Henrywood and Agarwal, Equation (3)

Percentage Accurate: 73.8% → 87.9%

Time: 11.6s

Alternatives: 10

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: 73.8% 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: 87.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [c0, A, V, l] = \mathsf{sort}([c0, A, V, l])\\ \\ \begin{array}{l} t_0 := c0 \cdot \frac{\sqrt{\frac{-A}{\ell}}}{\sqrt{-V}}\\ \mathbf{if}\;V \cdot \ell \leq -1 \cdot 10^{+306}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-287}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{-164}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{1}{V}}{\frac{\ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+306}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

NOTE: c0, A, V, and l should be sorted in increasing order before calling this function.
(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (* c0 (/ (sqrt (/ (- A) l)) (sqrt (- V))))))
   (if (<= (* V l) -1e+306)
     t_0
     (if (<= (* V l) -1e-287)
       (* c0 (/ (sqrt (- A)) (sqrt (* V (- l)))))
       (if (<= (* V l) 1e-164)
         (* c0 (sqrt (/ (/ 1.0 V) (/ l A))))
         (if (<= (* V l) 1e+306) (/ (* c0 (sqrt A)) (sqrt (* V l))) t_0))))))

C

assert(c0 < A && A < V && V < l);
double code(double c0, double A, double V, double l) {
	double t_0 = c0 * (sqrt((-A / l)) / sqrt(-V));
	double tmp;
	if ((V * l) <= -1e+306) {
		tmp = t_0;
	} else if ((V * l) <= -1e-287) {
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	} else if ((V * l) <= 1e-164) {
		tmp = c0 * sqrt(((1.0 / V) / (l / A)));
	} else if ((V * l) <= 1e+306) {
		tmp = (c0 * sqrt(A)) / sqrt((V * l));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

NOTE: c0, A, 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 = c0 * (sqrt((-a / l)) / sqrt(-v))
    if ((v * l) <= (-1d+306)) then
        tmp = t_0
    else if ((v * l) <= (-1d-287)) then
        tmp = c0 * (sqrt(-a) / sqrt((v * -l)))
    else if ((v * l) <= 1d-164) then
        tmp = c0 * sqrt(((1.0d0 / v) / (l / a)))
    else if ((v * l) <= 1d+306) then
        tmp = (c0 * sqrt(a)) / sqrt((v * l))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert c0 < A && A < V && V < l;
public static double code(double c0, double A, double V, double l) {
	double t_0 = c0 * (Math.sqrt((-A / l)) / Math.sqrt(-V));
	double tmp;
	if ((V * l) <= -1e+306) {
		tmp = t_0;
	} else if ((V * l) <= -1e-287) {
		tmp = c0 * (Math.sqrt(-A) / Math.sqrt((V * -l)));
	} else if ((V * l) <= 1e-164) {
		tmp = c0 * Math.sqrt(((1.0 / V) / (l / A)));
	} else if ((V * l) <= 1e+306) {
		tmp = (c0 * Math.sqrt(A)) / Math.sqrt((V * l));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[c0, A, V, l] = sort([c0, A, V, l])
def code(c0, A, V, l):
	t_0 = c0 * (math.sqrt((-A / l)) / math.sqrt(-V))
	tmp = 0
	if (V * l) <= -1e+306:
		tmp = t_0
	elif (V * l) <= -1e-287:
		tmp = c0 * (math.sqrt(-A) / math.sqrt((V * -l)))
	elif (V * l) <= 1e-164:
		tmp = c0 * math.sqrt(((1.0 / V) / (l / A)))
	elif (V * l) <= 1e+306:
		tmp = (c0 * math.sqrt(A)) / math.sqrt((V * l))
	else:
		tmp = t_0
	return tmp

Julia

c0, A, V, l = sort([c0, A, V, l])
function code(c0, A, V, l)
	t_0 = Float64(c0 * Float64(sqrt(Float64(Float64(-A) / l)) / sqrt(Float64(-V))))
	tmp = 0.0
	if (Float64(V * l) <= -1e+306)
		tmp = t_0;
	elseif (Float64(V * l) <= -1e-287)
		tmp = Float64(c0 * Float64(sqrt(Float64(-A)) / sqrt(Float64(V * Float64(-l)))));
	elseif (Float64(V * l) <= 1e-164)
		tmp = Float64(c0 * sqrt(Float64(Float64(1.0 / V) / Float64(l / A))));
	elseif (Float64(V * l) <= 1e+306)
		tmp = Float64(Float64(c0 * sqrt(A)) / sqrt(Float64(V * l)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

c0, A, V, l = num2cell(sort([c0, A, V, l])){:}
function tmp_2 = code(c0, A, V, l)
	t_0 = c0 * (sqrt((-A / l)) / sqrt(-V));
	tmp = 0.0;
	if ((V * l) <= -1e+306)
		tmp = t_0;
	elseif ((V * l) <= -1e-287)
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	elseif ((V * l) <= 1e-164)
		tmp = c0 * sqrt(((1.0 / V) / (l / A)));
	elseif ((V * l) <= 1e+306)
		tmp = (c0 * sqrt(A)) / sqrt((V * l));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: c0, A, V, and l should be sorted in increasing order before calling this function.
code[c0_, A_, V_, l_] := Block[{t$95$0 = N[(c0 * N[(N[Sqrt[N[((-A) / l), $MachinePrecision]], $MachinePrecision] / N[Sqrt[(-V)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(V * l), $MachinePrecision], -1e+306], t$95$0, If[LessEqual[N[(V * l), $MachinePrecision], -1e-287], N[(c0 * N[(N[Sqrt[(-A)], $MachinePrecision] / N[Sqrt[N[(V * (-l)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], 1e-164], N[(c0 * N[Sqrt[N[(N[(1.0 / V), $MachinePrecision] / N[(l / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], 1e+306], N[(N[(c0 * N[Sqrt[A], $MachinePrecision]), $MachinePrecision] / N[Sqrt[N[(V * l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 V l) < -1.00000000000000002e306 or 1.00000000000000002e306 < (*.f64 V l)

   1. Initial program 36.1%

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

      1. associate-/r* 58.7%

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

      2. div-inv 58.8%

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

   3. Applied egg-rr 58.8%

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{A}{V} \cdot \frac{1}{\ell}}} \]
   4. Step-by-step derivation

