Henrywood and Agarwal, Equation (3)

Percentage Accurate: 74.5% → 84.4%

Time: 10.2s

Alternatives: 9

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \end{array} \]

FPCore

(FPCore (c0 A V l) :precision binary64 (* c0 (sqrt (/ A (* V l)))))

C

double code(double c0, double A, double V, double l) {
	return c0 * sqrt((A / (V * l)));
}

Fortran

real(8) function code(c0, a, v, l)
    real(8), intent (in) :: c0
    real(8), intent (in) :: a
    real(8), intent (in) :: v
    real(8), intent (in) :: l
    code = c0 * sqrt((a / (v * l)))
end function

Java

public static double code(double c0, double A, double V, double l) {
	return c0 * Math.sqrt((A / (V * l)));
}

Python

def code(c0, A, V, l):
	return c0 * math.sqrt((A / (V * l)))

Julia

function code(c0, A, V, l)
	return Float64(c0 * sqrt(Float64(A / Float64(V * l))))
end

MATLAB

function tmp = code(c0, A, V, l)
	tmp = c0 * sqrt((A / (V * l)));
end

Wolfram

code[c0_, A_, V_, l_] := N[(c0 * N[Sqrt[N[(A / N[(V * l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \end{array} \]

FPCore

(FPCore (c0 A V l) :precision binary64 (* c0 (sqrt (/ A (* V l)))))

C

double code(double c0, double A, double V, double l) {
	return c0 * sqrt((A / (V * l)));
}

Fortran

real(8) function code(c0, a, v, l)
    real(8), intent (in) :: c0
    real(8), intent (in) :: a
    real(8), intent (in) :: v
    real(8), intent (in) :: l
    code = c0 * sqrt((a / (v * l)))
end function

Java

public static double code(double c0, double A, double V, double l) {
	return c0 * Math.sqrt((A / (V * l)));
}

Python

def code(c0, A, V, l):
	return c0 * math.sqrt((A / (V * l)))

Julia

function code(c0, A, V, l)
	return Float64(c0 * sqrt(Float64(A / Float64(V * l))))
end

MATLAB

function tmp = code(c0, A, V, l)
	tmp = c0 * sqrt((A / (V * l)));
end

Wolfram

code[c0_, A_, V_, l_] := N[(c0 * N[Sqrt[N[(A / N[(V * l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [V, l] = \mathsf{sort}([V, l])\\ \\ \begin{array}{l} \mathbf{if}\;\ell \leq -2 \cdot 10^{-310}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{-A}{V}}}{\sqrt{-\ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{A}} \cdot \sqrt{\ell}}\\ \end{array} \end{array} \]

FPCore

NOTE: V and l should be sorted in increasing order before calling this function.
(FPCore (c0 A V l)
 :precision binary64
 (if (<= l -2e-310)
   (* c0 (/ (sqrt (/ (- A) V)) (sqrt (- l))))
   (/ c0 (* (sqrt (/ V A)) (sqrt l)))))

C

assert(V < l);
double code(double c0, double A, double V, double l) {
	double tmp;
	if (l <= -2e-310) {
		tmp = c0 * (sqrt((-A / V)) / sqrt(-l));
	} else {
		tmp = c0 / (sqrt((V / A)) * sqrt(l));
	}
	return tmp;
}

Fortran

NOTE: V and l should be sorted in increasing order before calling this function.
real(8) function code(c0, a, v, l)
    real(8), intent (in) :: c0
    real(8), intent (in) :: a
    real(8), intent (in) :: v
    real(8), intent (in) :: l
    real(8) :: tmp
    if (l <= (-2d-310)) then
        tmp = c0 * (sqrt((-a / v)) / sqrt(-l))
    else
        tmp = c0 / (sqrt((v / a)) * sqrt(l))
    end if
    code = tmp
end function

Java

assert V < l;
public static double code(double c0, double A, double V, double l) {
	double tmp;
	if (l <= -2e-310) {
		tmp = c0 * (Math.sqrt((-A / V)) / Math.sqrt(-l));
	} else {
		tmp = c0 / (Math.sqrt((V / A)) * Math.sqrt(l));
	}
	return tmp;
}

Python

[V, l] = sort([V, l])
def code(c0, A, V, l):
	tmp = 0
	if l <= -2e-310:
		tmp = c0 * (math.sqrt((-A / V)) / math.sqrt(-l))
	else:
		tmp = c0 / (math.sqrt((V / A)) * math.sqrt(l))
	return tmp

Julia

V, l = sort([V, l])
function code(c0, A, V, l)
	tmp = 0.0
	if (l <= -2e-310)
		tmp = Float64(c0 * Float64(sqrt(Float64(Float64(-A) / V)) / sqrt(Float64(-l))));
	else
		tmp = Float64(c0 / Float64(sqrt(Float64(V / A)) * sqrt(l)));
	end
	return tmp
end

MATLAB

V, l = num2cell(sort([V, l])){:}
function tmp_2 = code(c0, A, V, l)
	tmp = 0.0;
	if (l <= -2e-310)
		tmp = c0 * (sqrt((-A / V)) / sqrt(-l));
	else
		tmp = c0 / (sqrt((V / A)) * sqrt(l));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: V and l should be sorted in increasing order before calling this function.
code[c0_, A_, V_, l_] := If[LessEqual[l, -2e-310], N[(c0 * N[(N[Sqrt[N[((-A) / V), $MachinePrecision]], $MachinePrecision] / N[Sqrt[(-l)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 / N[(N[Sqrt[N[(V / A), $MachinePrecision]], $MachinePrecision] * N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < -1.999999999999994e-310

   1. Initial program 74.6%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 74.6%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{A}{V \cdot \ell}\right)}^{0.5}} \]

      2. clear-num 74.3%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{1}{\frac{V \cdot \ell}{A}}\right)}}^{0.5} \]

      3. inv-pow 74.3%

         \[\leadsto c0 \cdot {\color{blue}{\left({\left(\frac{V \cdot \ell}{A}\right)}^{-1}\right)}}^{0.5} \]

      4. pow-pow 74.5%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V \cdot \ell}{A}\right)}^{\left(-1 \cdot 0.5\right)}} \]

      5. *-commutative 74.5%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{\ell \cdot V}}{A}\right)}^{\left(-1 \cdot 0.5\right)} \]

      6. associate-/l* 74.9%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell}{\frac{A}{V}}\right)}}^{\left(-1 \cdot 0.5\right)} \]

      7. metadata-eval 74.9%

         \[\leadsto c0 \cdot {\left(\frac{\ell}{\frac{A}{V}}\right)}^{\color{blue}{-0.5}} \]

   3. Applied egg-rr 74.9%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{\frac{A}{V}}\right)}^{-0.5}} \]
   4. Step-by-step derivation

      1. associate-/l* 74.5%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell \cdot V}{A}\right)}}^{-0.5} \]

      2. *-commutative 74.5%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{V \cdot \ell}}{A}\right)}^{-0.5} \]

      3. associate-/l* 77.4%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{V}{\frac{A}{\ell}}\right)}}^{-0.5} \]

      4. associate-/r/ 75.2%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{V}{A} \cdot \ell\right)}}^{-0.5} \]

   5. Simplified 75.2%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V}{A} \cdot \ell\right)}^{-0.5}} \]
   6. Step-by-step derivation

      1. metadata-eval 75.2%

         \[\leadsto c0 \cdot {\left(\frac{V}{A} \cdot \ell\right)}^{\color{blue}{\left(\frac{-1}{2}\right)}} \]

      2. sqrt-pow2 75.1%

         \[\leadsto c0 \cdot \color{blue}{{\left(\sqrt{\frac{V}{A} \cdot \ell}\right)}^{-1}} \]

      3. inv-pow 75.1%

         \[\leadsto c0 \cdot \color{blue}{\frac{1}{\sqrt{\frac{V}{A} \cdot \ell}}} \]

      4. sqrt-prod 0.0%

         \[\leadsto c0 \cdot \frac{1}{\color{blue}{\sqrt{\frac{V}{A}} \cdot \sqrt{\ell}}} \]

      5. associate-/r* 0.0%

         \[\leadsto c0 \cdot \color{blue}{\frac{\frac{1}{\sqrt{\frac{V}{A}}}}{\sqrt{\ell}}} \]

      6. metadata-eval 0.0%

         \[\leadsto c0 \cdot \frac{\frac{\color{blue}{\sqrt{1}}}{\sqrt{\frac{V}{A}}}}{\sqrt{\ell}} \]

      7. sqrt-div 0.0%

         \[\leadsto c0 \cdot \frac{\color{blue}{\sqrt{\frac{1}{\frac{V}{A}}}}}{\sqrt{\ell}} \]

      8. clear-num 0.0%

         \[\leadsto c0 \cdot \frac{\sqrt{\color{blue}{\frac{A}{V}}}}{\sqrt{\ell}} \]

      9. sqrt-div 74.8%

         \[\leadsto c0 \cdot \color{blue}{\sqrt{\frac{\frac{A}{V}}{\ell}}} \]

      10. frac-2neg 74.8%

          \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{-\frac{A}{V}}{-\ell}}} \]

      11. sqrt-div 82.4%

          \[\leadsto c0 \cdot \color{blue}{\frac{\sqrt{-\frac{A}{V}}}{\sqrt{-\ell}}} \]

      12. distribute-neg-frac 82.4%

          \[\leadsto c0 \cdot \frac{\sqrt{\color{blue}{\frac{-A}{V}}}}{\sqrt{-\ell}} \]

   7. Applied egg-rr 82.4%

      \[\leadsto c0 \cdot \color{blue}{\frac{\sqrt{\frac{-A}{V}}}{\sqrt{-\ell}}} \]

   if -1.999999999999994e-310 < l

   1. Initial program 72.1%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 72.1%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{A}{V \cdot \ell}\right)}^{0.5}} \]

