Average Error: 19.6 → 5.5
Time: 5.4s
Precision: binary64
\[ \begin{array}{c}[V, l] = \mathsf{sort}([V, l])\\ \end{array} \]
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
↓
\[\begin{array}{l} t_0 := c0 \cdot \frac{\sqrt{\frac{-1}{V}}}{\sqrt{\frac{-\ell}{A}}}\\ \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;t_0\\ \mathbf{elif}\;V \cdot \ell \leq -2 \cdot 10^{-292}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{\ell \cdot \left(-V\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;t_0\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+288}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left({1}^{0.5} \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\right)\\ \end{array} \]
(FPCore (c0 A V l) :precision binary64 (* c0 (sqrt (/ A (* V l)))))
↓
(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (* c0 (/ (sqrt (/ -1.0 V)) (sqrt (/ (- l) A))))))
   (if (<= (* V l) (- INFINITY))
     t_0
     (if (<= (* V l) -2e-292)
       (* c0 (/ (sqrt (- A)) (sqrt (* l (- V)))))
       (if (<= (* V l) 0.0)
         t_0
         (if (<= (* V l) 2e+288)
           (* c0 (/ (sqrt A) (sqrt (* V l))))
           (* c0 (* (pow 1.0 0.5) (sqrt (/ (/ A l) V))))))))))
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 = c0 * (sqrt((-1.0 / V)) / sqrt((-l / A)));
	double tmp;
	if ((V * l) <= -((double) INFINITY)) {
		tmp = t_0;
	} else if ((V * l) <= -2e-292) {
		tmp = c0 * (sqrt(-A) / sqrt((l * -V)));
	} else if ((V * l) <= 0.0) {
		tmp = t_0;
	} else if ((V * l) <= 2e+288) {
		tmp = c0 * (sqrt(A) / sqrt((V * l)));
	} else {
		tmp = c0 * (pow(1.0, 0.5) * sqrt(((A / l) / V)));
	}
	return tmp;
}

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 = c0 * (Math.sqrt((-1.0 / V)) / Math.sqrt((-l / A)));
	double tmp;
	if ((V * l) <= -Double.POSITIVE_INFINITY) {
		tmp = t_0;
	} else if ((V * l) <= -2e-292) {
		tmp = c0 * (Math.sqrt(-A) / Math.sqrt((l * -V)));
	} else if ((V * l) <= 0.0) {
		tmp = t_0;
	} else if ((V * l) <= 2e+288) {
		tmp = c0 * (Math.sqrt(A) / Math.sqrt((V * l)));
	} else {
		tmp = c0 * (Math.pow(1.0, 0.5) * Math.sqrt(((A / l) / V)));
	}
	return tmp;
}