      1. *-commutative 58.8%

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

      2. clear-num 58.8%

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

      3. un-div-inv 58.9%

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

   5. Applied egg-rr 58.9%

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\frac{1}{\ell}}{\frac{V}{A}}}} \]
   6. Step-by-step derivation

      1. associate-/l/ 58.8%

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

      2. associate-*l/ 36.1%

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

      3. clear-num 36.1%

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

      4. associate-/l/ 58.8%

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

      5. frac-2neg 58.8%

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

      6. sqrt-div 51.6%

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

      7. distribute-neg-frac 51.6%

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

   7. Applied egg-rr 51.6%

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

   if -1.00000000000000002e306 < (*.f64 V l) < -1.00000000000000002e-287

   1. Initial program 87.3%

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

      1. frac-2neg 87.3%

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

      2. sqrt-div 99.5%

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

      3. distribute-rgt-neg-in 99.5%

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

   3. Applied egg-rr 99.5%

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

      1. distribute-rgt-neg-out 99.5%

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

      2. *-commutative 99.5%

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

      3. distribute-rgt-neg-in 99.5%

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

   5. Simplified 99.5%

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

   if -1.00000000000000002e-287 < (*.f64 V l) < 9.99999999999999962e-165

   1. Initial program 60.0%

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

      1. associate-/r* 78.5%

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

      2. div-inv 78.5%

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

   3. Applied egg-rr 78.5%

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{A}{V} \cdot \frac{1}{\ell}}} \]
   4. Step-by-step derivation

      1. *-un-lft-identity 78.5%

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

      2. associate-*l/ 78.5%

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

      3. div-inv 78.5%

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

      4. associate-/l* 80.3%

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

   5. Applied egg-rr 80.3%

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

   if 9.99999999999999962e-165 < (*.f64 V l) < 1.00000000000000002e306

   1. Initial program 89.1%

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

      1. *-commutative 89.1%

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

      2. sqrt-div 99.3%

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

      3. associate-*l/ 97.9%

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

   3. Applied egg-rr 97.9%

      \[\leadsto \color{blue}{\frac{\sqrt{A} \cdot c0}{\sqrt{V \cdot \ell}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -1 \cdot 10^{+306}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{-A}{\ell}}}{\sqrt{-V}}\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-287}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{-164}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{1}{V}}{\frac{\ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{+306}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{-A}{\ell}}}{\sqrt{-V}}\\ \end{array} \]

Alternative 2: 89.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [c0, A, V, l] = \mathsf{sort}([c0, A, V, l])\\ \\ \begin{array}{l} \mathbf{if}\;A \leq -5 \cdot 10^{-310}:\\ \;\;\;\;c0 \cdot \left(\frac{\sqrt{-A}}{\sqrt{-V}} \cdot \frac{1}{\sqrt{\ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{A} \cdot \frac{c0}{\sqrt{V \cdot \ell}}\\ \end{array} \end{array} \]

FPCore

NOTE: c0, A, V, and l should be sorted in increasing order before calling this function.
(FPCore (c0 A V l)
 :precision binary64
 (if (<= A -5e-310)
   (* c0 (* (/ (sqrt (- A)) (sqrt (- V))) (/ 1.0 (sqrt l))))
   (* (sqrt A) (/ c0 (sqrt (* V l))))))

C

assert(c0 < A && A < V && V < l);
double code(double c0, double A, double V, double l) {
	double tmp;
	if (A <= -5e-310) {
		tmp = c0 * ((sqrt(-A) / sqrt(-V)) * (1.0 / sqrt(l)));
	} else {
		tmp = sqrt(A) * (c0 / sqrt((V * l)));
	}
	return tmp;
}

Fortran

NOTE: c0, A, 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 (a <= (-5d-310)) then
        tmp = c0 * ((sqrt(-a) / sqrt(-v)) * (1.0d0 / sqrt(l)))
    else
        tmp = sqrt(a) * (c0 / sqrt((v * l)))
    end if
    code = tmp
end function

Java

assert c0 < A && A < V && V < l;
public static double code(double c0, double A, double V, double l) {
	double tmp;
	if (A <= -5e-310) {
		tmp = c0 * ((Math.sqrt(-A) / Math.sqrt(-V)) * (1.0 / Math.sqrt(l)));
	} else {
		tmp = Math.sqrt(A) * (c0 / Math.sqrt((V * l)));
	}
	return tmp;
}

Python

[c0, A, V, l] = sort([c0, A, V, l])
def code(c0, A, V, l):
	tmp = 0
	if A <= -5e-310:
		tmp = c0 * ((math.sqrt(-A) / math.sqrt(-V)) * (1.0 / math.sqrt(l)))
	else:
		tmp = math.sqrt(A) * (c0 / math.sqrt((V * l)))
	return tmp

Julia

c0, A, V, l = sort([c0, A, V, l])
function code(c0, A, V, l)
	tmp = 0.0
	if (A <= -5e-310)
		tmp = Float64(c0 * Float64(Float64(sqrt(Float64(-A)) / sqrt(Float64(-V))) * Float64(1.0 / sqrt(l))));
	else
		tmp = Float64(sqrt(A) * Float64(c0 / sqrt(Float64(V * l))));
	end
	return tmp
end

MATLAB

c0, A, V, l = num2cell(sort([c0, A, V, l])){:}
function tmp_2 = code(c0, A, V, l)
	tmp = 0.0;
	if (A <= -5e-310)
		tmp = c0 * ((sqrt(-A) / sqrt(-V)) * (1.0 / sqrt(l)));
	else
		tmp = sqrt(A) * (c0 / sqrt((V * l)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: c0, A, V, and l should be sorted in increasing order before calling this function.
code[c0_, A_, V_, l_] := If[LessEqual[A, -5e-310], N[(c0 * N[(N[(N[Sqrt[(-A)], $MachinePrecision] / N[Sqrt[(-V)], $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[A], $MachinePrecision] * N[(c0 / N[Sqrt[N[(V * l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if A < -4.999999999999985e-310

