: 97.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ \begin{array}{l} \mathbf{if}\;\frac{t_m}{\ell} \leq -10:\\ \;\;\;\;\sin^{-1} \left(\frac{\ell}{\frac{-t_m}{\sqrt{0.5}}}\right)\\ \mathbf{elif}\;\frac{t_m}{\ell} \leq 0.01:\\ \;\;\;\;\sin^{-1} \left(\sqrt{1 - \frac{\frac{Om}{Omc}}{\frac{Omc}{Om}}}\right)\\ \mathbf{else}:\\ \;\;\;\;\sin^{-1} \left(\frac{\ell \cdot \sqrt{0.5}}{t_m}\right)\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
(FPCore (t_m l Om Omc)
 :precision binary64
 (if (<= (/ t_m l) -10.0)
   (asin (/ l (/ (- t_m) (sqrt 0.5))))
   (if (<= (/ t_m l) 0.01)
     (asin (sqrt (- 1.0 (/ (/ Om Omc) (/ Omc Om)))))
     (asin (/ (* l (sqrt 0.5)) t_m)))))

C

t_m = fabs(t);
double code(double t_m, double l, double Om, double Omc) {
	double tmp;
	if ((t_m / l) <= -10.0) {
		tmp = asin((l / (-t_m / sqrt(0.5))));
	} else if ((t_m / l) <= 0.01) {
		tmp = asin(sqrt((1.0 - ((Om / Omc) / (Omc / Om)))));
	} else {
		tmp = asin(((l * sqrt(0.5)) / t_m));
	}
	return tmp;
}

Fortran

t_m = abs(t)
real(8) function code(t_m, l, om, omc)
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: om
    real(8), intent (in) :: omc
    real(8) :: tmp
    if ((t_m / l) <= (-10.0d0)) then
        tmp = asin((l / (-t_m / sqrt(0.5d0))))
    else if ((t_m / l) <= 0.01d0) then
        tmp = asin(sqrt((1.0d0 - ((om / omc) / (omc / om)))))
    else
        tmp = asin(((l * sqrt(0.5d0)) / t_m))
    end if
    code = tmp
end function

Java

t_m = Math.abs(t);
public static double code(double t_m, double l, double Om, double Omc) {
	double tmp;
	if ((t_m / l) <= -10.0) {
		tmp = Math.asin((l / (-t_m / Math.sqrt(0.5))));
	} else if ((t_m / l) <= 0.01) {
		tmp = Math.asin(Math.sqrt((1.0 - ((Om / Omc) / (Omc / Om)))));
	} else {
		tmp = Math.asin(((l * Math.sqrt(0.5)) / t_m));
	}
	return tmp;
}

Python

t_m = math.fabs(t)
def code(t_m, l, Om, Omc):
	tmp = 0
	if (t_m / l) <= -10.0:
		tmp = math.asin((l / (-t_m / math.sqrt(0.5))))
	elif (t_m / l) <= 0.01:
		tmp = math.asin(math.sqrt((1.0 - ((Om / Omc) / (Omc / Om)))))
	else:
		tmp = math.asin(((l * math.sqrt(0.5)) / t_m))
	return tmp

Julia

t_m = abs(t)
function code(t_m, l, Om, Omc)
	tmp = 0.0
	if (Float64(t_m / l) <= -10.0)
		tmp = asin(Float64(l / Float64(Float64(-t_m) / sqrt(0.5))));
	elseif (Float64(t_m / l) <= 0.01)
		tmp = asin(sqrt(Float64(1.0 - Float64(Float64(Om / Omc) / Float64(Omc / Om)))));
	else
		tmp = asin(Float64(Float64(l * sqrt(0.5)) / t_m));
	end
	return tmp
end

MATLAB

t_m = abs(t);
function tmp_2 = code(t_m, l, Om, Omc)
	tmp = 0.0;
	if ((t_m / l) <= -10.0)
		tmp = asin((l / (-t_m / sqrt(0.5))));
	elseif ((t_m / l) <= 0.01)
		tmp = asin(sqrt((1.0 - ((Om / Omc) / (Omc / Om)))));
	else
		tmp = asin(((l * sqrt(0.5)) / t_m));
	end
	tmp_2 = tmp;
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
code[t$95$m_, l_, Om_, Omc_] := If[LessEqual[N[(t$95$m / l), $MachinePrecision], -10.0], N[ArcSin[N[(l / N[((-t$95$m) / N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[N[(t$95$m / l), $MachinePrecision], 0.01], N[ArcSin[N[Sqrt[N[(1.0 - N[(N[(Om / Omc), $MachinePrecision] / N[(Omc / Om), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision], N[ArcSin[N[(N[(l * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] / t$95$m), $MachinePrecision]], $MachinePrecision]]]

