Average Error: 18.8 → 7.7
Time: 6.6s
Precision: binary64
\[ \begin{array}{c}[V, l] = \mathsf{sort}([V, l])\\ \end{array} \]
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -1.417736747975075 \cdot 10^{-309}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;c0 \cdot {\left(e^{0.25 \cdot \left(\log \left(\frac{-A}{\ell}\right) + \log \left(\frac{-1}{V}\right)\right)}\right)}^{2}\\ \mathbf{elif}\;V \cdot \ell \leq 1.3567910861171497 \cdot 10^{+299}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left({\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.25}\right)}^{2}\\ \end{array} \]
(FPCore (c0 A V l) :precision binary64 (* c0 (sqrt (/ A (* V l)))))
↓
(FPCore (c0 A V l)
 :precision binary64
 (if (<= (* V l) -1.417736747975075e-309)
   (* c0 (/ (sqrt (- A)) (sqrt (* V (- l)))))
   (if (<= (* V l) 0.0)
     (* c0 (pow (exp (* 0.25 (+ (log (/ (- A) l)) (log (/ -1.0 V))))) 2.0))
     (if (<= (* V l) 1.3567910861171497e+299)
       (* c0 (/ (sqrt A) (sqrt (* V l))))
       (* c0 (pow (pow (/ (/ A V) l) 0.25) 2.0))))))
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 tmp;
	if ((V * l) <= -1.417736747975075e-309) {
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	} else if ((V * l) <= 0.0) {
		tmp = c0 * pow(exp((0.25 * (log((-A / l)) + log((-1.0 / V))))), 2.0);
	} else if ((V * l) <= 1.3567910861171497e+299) {
		tmp = c0 * (sqrt(A) / sqrt((V * l)));
	} else {
		tmp = c0 * pow(pow(((A / V) / l), 0.25), 2.0);
	}
	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) :: tmp
    if ((v * l) <= (-1.417736747975075d-309)) then
        tmp = c0 * (sqrt(-a) / sqrt((v * -l)))
    else if ((v * l) <= 0.0d0) then
        tmp = c0 * (exp((0.25d0 * (log((-a / l)) + log(((-1.0d0) / v))))) ** 2.0d0)
    else if ((v * l) <= 1.3567910861171497d+299) then
        tmp = c0 * (sqrt(a) / sqrt((v * l)))
    else
        tmp = c0 * ((((a / v) / l) ** 0.25d0) ** 2.0d0)
    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 tmp;
	if ((V * l) <= -1.417736747975075e-309) {
		tmp = c0 * (Math.sqrt(-A) / Math.sqrt((V * -l)));
	} else if ((V * l) <= 0.0) {
		tmp = c0 * Math.pow(Math.exp((0.25 * (Math.log((-A / l)) + Math.log((-1.0 / V))))), 2.0);
	} else if ((V * l) <= 1.3567910861171497e+299) {
		tmp = c0 * (Math.sqrt(A) / Math.sqrt((V * l)));
	} else {
		tmp = c0 * Math.pow(Math.pow(((A / V) / l), 0.25), 2.0);
	}
	return tmp;
}

def code(c0, A, V, l):
	return c0 * math.sqrt((A / (V * l)))
↓
def code(c0, A, V, l):
	tmp = 0
	if (V * l) <= -1.417736747975075e-309:
		tmp = c0 * (math.sqrt(-A) / math.sqrt((V * -l)))
	elif (V * l) <= 0.0:
		tmp = c0 * math.pow(math.exp((0.25 * (math.log((-A / l)) + math.log((-1.0 / V))))), 2.0)
	elif (V * l) <= 1.3567910861171497e+299:
		tmp = c0 * (math.sqrt(A) / math.sqrt((V * l)))
	else:
		tmp = c0 * math.pow(math.pow(((A / V) / l), 0.25), 2.0)
	return tmp