   1. Initial program 75.9%

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

      1. associate-/r* 77.3%

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

      2. sqrt-div 50.9%

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

      3. div-inv 50.8%

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

   3. Applied egg-rr 50.8%

      \[\leadsto c0 \cdot \color{blue}{\left(\sqrt{\frac{A}{V}} \cdot \frac{1}{\sqrt{\ell}}\right)} \]
   4. Step-by-step derivation

      1. frac-2neg 50.8%

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

      2. sqrt-div 56.2%

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

   5. Applied egg-rr 56.2%

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

   if -4.999999999999985e-310 < A

   1. Initial program 77.4%

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

      1. associate-/r* 76.0%

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

      2. div-inv 76.0%

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

   3. Applied egg-rr 76.0%

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{A}{V} \cdot \frac{1}{\ell}}} \]
   4. Step-by-step derivation

      1. un-div-inv 76.0%

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

      2. sqrt-div 46.6%

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

      3. associate-*r/ 45.0%

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

      4. sqrt-div 49.8%

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

      5. associate-*r/ 48.7%

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

      6. *-commutative 48.7%

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

      7. associate-/r* 48.7%

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

      8. sqrt-prod 80.9%

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

      9. clear-num 80.9%

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

      10. *-commutative 80.9%

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

   5. Applied egg-rr 80.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{\sqrt{V \cdot \ell}}{c0 \cdot \sqrt{A}}}} \]
   6. Step-by-step derivation

      1. associate-/r/ 80.9%

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

      2. associate-*l/ 80.9%

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

      3. *-lft-identity 80.9%

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

      4. associate-*l/ 81.6%

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

      5. *-commutative 81.6%

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

   7. Simplified 81.6%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;A \leq -5 \cdot 10^{-310}:\\ \;\;\;\;c0 \cdot \left(\frac{\sqrt{-A}}{\sqrt{-V}} \cdot \frac{1}{\sqrt{\ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{A} \cdot \frac{c0}{\sqrt{V \cdot \ell}}\\ \end{array} \]

Alternative 3: 88.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [c0, A, V, l] = \mathsf{sort}([c0, A, V, l])\\ \\ \begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -1 \cdot 10^{+306}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-287}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{-274}:\\ \;\;\;\;c0 \cdot \frac{1}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{A} \cdot \frac{c0}{\sqrt{V \cdot \ell}}\\ \end{array} \end{array} \]

FPCore

NOTE: c0, A, V, and l should be sorted in increasing order before calling this function.
(FPCore (c0 A V l)
 :precision binary64
 (if (<= (* V l) -1e+306)
   (/ (* c0 (sqrt (/ A V))) (sqrt l))
   (if (<= (* V l) -1e-287)
     (* c0 (/ (sqrt (- A)) (sqrt (* V (- l)))))
     (if (<= (* V l) 2e-274)
       (* c0 (/ 1.0 (sqrt (/ V (/ A l)))))
       (* (sqrt A) (/ c0 (sqrt (* V l))))))))

C

assert(c0 < A && A < V && V < l);
double code(double c0, double A, double V, double l) {
	double tmp;
	if ((V * l) <= -1e+306) {
		tmp = (c0 * sqrt((A / V))) / sqrt(l);
	} else if ((V * l) <= -1e-287) {
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	} else if ((V * l) <= 2e-274) {
		tmp = c0 * (1.0 / sqrt((V / (A / l))));
	} else {
		tmp = sqrt(A) * (c0 / sqrt((V * l)));
	}
	return tmp;
}

Fortran

NOTE: c0, A, 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 ((v * l) <= (-1d+306)) then
        tmp = (c0 * sqrt((a / v))) / sqrt(l)
    else if ((v * l) <= (-1d-287)) then
        tmp = c0 * (sqrt(-a) / sqrt((v * -l)))
    else if ((v * l) <= 2d-274) then
        tmp = c0 * (1.0d0 / sqrt((v / (a / l))))
    else
        tmp = sqrt(a) * (c0 / sqrt((v * l)))
    end if
    code = tmp
end function

Java

assert c0 < A && A < V && V < l;
public static double code(double c0, double A, double V, double l) {
	double tmp;
	if ((V * l) <= -1e+306) {
		tmp = (c0 * Math.sqrt((A / V))) / Math.sqrt(l);
	} else if ((V * l) <= -1e-287) {
		tmp = c0 * (Math.sqrt(-A) / Math.sqrt((V * -l)));
	} else if ((V * l) <= 2e-274) {
		tmp = c0 * (1.0 / Math.sqrt((V / (A / l))));
	} else {
		tmp = Math.sqrt(A) * (c0 / Math.sqrt((V * l)));
	}
	return tmp;
}

Python

[c0, A, V, l] = sort([c0, A, V, l])
def code(c0, A, V, l):
	tmp = 0
	if (V * l) <= -1e+306:
		tmp = (c0 * math.sqrt((A / V))) / math.sqrt(l)
	elif (V * l) <= -1e-287:
		tmp = c0 * (math.sqrt(-A) / math.sqrt((V * -l)))
	elif (V * l) <= 2e-274:
		tmp = c0 * (1.0 / math.sqrt((V / (A / l))))
	else:
		tmp = math.sqrt(A) * (c0 / math.sqrt((V * l)))
	return tmp

Julia

c0, A, V, l = sort([c0, A, V, l])
function code(c0, A, V, l)
	tmp = 0.0
	if (Float64(V * l) <= -1e+306)
		tmp = Float64(Float64(c0 * sqrt(Float64(A / V))) / sqrt(l));
	elseif (Float64(V * l) <= -1e-287)
		tmp = Float64(c0 * Float64(sqrt(Float64(-A)) / sqrt(Float64(V * Float64(-l)))));
	elseif (Float64(V * l) <= 2e-274)
		tmp = Float64(c0 * Float64(1.0 / sqrt(Float64(V / Float64(A / l)))));
	else
		tmp = Float64(sqrt(A) * Float64(c0 / sqrt(Float64(V * l))));
	end
	return tmp
end