Derivation

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

Alternative 10: 97.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ \begin{array}{l} \mathbf{if}\;\frac{t_m}{\ell} \leq -10:\\ \;\;\;\;\sin^{-1} \left(\frac{-\ell}{\sqrt{2} \cdot t_m}\right)\\ \mathbf{elif}\;\frac{t_m}{\ell} \leq 0.01:\\ \;\;\;\;\sin^{-1} \left(1 - {\left(\frac{t_m}{\ell}\right)}^{2}\right)\\ \mathbf{else}:\\ \;\;\;\;\sin^{-1} \left(\frac{\ell \cdot \sqrt{0.5}}{t_m}\right)\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
(FPCore (t_m l Om Omc)
 :precision binary64
 (if (<= (/ t_m l) -10.0)
   (asin (/ (- l) (* (sqrt 2.0) t_m)))
   (if (<= (/ t_m l) 0.01)
     (asin (- 1.0 (pow (/ t_m l) 2.0)))
     (asin (/ (* l (sqrt 0.5)) t_m)))))

C

t_m = fabs(t);
double code(double t_m, double l, double Om, double Omc) {
	double tmp;
	if ((t_m / l) <= -10.0) {
		tmp = asin((-l / (sqrt(2.0) * t_m)));
	} else if ((t_m / l) <= 0.01) {
		tmp = asin((1.0 - pow((t_m / l), 2.0)));
	} else {
		tmp = asin(((l * sqrt(0.5)) / t_m));
	}
	return tmp;
}

Fortran

t_m = abs(t)
real(8) function code(t_m, l, om, omc)
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: om
    real(8), intent (in) :: omc
    real(8) :: tmp
    if ((t_m / l) <= (-10.0d0)) then
        tmp = asin((-l / (sqrt(2.0d0) * t_m)))
    else if ((t_m / l) <= 0.01d0) then
        tmp = asin((1.0d0 - ((t_m / l) ** 2.0d0)))
    else
        tmp = asin(((l * sqrt(0.5d0)) / t_m))
    end if
    code = tmp
end function

Java

t_m = Math.abs(t);
public static double code(double t_m, double l, double Om, double Omc) {
	double tmp;
	if ((t_m / l) <= -10.0) {
		tmp = Math.asin((-l / (Math.sqrt(2.0) * t_m)));
	} else if ((t_m / l) <= 0.01) {
		tmp = Math.asin((1.0 - Math.pow((t_m / l), 2.0)));
	} else {
		tmp = Math.asin(((l * Math.sqrt(0.5)) / t_m));
	}
	return tmp;
}

Python

t_m = math.fabs(t)
def code(t_m, l, Om, Omc):
	tmp = 0
	if (t_m / l) <= -10.0:
		tmp = math.asin((-l / (math.sqrt(2.0) * t_m)))
	elif (t_m / l) <= 0.01:
		tmp = math.asin((1.0 - math.pow((t_m / l), 2.0)))
	else:
		tmp = math.asin(((l * math.sqrt(0.5)) / t_m))
	return tmp

Julia

t_m = abs(t)
function code(t_m, l, Om, Omc)
	tmp = 0.0
	if (Float64(t_m / l) <= -10.0)
		tmp = asin(Float64(Float64(-l) / Float64(sqrt(2.0) * t_m)));
	elseif (Float64(t_m / l) <= 0.01)
		tmp = asin(Float64(1.0 - (Float64(t_m / l) ^ 2.0)));
	else
		tmp = asin(Float64(Float64(l * sqrt(0.5)) / t_m));
	end
	return tmp
end