      2. clear-num 72.1%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{1}{\frac{V \cdot \ell}{A}}\right)}}^{0.5} \]

      3. inv-pow 72.1%

         \[\leadsto c0 \cdot {\color{blue}{\left({\left(\frac{V \cdot \ell}{A}\right)}^{-1}\right)}}^{0.5} \]

      4. pow-pow 72.1%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V \cdot \ell}{A}\right)}^{\left(-1 \cdot 0.5\right)}} \]

      5. *-commutative 72.1%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{\ell \cdot V}}{A}\right)}^{\left(-1 \cdot 0.5\right)} \]

      6. associate-/l* 73.5%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell}{\frac{A}{V}}\right)}}^{\left(-1 \cdot 0.5\right)} \]

      7. metadata-eval 73.5%

         \[\leadsto c0 \cdot {\left(\frac{\ell}{\frac{A}{V}}\right)}^{\color{blue}{-0.5}} \]

   3. Applied egg-rr 73.5%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{\frac{A}{V}}\right)}^{-0.5}} \]
   4. Step-by-step derivation

      1. associate-/l* 72.1%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell \cdot V}{A}\right)}}^{-0.5} \]

      2. *-commutative 72.1%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{V \cdot \ell}}{A}\right)}^{-0.5} \]

      3. associate-/l* 72.4%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{V}{\frac{A}{\ell}}\right)}}^{-0.5} \]

      4. associate-/r/ 74.7%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{V}{A} \cdot \ell\right)}}^{-0.5} \]

   5. Simplified 74.7%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V}{A} \cdot \ell\right)}^{-0.5}} \]
   6. Step-by-step derivation

      1. metadata-eval 74.7%

         \[\leadsto c0 \cdot {\left(\frac{V}{A} \cdot \ell\right)}^{\color{blue}{\left(\frac{-1}{2}\right)}} \]

      2. sqrt-pow2 74.6%

         \[\leadsto c0 \cdot \color{blue}{{\left(\sqrt{\frac{V}{A} \cdot \ell}\right)}^{-1}} \]

      3. inv-pow 74.6%

         \[\leadsto c0 \cdot \color{blue}{\frac{1}{\sqrt{\frac{V}{A} \cdot \ell}}} \]

      4. un-div-inv 74.7%

         \[\leadsto \color{blue}{\frac{c0}{\sqrt{\frac{V}{A} \cdot \ell}}} \]

      5. sqrt-prod 87.4%

         \[\leadsto \frac{c0}{\color{blue}{\sqrt{\frac{V}{A}} \cdot \sqrt{\ell}}} \]

      6. associate-/r* 85.7%

         \[\leadsto \color{blue}{\frac{\frac{c0}{\sqrt{\frac{V}{A}}}}{\sqrt{\ell}}} \]

   7. Applied egg-rr 85.7%

      \[\leadsto \color{blue}{\frac{\frac{c0}{\sqrt{\frac{V}{A}}}}{\sqrt{\ell}}} \]
   8. Step-by-step derivation

      1. associate-/r* 87.4%

         \[\leadsto \color{blue}{\frac{c0}{\sqrt{\frac{V}{A}} \cdot \sqrt{\ell}}} \]

   9. Simplified 87.4%

      \[\leadsto \color{blue}{\frac{c0}{\sqrt{\frac{V}{A}} \cdot \sqrt{\ell}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -2 \cdot 10^{-310}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{-A}{V}}}{\sqrt{-\ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{A}} \cdot \sqrt{\ell}}\\ \end{array} \]

Alternative 2: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [V, l] = \mathsf{sort}([V, l])\\ \\ \begin{array}{l} \mathbf{if}\;\ell \leq -2.6 \cdot 10^{+43}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{elif}\;\ell \leq -2 \cdot 10^{-310}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\ell \cdot V}}{\sqrt{A}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{A}} \cdot \sqrt{\ell}}\\ \end{array} \end{array} \]

FPCore

NOTE: V and l should be sorted in increasing order before calling this function.
(FPCore (c0 A V l)
 :precision binary64
 (if (<= l -2.6e+43)
   (* c0 (sqrt (/ (/ A l) V)))
   (if (<= l -2e-310)
     (/ c0 (/ (sqrt (* l V)) (sqrt A)))
     (/ c0 (* (sqrt (/ V A)) (sqrt l))))))

C

assert(V < l);
double code(double c0, double A, double V, double l) {
	double tmp;
	if (l <= -2.6e+43) {
		tmp = c0 * sqrt(((A / l) / V));
	} else if (l <= -2e-310) {
		tmp = c0 / (sqrt((l * V)) / sqrt(A));
	} else {
		tmp = c0 / (sqrt((V / A)) * sqrt(l));
	}
	return tmp;
}

Fortran

NOTE: V and l should be sorted in increasing order before calling this function.
real(8) function code(c0, a, v, l)
    real(8), intent (in) :: c0
    real(8), intent (in) :: a
    real(8), intent (in) :: v
    real(8), intent (in) :: l
    real(8) :: tmp
    if (l <= (-2.6d+43)) then
        tmp = c0 * sqrt(((a / l) / v))
    else if (l <= (-2d-310)) then
        tmp = c0 / (sqrt((l * v)) / sqrt(a))
    else
        tmp = c0 / (sqrt((v / a)) * sqrt(l))
    end if
    code = tmp
end function

Java

assert V < l;
public static double code(double c0, double A, double V, double l) {
	double tmp;
	if (l <= -2.6e+43) {
		tmp = c0 * Math.sqrt(((A / l) / V));
	} else if (l <= -2e-310) {
		tmp = c0 / (Math.sqrt((l * V)) / Math.sqrt(A));
	} else {
		tmp = c0 / (Math.sqrt((V / A)) * Math.sqrt(l));
	}
	return tmp;
}

Python

[V, l] = sort([V, l])
def code(c0, A, V, l):
	tmp = 0
	if l <= -2.6e+43:
		tmp = c0 * math.sqrt(((A / l) / V))
	elif l <= -2e-310:
		tmp = c0 / (math.sqrt((l * V)) / math.sqrt(A))
	else:
		tmp = c0 / (math.sqrt((V / A)) * math.sqrt(l))
	return tmp

Julia

V, l = sort([V, l])
function code(c0, A, V, l)
	tmp = 0.0
	if (l <= -2.6e+43)
		tmp = Float64(c0 * sqrt(Float64(Float64(A / l) / V)));
	elseif (l <= -2e-310)
		tmp = Float64(c0 / Float64(sqrt(Float64(l * V)) / sqrt(A)));
	else
		tmp = Float64(c0 / Float64(sqrt(Float64(V / A)) * sqrt(l)));
	end
	return tmp
end

MATLAB

V, l = num2cell(sort([V, l])){:}
function tmp_2 = code(c0, A, V, l)
	tmp = 0.0;
	if (l <= -2.6e+43)
		tmp = c0 * sqrt(((A / l) / V));
	elseif (l <= -2e-310)
		tmp = c0 / (sqrt((l * V)) / sqrt(A));
	else
		tmp = c0 / (sqrt((V / A)) * sqrt(l));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: V and l should be sorted in increasing order before calling this function.
code[c0_, A_, V_, l_] := If[LessEqual[l, -2.6e+43], N[(c0 * N[Sqrt[N[(N[(A / l), $MachinePrecision] / V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[l, -2e-310], N[(c0 / N[(N[Sqrt[N[(l * V), $MachinePrecision]], $MachinePrecision] / N[Sqrt[A], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 / N[(N[Sqrt[N[(V / A), $MachinePrecision]], $MachinePrecision] * N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if l < -2.60000000000000021e43

   1. Initial program 67.3%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. add-sqr-sqrt 33.9%

         \[\leadsto \color{blue}{\sqrt{c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}} \cdot \sqrt{c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}}} \]

      2. sqrt-unprod 32.5%

         \[\leadsto \color{blue}{\sqrt{\left(c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\right) \cdot \left(c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\right)}} \]

      3. *-commutative 32.5%

         \[\leadsto \sqrt{\color{blue}{\left(\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\right)} \cdot \left(c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\right)} \]

      4. *-commutative 32.5%

         \[\leadsto \sqrt{\left(\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\right) \cdot \color{blue}{\left(\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\right)}} \]

      5. swap-sqr 28.7%

         \[\leadsto \sqrt{\color{blue}{\left(\sqrt{\frac{A}{V \cdot \ell}} \cdot \sqrt{\frac{A}{V \cdot \ell}}\right) \cdot \left(c0 \cdot c0\right)}} \]

      6. add-sqr-sqrt 28.7%

         \[\leadsto \sqrt{\color{blue}{\frac{A}{V \cdot \ell}} \cdot \left(c0 \cdot c0\right)} \]

      7. associate-/r* 25.7%

         \[\leadsto \sqrt{\color{blue}{\frac{\frac{A}{V}}{\ell}} \cdot \left(c0 \cdot c0\right)} \]

      8. pow2 25.7%

         \[\leadsto \sqrt{\frac{\frac{A}{V}}{\ell} \cdot \color{blue}{{c0}^{2}}} \]

   3. Applied egg-rr 25.7%

      \[\leadsto \color{blue}{\sqrt{\frac{\frac{A}{V}}{\ell} \cdot {c0}^{2}}} \]
   4. Step-by-step derivation

      1. sqrt-prod 27.4%

         \[\leadsto \color{blue}{\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot \sqrt{{c0}^{2}}} \]

      2. sqrt-div 0.0%

         \[\leadsto \color{blue}{\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}} \cdot \sqrt{{c0}^{2}} \]