MATLAB

c0, A, V, l = num2cell(sort([c0, A, V, l])){:}
function tmp_2 = code(c0, A, V, l)
	tmp = 0.0;
	if ((V * l) <= -1e+306)
		tmp = (c0 * sqrt((A / V))) / sqrt(l);
	elseif ((V * l) <= -1e-287)
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	elseif ((V * l) <= 2e-274)
		tmp = c0 * (1.0 / sqrt((V / (A / l))));
	else
		tmp = sqrt(A) * (c0 / sqrt((V * l)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: c0, A, V, and l should be sorted in increasing order before calling this function.
code[c0_, A_, V_, l_] := If[LessEqual[N[(V * l), $MachinePrecision], -1e+306], N[(N[(c0 * N[Sqrt[N[(A / V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], -1e-287], N[(c0 * N[(N[Sqrt[(-A)], $MachinePrecision] / N[Sqrt[N[(V * (-l)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], 2e-274], N[(c0 * N[(1.0 / N[Sqrt[N[(V / N[(A / l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[A], $MachinePrecision] * N[(c0 / N[Sqrt[N[(V * l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 V l) < -1.00000000000000002e306

   1. Initial program 43.7%

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

      1. *-commutative 43.7%

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

      2. associate-/r* 66.5%

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

      3. sqrt-div 47.4%

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

      4. associate-*l/ 47.5%

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

   3. Applied egg-rr 47.5%

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

   if -1.00000000000000002e306 < (*.f64 V l) < -1.00000000000000002e-287

   1. Initial program 87.3%

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

      1. frac-2neg 87.3%

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

      2. sqrt-div 99.5%

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

      3. distribute-rgt-neg-in 99.5%

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

   3. Applied egg-rr 99.5%

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

      1. distribute-rgt-neg-out 99.5%

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

      2. *-commutative 99.5%

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

      3. distribute-rgt-neg-in 99.5%

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

   5. Simplified 99.5%

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

   if -1.00000000000000002e-287 < (*.f64 V l) < 1.99999999999999993e-274

   1. Initial program 48.3%

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

      1. associate-/r* 76.0%

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

      2. div-inv 75.9%

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

   3. Applied egg-rr 75.9%

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{A}{V} \cdot \frac{1}{\ell}}} \]
   4. Step-by-step derivation

      1. *-commutative 75.9%

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

      2. clear-num 75.9%

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

      3. un-div-inv 75.9%

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

   5. Applied egg-rr 75.9%

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\frac{1}{\ell}}{\frac{V}{A}}}} \]
   6. Step-by-step derivation

      1. clear-num 75.9%

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

      2. sqrt-div 75.9%

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

      3. metadata-eval 75.9%

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

      4. clear-num 75.9%

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

      5. associate-/l/ 75.9%

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

      6. associate-*l/ 48.3%

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

      7. clear-num 48.3%

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

      8. associate-/l/ 76.0%

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

      9. clear-num 76.0%

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

      10. div-inv 76.0%

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

      11. clear-num 75.9%

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

   7. Applied egg-rr 75.9%

      \[\leadsto c0 \cdot \color{blue}{\frac{1}{\sqrt{V \cdot \frac{\ell}{A}}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 48.3%

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

      2. associate-/l* 76.0%

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

   9. Simplified 76.0%

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

   if 1.99999999999999993e-274 < (*.f64 V l)

   1. Initial program 81.1%

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

      1. associate-/r* 75.0%

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

      2. div-inv 75.0%

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

   3. Applied egg-rr 75.0%

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{A}{V} \cdot \frac{1}{\ell}}} \]
   4. Step-by-step derivation

      1. un-div-inv 75.0%

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

      2. sqrt-div 44.9%

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

      3. associate-*r/ 43.9%

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

      4. sqrt-div 48.7%

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

      5. associate-*r/ 47.3%

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

      6. *-commutative 47.3%

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

      7. associate-/r* 47.4%

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

      8. sqrt-prod 85.4%

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

      9. clear-num 85.4%

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

      10. *-commutative 85.4%

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

   5. Applied egg-rr 85.4%

      \[\leadsto \color{blue}{\frac{1}{\frac{\sqrt{V \cdot \ell}}{c0 \cdot \sqrt{A}}}} \]
   6. Step-by-step derivation

      1. associate-/r/ 85.4%

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

      2. associate-*l/ 85.4%

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

      3. *-lft-identity 85.4%

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

      4. associate-*l/ 87.1%

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

      5. *-commutative 87.1%

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

   7. Simplified 87.1%

      \[\leadsto \color{blue}{\sqrt{A} \cdot \frac{c0}{\sqrt{V \cdot \ell}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -1 \cdot 10^{+306}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-287}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{-274}:\\ \;\;\;\;c0 \cdot \frac{1}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{A} \cdot \frac{c0}{\sqrt{V \cdot \ell}}\\ \end{array} \]

Alternative 4: 82.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: c0, A, 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 = sqrt(a) * (c0 / sqrt((v * l)))
    else
        tmp = c0 / (sqrt(l) / sqrt((a / v)))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if l < -1.999999999999994e-310

   1. Initial program 73.9%

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

      1. associate-/r* 72.1%

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

      2. div-inv 72.1%

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

   3. Applied egg-rr 72.1%

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{A}{V} \cdot \frac{1}{\ell}}} \]
   4. Step-by-step derivation

      1. un-div-inv 72.1%

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

      2. sqrt-div 0.0%

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

      3. associate-*r/ 0.0%

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

      4. sqrt-div 0.0%

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

      5. associate-*r/ 0.0%

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

      6. *-commutative 0.0%

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

      7. associate-/r* 0.0%

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

      8. sqrt-prod 36.0%

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

      9. clear-num 35.9%

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

      10. *-commutative 35.9%

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

   5. Applied egg-rr 35.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{\sqrt{V \cdot \ell}}{c0 \cdot \sqrt{A}}}} \]
   6. Step-by-step derivation

      1. associate-/r/ 35.9%

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

      2. associate-*l/ 36.0%

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

      3. *-lft-identity 36.0%

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

      4. associate-*l/ 37.7%

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

      5. *-commutative 37.7%

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

   7. Simplified 37.7%

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

   if -1.999999999999994e-310 < l

   1. Initial program 78.8%

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

      1. associate-/r* 80.5%

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

      2. sqrt-div 90.1%

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

      3. associate-*r/ 88.4%

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

   3. Applied egg-rr 88.4%

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

      1. associate-/l* 90.1%

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

   5. Simplified 90.1%

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

4. Final simplification 66.1%

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

Alternative 5: 79.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [c0, A, V, l] = \mathsf{sort}([c0, A, V, l])\\ \\ \begin{array}{l} t_0 := V \cdot \frac{\ell}{A}\\ t_1 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_1 \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{t_0}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+247}:\\ \;\;\;\;c0 \cdot \sqrt{t_1}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{1}{\sqrt{t_0}}\\ \end{array} \end{array} \]