MATLAB

t_m = abs(t);
function tmp_2 = code(t_m, l, Om, Omc)
	tmp = 0.0;
	if ((t_m / l) <= -10.0)
		tmp = asin((-l / (sqrt(2.0) * t_m)));
	elseif ((t_m / l) <= 0.01)
		tmp = asin((1.0 - ((t_m / l) ^ 2.0)));
	else
		tmp = asin(((l * sqrt(0.5)) / t_m));
	end
	tmp_2 = tmp;
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
code[t$95$m_, l_, Om_, Omc_] := If[LessEqual[N[(t$95$m / l), $MachinePrecision], -10.0], N[ArcSin[N[((-l) / N[(N[Sqrt[2.0], $MachinePrecision] * t$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[N[(t$95$m / l), $MachinePrecision], 0.01], N[ArcSin[N[(1.0 - N[Power[N[(t$95$m / l), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[ArcSin[N[(N[(l * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] / t$95$m), $MachinePrecision]], $MachinePrecision]]]

Derivation

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

Alternative 11: 97.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ \begin{array}{l} \mathbf{if}\;\frac{t_m}{\ell} \leq -10:\\ \;\;\;\;\sin^{-1} \left(\frac{\ell}{\frac{-t_m}{\sqrt{0.5}}}\right)\\ \mathbf{elif}\;\frac{t_m}{\ell} \leq 0.01:\\ \;\;\;\;\sin^{-1} \left(1 - {\left(\frac{t_m}{\ell}\right)}^{2}\right)\\ \mathbf{else}:\\ \;\;\;\;\sin^{-1} \left(\frac{\ell \cdot \sqrt{0.5}}{t_m}\right)\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
(FPCore (t_m l Om Omc)
 :precision binary64
 (if (<= (/ t_m l) -10.0)
   (asin (/ l (/ (- t_m) (sqrt 0.5))))
   (if (<= (/ t_m l) 0.01)
     (asin (- 1.0 (pow (/ t_m l) 2.0)))
     (asin (/ (* l (sqrt 0.5)) t_m)))))

C

t_m = fabs(t);
double code(double t_m, double l, double Om, double Omc) {
	double tmp;
	if ((t_m / l) <= -10.0) {
		tmp = asin((l / (-t_m / sqrt(0.5))));
	} else if ((t_m / l) <= 0.01) {
		tmp = asin((1.0 - pow((t_m / l), 2.0)));
	} else {
		tmp = asin(((l * sqrt(0.5)) / t_m));
	}
	return tmp;
}

Fortran

t_m = abs(t)
real(8) function code(t_m, l, om, omc)
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: om
    real(8), intent (in) :: omc
    real(8) :: tmp
    if ((t_m / l) <= (-10.0d0)) then
        tmp = asin((l / (-t_m / sqrt(0.5d0))))
    else if ((t_m / l) <= 0.01d0) then
        tmp = asin((1.0d0 - ((t_m / l) ** 2.0d0)))
    else
        tmp = asin(((l * sqrt(0.5d0)) / t_m))
    end if
    code = tmp
end function

Java

t_m = Math.abs(t);
public static double code(double t_m, double l, double Om, double Omc) {
	double tmp;
	if ((t_m / l) <= -10.0) {
		tmp = Math.asin((l / (-t_m / Math.sqrt(0.5))));
	} else if ((t_m / l) <= 0.01) {
		tmp = Math.asin((1.0 - Math.pow((t_m / l), 2.0)));
	} else {
		tmp = Math.asin(((l * Math.sqrt(0.5)) / t_m));
	}
	return tmp;
}

Python

t_m = math.fabs(t)
def code(t_m, l, Om, Omc):
	tmp = 0
	if (t_m / l) <= -10.0:
		tmp = math.asin((l / (-t_m / math.sqrt(0.5))))
	elif (t_m / l) <= 0.01:
		tmp = math.asin((1.0 - math.pow((t_m / l), 2.0)))
	else:
		tmp = math.asin(((l * math.sqrt(0.5)) / t_m))
	return tmp

Julia

t_m = abs(t)
function code(t_m, l, Om, Omc)
	tmp = 0.0
	if (Float64(t_m / l) <= -10.0)
		tmp = asin(Float64(l / Float64(Float64(-t_m) / sqrt(0.5))));
	elseif (Float64(t_m / l) <= 0.01)
		tmp = asin(Float64(1.0 - (Float64(t_m / l) ^ 2.0)));
	else
		tmp = asin(Float64(Float64(l * sqrt(0.5)) / t_m));
	end
	return tmp
end