      3. clear-num 0.0%

         \[\leadsto \frac{\sqrt{\color{blue}{\frac{1}{\frac{V}{A}}}}}{\sqrt{\ell}} \cdot \sqrt{{c0}^{2}} \]

      4. sqrt-div 0.0%

         \[\leadsto \frac{\color{blue}{\frac{\sqrt{1}}{\sqrt{\frac{V}{A}}}}}{\sqrt{\ell}} \cdot \sqrt{{c0}^{2}} \]

      5. metadata-eval 0.0%

         \[\leadsto \frac{\frac{\color{blue}{1}}{\sqrt{\frac{V}{A}}}}{\sqrt{\ell}} \cdot \sqrt{{c0}^{2}} \]

      6. associate-/r* 0.0%

         \[\leadsto \color{blue}{\frac{1}{\sqrt{\frac{V}{A}} \cdot \sqrt{\ell}}} \cdot \sqrt{{c0}^{2}} \]

      7. sqrt-prod 27.3%

         \[\leadsto \frac{1}{\color{blue}{\sqrt{\frac{V}{A} \cdot \ell}}} \cdot \sqrt{{c0}^{2}} \]

      8. unpow2 27.3%

         \[\leadsto \frac{1}{\sqrt{\frac{V}{A} \cdot \ell}} \cdot \sqrt{\color{blue}{c0 \cdot c0}} \]

      9. sqrt-prod 32.0%

         \[\leadsto \frac{1}{\sqrt{\frac{V}{A} \cdot \ell}} \cdot \color{blue}{\left(\sqrt{c0} \cdot \sqrt{c0}\right)} \]

      10. add-sqr-sqrt 67.7%

          \[\leadsto \frac{1}{\sqrt{\frac{V}{A} \cdot \ell}} \cdot \color{blue}{c0} \]

   5. Applied egg-rr 76.6%

      \[\leadsto \color{blue}{\sqrt{\frac{\frac{A}{\ell}}{V}} \cdot c0} \]

   if -2.60000000000000021e43 < l < -1.999999999999994e-310

   1. Initial program 79.3%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. sqrt-div 50.7%

         \[\leadsto c0 \cdot \color{blue}{\frac{\sqrt{A}}{\sqrt{V \cdot \ell}}} \]

      2. associate-*r/ 48.9%

         \[\leadsto \color{blue}{\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}} \]

   3. Applied egg-rr 48.9%

      \[\leadsto \color{blue}{\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}} \]
   4. Step-by-step derivation

      1. associate-/l* 50.6%

         \[\leadsto \color{blue}{\frac{c0}{\frac{\sqrt{V \cdot \ell}}{\sqrt{A}}}} \]

   5. Simplified 50.6%

      \[\leadsto \color{blue}{\frac{c0}{\frac{\sqrt{V \cdot \ell}}{\sqrt{A}}}} \]

   if -1.999999999999994e-310 < l

   1. Initial program 72.1%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 72.1%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{A}{V \cdot \ell}\right)}^{0.5}} \]

      2. clear-num 72.1%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{1}{\frac{V \cdot \ell}{A}}\right)}}^{0.5} \]

      3. inv-pow 72.1%

         \[\leadsto c0 \cdot {\color{blue}{\left({\left(\frac{V \cdot \ell}{A}\right)}^{-1}\right)}}^{0.5} \]

      4. pow-pow 72.1%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V \cdot \ell}{A}\right)}^{\left(-1 \cdot 0.5\right)}} \]

      5. *-commutative 72.1%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{\ell \cdot V}}{A}\right)}^{\left(-1 \cdot 0.5\right)} \]

      6. associate-/l* 73.5%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell}{\frac{A}{V}}\right)}}^{\left(-1 \cdot 0.5\right)} \]

      7. metadata-eval 73.5%

         \[\leadsto c0 \cdot {\left(\frac{\ell}{\frac{A}{V}}\right)}^{\color{blue}{-0.5}} \]

   3. Applied egg-rr 73.5%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{\frac{A}{V}}\right)}^{-0.5}} \]
   4. Step-by-step derivation

      1. associate-/l* 72.1%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell \cdot V}{A}\right)}}^{-0.5} \]

      2. *-commutative 72.1%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{V \cdot \ell}}{A}\right)}^{-0.5} \]

      3. associate-/l* 72.4%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{V}{\frac{A}{\ell}}\right)}}^{-0.5} \]

      4. associate-/r/ 74.7%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{V}{A} \cdot \ell\right)}}^{-0.5} \]

   5. Simplified 74.7%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V}{A} \cdot \ell\right)}^{-0.5}} \]
   6. Step-by-step derivation

      1. metadata-eval 74.7%

         \[\leadsto c0 \cdot {\left(\frac{V}{A} \cdot \ell\right)}^{\color{blue}{\left(\frac{-1}{2}\right)}} \]

      2. sqrt-pow2 74.6%

         \[\leadsto c0 \cdot \color{blue}{{\left(\sqrt{\frac{V}{A} \cdot \ell}\right)}^{-1}} \]

      3. inv-pow 74.6%

         \[\leadsto c0 \cdot \color{blue}{\frac{1}{\sqrt{\frac{V}{A} \cdot \ell}}} \]

      4. un-div-inv 74.7%

         \[\leadsto \color{blue}{\frac{c0}{\sqrt{\frac{V}{A} \cdot \ell}}} \]

      5. sqrt-prod 87.4%

         \[\leadsto \frac{c0}{\color{blue}{\sqrt{\frac{V}{A}} \cdot \sqrt{\ell}}} \]

      6. associate-/r* 85.7%

         \[\leadsto \color{blue}{\frac{\frac{c0}{\sqrt{\frac{V}{A}}}}{\sqrt{\ell}}} \]

   7. Applied egg-rr 85.7%

      \[\leadsto \color{blue}{\frac{\frac{c0}{\sqrt{\frac{V}{A}}}}{\sqrt{\ell}}} \]
   8. Step-by-step derivation

      1. associate-/r* 87.4%

         \[\leadsto \color{blue}{\frac{c0}{\sqrt{\frac{V}{A}} \cdot \sqrt{\ell}}} \]

   9. Simplified 87.4%

      \[\leadsto \color{blue}{\frac{c0}{\sqrt{\frac{V}{A}} \cdot \sqrt{\ell}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -2.6 \cdot 10^{+43}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{elif}\;\ell \leq -2 \cdot 10^{-310}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\ell \cdot V}}{\sqrt{A}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{A}} \cdot \sqrt{\ell}}\\ \end{array} \]

Alternative 3: 81.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [V, l] = \mathsf{sort}([V, l])\\ \\ \begin{array}{l} \mathbf{if}\;\ell \leq -2 \cdot 10^{-310}:\\ \;\;\;\;c0 \cdot {\left(\ell \cdot \frac{V}{A}\right)}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \end{array} \end{array} \]

FPCore

NOTE: V and l should be sorted in increasing order before calling this function.
(FPCore (c0 A V l)
 :precision binary64
 (if (<= l -2e-310)
   (* c0 (pow (* l (/ V A)) -0.5))
   (* c0 (/ (sqrt (/ A V)) (sqrt l)))))

C

assert(V < l);
double code(double c0, double A, double V, double l) {
	double tmp;
	if (l <= -2e-310) {
		tmp = c0 * pow((l * (V / A)), -0.5);
	} else {
		tmp = c0 * (sqrt((A / V)) / sqrt(l));
	}
	return tmp;
}

Fortran

NOTE: V and l should be sorted in increasing order before calling this function.
real(8) function code(c0, a, v, l)
    real(8), intent (in) :: c0
    real(8), intent (in) :: a
    real(8), intent (in) :: v
    real(8), intent (in) :: l
    real(8) :: tmp
    if (l <= (-2d-310)) then
        tmp = c0 * ((l * (v / a)) ** (-0.5d0))
    else
        tmp = c0 * (sqrt((a / v)) / sqrt(l))
    end if
    code = tmp
end function

Java

assert V < l;
public static double code(double c0, double A, double V, double l) {
	double tmp;
	if (l <= -2e-310) {
		tmp = c0 * Math.pow((l * (V / A)), -0.5);
	} else {
		tmp = c0 * (Math.sqrt((A / V)) / Math.sqrt(l));
	}
	return tmp;
}

Python

[V, l] = sort([V, l])
def code(c0, A, V, l):
	tmp = 0
	if l <= -2e-310:
		tmp = c0 * math.pow((l * (V / A)), -0.5)
	else:
		tmp = c0 * (math.sqrt((A / V)) / math.sqrt(l))
	return tmp

Julia

V, l = sort([V, l])
function code(c0, A, V, l)
	tmp = 0.0
	if (l <= -2e-310)
		tmp = Float64(c0 * (Float64(l * Float64(V / A)) ^ -0.5));
	else
		tmp = Float64(c0 * Float64(sqrt(Float64(A / V)) / sqrt(l)));
	end
	return tmp
end

MATLAB

V, l = num2cell(sort([V, l])){:}
function tmp_2 = code(c0, A, V, l)
	tmp = 0.0;
	if (l <= -2e-310)
		tmp = c0 * ((l * (V / A)) ^ -0.5);
	else
		tmp = c0 * (sqrt((A / V)) / sqrt(l));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: V and l should be sorted in increasing order before calling this function.
code[c0_, A_, V_, l_] := If[LessEqual[l, -2e-310], N[(c0 * N[Power[N[(l * N[(V / A), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision], N[(c0 * N[(N[Sqrt[N[(A / V), $MachinePrecision]], $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < -1.999999999999994e-310

   1. Initial program 74.6%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 74.6%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{A}{V \cdot \ell}\right)}^{0.5}} \]

