Average Error: 19.7 → 7.2
Time: 4.9s
Precision: binary64
\[ \begin{array}{c}[V, l] = \mathsf{sort}([V, l])\\ \end{array} \]
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
↓
\[\begin{array}{l} t_0 := \sqrt{\frac{A}{V}}\\ \mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{+253}:\\ \;\;\;\;c0 \cdot \left({\ell}^{-0.5} \cdot t_0\right)\\ \mathbf{elif}\;V \cdot \ell \leq -5 \cdot 10^{-295}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;c0 \cdot \frac{t_0}{\sqrt{\ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \end{array} \]
(FPCore (c0 A V l) :precision binary64 (* c0 (sqrt (/ A (* V l)))))
↓
(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (sqrt (/ A V))))
   (if (<= (* V l) -2e+253)
     (* c0 (* (pow l -0.5) t_0))
     (if (<= (* V l) -5e-295)
       (* c0 (/ (sqrt (- A)) (sqrt (* V (- l)))))
       (if (<= (* V l) 0.0)
         (* c0 (/ t_0 (sqrt l)))
         (* c0 (/ (sqrt A) (sqrt (* V l)))))))))
double code(double c0, double A, double V, double l) {
	return c0 * sqrt((A / (V * l)));
}
↓
double code(double c0, double A, double V, double l) {
	double t_0 = sqrt((A / V));
	double tmp;
	if ((V * l) <= -2e+253) {
		tmp = c0 * (pow(l, -0.5) * t_0);
	} else if ((V * l) <= -5e-295) {
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	} else if ((V * l) <= 0.0) {
		tmp = c0 * (t_0 / sqrt(l));
	} else {
		tmp = c0 * (sqrt(A) / sqrt((V * l)));
	}
	return tmp;
}

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
↓
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 = sqrt((a / v))
    if ((v * l) <= (-2d+253)) then
        tmp = c0 * ((l ** (-0.5d0)) * t_0)
    else if ((v * l) <= (-5d-295)) then
        tmp = c0 * (sqrt(-a) / sqrt((v * -l)))
    else if ((v * l) <= 0.0d0) then
        tmp = c0 * (t_0 / sqrt(l))
    else
        tmp = c0 * (sqrt(a) / sqrt((v * l)))
    end if
    code = tmp
end function

public static double code(double c0, double A, double V, double l) {
	return c0 * Math.sqrt((A / (V * l)));
}
↓
public static double code(double c0, double A, double V, double l) {
	double t_0 = Math.sqrt((A / V));
	double tmp;
	if ((V * l) <= -2e+253) {
		tmp = c0 * (Math.pow(l, -0.5) * t_0);
	} else if ((V * l) <= -5e-295) {
		tmp = c0 * (Math.sqrt(-A) / Math.sqrt((V * -l)));
	} else if ((V * l) <= 0.0) {
		tmp = c0 * (t_0 / Math.sqrt(l));
	} else {
		tmp = c0 * (Math.sqrt(A) / Math.sqrt((V * l)));
	}
	return tmp;
}

def code(c0, A, V, l):
	return c0 * math.sqrt((A / (V * l)))
↓
def code(c0, A, V, l):
	t_0 = math.sqrt((A / V))
	tmp = 0
	if (V * l) <= -2e+253:
		tmp = c0 * (math.pow(l, -0.5) * t_0)
	elif (V * l) <= -5e-295:
		tmp = c0 * (math.sqrt(-A) / math.sqrt((V * -l)))
	elif (V * l) <= 0.0:
		tmp = c0 * (t_0 / math.sqrt(l))
	else:
		tmp = c0 * (math.sqrt(A) / math.sqrt((V * l)))
	return tmp

function code(c0, A, V, l)
	return Float64(c0 * sqrt(Float64(A / Float64(V * l))))
end
↓
function code(c0, A, V, l)
	t_0 = sqrt(Float64(A / V))
	tmp = 0.0
	if (Float64(V * l) <= -2e+253)
		tmp = Float64(c0 * Float64((l ^ -0.5) * t_0));
	elseif (Float64(V * l) <= -5e-295)
		tmp = Float64(c0 * Float64(sqrt(Float64(-A)) / sqrt(Float64(V * Float64(-l)))));
	elseif (Float64(V * l) <= 0.0)
		tmp = Float64(c0 * Float64(t_0 / sqrt(l)));
	else
		tmp = Float64(c0 * Float64(sqrt(A) / sqrt(Float64(V * l))));
	end
	return tmp
end

function tmp = code(c0, A, V, l)
	tmp = c0 * sqrt((A / (V * l)));
end
↓
function tmp_2 = code(c0, A, V, l)
	t_0 = sqrt((A / V));
	tmp = 0.0;
	if ((V * l) <= -2e+253)
		tmp = c0 * ((l ^ -0.5) * t_0);
	elseif ((V * l) <= -5e-295)
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	elseif ((V * l) <= 0.0)
		tmp = c0 * (t_0 / sqrt(l));
	else
		tmp = c0 * (sqrt(A) / sqrt((V * l)));
	end
	tmp_2 = tmp;
end

code[c0_, A_, V_, l_] := N[(c0 * N[Sqrt[N[(A / N[(V * l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
↓
code[c0_, A_, V_, l_] := Block[{t$95$0 = N[Sqrt[N[(A / V), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(V * l), $MachinePrecision], -2e+253], N[(c0 * N[(N[Power[l, -0.5], $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], -5e-295], N[(c0 * N[(N[Sqrt[(-A)], $MachinePrecision] / N[Sqrt[N[(V * (-l)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], 0.0], N[(c0 * N[(t$95$0 / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 * N[(N[Sqrt[A], $MachinePrecision] / N[Sqrt[N[(V * l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
t_0 := \sqrt{\frac{A}{V}}\\
\mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{+253}:\\
\;\;\;\;c0 \cdot \left({\ell}^{-0.5} \cdot t_0\right)\\

\mathbf{elif}\;V \cdot \ell \leq -5 \cdot 10^{-295}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\

\mathbf{elif}\;V \cdot \ell \leq 0:\\
\;\;\;\;c0 \cdot \frac{t_0}{\sqrt{\ell}}\\

\mathbf{else}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\


\end{array}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 4 regimes

  2. if (*.f64 V l) < -1.9999999999999999e253

    1. Initial program 36.9

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

    2. Applied egg-rr23.7

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

    3. Applied egg-rr10.5

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

    if -1.9999999999999999e253 < (*.f64 V l) < -5.00000000000000008e-295

    1. Initial program 9.8

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

    2. Applied egg-rr0.4

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

    if -5.00000000000000008e-295 < (*.f64 V l) < -0.0

    1. Initial program 60.2

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

    2. Applied egg-rr28.4

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

    if -0.0 < (*.f64 V l)

    1. Initial program 15.3

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

    2. Applied egg-rr7.3

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

  4. Final simplification7.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -2 \cdot 10^{+253}:\\ \;\;\;\;c0 \cdot \left({\ell}^{-0.5} \cdot \sqrt{\frac{A}{V}}\right)\\ \mathbf{elif}\;V \cdot \ell \leq -5 \cdot 10^{-295}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022210 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))