FPCore

NOTE: c0, A, V, and l should be sorted in increasing order before calling this function.
(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (* V (/ l A))) (t_1 (/ A (* V l))))
   (if (<= t_1 0.0)
     (* c0 (sqrt (/ 1.0 t_0)))
     (if (<= t_1 5e+247) (* c0 (sqrt t_1)) (* c0 (/ 1.0 (sqrt t_0)))))))

C

assert(c0 < A && A < V && V < l);
double code(double c0, double A, double V, double l) {
	double t_0 = V * (l / A);
	double t_1 = A / (V * l);
	double tmp;
	if (t_1 <= 0.0) {
		tmp = c0 * sqrt((1.0 / t_0));
	} else if (t_1 <= 5e+247) {
		tmp = c0 * sqrt(t_1);
	} else {
		tmp = c0 * (1.0 / sqrt(t_0));
	}
	return tmp;
}

Fortran

NOTE: c0, A, 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) :: t_1
    real(8) :: tmp
    t_0 = v * (l / a)
    t_1 = a / (v * l)
    if (t_1 <= 0.0d0) then
        tmp = c0 * sqrt((1.0d0 / t_0))
    else if (t_1 <= 5d+247) then
        tmp = c0 * sqrt(t_1)
    else
        tmp = c0 * (1.0d0 / sqrt(t_0))
    end if
    code = tmp
end function

Java

assert c0 < A && A < V && V < l;
public static double code(double c0, double A, double V, double l) {
	double t_0 = V * (l / A);
	double t_1 = A / (V * l);
	double tmp;
	if (t_1 <= 0.0) {
		tmp = c0 * Math.sqrt((1.0 / t_0));
	} else if (t_1 <= 5e+247) {
		tmp = c0 * Math.sqrt(t_1);
	} else {
		tmp = c0 * (1.0 / Math.sqrt(t_0));
	}
	return tmp;
}

Python

[c0, A, V, l] = sort([c0, A, V, l])
def code(c0, A, V, l):
	t_0 = V * (l / A)
	t_1 = A / (V * l)
	tmp = 0
	if t_1 <= 0.0:
		tmp = c0 * math.sqrt((1.0 / t_0))
	elif t_1 <= 5e+247:
		tmp = c0 * math.sqrt(t_1)
	else:
		tmp = c0 * (1.0 / math.sqrt(t_0))
	return tmp

Julia

c0, A, V, l = sort([c0, A, V, l])
function code(c0, A, V, l)
	t_0 = Float64(V * Float64(l / A))
	t_1 = Float64(A / Float64(V * l))
	tmp = 0.0
	if (t_1 <= 0.0)
		tmp = Float64(c0 * sqrt(Float64(1.0 / t_0)));
	elseif (t_1 <= 5e+247)
		tmp = Float64(c0 * sqrt(t_1));
	else
		tmp = Float64(c0 * Float64(1.0 / sqrt(t_0)));
	end
	return tmp
end

MATLAB

c0, A, V, l = num2cell(sort([c0, A, V, l])){:}
function tmp_2 = code(c0, A, V, l)
	t_0 = V * (l / A);
	t_1 = A / (V * l);
	tmp = 0.0;
	if (t_1 <= 0.0)
		tmp = c0 * sqrt((1.0 / t_0));
	elseif (t_1 <= 5e+247)
		tmp = c0 * sqrt(t_1);
	else
		tmp = c0 * (1.0 / sqrt(t_0));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: c0, A, V, and l should be sorted in increasing order before calling this function.
code[c0_, A_, V_, l_] := Block[{t$95$0 = N[(V * N[(l / A), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(A / N[(V * l), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.0], N[(c0 * N[Sqrt[N[(1.0 / t$95$0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+247], N[(c0 * N[Sqrt[t$95$1], $MachinePrecision]), $MachinePrecision], N[(c0 * N[(1.0 / N[Sqrt[t$95$0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 38.0%

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

      1. associate-/r* 53.8%

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

      2. div-inv 53.8%

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

   3. Applied egg-rr 53.8%

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{A}{V} \cdot \frac{1}{\ell}}} \]
   4. Step-by-step derivation

      1. *-commutative 53.8%

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

      2. div-inv 53.8%

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

      3. associate-*r* 53.8%

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

      4. associate-/r/ 53.8%

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

      5. frac-times 53.8%

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

      6. metadata-eval 53.8%

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

   5. Applied egg-rr 53.8%

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

   if 0.0 < (/.f64 A (*.f64 V l)) < 5.00000000000000023e247

   1. Initial program 97.5%

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

   if 5.00000000000000023e247 < (/.f64 A (*.f64 V l))

   1. Initial program 47.4%

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

      1. associate-/r* 62.3%

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

      2. clear-num 62.3%

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

      3. sqrt-div 63.7%

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

      4. metadata-eval 63.7%

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

      5. div-inv 63.7%

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

      6. clear-num 65.4%

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

   3. Applied egg-rr 65.4%

      \[\leadsto c0 \cdot \color{blue}{\frac{1}{\sqrt{\ell \cdot \frac{V}{A}}}} \]
   4. Step-by-step derivation

      1. associate-*r/ 48.9%

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

      2. *-commutative 48.9%

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

      3. *-lft-identity 48.9%

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

      4. times-frac 60.6%

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

      5. remove-double-div 60.6%

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

      6. associate-/r* 60.6%

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

      7. *-rgt-identity 60.6%

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

      8. remove-double-div 60.6%

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

   5. Simplified 60.6%

      \[\leadsto c0 \cdot \color{blue}{\frac{1}{\sqrt{V \cdot \frac{\ell}{A}}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{V \cdot \ell} \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{V \cdot \frac{\ell}{A}}}\\ \mathbf{elif}\;\frac{A}{V \cdot \ell} \leq 5 \cdot 10^{+247}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{1}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \end{array} \]

