Toniolo and Linder, Equation (2)

Percentage Accurate: 83.8% → 83.8%

Time: 4.0s

Alternatives: 5

Speedup: 1.0×

Specification

\[\mathsf{TRUE}\left(\right)\]

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: 83.8% 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: 83.8% 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]

Derivation

1. Initial program 82.3%

   \[\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 62.4% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (t l Om Omc)
 :precision binary64
 (asin (/ (- 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(((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(((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(((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(((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(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(((1.0 - ((Om / Omc) ^ 2.0)) / (1.0 + (2.0 * ((t / l) ^ 2.0)))));
end

Wolfram

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

Derivation

1. Initial program 82.3%

   \[\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right) \]
2. Add Preprocessing

3. Taylor expanded in t around 0

   \[\leadsto \sin^{-1} \color{blue}{\left(\sqrt{1 - \frac{{Om}^{2}}{{Omc}^{2}}} + -1 \cdot \left(\frac{{t}^{2}}{{\ell}^{2}} \cdot \sqrt{1 - \frac{{Om}^{2}}{{Omc}^{2}}}\right)\right)} \]

5. Applied rewrites 61.6%

   \[\leadsto \sin^{-1} \color{blue}{\left(\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}\right)} \]
6. Add Preprocessing

Alternative 3: 57.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {\left(\frac{Om}{Omc}\right)}^{2}\\ \mathbf{if}\;{\left(\frac{t}{\ell}\right)}^{2} \leq 4 \cdot 10^{+224}:\\ \;\;\;\;\sin^{-1} \left(1 - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\sin^{-1} t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (t l Om Omc)
 :precision binary64
 (let* ((t_1 (pow (/ Om Omc) 2.0)))
   (if (<= (pow (/ t l) 2.0) 4e+224) (asin (- 1.0 t_1)) (asin t_1))))

C

double code(double t, double l, double Om, double Omc) {
	double t_1 = pow((Om / Omc), 2.0);
	double tmp;
	if (pow((t / l), 2.0) <= 4e+224) {
		tmp = asin((1.0 - t_1));
	} else {
		tmp = asin(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 = (om / omc) ** 2.0d0
    if (((t / l) ** 2.0d0) <= 4d+224) then
        tmp = asin((1.0d0 - t_1))
    else
        tmp = asin(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.pow((Om / Omc), 2.0);
	double tmp;
	if (Math.pow((t / l), 2.0) <= 4e+224) {
		tmp = Math.asin((1.0 - t_1));
	} else {
		tmp = Math.asin(t_1);
	}
	return tmp;
}

Python

def code(t, l, Om, Omc):
	t_1 = math.pow((Om / Omc), 2.0)
	tmp = 0
	if math.pow((t / l), 2.0) <= 4e+224:
		tmp = math.asin((1.0 - t_1))
	else:
		tmp = math.asin(t_1)
	return tmp

Julia

function code(t, l, Om, Omc)
	t_1 = Float64(Om / Omc) ^ 2.0
	tmp = 0.0
	if ((Float64(t / l) ^ 2.0) <= 4e+224)
		tmp = asin(Float64(1.0 - t_1));
	else
		tmp = asin(t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(t, l, Om, Omc)
	t_1 = (Om / Omc) ^ 2.0;
	tmp = 0.0;
	if (((t / l) ^ 2.0) <= 4e+224)
		tmp = asin((1.0 - t_1));
	else
		tmp = asin(t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[t_, l_, Om_, Omc_] := Block[{t$95$1 = N[Power[N[(Om / Omc), $MachinePrecision], 2.0], $MachinePrecision]}, If[LessEqual[N[Power[N[(t / l), $MachinePrecision], 2.0], $MachinePrecision], 4e+224], N[ArcSin[N[(1.0 - t$95$1), $MachinePrecision]], $MachinePrecision], N[ArcSin[t$95$1], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (pow.f64 (/.f64 t l) #s(literal 2 binary64)) < 3.99999999999999988e224