MATLAB

t_m = abs(t);
function tmp_2 = code(t_m, l, Om, Omc)
	tmp = 0.0;
	if ((t_m / l) <= -10.0)
		tmp = asin((l / (-t_m / sqrt(0.5))));
	elseif ((t_m / l) <= 0.01)
		tmp = asin((1.0 - ((t_m / l) ^ 2.0)));
	else
		tmp = asin(((l * sqrt(0.5)) / t_m));
	end
	tmp_2 = tmp;
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
code[t$95$m_, l_, Om_, Omc_] := If[LessEqual[N[(t$95$m / l), $MachinePrecision], -10.0], N[ArcSin[N[(l / N[((-t$95$m) / N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[N[(t$95$m / l), $MachinePrecision], 0.01], N[ArcSin[N[(1.0 - N[Power[N[(t$95$m / l), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[ArcSin[N[(N[(l * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] / t$95$m), $MachinePrecision]], $MachinePrecision]]]

Derivation

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

Alternative 12: 79.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ \begin{array}{l} \mathbf{if}\;\frac{t_m}{\ell} \leq -5 \cdot 10^{+210}:\\ \;\;\;\;\sin^{-1} \left(\frac{\ell}{t_m} \cdot \sqrt{0.5}\right)\\ \mathbf{elif}\;\frac{t_m}{\ell} \leq 0.01:\\ \;\;\;\;\sin^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\sin^{-1} \left(\ell \cdot \frac{\sqrt{0.5}}{t_m}\right)\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
(FPCore (t_m l Om Omc)
 :precision binary64
 (if (<= (/ t_m l) -5e+210)
   (asin (* (/ l t_m) (sqrt 0.5)))
   (if (<= (/ t_m l) 0.01) (asin 1.0) (asin (* l (/ (sqrt 0.5) t_m))))))

C

t_m = fabs(t);
double code(double t_m, double l, double Om, double Omc) {
	double tmp;
	if ((t_m / l) <= -5e+210) {
		tmp = asin(((l / t_m) * sqrt(0.5)));
	} else if ((t_m / l) <= 0.01) {
		tmp = asin(1.0);
	} else {
		tmp = asin((l * (sqrt(0.5) / t_m)));
	}
	return tmp;
}

Fortran

t_m = abs(t)
real(8) function code(t_m, l, om, omc)
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: om
    real(8), intent (in) :: omc
    real(8) :: tmp
    if ((t_m / l) <= (-5d+210)) then
        tmp = asin(((l / t_m) * sqrt(0.5d0)))
    else if ((t_m / l) <= 0.01d0) then
        tmp = asin(1.0d0)
    else
        tmp = asin((l * (sqrt(0.5d0) / t_m)))
    end if
    code = tmp
end function

Java

t_m = Math.abs(t);
public static double code(double t_m, double l, double Om, double Omc) {
	double tmp;
	if ((t_m / l) <= -5e+210) {
		tmp = Math.asin(((l / t_m) * Math.sqrt(0.5)));
	} else if ((t_m / l) <= 0.01) {
		tmp = Math.asin(1.0);
	} else {
		tmp = Math.asin((l * (Math.sqrt(0.5) / t_m)));
	}
	return tmp;
}

Python

t_m = math.fabs(t)
def code(t_m, l, Om, Omc):
	tmp = 0
	if (t_m / l) <= -5e+210:
		tmp = math.asin(((l / t_m) * math.sqrt(0.5)))
	elif (t_m / l) <= 0.01:
		tmp = math.asin(1.0)
	else:
		tmp = math.asin((l * (math.sqrt(0.5) / t_m)))
	return tmp

Julia

t_m = abs(t)
function code(t_m, l, Om, Omc)
	tmp = 0.0
	if (Float64(t_m / l) <= -5e+210)
		tmp = asin(Float64(Float64(l / t_m) * sqrt(0.5)));
	elseif (Float64(t_m / l) <= 0.01)
		tmp = asin(1.0);
	else
		tmp = asin(Float64(l * Float64(sqrt(0.5) / t_m)));
	end
	return tmp
end