def code(c0, A, V, l):
	return c0 * math.sqrt((A / (V * l)))
↓
def code(c0, A, V, l):
	t_0 = c0 * (math.sqrt((-1.0 / V)) / math.sqrt((-l / A)))
	tmp = 0
	if (V * l) <= -math.inf:
		tmp = t_0
	elif (V * l) <= -2e-292:
		tmp = c0 * (math.sqrt(-A) / math.sqrt((l * -V)))
	elif (V * l) <= 0.0:
		tmp = t_0
	elif (V * l) <= 2e+288:
		tmp = c0 * (math.sqrt(A) / math.sqrt((V * l)))
	else:
		tmp = c0 * (math.pow(1.0, 0.5) * math.sqrt(((A / l) / V)))
	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 = Float64(c0 * Float64(sqrt(Float64(-1.0 / V)) / sqrt(Float64(Float64(-l) / A))))
	tmp = 0.0
	if (Float64(V * l) <= Float64(-Inf))
		tmp = t_0;
	elseif (Float64(V * l) <= -2e-292)
		tmp = Float64(c0 * Float64(sqrt(Float64(-A)) / sqrt(Float64(l * Float64(-V)))));
	elseif (Float64(V * l) <= 0.0)
		tmp = t_0;
	elseif (Float64(V * l) <= 2e+288)
		tmp = Float64(c0 * Float64(sqrt(A) / sqrt(Float64(V * l))));
	else
		tmp = Float64(c0 * Float64((1.0 ^ 0.5) * sqrt(Float64(Float64(A / l) / V))));
	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 = c0 * (sqrt((-1.0 / V)) / sqrt((-l / A)));
	tmp = 0.0;
	if ((V * l) <= -Inf)
		tmp = t_0;
	elseif ((V * l) <= -2e-292)
		tmp = c0 * (sqrt(-A) / sqrt((l * -V)));
	elseif ((V * l) <= 0.0)
		tmp = t_0;
	elseif ((V * l) <= 2e+288)
		tmp = c0 * (sqrt(A) / sqrt((V * l)));
	else
		tmp = c0 * ((1.0 ^ 0.5) * sqrt(((A / l) / V)));
	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[(c0 * N[(N[Sqrt[N[(-1.0 / V), $MachinePrecision]], $MachinePrecision] / N[Sqrt[N[((-l) / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(V * l), $MachinePrecision], (-Infinity)], t$95$0, If[LessEqual[N[(V * l), $MachinePrecision], -2e-292], N[(c0 * N[(N[Sqrt[(-A)], $MachinePrecision] / N[Sqrt[N[(l * (-V)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], 0.0], t$95$0, If[LessEqual[N[(V * l), $MachinePrecision], 2e+288], N[(c0 * N[(N[Sqrt[A], $MachinePrecision] / N[Sqrt[N[(V * l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 * N[(N[Power[1.0, 0.5], $MachinePrecision] * N[Sqrt[N[(N[(A / l), $MachinePrecision] / V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
t_0 := c0 \cdot \frac{\sqrt{\frac{-1}{V}}}{\sqrt{\frac{-\ell}{A}}}\\
\mathbf{if}\;V \cdot \ell \leq -\infty:\\
\;\;\;\;t_0\\

\mathbf{elif}\;V \cdot \ell \leq -2 \cdot 10^{-292}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{\ell \cdot \left(-V\right)}}\\

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

\mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+288}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\

\mathbf{else}:\\
\;\;\;\;c0 \cdot \left({1}^{0.5} \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\right)\\


\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) < -inf.0 or -2.0000000000000001e-292 < (*.f64 V l) < -0.0

    1. Initial program 52.7

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

    2. Applied egg-rr30.6

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

    3. Applied egg-rr30.6

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

    4. Applied egg-rr20.1

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

    if -inf.0 < (*.f64 V l) < -2.0000000000000001e-292

    1. Initial program 10.0

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

    2. Applied egg-rr0.4

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

    if -0.0 < (*.f64 V l) < 2e288

    1. Initial program 10.5

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

    2. Applied egg-rr15.5

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{{\left(\sqrt[3]{A}\right)}^{2}}{\ell} \cdot \frac{\sqrt[3]{A}}{V}}} \]

    3. Applied egg-rr0.7

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

    if 2e288 < (*.f64 V l)

    1. Initial program 38.0

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

    2. Applied egg-rr21.9

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{{\left(\sqrt[3]{A}\right)}^{2}}{\ell} \cdot \frac{\sqrt[3]{A}}{V}}} \]

    3. Applied egg-rr21.7

      \[\leadsto c0 \cdot \color{blue}{\left({1}^{0.5} \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\right)} \]
  3. Recombined 4 regimes into one program.

  4. Final simplification5.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{-1}{V}}}{\sqrt{\frac{-\ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq -2 \cdot 10^{-292}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{\ell \cdot \left(-V\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{-1}{V}}}{\sqrt{\frac{-\ell}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+288}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left({1}^{0.5} \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\right)\\ \end{array} \]

Reproduce

herbie shell --seed 2022169 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))