      2. clear-num 74.3%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{1}{\frac{V \cdot \ell}{A}}\right)}}^{0.5} \]

      3. inv-pow 74.3%

         \[\leadsto c0 \cdot {\color{blue}{\left({\left(\frac{V \cdot \ell}{A}\right)}^{-1}\right)}}^{0.5} \]

      4. pow-pow 74.5%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V \cdot \ell}{A}\right)}^{\left(-1 \cdot 0.5\right)}} \]

      5. *-commutative 74.5%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{\ell \cdot V}}{A}\right)}^{\left(-1 \cdot 0.5\right)} \]

      6. associate-/l* 74.9%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell}{\frac{A}{V}}\right)}}^{\left(-1 \cdot 0.5\right)} \]

      7. metadata-eval 74.9%

         \[\leadsto c0 \cdot {\left(\frac{\ell}{\frac{A}{V}}\right)}^{\color{blue}{-0.5}} \]

   3. Applied egg-rr 74.9%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{\frac{A}{V}}\right)}^{-0.5}} \]
   4. Step-by-step derivation

      1. associate-/l* 74.5%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell \cdot V}{A}\right)}}^{-0.5} \]

      2. *-commutative 74.5%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{V \cdot \ell}}{A}\right)}^{-0.5} \]

      3. associate-/l* 77.4%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{V}{\frac{A}{\ell}}\right)}}^{-0.5} \]

      4. associate-/r/ 75.2%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{V}{A} \cdot \ell\right)}}^{-0.5} \]

   5. Simplified 75.2%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V}{A} \cdot \ell\right)}^{-0.5}} \]

   if -1.999999999999994e-310 < l

   1. Initial program 72.1%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. associate-/r* 73.8%

         \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\frac{A}{V}}{\ell}}} \]

      2. sqrt-div 85.4%

         \[\leadsto c0 \cdot \color{blue}{\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}} \]

   3. Applied egg-rr 85.4%

      \[\leadsto c0 \cdot \color{blue}{\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -2 \cdot 10^{-310}:\\ \;\;\;\;c0 \cdot {\left(\ell \cdot \frac{V}{A}\right)}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \end{array} \]

Alternative 4: 81.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [V, l] = \mathsf{sort}([V, l])\\ \\ \begin{array}{l} \mathbf{if}\;\ell \leq -2 \cdot 10^{-310}:\\ \;\;\;\;c0 \cdot {\left(\ell \cdot \frac{V}{A}\right)}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{A}} \cdot \sqrt{\ell}}\\ \end{array} \end{array} \]

FPCore

NOTE: V and l should be sorted in increasing order before calling this function.
(FPCore (c0 A V l)
 :precision binary64
 (if (<= l -2e-310)
   (* c0 (pow (* l (/ V A)) -0.5))
   (/ c0 (* (sqrt (/ V A)) (sqrt l)))))

C

assert(V < l);
double code(double c0, double A, double V, double l) {
	double tmp;
	if (l <= -2e-310) {
		tmp = c0 * pow((l * (V / A)), -0.5);
	} else {
		tmp = c0 / (sqrt((V / A)) * sqrt(l));
	}
	return tmp;
}

Fortran

NOTE: V and l should be sorted in increasing order before calling this function.
real(8) function code(c0, a, v, l)
    real(8), intent (in) :: c0
    real(8), intent (in) :: a
    real(8), intent (in) :: v
    real(8), intent (in) :: l
    real(8) :: tmp
    if (l <= (-2d-310)) then
        tmp = c0 * ((l * (v / a)) ** (-0.5d0))
    else
        tmp = c0 / (sqrt((v / a)) * sqrt(l))
    end if
    code = tmp
end function

Java

assert V < l;
public static double code(double c0, double A, double V, double l) {
	double tmp;
	if (l <= -2e-310) {
		tmp = c0 * Math.pow((l * (V / A)), -0.5);
	} else {
		tmp = c0 / (Math.sqrt((V / A)) * Math.sqrt(l));
	}
	return tmp;
}

Python

[V, l] = sort([V, l])
def code(c0, A, V, l):
	tmp = 0
	if l <= -2e-310:
		tmp = c0 * math.pow((l * (V / A)), -0.5)
	else:
		tmp = c0 / (math.sqrt((V / A)) * math.sqrt(l))
	return tmp

Julia

V, l = sort([V, l])
function code(c0, A, V, l)
	tmp = 0.0
	if (l <= -2e-310)
		tmp = Float64(c0 * (Float64(l * Float64(V / A)) ^ -0.5));
	else
		tmp = Float64(c0 / Float64(sqrt(Float64(V / A)) * sqrt(l)));
	end
	return tmp
end

MATLAB

V, l = num2cell(sort([V, l])){:}
function tmp_2 = code(c0, A, V, l)
	tmp = 0.0;
	if (l <= -2e-310)
		tmp = c0 * ((l * (V / A)) ^ -0.5);
	else
		tmp = c0 / (sqrt((V / A)) * sqrt(l));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: V and l should be sorted in increasing order before calling this function.
code[c0_, A_, V_, l_] := If[LessEqual[l, -2e-310], N[(c0 * N[Power[N[(l * N[(V / A), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision], N[(c0 / N[(N[Sqrt[N[(V / A), $MachinePrecision]], $MachinePrecision] * N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < -1.999999999999994e-310

   1. Initial program 74.6%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 74.6%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{A}{V \cdot \ell}\right)}^{0.5}} \]

      2. clear-num 74.3%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{1}{\frac{V \cdot \ell}{A}}\right)}}^{0.5} \]

      3. inv-pow 74.3%

         \[\leadsto c0 \cdot {\color{blue}{\left({\left(\frac{V \cdot \ell}{A}\right)}^{-1}\right)}}^{0.5} \]

      4. pow-pow 74.5%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V \cdot \ell}{A}\right)}^{\left(-1 \cdot 0.5\right)}} \]

      5. *-commutative 74.5%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{\ell \cdot V}}{A}\right)}^{\left(-1 \cdot 0.5\right)} \]

      6. associate-/l* 74.9%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell}{\frac{A}{V}}\right)}}^{\left(-1 \cdot 0.5\right)} \]

      7. metadata-eval 74.9%

         \[\leadsto c0 \cdot {\left(\frac{\ell}{\frac{A}{V}}\right)}^{\color{blue}{-0.5}} \]

   3. Applied egg-rr 74.9%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{\frac{A}{V}}\right)}^{-0.5}} \]
   4. Step-by-step derivation

      1. associate-/l* 74.5%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell \cdot V}{A}\right)}}^{-0.5} \]

      2. *-commutative 74.5%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{V \cdot \ell}}{A}\right)}^{-0.5} \]

      3. associate-/l* 77.4%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{V}{\frac{A}{\ell}}\right)}}^{-0.5} \]

      4. associate-/r/ 75.2%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{V}{A} \cdot \ell\right)}}^{-0.5} \]

   5. Simplified 75.2%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V}{A} \cdot \ell\right)}^{-0.5}} \]

   if -1.999999999999994e-310 < l

   1. Initial program 72.1%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 72.1%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{A}{V \cdot \ell}\right)}^{0.5}} \]

      2. clear-num 72.1%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{1}{\frac{V \cdot \ell}{A}}\right)}}^{0.5} \]

      3. inv-pow 72.1%

         \[\leadsto c0 \cdot {\color{blue}{\left({\left(\frac{V \cdot \ell}{A}\right)}^{-1}\right)}}^{0.5} \]

      4. pow-pow 72.1%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V \cdot \ell}{A}\right)}^{\left(-1 \cdot 0.5\right)}} \]

      5. *-commutative 72.1%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{\ell \cdot V}}{A}\right)}^{\left(-1 \cdot 0.5\right)} \]

      6. associate-/l* 73.5%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell}{\frac{A}{V}}\right)}}^{\left(-1 \cdot 0.5\right)} \]

      7. metadata-eval 73.5%

         \[\leadsto c0 \cdot {\left(\frac{\ell}{\frac{A}{V}}\right)}^{\color{blue}{-0.5}} \]

   3. Applied egg-rr 73.5%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{\frac{A}{V}}\right)}^{-0.5}} \]
   4. Step-by-step derivation

      1. associate-/l* 72.1%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell \cdot V}{A}\right)}}^{-0.5} \]

      2. *-commutative 72.1%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{V \cdot \ell}}{A}\right)}^{-0.5} \]

      3. associate-/l* 72.4%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{V}{\frac{A}{\ell}}\right)}}^{-0.5} \]

      4. associate-/r/ 74.7%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{V}{A} \cdot \ell\right)}}^{-0.5} \]

   5. Simplified 74.7%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V}{A} \cdot \ell\right)}^{-0.5}} \]
   6. Step-by-step derivation

      1. metadata-eval 74.7%

         \[\leadsto c0 \cdot {\left(\frac{V}{A} \cdot \ell\right)}^{\color{blue}{\left(\frac{-1}{2}\right)}} \]

      2. sqrt-pow2 74.6%

         \[\leadsto c0 \cdot \color{blue}{{\left(\sqrt{\frac{V}{A} \cdot \ell}\right)}^{-1}} \]

      3. inv-pow 74.6%

         \[\leadsto c0 \cdot \color{blue}{\frac{1}{\sqrt{\frac{V}{A} \cdot \ell}}} \]

      4. un-div-inv 74.7%

         \[\leadsto \color{blue}{\frac{c0}{\sqrt{\frac{V}{A} \cdot \ell}}} \]

      5. sqrt-prod 87.4%

         \[\leadsto \frac{c0}{\color{blue}{\sqrt{\frac{V}{A}} \cdot \sqrt{\ell}}} \]