   1. Initial program 98.9%

      \[\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \sin^{-1} \color{blue}{\left(\sqrt{1 - \frac{{Om}^{2}}{{Omc}^{2}}} + {t}^{2} \cdot \left(-1 \cdot \left(\frac{1}{{\ell}^{2}} \cdot \sqrt{1 - \frac{{Om}^{2}}{{Omc}^{2}}}\right) + \frac{1}{2} \cdot \left(\left({t}^{2} \cdot \left(\frac{{Om}^{2}}{{Omc}^{2} \cdot {\ell}^{4}} - \left(-4 \cdot \frac{1 - \frac{{Om}^{2}}{{Omc}^{2}}}{{\ell}^{4}} + \frac{1}{{\ell}^{4}}\right)\right)\right) \cdot \sqrt{\frac{1}{1 - \frac{{Om}^{2}}{{Omc}^{2}}}}\right)\right)\right)} \]

   5. Applied rewrites 73.8%

      \[\leadsto \sin^{-1} \color{blue}{\left(1 - {\left(\frac{Om}{Omc}\right)}^{2}\right)} \]

   if 3.99999999999999988e224 < (pow.f64 (/.f64 t l) #s(literal 2 binary64))

   1. Initial program 49.5%

      \[\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \sin^{-1} \color{blue}{\left(\sqrt{1 - \frac{{Om}^{2}}{{Omc}^{2}}} + {t}^{2} \cdot \left(-1 \cdot \left(\frac{1}{{\ell}^{2}} \cdot \sqrt{1 - \frac{{Om}^{2}}{{Omc}^{2}}}\right) + {t}^{2} \cdot \left(\frac{-1}{2} \cdot \left(\left({t}^{2} \cdot \left(-1 \cdot \frac{\frac{{Om}^{2}}{{Omc}^{2} \cdot {\ell}^{4}} - \left(-4 \cdot \frac{1 - \frac{{Om}^{2}}{{Omc}^{2}}}{{\ell}^{4}} + \frac{1}{{\ell}^{4}}\right)}{{\ell}^{2}} + 8 \cdot \frac{1 - \frac{{Om}^{2}}{{Omc}^{2}}}{{\ell}^{6}}\right)\right) \cdot \sqrt{\frac{1}{1 - \frac{{Om}^{2}}{{Omc}^{2}}}}\right) + \frac{1}{2} \cdot \left(\sqrt{\frac{1}{1 - \frac{{Om}^{2}}{{Omc}^{2}}}} \cdot \left(\frac{{Om}^{2}}{{Omc}^{2} \cdot {\ell}^{4}} - \left(-4 \cdot \frac{1 - \frac{{Om}^{2}}{{Omc}^{2}}}{{\ell}^{4}} + \frac{1}{{\ell}^{4}}\right)\right)\right)\right)\right)\right)} \]

   5. Applied rewrites 24.4%

      \[\leadsto \sin^{-1} \color{blue}{\left({\left(\frac{Om}{Omc}\right)}^{2}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 10.6% accurate, 1.7× speedup

Math

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

FPCore

(FPCore (t l Om Omc) :precision binary64 (asin (pow (/ Om Omc) 2.0)))

C

double code(double t, double l, double Om, double Omc) {
	return asin(pow((Om / Omc), 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(((om / omc) ** 2.0d0))
end function

Java

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

Python

def code(t, l, Om, Omc):
	return math.asin(math.pow((Om / Omc), 2.0))

Julia

function code(t, l, Om, Omc)
	return asin((Float64(Om / Omc) ^ 2.0))
end

MATLAB

function tmp = code(t, l, Om, Omc)
	tmp = asin(((Om / Omc) ^ 2.0));
end

Wolfram

code[t_, l_, Om_, Omc_] := N[ArcSin[N[Power[N[(Om / Omc), $MachinePrecision], 2.0], $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 82.3%

   \[\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right) \]
2. Add Preprocessing