Alternative 6: 79.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [c0, A, V, l] = \mathsf{sort}([c0, A, V, l])\\ \\ \begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{V \cdot \frac{\ell}{A}}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+247}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{1}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \end{array} \end{array} \]

FPCore

NOTE: c0, A, V, and l should be sorted in increasing order before calling this function.
(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (/ A (* V l))))
   (if (<= t_0 0.0)
     (* c0 (sqrt (/ 1.0 (* V (/ l A)))))
     (if (<= t_0 5e+247)
       (* c0 (sqrt t_0))
       (* c0 (/ 1.0 (sqrt (/ V (/ A l)))))))))

C

assert(c0 < A && A < V && V < l);
double code(double c0, double A, double V, double l) {
	double t_0 = A / (V * l);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = c0 * sqrt((1.0 / (V * (l / A))));
	} else if (t_0 <= 5e+247) {
		tmp = c0 * sqrt(t_0);
	} else {
		tmp = c0 * (1.0 / sqrt((V / (A / l))));
	}
	return tmp;
}

Fortran

NOTE: c0, A, 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 / (v * l)
    if (t_0 <= 0.0d0) then
        tmp = c0 * sqrt((1.0d0 / (v * (l / a))))
    else if (t_0 <= 5d+247) then
        tmp = c0 * sqrt(t_0)
    else
        tmp = c0 * (1.0d0 / sqrt((v / (a / l))))
    end if
    code = tmp
end function

Java

assert c0 < A && A < V && V < l;
public static double code(double c0, double A, double V, double l) {
	double t_0 = A / (V * l);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = c0 * Math.sqrt((1.0 / (V * (l / A))));
	} else if (t_0 <= 5e+247) {
		tmp = c0 * Math.sqrt(t_0);
	} else {
		tmp = c0 * (1.0 / Math.sqrt((V / (A / l))));
	}
	return tmp;
}

Python

[c0, A, V, l] = sort([c0, A, V, l])
def code(c0, A, V, l):
	t_0 = A / (V * l)
	tmp = 0
	if t_0 <= 0.0:
		tmp = c0 * math.sqrt((1.0 / (V * (l / A))))
	elif t_0 <= 5e+247:
		tmp = c0 * math.sqrt(t_0)
	else:
		tmp = c0 * (1.0 / math.sqrt((V / (A / l))))
	return tmp

Julia

c0, A, V, l = sort([c0, A, V, l])
function code(c0, A, V, l)
	t_0 = Float64(A / Float64(V * l))
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = Float64(c0 * sqrt(Float64(1.0 / Float64(V * Float64(l / A)))));
	elseif (t_0 <= 5e+247)
		tmp = Float64(c0 * sqrt(t_0));
	else
		tmp = Float64(c0 * Float64(1.0 / sqrt(Float64(V / Float64(A / l)))));
	end
	return tmp
end

MATLAB

c0, A, V, l = num2cell(sort([c0, A, V, l])){:}
function tmp_2 = code(c0, A, V, l)
	t_0 = A / (V * l);
	tmp = 0.0;
	if (t_0 <= 0.0)
		tmp = c0 * sqrt((1.0 / (V * (l / A))));
	elseif (t_0 <= 5e+247)
		tmp = c0 * sqrt(t_0);
	else
		tmp = c0 * (1.0 / sqrt((V / (A / l))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: c0, A, 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[(V * l), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.0], N[(c0 * N[Sqrt[N[(1.0 / N[(V * N[(l / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+247], N[(c0 * N[Sqrt[t$95$0], $MachinePrecision]), $MachinePrecision], N[(c0 * N[(1.0 / N[Sqrt[N[(V / N[(A / l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 38.0%

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

      1. associate-/r* 53.8%

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

      2. div-inv 53.8%

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

   3. Applied egg-rr 53.8%

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{A}{V} \cdot \frac{1}{\ell}}} \]
   4. Step-by-step derivation

      1. *-commutative 53.8%

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

      2. div-inv 53.8%

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

      3. associate-*r* 53.8%

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

      4. associate-/r/ 53.8%

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

      5. frac-times 53.8%

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

      6. metadata-eval 53.8%

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

   5. Applied egg-rr 53.8%

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

   if 0.0 < (/.f64 A (*.f64 V l)) < 5.00000000000000023e247

   1. Initial program 97.5%

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

   if 5.00000000000000023e247 < (/.f64 A (*.f64 V l))

   1. Initial program 47.4%

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

      1. associate-/r* 62.3%

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

      2. div-inv 62.3%

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

   3. Applied egg-rr 62.3%

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{A}{V} \cdot \frac{1}{\ell}}} \]
   4. Step-by-step derivation

      1. *-commutative 62.3%

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

      2. clear-num 62.3%

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

      3. un-div-inv 63.9%

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

   5. Applied egg-rr 63.9%

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\frac{1}{\ell}}{\frac{V}{A}}}} \]
   6. Step-by-step derivation

      1. clear-num 63.9%

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

      2. sqrt-div 65.4%

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

      3. metadata-eval 65.4%

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

      4. clear-num 63.9%

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

      5. associate-/l/ 63.9%

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

      6. associate-*l/ 47.4%

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

      7. clear-num 47.4%

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

      8. associate-/l/ 60.6%

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

      9. clear-num 60.6%

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

      10. div-inv 60.6%

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

      11. clear-num 60.6%

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

   7. Applied egg-rr 60.6%

      \[\leadsto c0 \cdot \color{blue}{\frac{1}{\sqrt{V \cdot \frac{\ell}{A}}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 48.9%

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

      2. associate-/l* 60.6%

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

   9. Simplified 60.6%

      \[\leadsto c0 \cdot \color{blue}{\frac{1}{\sqrt{\frac{V}{\frac{A}{\ell}}}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{V \cdot \ell} \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{V \cdot \frac{\ell}{A}}}\\ \mathbf{elif}\;\frac{A}{V \cdot \ell} \leq 5 \cdot 10^{+247}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{1}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \end{array} \]

Alternative 7: 79.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [c0, A, V, l] = \mathsf{sort}([c0, A, V, l])\\ \\ \begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 0 \lor \neg \left(t_0 \leq 2 \cdot 10^{+281}\right):\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \end{array} \end{array} \]