      6. associate-/r* 85.7%

         \[\leadsto \color{blue}{\frac{\frac{c0}{\sqrt{\frac{V}{A}}}}{\sqrt{\ell}}} \]

   7. Applied egg-rr 85.7%

      \[\leadsto \color{blue}{\frac{\frac{c0}{\sqrt{\frac{V}{A}}}}{\sqrt{\ell}}} \]
   8. Step-by-step derivation

      1. associate-/r* 87.4%

         \[\leadsto \color{blue}{\frac{c0}{\sqrt{\frac{V}{A}} \cdot \sqrt{\ell}}} \]

   9. Simplified 87.4%

      \[\leadsto \color{blue}{\frac{c0}{\sqrt{\frac{V}{A}} \cdot \sqrt{\ell}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -2 \cdot 10^{-310}:\\ \;\;\;\;c0 \cdot {\left(\ell \cdot \frac{V}{A}\right)}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{A}} \cdot \sqrt{\ell}}\\ \end{array} \]

Alternative 5: 80.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [V, l] = \mathsf{sort}([V, l])\\ \\ \begin{array}{l} t_0 := \frac{A}{\ell \cdot V}\\ \mathbf{if}\;t_0 \leq 0 \lor \neg \left(t_0 \leq 5 \cdot 10^{+302}\right):\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \end{array} \end{array} \]

FPCore

NOTE: V and l should be sorted in increasing order before calling this function.
(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (/ A (* l V))))
   (if (or (<= t_0 0.0) (not (<= t_0 5e+302)))
     (* c0 (sqrt (/ (/ A l) V)))
     (* c0 (sqrt t_0)))))

C

assert(V < l);
double code(double c0, double A, double V, double l) {
	double t_0 = A / (l * V);
	double tmp;
	if ((t_0 <= 0.0) || !(t_0 <= 5e+302)) {
		tmp = c0 * sqrt(((A / l) / V));
	} else {
		tmp = c0 * sqrt(t_0);
	}
	return tmp;
}

Fortran

NOTE: V and l should be sorted in increasing order before calling this function.
real(8) function code(c0, a, v, l)
    real(8), intent (in) :: c0
    real(8), intent (in) :: a
    real(8), intent (in) :: v
    real(8), intent (in) :: l
    real(8) :: t_0
    real(8) :: tmp
    t_0 = a / (l * v)
    if ((t_0 <= 0.0d0) .or. (.not. (t_0 <= 5d+302))) then
        tmp = c0 * sqrt(((a / l) / v))
    else
        tmp = c0 * sqrt(t_0)
    end if
    code = tmp
end function

Java

assert V < l;
public static double code(double c0, double A, double V, double l) {
	double t_0 = A / (l * V);
	double tmp;
	if ((t_0 <= 0.0) || !(t_0 <= 5e+302)) {
		tmp = c0 * Math.sqrt(((A / l) / V));
	} else {
		tmp = c0 * Math.sqrt(t_0);
	}
	return tmp;
}

Python

[V, l] = sort([V, l])
def code(c0, A, V, l):
	t_0 = A / (l * V)
	tmp = 0
	if (t_0 <= 0.0) or not (t_0 <= 5e+302):
		tmp = c0 * math.sqrt(((A / l) / V))
	else:
		tmp = c0 * math.sqrt(t_0)
	return tmp

Julia

V, l = sort([V, l])
function code(c0, A, V, l)
	t_0 = Float64(A / Float64(l * V))
	tmp = 0.0
	if ((t_0 <= 0.0) || !(t_0 <= 5e+302))
		tmp = Float64(c0 * sqrt(Float64(Float64(A / l) / V)));
	else
		tmp = Float64(c0 * sqrt(t_0));
	end
	return tmp
end

MATLAB

V, l = num2cell(sort([V, l])){:}
function tmp_2 = code(c0, A, V, l)
	t_0 = A / (l * V);
	tmp = 0.0;
	if ((t_0 <= 0.0) || ~((t_0 <= 5e+302)))
		tmp = c0 * sqrt(((A / l) / V));
	else
		tmp = c0 * sqrt(t_0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: V and l should be sorted in increasing order before calling this function.
code[c0_, A_, V_, l_] := Block[{t$95$0 = N[(A / N[(l * V), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 0.0], N[Not[LessEqual[t$95$0, 5e+302]], $MachinePrecision]], N[(c0 * N[Sqrt[N[(N[(A / l), $MachinePrecision] / V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(c0 * N[Sqrt[t$95$0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 A (*.f64 V l)) < 0.0 or 5e302 < (/.f64 A (*.f64 V l))

   1. Initial program 37.1%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. add-sqr-sqrt 27.8%

         \[\leadsto \color{blue}{\sqrt{c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}} \cdot \sqrt{c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}}} \]

      2. sqrt-unprod 27.9%

         \[\leadsto \color{blue}{\sqrt{\left(c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\right) \cdot \left(c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\right)}} \]

      3. *-commutative 27.9%

         \[\leadsto \sqrt{\color{blue}{\left(\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\right)} \cdot \left(c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\right)} \]

      4. *-commutative 27.9%

         \[\leadsto \sqrt{\left(\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\right) \cdot \color{blue}{\left(\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\right)}} \]

      5. swap-sqr 27.2%

         \[\leadsto \sqrt{\color{blue}{\left(\sqrt{\frac{A}{V \cdot \ell}} \cdot \sqrt{\frac{A}{V \cdot \ell}}\right) \cdot \left(c0 \cdot c0\right)}} \]

      6. add-sqr-sqrt 27.2%

         \[\leadsto \sqrt{\color{blue}{\frac{A}{V \cdot \ell}} \cdot \left(c0 \cdot c0\right)} \]

      7. associate-/r* 32.0%

         \[\leadsto \sqrt{\color{blue}{\frac{\frac{A}{V}}{\ell}} \cdot \left(c0 \cdot c0\right)} \]

      8. pow2 32.0%

         \[\leadsto \sqrt{\frac{\frac{A}{V}}{\ell} \cdot \color{blue}{{c0}^{2}}} \]

   3. Applied egg-rr 32.0%

      \[\leadsto \color{blue}{\sqrt{\frac{\frac{A}{V}}{\ell} \cdot {c0}^{2}}} \]
   4. Step-by-step derivation

      1. sqrt-prod 35.1%

         \[\leadsto \color{blue}{\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot \sqrt{{c0}^{2}}} \]

      2. sqrt-div 24.4%

         \[\leadsto \color{blue}{\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}} \cdot \sqrt{{c0}^{2}} \]

      3. clear-num 24.4%

         \[\leadsto \frac{\sqrt{\color{blue}{\frac{1}{\frac{V}{A}}}}}{\sqrt{\ell}} \cdot \sqrt{{c0}^{2}} \]

      4. sqrt-div 25.1%

         \[\leadsto \frac{\color{blue}{\frac{\sqrt{1}}{\sqrt{\frac{V}{A}}}}}{\sqrt{\ell}} \cdot \sqrt{{c0}^{2}} \]

      5. metadata-eval 25.1%

         \[\leadsto \frac{\frac{\color{blue}{1}}{\sqrt{\frac{V}{A}}}}{\sqrt{\ell}} \cdot \sqrt{{c0}^{2}} \]

      6. associate-/r* 25.2%

         \[\leadsto \color{blue}{\frac{1}{\sqrt{\frac{V}{A}} \cdot \sqrt{\ell}}} \cdot \sqrt{{c0}^{2}} \]

      7. sqrt-prod 34.7%

         \[\leadsto \frac{1}{\color{blue}{\sqrt{\frac{V}{A} \cdot \ell}}} \cdot \sqrt{{c0}^{2}} \]

      8. unpow2 34.7%

         \[\leadsto \frac{1}{\sqrt{\frac{V}{A} \cdot \ell}} \cdot \sqrt{\color{blue}{c0 \cdot c0}} \]

      9. sqrt-prod 33.3%

         \[\leadsto \frac{1}{\sqrt{\frac{V}{A} \cdot \ell}} \cdot \color{blue}{\left(\sqrt{c0} \cdot \sqrt{c0}\right)} \]

      10. add-sqr-sqrt 55.2%

          \[\leadsto \frac{1}{\sqrt{\frac{V}{A} \cdot \ell}} \cdot \color{blue}{c0} \]

   5. Applied egg-rr 55.3%

      \[\leadsto \color{blue}{\sqrt{\frac{\frac{A}{\ell}}{V}} \cdot c0} \]

   if 0.0 < (/.f64 A (*.f64 V l)) < 5e302

   1. Initial program 98.8%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{\ell \cdot V} \leq 0 \lor \neg \left(\frac{A}{\ell \cdot V} \leq 5 \cdot 10^{+302}\right):\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \end{array} \]

Alternative 6: 81.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [V, l] = \mathsf{sort}([V, l])\\ \\ \begin{array}{l} t_0 := \frac{A}{\ell \cdot V}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \end{array} \end{array} \]

FPCore

NOTE: V and l should be sorted in increasing order before calling this function.
(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (/ A (* l V))))
   (if (<= t_0 0.0)
     (* c0 (sqrt (/ (/ A l) V)))
     (if (<= t_0 5e+302) (* c0 (sqrt t_0)) (/ c0 (sqrt (* V (/ l A))))))))

C

assert(V < l);
double code(double c0, double A, double V, double l) {
	double t_0 = A / (l * V);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = c0 * sqrt(((A / l) / V));
	} else if (t_0 <= 5e+302) {
		tmp = c0 * sqrt(t_0);
	} else {
		tmp = c0 / sqrt((V * (l / A)));
	}
	return tmp;
}