3. Taylor expanded in t around 0

   \[\leadsto \sin^{-1} \color{blue}{\left(\sqrt{1 - \frac{{Om}^{2}}{{Omc}^{2}}} + {t}^{2} \cdot \left(-1 \cdot \left(\frac{1}{{\ell}^{2}} \cdot \sqrt{1 - \frac{{Om}^{2}}{{Omc}^{2}}}\right) + {t}^{2} \cdot \left(\frac{-1}{2} \cdot \left(\left({t}^{2} \cdot \left(-1 \cdot \frac{\frac{{Om}^{2}}{{Omc}^{2} \cdot {\ell}^{4}} - \left(-4 \cdot \frac{1 - \frac{{Om}^{2}}{{Omc}^{2}}}{{\ell}^{4}} + \frac{1}{{\ell}^{4}}\right)}{{\ell}^{2}} + 8 \cdot \frac{1 - \frac{{Om}^{2}}{{Omc}^{2}}}{{\ell}^{6}}\right)\right) \cdot \sqrt{\frac{1}{1 - \frac{{Om}^{2}}{{Omc}^{2}}}}\right) + \frac{1}{2} \cdot \left(\sqrt{\frac{1}{1 - \frac{{Om}^{2}}{{Omc}^{2}}}} \cdot \left(\frac{{Om}^{2}}{{Omc}^{2} \cdot {\ell}^{4}} - \left(-4 \cdot \frac{1 - \frac{{Om}^{2}}{{Omc}^{2}}}{{\ell}^{4}} + \frac{1}{{\ell}^{4}}\right)\right)\right)\right)\right)\right)} \]

5. Applied rewrites 11.1%

   \[\leadsto \sin^{-1} \color{blue}{\left({\left(\frac{Om}{Omc}\right)}^{2}\right)} \]
6. Add Preprocessing

Alternative 5: 6.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \sin^{-1} \left(\frac{Om}{Omc}\right) \end{array} \]

FPCore

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

C

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

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((om / omc))
end function

Java

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

Python

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

Julia

function code(t, l, Om, Omc)
	return asin(Float64(Om / Omc))
end

MATLAB

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

Wolfram

code[t_, l_, Om_, Omc_] := N[ArcSin[N[(Om / Omc), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 82.3%

   \[\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right) \]
2. Add Preprocessing

3. Taylor expanded in t around 0

   \[\leadsto \sin^{-1} \color{blue}{\left(\sqrt{1 - \frac{{Om}^{2}}{{Omc}^{2}}} + {t}^{2} \cdot \left(-1 \cdot \left(\frac{1}{{\ell}^{2}} \cdot \sqrt{1 - \frac{{Om}^{2}}{{Omc}^{2}}}\right) + \frac{1}{2} \cdot \left(\left({t}^{2} \cdot \left(\frac{{Om}^{2}}{{Omc}^{2} \cdot {\ell}^{4}} - \left(-4 \cdot \frac{1 - \frac{{Om}^{2}}{{Omc}^{2}}}{{\ell}^{4}} + \frac{1}{{\ell}^{4}}\right)\right)\right) \cdot \sqrt{\frac{1}{1 - \frac{{Om}^{2}}{{Omc}^{2}}}}\right)\right)\right)} \]

5. Applied rewrites 50.3%

   \[\leadsto \sin^{-1} \color{blue}{\left(1 - {\left(\frac{Om}{Omc}\right)}^{2}\right)} \]

6. Taylor expanded in t around inf

   \[\leadsto \sin^{-1} \color{blue}{\left(\frac{\ell \cdot \sqrt{\frac{1}{2}}}{t} \cdot \sqrt{1 - \frac{{Om}^{2}}{{Omc}^{2}}}\right)} \]

8. Applied rewrites 6.9%

   \[\leadsto \sin^{-1} \color{blue}{\left(\frac{Om}{Omc}\right)} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024321 
(FPCore (t l Om Omc)
  :name "Toniolo and Linder, Equation (2)"
  :precision binary64
  :pre (TRUE)
  (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))