FPCore

NOTE: c0, A, V, and l should be sorted in increasing order before calling this function.
(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (/ A (* V l))))
   (if (or (<= t_0 0.0) (not (<= t_0 2e+281)))
     (* c0 (sqrt (/ (/ A V) l)))
     (* c0 (sqrt t_0)))))

C

assert(c0 < A && A < V && V < l);
double code(double c0, double A, double V, double l) {
	double t_0 = A / (V * l);
	double tmp;
	if ((t_0 <= 0.0) || !(t_0 <= 2e+281)) {
		tmp = c0 * sqrt(((A / V) / l));
	} else {
		tmp = c0 * sqrt(t_0);
	}
	return tmp;
}

Fortran

NOTE: c0, A, 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 / (v * l)
    if ((t_0 <= 0.0d0) .or. (.not. (t_0 <= 2d+281))) then
        tmp = c0 * sqrt(((a / v) / l))
    else
        tmp = c0 * sqrt(t_0)
    end if
    code = tmp
end function

Java

assert c0 < A && A < V && V < l;
public static double code(double c0, double A, double V, double l) {
	double t_0 = A / (V * l);
	double tmp;
	if ((t_0 <= 0.0) || !(t_0 <= 2e+281)) {
		tmp = c0 * Math.sqrt(((A / V) / l));
	} else {
		tmp = c0 * Math.sqrt(t_0);
	}
	return tmp;
}

Python

[c0, A, V, l] = sort([c0, A, V, l])
def code(c0, A, V, l):
	t_0 = A / (V * l)
	tmp = 0
	if (t_0 <= 0.0) or not (t_0 <= 2e+281):
		tmp = c0 * math.sqrt(((A / V) / l))
	else:
		tmp = c0 * math.sqrt(t_0)
	return tmp

Julia

c0, A, V, l = sort([c0, A, V, l])
function code(c0, A, V, l)
	t_0 = Float64(A / Float64(V * l))
	tmp = 0.0
	if ((t_0 <= 0.0) || !(t_0 <= 2e+281))
		tmp = Float64(c0 * sqrt(Float64(Float64(A / V) / l)));
	else
		tmp = Float64(c0 * sqrt(t_0));
	end
	return tmp
end

MATLAB

c0, A, V, l = num2cell(sort([c0, A, V, l])){:}
function tmp_2 = code(c0, A, V, l)
	t_0 = A / (V * l);
	tmp = 0.0;
	if ((t_0 <= 0.0) || ~((t_0 <= 2e+281)))
		tmp = c0 * sqrt(((A / V) / l));
	else
		tmp = c0 * sqrt(t_0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: c0, A, 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[(V * l), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 0.0], N[Not[LessEqual[t$95$0, 2e+281]], $MachinePrecision]], N[(c0 * N[Sqrt[N[(N[(A / V), $MachinePrecision] / l), $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 2.0000000000000001e281 < (/.f64 A (*.f64 V l))

   1. Initial program 40.5%

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

      1. associate-/r* 57.4%

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

   3. Simplified 57.4%

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

   if 0.0 < (/.f64 A (*.f64 V l)) < 2.0000000000000001e281

   1. Initial program 97.5%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{V \cdot \ell} \leq 0 \lor \neg \left(\frac{A}{V \cdot \ell} \leq 2 \cdot 10^{+281}\right):\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \end{array} \]

Alternative 8: 79.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [c0, A, V, l] = \mathsf{sort}([c0, A, V, l])\\ \\ \begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+247}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array} \end{array} \]

FPCore

NOTE: c0, A, V, and l should be sorted in increasing order before calling this function.
(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (/ A (* V l))))
   (if (<= t_0 0.0)
     (* c0 (sqrt (/ (/ A V) l)))
     (if (<= t_0 5e+247) (* c0 (sqrt t_0)) (* c0 (sqrt (/ (/ A l) V)))))))

C

assert(c0 < A && A < V && V < l);
double code(double c0, double A, double V, double l) {
	double t_0 = A / (V * l);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = c0 * sqrt(((A / V) / l));
	} else if (t_0 <= 5e+247) {
		tmp = c0 * sqrt(t_0);
	} else {
		tmp = c0 * sqrt(((A / l) / V));
	}
	return tmp;
}

Fortran

NOTE: c0, A, 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 / (v * l)
    if (t_0 <= 0.0d0) then
        tmp = c0 * sqrt(((a / v) / l))
    else if (t_0 <= 5d+247) then
        tmp = c0 * sqrt(t_0)
    else
        tmp = c0 * sqrt(((a / l) / v))
    end if
    code = tmp
end function

Java

assert c0 < A && A < V && V < l;
public static double code(double c0, double A, double V, double l) {
	double t_0 = A / (V * l);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = c0 * Math.sqrt(((A / V) / l));
	} else if (t_0 <= 5e+247) {
		tmp = c0 * Math.sqrt(t_0);
	} else {
		tmp = c0 * Math.sqrt(((A / l) / V));
	}
	return tmp;
}

Python

[c0, A, V, l] = sort([c0, A, V, l])
def code(c0, A, V, l):
	t_0 = A / (V * l)
	tmp = 0
	if t_0 <= 0.0:
		tmp = c0 * math.sqrt(((A / V) / l))
	elif t_0 <= 5e+247:
		tmp = c0 * math.sqrt(t_0)
	else:
		tmp = c0 * math.sqrt(((A / l) / V))
	return tmp

Julia

c0, A, V, l = sort([c0, A, V, l])
function code(c0, A, V, l)
	t_0 = Float64(A / Float64(V * l))
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = Float64(c0 * sqrt(Float64(Float64(A / V) / l)));
	elseif (t_0 <= 5e+247)
		tmp = Float64(c0 * sqrt(t_0));
	else
		tmp = Float64(c0 * sqrt(Float64(Float64(A / l) / V)));
	end
	return tmp
end

MATLAB

c0, A, V, l = num2cell(sort([c0, A, V, l])){:}
function tmp_2 = code(c0, A, V, l)
	t_0 = A / (V * l);
	tmp = 0.0;
	if (t_0 <= 0.0)
		tmp = c0 * sqrt(((A / V) / l));
	elseif (t_0 <= 5e+247)
		tmp = c0 * sqrt(t_0);
	else
		tmp = c0 * sqrt(((A / l) / V));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: c0, A, 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[(V * l), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.0], N[(c0 * N[Sqrt[N[(N[(A / V), $MachinePrecision] / l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+247], N[(c0 * N[Sqrt[t$95$0], $MachinePrecision]), $MachinePrecision], N[(c0 * N[Sqrt[N[(N[(A / l), $MachinePrecision] / V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 38.0%