MATLAB

t_m = abs(t);
function tmp_2 = code(t_m, l, Om, Omc)
	tmp = 0.0;
	if ((t_m / l) <= -5e+210)
		tmp = asin(((l / t_m) * sqrt(0.5)));
	elseif ((t_m / l) <= 0.01)
		tmp = asin(1.0);
	else
		tmp = asin((l * (sqrt(0.5) / t_m)));
	end
	tmp_2 = tmp;
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
code[t$95$m_, l_, Om_, Omc_] := If[LessEqual[N[(t$95$m / l), $MachinePrecision], -5e+210], N[ArcSin[N[(N[(l / t$95$m), $MachinePrecision] * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[N[(t$95$m / l), $MachinePrecision], 0.01], N[ArcSin[1.0], $MachinePrecision], N[ArcSin[N[(l * N[(N[Sqrt[0.5], $MachinePrecision] / t$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]

Derivation

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

Alternative 13: 79.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ \begin{array}{l} \mathbf{if}\;\frac{t_m}{\ell} \leq -5 \cdot 10^{+210}:\\ \;\;\;\;\sin^{-1} \left(\frac{\ell}{t_m} \cdot \sqrt{0.5}\right)\\ \mathbf{elif}\;\frac{t_m}{\ell} \leq 0.01:\\ \;\;\;\;\sin^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\sin^{-1} \left(\frac{\ell \cdot \sqrt{0.5}}{t_m}\right)\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
(FPCore (t_m l Om Omc)
 :precision binary64
 (if (<= (/ t_m l) -5e+210)
   (asin (* (/ l t_m) (sqrt 0.5)))
   (if (<= (/ t_m l) 0.01) (asin 1.0) (asin (/ (* l (sqrt 0.5)) t_m)))))

C

t_m = fabs(t);
double code(double t_m, double l, double Om, double Omc) {
	double tmp;
	if ((t_m / l) <= -5e+210) {
		tmp = asin(((l / t_m) * sqrt(0.5)));
	} else if ((t_m / l) <= 0.01) {
		tmp = asin(1.0);
	} else {
		tmp = asin(((l * sqrt(0.5)) / t_m));
	}
	return tmp;
}

Fortran

t_m = abs(t)
real(8) function code(t_m, l, om, omc)
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: om
    real(8), intent (in) :: omc
    real(8) :: tmp
    if ((t_m / l) <= (-5d+210)) then
        tmp = asin(((l / t_m) * sqrt(0.5d0)))
    else if ((t_m / l) <= 0.01d0) then
        tmp = asin(1.0d0)
    else
        tmp = asin(((l * sqrt(0.5d0)) / t_m))
    end if
    code = tmp
end function

Java

t_m = Math.abs(t);
public static double code(double t_m, double l, double Om, double Omc) {
	double tmp;
	if ((t_m / l) <= -5e+210) {
		tmp = Math.asin(((l / t_m) * Math.sqrt(0.5)));
	} else if ((t_m / l) <= 0.01) {
		tmp = Math.asin(1.0);
	} else {
		tmp = Math.asin(((l * Math.sqrt(0.5)) / t_m));
	}
	return tmp;
}

Python

t_m = math.fabs(t)
def code(t_m, l, Om, Omc):
	tmp = 0
	if (t_m / l) <= -5e+210:
		tmp = math.asin(((l / t_m) * math.sqrt(0.5)))
	elif (t_m / l) <= 0.01:
		tmp = math.asin(1.0)
	else:
		tmp = math.asin(((l * math.sqrt(0.5)) / t_m))
	return tmp

Julia

t_m = abs(t)
function code(t_m, l, Om, Omc)
	tmp = 0.0
	if (Float64(t_m / l) <= -5e+210)
		tmp = asin(Float64(Float64(l / t_m) * sqrt(0.5)));
	elseif (Float64(t_m / l) <= 0.01)
		tmp = asin(1.0);
	else
		tmp = asin(Float64(Float64(l * sqrt(0.5)) / t_m));
	end
	return tmp
end

MATLAB

t_m = abs(t);
function tmp_2 = code(t_m, l, Om, Omc)
	tmp = 0.0;
	if ((t_m / l) <= -5e+210)
		tmp = asin(((l / t_m) * sqrt(0.5)));
	elseif ((t_m / l) <= 0.01)
		tmp = asin(1.0);
	else
		tmp = asin(((l * sqrt(0.5)) / t_m));
	end
	tmp_2 = tmp;
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
code[t$95$m_, l_, Om_, Omc_] := If[LessEqual[N[(t$95$m / l), $MachinePrecision], -5e+210], N[ArcSin[N[(N[(l / t$95$m), $MachinePrecision] * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[N[(t$95$m / l), $MachinePrecision], 0.01], N[ArcSin[1.0], $MachinePrecision], N[ArcSin[N[(N[(l * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] / t$95$m), $MachinePrecision]], $MachinePrecision]]]