Fortran

NOTE: V and l should be sorted in increasing order before calling this function.
real(8) function code(c0, a, v, l)
    real(8), intent (in) :: c0
    real(8), intent (in) :: a
    real(8), intent (in) :: v
    real(8), intent (in) :: l
    real(8) :: t_0
    real(8) :: tmp
    t_0 = a / (l * v)
    if (t_0 <= 0.0d0) then
        tmp = c0 * sqrt(((a / l) / v))
    else if (t_0 <= 5d+302) then
        tmp = c0 * sqrt(t_0)
    else
        tmp = c0 / sqrt((v * (l / a)))
    end if
    code = tmp
end function

Java

assert V < l;
public static double code(double c0, double A, double V, double l) {
	double t_0 = A / (l * V);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = c0 * Math.sqrt(((A / l) / V));
	} else if (t_0 <= 5e+302) {
		tmp = c0 * Math.sqrt(t_0);
	} else {
		tmp = c0 / Math.sqrt((V * (l / A)));
	}
	return tmp;
}

Python

[V, l] = sort([V, l])
def code(c0, A, V, l):
	t_0 = A / (l * V)
	tmp = 0
	if t_0 <= 0.0:
		tmp = c0 * math.sqrt(((A / l) / V))
	elif t_0 <= 5e+302:
		tmp = c0 * math.sqrt(t_0)
	else:
		tmp = c0 / math.sqrt((V * (l / A)))
	return tmp

Julia

V, l = sort([V, l])
function code(c0, A, V, l)
	t_0 = Float64(A / Float64(l * V))
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = Float64(c0 * sqrt(Float64(Float64(A / l) / V)));
	elseif (t_0 <= 5e+302)
		tmp = Float64(c0 * sqrt(t_0));
	else
		tmp = Float64(c0 / sqrt(Float64(V * Float64(l / A))));
	end
	return tmp
end

MATLAB

V, l = num2cell(sort([V, l])){:}
function tmp_2 = code(c0, A, V, l)
	t_0 = A / (l * V);
	tmp = 0.0;
	if (t_0 <= 0.0)
		tmp = c0 * sqrt(((A / l) / V));
	elseif (t_0 <= 5e+302)
		tmp = c0 * sqrt(t_0);
	else
		tmp = c0 / sqrt((V * (l / A)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: V and l should be sorted in increasing order before calling this function.
code[c0_, A_, V_, l_] := Block[{t$95$0 = N[(A / N[(l * V), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.0], N[(c0 * N[Sqrt[N[(N[(A / l), $MachinePrecision] / V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+302], N[(c0 * N[Sqrt[t$95$0], $MachinePrecision]), $MachinePrecision], N[(c0 / N[Sqrt[N[(V * N[(l / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 A (*.f64 V l)) < 0.0

   1. Initial program 31.4%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. add-sqr-sqrt 31.4%

         \[\leadsto \color{blue}{\sqrt{c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}} \cdot \sqrt{c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}}} \]

      2. sqrt-unprod 31.4%

         \[\leadsto \color{blue}{\sqrt{\left(c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\right) \cdot \left(c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\right)}} \]

      3. *-commutative 31.4%

         \[\leadsto \sqrt{\color{blue}{\left(\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\right)} \cdot \left(c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\right)} \]

      4. *-commutative 31.4%

         \[\leadsto \sqrt{\left(\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\right) \cdot \color{blue}{\left(\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\right)}} \]

      5. swap-sqr 30.6%

         \[\leadsto \sqrt{\color{blue}{\left(\sqrt{\frac{A}{V \cdot \ell}} \cdot \sqrt{\frac{A}{V \cdot \ell}}\right) \cdot \left(c0 \cdot c0\right)}} \]

      6. add-sqr-sqrt 30.6%

         \[\leadsto \sqrt{\color{blue}{\frac{A}{V \cdot \ell}} \cdot \left(c0 \cdot c0\right)} \]

      7. associate-/r* 34.7%

         \[\leadsto \sqrt{\color{blue}{\frac{\frac{A}{V}}{\ell}} \cdot \left(c0 \cdot c0\right)} \]

      8. pow2 34.7%

         \[\leadsto \sqrt{\frac{\frac{A}{V}}{\ell} \cdot \color{blue}{{c0}^{2}}} \]

   3. Applied egg-rr 34.7%

      \[\leadsto \color{blue}{\sqrt{\frac{\frac{A}{V}}{\ell} \cdot {c0}^{2}}} \]
   4. Step-by-step derivation

      1. sqrt-prod 37.2%

         \[\leadsto \color{blue}{\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot \sqrt{{c0}^{2}}} \]

      2. sqrt-div 27.8%

         \[\leadsto \color{blue}{\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}} \cdot \sqrt{{c0}^{2}} \]

      3. clear-num 27.8%

         \[\leadsto \frac{\sqrt{\color{blue}{\frac{1}{\frac{V}{A}}}}}{\sqrt{\ell}} \cdot \sqrt{{c0}^{2}} \]

      4. sqrt-div 27.8%

         \[\leadsto \frac{\color{blue}{\frac{\sqrt{1}}{\sqrt{\frac{V}{A}}}}}{\sqrt{\ell}} \cdot \sqrt{{c0}^{2}} \]

      5. metadata-eval 27.8%

         \[\leadsto \frac{\frac{\color{blue}{1}}{\sqrt{\frac{V}{A}}}}{\sqrt{\ell}} \cdot \sqrt{{c0}^{2}} \]

      6. associate-/r* 27.8%

         \[\leadsto \color{blue}{\frac{1}{\sqrt{\frac{V}{A}} \cdot \sqrt{\ell}}} \cdot \sqrt{{c0}^{2}} \]

      7. sqrt-prod 36.5%

         \[\leadsto \frac{1}{\color{blue}{\sqrt{\frac{V}{A} \cdot \ell}}} \cdot \sqrt{{c0}^{2}} \]

      8. unpow2 36.5%

         \[\leadsto \frac{1}{\sqrt{\frac{V}{A} \cdot \ell}} \cdot \sqrt{\color{blue}{c0 \cdot c0}} \]

      9. sqrt-prod 31.5%

         \[\leadsto \frac{1}{\sqrt{\frac{V}{A} \cdot \ell}} \cdot \color{blue}{\left(\sqrt{c0} \cdot \sqrt{c0}\right)} \]

      10. add-sqr-sqrt 51.9%

          \[\leadsto \frac{1}{\sqrt{\frac{V}{A} \cdot \ell}} \cdot \color{blue}{c0} \]

   5. Applied egg-rr 53.6%

      \[\leadsto \color{blue}{\sqrt{\frac{\frac{A}{\ell}}{V}} \cdot c0} \]

   if 0.0 < (/.f64 A (*.f64 V l)) < 5e302

   1. Initial program 98.8%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]

   if 5e302 < (/.f64 A (*.f64 V l))

   1. Initial program 42.6%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 42.6%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{A}{V \cdot \ell}\right)}^{0.5}} \]

      2. clear-num 42.6%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{1}{\frac{V \cdot \ell}{A}}\right)}}^{0.5} \]

      3. inv-pow 42.6%

         \[\leadsto c0 \cdot {\color{blue}{\left({\left(\frac{V \cdot \ell}{A}\right)}^{-1}\right)}}^{0.5} \]

      4. pow-pow 43.0%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V \cdot \ell}{A}\right)}^{\left(-1 \cdot 0.5\right)}} \]

      5. *-commutative 43.0%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{\ell \cdot V}}{A}\right)}^{\left(-1 \cdot 0.5\right)} \]

      6. associate-/l* 58.5%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell}{\frac{A}{V}}\right)}}^{\left(-1 \cdot 0.5\right)} \]

      7. metadata-eval 58.5%

         \[\leadsto c0 \cdot {\left(\frac{\ell}{\frac{A}{V}}\right)}^{\color{blue}{-0.5}} \]

   3. Applied egg-rr 58.5%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{\frac{A}{V}}\right)}^{-0.5}} \]
   4. Step-by-step derivation

      1. associate-/l* 43.0%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell \cdot V}{A}\right)}}^{-0.5} \]

      2. *-commutative 43.0%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{V \cdot \ell}}{A}\right)}^{-0.5} \]

      3. associate-/l* 58.1%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{V}{\frac{A}{\ell}}\right)}}^{-0.5} \]

      4. associate-/r/ 58.5%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{V}{A} \cdot \ell\right)}}^{-0.5} \]

   5. Simplified 58.5%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V}{A} \cdot \ell\right)}^{-0.5}} \]
   6. Step-by-step derivation

      1. metadata-eval 58.5%

         \[\leadsto c0 \cdot {\left(\frac{V}{A} \cdot \ell\right)}^{\color{blue}{\left(\frac{-1}{2}\right)}} \]

      2. sqrt-pow2 58.5%

         \[\leadsto c0 \cdot \color{blue}{{\left(\sqrt{\frac{V}{A} \cdot \ell}\right)}^{-1}} \]

      3. inv-pow 58.5%

         \[\leadsto c0 \cdot \color{blue}{\frac{1}{\sqrt{\frac{V}{A} \cdot \ell}}} \]

      4. un-div-inv 58.5%

         \[\leadsto \color{blue}{\frac{c0}{\sqrt{\frac{V}{A} \cdot \ell}}} \]

      5. associate-*l/ 43.0%

         \[\leadsto \frac{c0}{\sqrt{\color{blue}{\frac{V \cdot \ell}{A}}}} \]

      6. sqrt-div 27.5%

         \[\leadsto \frac{c0}{\color{blue}{\frac{\sqrt{V \cdot \ell}}{\sqrt{A}}}} \]

      7. *-commutative 27.5%

         \[\leadsto \frac{c0}{\frac{\sqrt{\color{blue}{\ell \cdot V}}}{\sqrt{A}}} \]