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

      1. associate-/r* 53.8%

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

   3. Simplified 53.8%

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

   if 0.0 < (/.f64 A (*.f64 V l)) < 5.00000000000000023e247

   1. Initial program 97.5%

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

   if 5.00000000000000023e247 < (/.f64 A (*.f64 V l))

   1. Initial program 47.4%

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

      1. associate-/r* 62.3%

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

      2. div-inv 62.3%

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

   3. Applied egg-rr 62.3%

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{A}{V} \cdot \frac{1}{\ell}}} \]
   4. Step-by-step derivation

      1. associate-*l/ 60.6%

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

      2. div-inv 60.6%

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

   5. Applied egg-rr 60.6%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{V \cdot \ell} \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;\frac{A}{V \cdot \ell} \leq 5 \cdot 10^{+247}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array} \]

Alternative 9: 79.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [c0, A, V, l] = \mathsf{sort}([c0, A, V, l])\\ \\ \begin{array}{l} t_0 := \frac{A}{V \cdot \ell}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{V \cdot \frac{\ell}{A}}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+247}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array} \end{array} \]

FPCore

NOTE: c0, A, V, and l should be sorted in increasing order before calling this function.
(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (/ A (* V l))))
   (if (<= t_0 0.0)
     (* c0 (sqrt (/ 1.0 (* V (/ l A)))))
     (if (<= t_0 5e+247) (* c0 (sqrt t_0)) (* c0 (sqrt (/ (/ A l) V)))))))

C

assert(c0 < A && A < V && V < l);
double code(double c0, double A, double V, double l) {
	double t_0 = A / (V * l);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = c0 * sqrt((1.0 / (V * (l / A))));
	} else if (t_0 <= 5e+247) {
		tmp = c0 * sqrt(t_0);
	} else {
		tmp = c0 * sqrt(((A / l) / V));
	}
	return tmp;
}

Fortran

NOTE: c0, A, 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 / (v * l)
    if (t_0 <= 0.0d0) then
        tmp = c0 * sqrt((1.0d0 / (v * (l / a))))
    else if (t_0 <= 5d+247) then
        tmp = c0 * sqrt(t_0)
    else
        tmp = c0 * sqrt(((a / l) / v))
    end if
    code = tmp
end function

Java

assert c0 < A && A < V && V < l;
public static double code(double c0, double A, double V, double l) {
	double t_0 = A / (V * l);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = c0 * Math.sqrt((1.0 / (V * (l / A))));
	} else if (t_0 <= 5e+247) {
		tmp = c0 * Math.sqrt(t_0);
	} else {
		tmp = c0 * Math.sqrt(((A / l) / V));
	}
	return tmp;
}

Python

[c0, A, V, l] = sort([c0, A, V, l])
def code(c0, A, V, l):
	t_0 = A / (V * l)
	tmp = 0
	if t_0 <= 0.0:
		tmp = c0 * math.sqrt((1.0 / (V * (l / A))))
	elif t_0 <= 5e+247:
		tmp = c0 * math.sqrt(t_0)
	else:
		tmp = c0 * math.sqrt(((A / l) / V))
	return tmp

Julia

c0, A, V, l = sort([c0, A, V, l])
function code(c0, A, V, l)
	t_0 = Float64(A / Float64(V * l))
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = Float64(c0 * sqrt(Float64(1.0 / Float64(V * Float64(l / A)))));
	elseif (t_0 <= 5e+247)
		tmp = Float64(c0 * sqrt(t_0));
	else
		tmp = Float64(c0 * sqrt(Float64(Float64(A / l) / V)));
	end
	return tmp
end

MATLAB

c0, A, V, l = num2cell(sort([c0, A, V, l])){:}
function tmp_2 = code(c0, A, V, l)
	t_0 = A / (V * l);
	tmp = 0.0;
	if (t_0 <= 0.0)
		tmp = c0 * sqrt((1.0 / (V * (l / A))));
	elseif (t_0 <= 5e+247)
		tmp = c0 * sqrt(t_0);
	else
		tmp = c0 * sqrt(((A / l) / V));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: c0, A, 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[(V * l), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.0], N[(c0 * N[Sqrt[N[(1.0 / N[(V * N[(l / A), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+247], N[(c0 * N[Sqrt[t$95$0], $MachinePrecision]), $MachinePrecision], N[(c0 * N[Sqrt[N[(N[(A / l), $MachinePrecision] / V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 38.0%

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

      1. associate-/r* 53.8%

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

      2. div-inv 53.8%

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

   3. Applied egg-rr 53.8%

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{A}{V} \cdot \frac{1}{\ell}}} \]
   4. Step-by-step derivation

      1. *-commutative 53.8%

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

      2. div-inv 53.8%

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

      3. associate-*r* 53.8%

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

      4. associate-/r/ 53.8%

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

      5. frac-times 53.8%

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

      6. metadata-eval 53.8%

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

   5. Applied egg-rr 53.8%

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

   if 0.0 < (/.f64 A (*.f64 V l)) < 5.00000000000000023e247

   1. Initial program 97.5%

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

   if 5.00000000000000023e247 < (/.f64 A (*.f64 V l))

   1. Initial program 47.4%

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

      1. associate-/r* 62.3%

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

      2. div-inv 62.3%

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

   3. Applied egg-rr 62.3%

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{A}{V} \cdot \frac{1}{\ell}}} \]
   4. Step-by-step derivation

      1. associate-*l/ 60.6%

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

      2. div-inv 60.6%

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

   5. Applied egg-rr 60.6%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{V \cdot \ell} \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{V \cdot \frac{\ell}{A}}}\\ \mathbf{elif}\;\frac{A}{V \cdot \ell} \leq 5 \cdot 10^{+247}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array} \]

Alternative 10: 73.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: c0, A, 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 / (v * l)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: c0, A, 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[(V * l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.6%

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

2. Final simplification 76.6%

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

Reproduce

herbie shell --seed 2023333 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))