Derivation

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

Alternative 14: 96.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ \begin{array}{l} \mathbf{if}\;\frac{t_m}{\ell} \leq -10:\\ \;\;\;\;\sin^{-1} \left(\frac{-\ell}{\sqrt{2} \cdot t_m}\right)\\ \mathbf{elif}\;\frac{t_m}{\ell} \leq 0.01:\\ \;\;\;\;\sin^{-1} 1\\ \mathbf{else}:\\ \;\;\;\;\sin^{-1} \left(\frac{\ell \cdot \sqrt{0.5}}{t_m}\right)\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
(FPCore (t_m l Om Omc)
 :precision binary64
 (if (<= (/ t_m l) -10.0)
   (asin (/ (- l) (* (sqrt 2.0) t_m)))
   (if (<= (/ t_m l) 0.01) (asin 1.0) (asin (/ (* l (sqrt 0.5)) t_m)))))

C

t_m = fabs(t);
double code(double t_m, double l, double Om, double Omc) {
	double tmp;
	if ((t_m / l) <= -10.0) {
		tmp = asin((-l / (sqrt(2.0) * t_m)));
	} else if ((t_m / l) <= 0.01) {
		tmp = asin(1.0);
	} else {
		tmp = asin(((l * sqrt(0.5)) / t_m));
	}
	return tmp;
}

Fortran

t_m = abs(t)
real(8) function code(t_m, l, om, omc)
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: om
    real(8), intent (in) :: omc
    real(8) :: tmp
    if ((t_m / l) <= (-10.0d0)) then
        tmp = asin((-l / (sqrt(2.0d0) * t_m)))
    else if ((t_m / l) <= 0.01d0) then
        tmp = asin(1.0d0)
    else
        tmp = asin(((l * sqrt(0.5d0)) / t_m))
    end if
    code = tmp
end function

Java

t_m = Math.abs(t);
public static double code(double t_m, double l, double Om, double Omc) {
	double tmp;
	if ((t_m / l) <= -10.0) {
		tmp = Math.asin((-l / (Math.sqrt(2.0) * t_m)));
	} else if ((t_m / l) <= 0.01) {
		tmp = Math.asin(1.0);
	} else {
		tmp = Math.asin(((l * Math.sqrt(0.5)) / t_m));
	}
	return tmp;
}

Python

t_m = math.fabs(t)
def code(t_m, l, Om, Omc):
	tmp = 0
	if (t_m / l) <= -10.0:
		tmp = math.asin((-l / (math.sqrt(2.0) * t_m)))
	elif (t_m / l) <= 0.01:
		tmp = math.asin(1.0)
	else:
		tmp = math.asin(((l * math.sqrt(0.5)) / t_m))
	return tmp

Julia

t_m = abs(t)
function code(t_m, l, Om, Omc)
	tmp = 0.0
	if (Float64(t_m / l) <= -10.0)
		tmp = asin(Float64(Float64(-l) / Float64(sqrt(2.0) * t_m)));
	elseif (Float64(t_m / l) <= 0.01)
		tmp = asin(1.0);
	else
		tmp = asin(Float64(Float64(l * sqrt(0.5)) / t_m));
	end
	return tmp
end

MATLAB

t_m = abs(t);
function tmp_2 = code(t_m, l, Om, Omc)
	tmp = 0.0;
	if ((t_m / l) <= -10.0)
		tmp = asin((-l / (sqrt(2.0) * t_m)));
	elseif ((t_m / l) <= 0.01)
		tmp = asin(1.0);
	else
		tmp = asin(((l * sqrt(0.5)) / t_m));
	end
	tmp_2 = tmp;
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
code[t$95$m_, l_, Om_, Omc_] := If[LessEqual[N[(t$95$m / l), $MachinePrecision], -10.0], N[ArcSin[N[((-l) / N[(N[Sqrt[2.0], $MachinePrecision] * t$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[N[(t$95$m / l), $MachinePrecision], 0.01], N[ArcSin[1.0], $MachinePrecision], N[ArcSin[N[(N[(l * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] / t$95$m), $MachinePrecision]], $MachinePrecision]]]