      8. sqrt-div 43.0%

         \[\leadsto \frac{c0}{\color{blue}{\sqrt{\frac{\ell \cdot V}{A}}}} \]

      9. associate-*l/ 58.1%

         \[\leadsto \frac{c0}{\sqrt{\color{blue}{\frac{\ell}{A} \cdot V}}} \]

      10. *-commutative 58.1%

          \[\leadsto \frac{c0}{\sqrt{\color{blue}{V \cdot \frac{\ell}{A}}}} \]

   7. Applied egg-rr 58.1%

      \[\leadsto \color{blue}{\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{\ell \cdot V} \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{elif}\;\frac{A}{\ell \cdot V} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \end{array} \]

Alternative 7: 80.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} [V, l] = \mathsf{sort}([V, l])\\ \\ \begin{array}{l} t_0 := \frac{A}{\ell \cdot V}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{elif}\;t_0 \leq 2 \cdot 10^{+282}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \end{array} \]

FPCore

NOTE: V and l should be sorted in increasing order before calling this function.
(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (/ A (* l V))))
   (if (<= t_0 0.0)
     (* c0 (sqrt (/ (/ A l) V)))
     (if (<= t_0 2e+282) (* c0 (sqrt t_0)) (/ c0 (sqrt (* l (/ V A))))))))

C

assert(V < l);
double code(double c0, double A, double V, double l) {
	double t_0 = A / (l * V);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = c0 * sqrt(((A / l) / V));
	} else if (t_0 <= 2e+282) {
		tmp = c0 * sqrt(t_0);
	} else {
		tmp = c0 / sqrt((l * (V / A)));
	}
	return tmp;
}

Fortran

NOTE: V and l should be sorted in increasing order before calling this function.
real(8) function code(c0, a, v, l)
    real(8), intent (in) :: c0
    real(8), intent (in) :: a
    real(8), intent (in) :: v
    real(8), intent (in) :: l
    real(8) :: t_0
    real(8) :: tmp
    t_0 = a / (l * v)
    if (t_0 <= 0.0d0) then
        tmp = c0 * sqrt(((a / l) / v))
    else if (t_0 <= 2d+282) then
        tmp = c0 * sqrt(t_0)
    else
        tmp = c0 / sqrt((l * (v / a)))
    end if
    code = tmp
end function

Java

assert V < l;
public static double code(double c0, double A, double V, double l) {
	double t_0 = A / (l * V);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = c0 * Math.sqrt(((A / l) / V));
	} else if (t_0 <= 2e+282) {
		tmp = c0 * Math.sqrt(t_0);
	} else {
		tmp = c0 / Math.sqrt((l * (V / A)));
	}
	return tmp;
}

Python

[V, l] = sort([V, l])
def code(c0, A, V, l):
	t_0 = A / (l * V)
	tmp = 0
	if t_0 <= 0.0:
		tmp = c0 * math.sqrt(((A / l) / V))
	elif t_0 <= 2e+282:
		tmp = c0 * math.sqrt(t_0)
	else:
		tmp = c0 / math.sqrt((l * (V / A)))
	return tmp

Julia

V, l = sort([V, l])
function code(c0, A, V, l)
	t_0 = Float64(A / Float64(l * V))
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = Float64(c0 * sqrt(Float64(Float64(A / l) / V)));
	elseif (t_0 <= 2e+282)
		tmp = Float64(c0 * sqrt(t_0));
	else
		tmp = Float64(c0 / sqrt(Float64(l * Float64(V / A))));
	end
	return tmp
end

MATLAB

V, l = num2cell(sort([V, l])){:}
function tmp_2 = code(c0, A, V, l)
	t_0 = A / (l * V);
	tmp = 0.0;
	if (t_0 <= 0.0)
		tmp = c0 * sqrt(((A / l) / V));
	elseif (t_0 <= 2e+282)
		tmp = c0 * sqrt(t_0);
	else
		tmp = c0 / sqrt((l * (V / A)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: V and l should be sorted in increasing order before calling this function.
code[c0_, A_, V_, l_] := Block[{t$95$0 = N[(A / N[(l * V), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.0], N[(c0 * N[Sqrt[N[(N[(A / l), $MachinePrecision] / V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2e+282], N[(c0 * N[Sqrt[t$95$0], $MachinePrecision]), $MachinePrecision], N[(c0 / N[Sqrt[N[(l * N[(V / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 A (*.f64 V l)) < 0.0

   1. Initial program 31.4%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. add-sqr-sqrt 31.4%

         \[\leadsto \color{blue}{\sqrt{c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}} \cdot \sqrt{c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}}} \]

      2. sqrt-unprod 31.4%

         \[\leadsto \color{blue}{\sqrt{\left(c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\right) \cdot \left(c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\right)}} \]

      3. *-commutative 31.4%

         \[\leadsto \sqrt{\color{blue}{\left(\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\right)} \cdot \left(c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\right)} \]

      4. *-commutative 31.4%

         \[\leadsto \sqrt{\left(\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\right) \cdot \color{blue}{\left(\sqrt{\frac{A}{V \cdot \ell}} \cdot c0\right)}} \]

      5. swap-sqr 30.6%

         \[\leadsto \sqrt{\color{blue}{\left(\sqrt{\frac{A}{V \cdot \ell}} \cdot \sqrt{\frac{A}{V \cdot \ell}}\right) \cdot \left(c0 \cdot c0\right)}} \]

      6. add-sqr-sqrt 30.6%

         \[\leadsto \sqrt{\color{blue}{\frac{A}{V \cdot \ell}} \cdot \left(c0 \cdot c0\right)} \]

      7. associate-/r* 34.7%

         \[\leadsto \sqrt{\color{blue}{\frac{\frac{A}{V}}{\ell}} \cdot \left(c0 \cdot c0\right)} \]

      8. pow2 34.7%

         \[\leadsto \sqrt{\frac{\frac{A}{V}}{\ell} \cdot \color{blue}{{c0}^{2}}} \]

   3. Applied egg-rr 34.7%

      \[\leadsto \color{blue}{\sqrt{\frac{\frac{A}{V}}{\ell} \cdot {c0}^{2}}} \]
   4. Step-by-step derivation

      1. sqrt-prod 37.2%

         \[\leadsto \color{blue}{\sqrt{\frac{\frac{A}{V}}{\ell}} \cdot \sqrt{{c0}^{2}}} \]

      2. sqrt-div 27.8%

         \[\leadsto \color{blue}{\frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}} \cdot \sqrt{{c0}^{2}} \]

      3. clear-num 27.8%

         \[\leadsto \frac{\sqrt{\color{blue}{\frac{1}{\frac{V}{A}}}}}{\sqrt{\ell}} \cdot \sqrt{{c0}^{2}} \]

      4. sqrt-div 27.8%

         \[\leadsto \frac{\color{blue}{\frac{\sqrt{1}}{\sqrt{\frac{V}{A}}}}}{\sqrt{\ell}} \cdot \sqrt{{c0}^{2}} \]

      5. metadata-eval 27.8%

         \[\leadsto \frac{\frac{\color{blue}{1}}{\sqrt{\frac{V}{A}}}}{\sqrt{\ell}} \cdot \sqrt{{c0}^{2}} \]

      6. associate-/r* 27.8%

         \[\leadsto \color{blue}{\frac{1}{\sqrt{\frac{V}{A}} \cdot \sqrt{\ell}}} \cdot \sqrt{{c0}^{2}} \]

      7. sqrt-prod 36.5%

         \[\leadsto \frac{1}{\color{blue}{\sqrt{\frac{V}{A} \cdot \ell}}} \cdot \sqrt{{c0}^{2}} \]

      8. unpow2 36.5%

         \[\leadsto \frac{1}{\sqrt{\frac{V}{A} \cdot \ell}} \cdot \sqrt{\color{blue}{c0 \cdot c0}} \]

      9. sqrt-prod 31.5%

         \[\leadsto \frac{1}{\sqrt{\frac{V}{A} \cdot \ell}} \cdot \color{blue}{\left(\sqrt{c0} \cdot \sqrt{c0}\right)} \]

      10. add-sqr-sqrt 51.9%

          \[\leadsto \frac{1}{\sqrt{\frac{V}{A} \cdot \ell}} \cdot \color{blue}{c0} \]

   5. Applied egg-rr 53.6%

      \[\leadsto \color{blue}{\sqrt{\frac{\frac{A}{\ell}}{V}} \cdot c0} \]

   if 0.0 < (/.f64 A (*.f64 V l)) < 2.00000000000000007e282

   1. Initial program 98.8%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]

   if 2.00000000000000007e282 < (/.f64 A (*.f64 V l))

   1. Initial program 48.4%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 48.4%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{A}{V \cdot \ell}\right)}^{0.5}} \]

      2. clear-num 48.4%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{1}{\frac{V \cdot \ell}{A}}\right)}}^{0.5} \]

      3. inv-pow 48.4%

         \[\leadsto c0 \cdot {\color{blue}{\left({\left(\frac{V \cdot \ell}{A}\right)}^{-1}\right)}}^{0.5} \]

      4. pow-pow 48.7%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V \cdot \ell}{A}\right)}^{\left(-1 \cdot 0.5\right)}} \]

      5. *-commutative 48.7%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{\ell \cdot V}}{A}\right)}^{\left(-1 \cdot 0.5\right)} \]

      6. associate-/l* 61.0%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell}{\frac{A}{V}}\right)}}^{\left(-1 \cdot 0.5\right)} \]

      7. metadata-eval 61.0%

         \[\leadsto c0 \cdot {\left(\frac{\ell}{\frac{A}{V}}\right)}^{\color{blue}{-0.5}} \]