function code(c0, A, V, l)
	return Float64(c0 * sqrt(Float64(A / Float64(V * l))))
end
↓
function code(c0, A, V, l)
	tmp = 0.0
	if (Float64(V * l) <= -1.417736747975075e-309)
		tmp = Float64(c0 * Float64(sqrt(Float64(-A)) / sqrt(Float64(V * Float64(-l)))));
	elseif (Float64(V * l) <= 0.0)
		tmp = Float64(c0 * (exp(Float64(0.25 * Float64(log(Float64(Float64(-A) / l)) + log(Float64(-1.0 / V))))) ^ 2.0));
	elseif (Float64(V * l) <= 1.3567910861171497e+299)
		tmp = Float64(c0 * Float64(sqrt(A) / sqrt(Float64(V * l))));
	else
		tmp = Float64(c0 * ((Float64(Float64(A / V) / l) ^ 0.25) ^ 2.0));
	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)
	tmp = 0.0;
	if ((V * l) <= -1.417736747975075e-309)
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	elseif ((V * l) <= 0.0)
		tmp = c0 * (exp((0.25 * (log((-A / l)) + log((-1.0 / V))))) ^ 2.0);
	elseif ((V * l) <= 1.3567910861171497e+299)
		tmp = c0 * (sqrt(A) / sqrt((V * l)));
	else
		tmp = c0 * ((((A / V) / l) ^ 0.25) ^ 2.0);
	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_] := If[LessEqual[N[(V * l), $MachinePrecision], -1.417736747975075e-309], 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[Power[N[Exp[N[(0.25 * N[(N[Log[N[((-A) / l), $MachinePrecision]], $MachinePrecision] + N[Log[N[(-1.0 / V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], 1.3567910861171497e+299], N[(c0 * N[(N[Sqrt[A], $MachinePrecision] / N[Sqrt[N[(V * l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 * N[Power[N[Power[N[(N[(A / V), $MachinePrecision] / l), $MachinePrecision], 0.25], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]]]]

c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \leq -1.417736747975075 \cdot 10^{-309}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\

\mathbf{elif}\;V \cdot \ell \leq 0:\\
\;\;\;\;c0 \cdot {\left(e^{0.25 \cdot \left(\log \left(\frac{-A}{\ell}\right) + \log \left(\frac{-1}{V}\right)\right)}\right)}^{2}\\

\mathbf{elif}\;V \cdot \ell \leq 1.3567910861171497 \cdot 10^{+299}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\

\mathbf{else}:\\
\;\;\;\;c0 \cdot {\left({\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.25}\right)}^{2}\\


\end{array}

Error

Bits error versus c0

Bits error versus A

Bits error versus V

Bits error versus l

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) < -1.417736747975075e-309

    1. Initial program 14.4

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

    2. Applied egg-rr6.8

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

    if -1.417736747975075e-309 < (*.f64 V l) < -0.0

    1. Initial program 63.1

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

    2. Applied egg-rr37.2

      \[\leadsto c0 \cdot \color{blue}{{\left({\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.25}\right)}^{2}} \]

    3. Taylor expanded in V around -inf 31.5

      \[\leadsto c0 \cdot {\color{blue}{\left(e^{0.25 \cdot \left(\log \left(-1 \cdot \frac{A}{\ell}\right) + \log \left(\frac{-1}{V}\right)\right)}\right)}}^{2} \]

    if -0.0 < (*.f64 V l) < 1.3567910861171497e299

    1. Initial program 10.3

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

    2. Applied egg-rr0.7

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

    if 1.3567910861171497e299 < (*.f64 V l)

    1. Initial program 39.3

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

    2. Applied egg-rr21.5

      \[\leadsto c0 \cdot \color{blue}{{\left({\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.25}\right)}^{2}} \]
  3. Recombined 4 regimes into one program.

  4. Final simplification7.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -1.417736747975075 \cdot 10^{-309}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;c0 \cdot {\left(e^{0.25 \cdot \left(\log \left(\frac{-A}{\ell}\right) + \log \left(\frac{-1}{V}\right)\right)}\right)}^{2}\\ \mathbf{elif}\;V \cdot \ell \leq 1.3567910861171497 \cdot 10^{+299}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left({\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.25}\right)}^{2}\\ \end{array} \]

Reproduce

herbie shell --seed 2022153 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))