Derivation

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

Alternative 15: 64.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ \begin{array}{l} \mathbf{if}\;\ell \leq -1.85 \cdot 10^{-93}:\\ \;\;\;\;\sin^{-1} 1\\ \mathbf{elif}\;\ell \leq 3.3 \cdot 10^{-16}:\\ \;\;\;\;\sin^{-1} \left(\frac{\ell}{t_m} \cdot \sqrt{0.5}\right)\\ \mathbf{else}:\\ \;\;\;\;\sin^{-1} 1\\ \end{array} \end{array} \]

FPCore

t_m = (fabs.f64 t)
(FPCore (t_m l Om Omc)
 :precision binary64
 (if (<= l -1.85e-93)
   (asin 1.0)
   (if (<= l 3.3e-16) (asin (* (/ l t_m) (sqrt 0.5))) (asin 1.0))))

C

t_m = fabs(t);
double code(double t_m, double l, double Om, double Omc) {
	double tmp;
	if (l <= -1.85e-93) {
		tmp = asin(1.0);
	} else if (l <= 3.3e-16) {
		tmp = asin(((l / t_m) * sqrt(0.5)));
	} else {
		tmp = asin(1.0);
	}
	return tmp;
}

Fortran

t_m = abs(t)
real(8) function code(t_m, l, om, omc)
    real(8), intent (in) :: t_m
    real(8), intent (in) :: l
    real(8), intent (in) :: om
    real(8), intent (in) :: omc
    real(8) :: tmp
    if (l <= (-1.85d-93)) then
        tmp = asin(1.0d0)
    else if (l <= 3.3d-16) then
        tmp = asin(((l / t_m) * sqrt(0.5d0)))
    else
        tmp = asin(1.0d0)
    end if
    code = tmp
end function

Java

t_m = Math.abs(t);
public static double code(double t_m, double l, double Om, double Omc) {
	double tmp;
	if (l <= -1.85e-93) {
		tmp = Math.asin(1.0);
	} else if (l <= 3.3e-16) {
		tmp = Math.asin(((l / t_m) * Math.sqrt(0.5)));
	} else {
		tmp = Math.asin(1.0);
	}
	return tmp;
}

Python

t_m = math.fabs(t)
def code(t_m, l, Om, Omc):
	tmp = 0
	if l <= -1.85e-93:
		tmp = math.asin(1.0)
	elif l <= 3.3e-16:
		tmp = math.asin(((l / t_m) * math.sqrt(0.5)))
	else:
		tmp = math.asin(1.0)
	return tmp

Julia

t_m = abs(t)
function code(t_m, l, Om, Omc)
	tmp = 0.0
	if (l <= -1.85e-93)
		tmp = asin(1.0);
	elseif (l <= 3.3e-16)
		tmp = asin(Float64(Float64(l / t_m) * sqrt(0.5)));
	else
		tmp = asin(1.0);
	end
	return tmp
end

MATLAB

t_m = abs(t);
function tmp_2 = code(t_m, l, Om, Omc)
	tmp = 0.0;
	if (l <= -1.85e-93)
		tmp = asin(1.0);
	elseif (l <= 3.3e-16)
		tmp = asin(((l / t_m) * sqrt(0.5)));
	else
		tmp = asin(1.0);
	end
	tmp_2 = tmp;
end

Wolfram

t_m = N[Abs[t], $MachinePrecision]
code[t$95$m_, l_, Om_, Omc_] := If[LessEqual[l, -1.85e-93], N[ArcSin[1.0], $MachinePrecision], If[LessEqual[l, 3.3e-16], N[ArcSin[N[(N[(l / t$95$m), $MachinePrecision] * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[ArcSin[1.0], $MachinePrecision]]]

Derivation

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

Alternative 16: 50.3% accurate, 4.1× speedup

Math

\[\begin{array}{l} t_m = \left|t\right| \\ \sin^{-1} 1 \end{array} \]

FPCore

t_m = (fabs.f64 t)
(FPCore (t_m l Om Omc) :precision binary64 (asin 1.0))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

t_m = N[Abs[t], $MachinePrecision]
code[t$95$m_, l_, Om_, Omc_] := N[ArcSin[1.0], $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2023347 
(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)))))))