   3. Applied egg-rr 61.0%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{\frac{A}{V}}\right)}^{-0.5}} \]

   5. Applied egg-rr 61.0%

      \[\leadsto \color{blue}{\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{\ell \cdot V} \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{elif}\;\frac{A}{\ell \cdot V} \leq 2 \cdot 10^{+282}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \]

Alternative 8: 80.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [V, l] = \mathsf{sort}([V, l])\\ \\ \begin{array}{l} t_0 := \frac{A}{\ell \cdot V}\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{-297}:\\ \;\;\;\;c0 \cdot {\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.5}\\ \mathbf{elif}\;t_0 \leq 2 \cdot 10^{+282}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{\ell \cdot V}{A}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \end{array} \]

FPCore

NOTE: V and l should be sorted in increasing order before calling this function.
(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (/ A (* l V))))
   (if (<= t_0 5e-297)
     (* c0 (pow (/ (/ A V) l) 0.5))
     (if (<= t_0 2e+282)
       (/ c0 (sqrt (/ (* l V) A)))
       (/ c0 (sqrt (* l (/ V A))))))))

C

assert(V < l);
double code(double c0, double A, double V, double l) {
	double t_0 = A / (l * V);
	double tmp;
	if (t_0 <= 5e-297) {
		tmp = c0 * pow(((A / V) / l), 0.5);
	} else if (t_0 <= 2e+282) {
		tmp = c0 / sqrt(((l * V) / A));
	} else {
		tmp = c0 / sqrt((l * (V / A)));
	}
	return tmp;
}

Fortran

NOTE: V and l should be sorted in increasing order before calling this function.
real(8) function code(c0, a, v, l)
    real(8), intent (in) :: c0
    real(8), intent (in) :: a
    real(8), intent (in) :: v
    real(8), intent (in) :: l
    real(8) :: t_0
    real(8) :: tmp
    t_0 = a / (l * v)
    if (t_0 <= 5d-297) then
        tmp = c0 * (((a / v) / l) ** 0.5d0)
    else if (t_0 <= 2d+282) then
        tmp = c0 / sqrt(((l * v) / a))
    else
        tmp = c0 / sqrt((l * (v / a)))
    end if
    code = tmp
end function

Java

assert V < l;
public static double code(double c0, double A, double V, double l) {
	double t_0 = A / (l * V);
	double tmp;
	if (t_0 <= 5e-297) {
		tmp = c0 * Math.pow(((A / V) / l), 0.5);
	} else if (t_0 <= 2e+282) {
		tmp = c0 / Math.sqrt(((l * V) / A));
	} else {
		tmp = c0 / Math.sqrt((l * (V / A)));
	}
	return tmp;
}

Python

[V, l] = sort([V, l])
def code(c0, A, V, l):
	t_0 = A / (l * V)
	tmp = 0
	if t_0 <= 5e-297:
		tmp = c0 * math.pow(((A / V) / l), 0.5)
	elif t_0 <= 2e+282:
		tmp = c0 / math.sqrt(((l * V) / A))
	else:
		tmp = c0 / math.sqrt((l * (V / A)))
	return tmp

Julia

V, l = sort([V, l])
function code(c0, A, V, l)
	t_0 = Float64(A / Float64(l * V))
	tmp = 0.0
	if (t_0 <= 5e-297)
		tmp = Float64(c0 * (Float64(Float64(A / V) / l) ^ 0.5));
	elseif (t_0 <= 2e+282)
		tmp = Float64(c0 / sqrt(Float64(Float64(l * V) / A)));
	else
		tmp = Float64(c0 / sqrt(Float64(l * Float64(V / A))));
	end
	return tmp
end

MATLAB

V, l = num2cell(sort([V, l])){:}
function tmp_2 = code(c0, A, V, l)
	t_0 = A / (l * V);
	tmp = 0.0;
	if (t_0 <= 5e-297)
		tmp = c0 * (((A / V) / l) ^ 0.5);
	elseif (t_0 <= 2e+282)
		tmp = c0 / sqrt(((l * V) / A));
	else
		tmp = c0 / sqrt((l * (V / A)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: V and l should be sorted in increasing order before calling this function.
code[c0_, A_, V_, l_] := Block[{t$95$0 = N[(A / N[(l * V), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 5e-297], N[(c0 * N[Power[N[(N[(A / V), $MachinePrecision] / l), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2e+282], N[(c0 / N[Sqrt[N[(N[(l * V), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(c0 / N[Sqrt[N[(l * N[(V / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 A (*.f64 V l)) < 5e-297

   1. Initial program 32.8%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 32.8%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{A}{V \cdot \ell}\right)}^{0.5}} \]

      2. associate-/r* 53.5%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\frac{A}{V}}{\ell}\right)}}^{0.5} \]

   3. Applied egg-rr 53.5%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.5}} \]

   if 5e-297 < (/.f64 A (*.f64 V l)) < 2.00000000000000007e282

   1. Initial program 99.2%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 99.2%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{A}{V \cdot \ell}\right)}^{0.5}} \]

      2. clear-num 99.1%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{1}{\frac{V \cdot \ell}{A}}\right)}}^{0.5} \]

      3. inv-pow 99.1%

         \[\leadsto c0 \cdot {\color{blue}{\left({\left(\frac{V \cdot \ell}{A}\right)}^{-1}\right)}}^{0.5} \]

      4. pow-pow 99.2%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V \cdot \ell}{A}\right)}^{\left(-1 \cdot 0.5\right)}} \]

      5. *-commutative 99.2%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{\ell \cdot V}}{A}\right)}^{\left(-1 \cdot 0.5\right)} \]

      6. associate-/l* 88.3%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell}{\frac{A}{V}}\right)}}^{\left(-1 \cdot 0.5\right)} \]

      7. metadata-eval 88.3%

         \[\leadsto c0 \cdot {\left(\frac{\ell}{\frac{A}{V}}\right)}^{\color{blue}{-0.5}} \]

   3. Applied egg-rr 88.3%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{\frac{A}{V}}\right)}^{-0.5}} \]

   5. Applied egg-rr 89.5%

      \[\leadsto \color{blue}{\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}} \]
   6. Step-by-step derivation

      1. associate-*r/ 99.2%

         \[\leadsto \frac{c0}{\sqrt{\color{blue}{\frac{\ell \cdot V}{A}}}} \]

   7. Applied egg-rr 99.2%

      \[\leadsto \frac{c0}{\sqrt{\color{blue}{\frac{\ell \cdot V}{A}}}} \]

   if 2.00000000000000007e282 < (/.f64 A (*.f64 V l))

   1. Initial program 48.4%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 48.4%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{A}{V \cdot \ell}\right)}^{0.5}} \]

      2. clear-num 48.4%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{1}{\frac{V \cdot \ell}{A}}\right)}}^{0.5} \]

      3. inv-pow 48.4%

         \[\leadsto c0 \cdot {\color{blue}{\left({\left(\frac{V \cdot \ell}{A}\right)}^{-1}\right)}}^{0.5} \]

      4. pow-pow 48.7%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V \cdot \ell}{A}\right)}^{\left(-1 \cdot 0.5\right)}} \]

      5. *-commutative 48.7%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{\ell \cdot V}}{A}\right)}^{\left(-1 \cdot 0.5\right)} \]

      6. associate-/l* 61.0%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell}{\frac{A}{V}}\right)}}^{\left(-1 \cdot 0.5\right)} \]

      7. metadata-eval 61.0%

         \[\leadsto c0 \cdot {\left(\frac{\ell}{\frac{A}{V}}\right)}^{\color{blue}{-0.5}} \]

   3. Applied egg-rr 61.0%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{\frac{A}{V}}\right)}^{-0.5}} \]

   5. Applied egg-rr 61.0%

      \[\leadsto \color{blue}{\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{\ell \cdot V} \leq 5 \cdot 10^{-297}:\\ \;\;\;\;c0 \cdot {\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.5}\\ \mathbf{elif}\;\frac{A}{\ell \cdot V} \leq 2 \cdot 10^{+282}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{\ell \cdot V}{A}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \]

Alternative 9: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [V, l] = \mathsf{sort}([V, l])\\ \\ c0 \cdot \sqrt{\frac{A}{\ell \cdot V}} \end{array} \]

FPCore

NOTE: V and l should be sorted in increasing order before calling this function.
(FPCore (c0 A V l) :precision binary64 (* c0 (sqrt (/ A (* l V)))))

C

assert(V < l);
double code(double c0, double A, double V, double l) {
	return c0 * sqrt((A / (l * V)));
}

Fortran

NOTE: V and l should be sorted in increasing order before calling this function.
real(8) function code(c0, a, v, l)
    real(8), intent (in) :: c0
    real(8), intent (in) :: a
    real(8), intent (in) :: v
    real(8), intent (in) :: l
    code = c0 * sqrt((a / (l * v)))
end function

Java

assert V < l;
public static double code(double c0, double A, double V, double l) {
	return c0 * Math.sqrt((A / (l * V)));
}

Python

[V, l] = sort([V, l])
def code(c0, A, V, l):
	return c0 * math.sqrt((A / (l * V)))

Julia

V, l = sort([V, l])
function code(c0, A, V, l)
	return Float64(c0 * sqrt(Float64(A / Float64(l * V))))
end

MATLAB

V, l = num2cell(sort([V, l])){:}
function tmp = code(c0, A, V, l)
	tmp = c0 * sqrt((A / (l * V)));
end

Wolfram

NOTE: V and l should be sorted in increasing order before calling this function.
code[c0_, A_, V_, l_] := N[(c0 * N[Sqrt[N[(A / N[(l * V), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 73.5%

   \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]

2. Final simplification 73.5%

   \[\leadsto c0 \cdot \sqrt{\frac{A}{\ell \cdot V}} \]

Reproduce

herbie shell --seed 2023313 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))