Average Error: 18.7 → 6.2
Time: 4.6s
Precision: binary64
\[ \begin{array}{c}[V, l] = \mathsf{sort}([V, l])\\ \end{array} \]
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{\ell}{\frac{A}{V}}}}\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-275}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{-317}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+303}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \end{array} \]
(FPCore (c0 A V l) :precision binary64 (* c0 (sqrt (/ A (* V l)))))
↓
(FPCore (c0 A V l)
 :precision binary64
 (if (<= (* V l) (- INFINITY))
   (/ c0 (sqrt (/ l (/ A V))))
   (if (<= (* V l) -1e-275)
     (* c0 (/ (sqrt (- A)) (sqrt (* V (- l)))))
     (if (<= (* V l) 1e-317)
       (* c0 (/ (sqrt (/ A V)) (sqrt l)))
       (if (<= (* V l) 2e+303)
         (* c0 (/ (sqrt A) (sqrt (* V l))))
         (/ c0 (sqrt (* V (/ l A)))))))))
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) <= -((double) INFINITY)) {
		tmp = c0 / sqrt((l / (A / V)));
	} else if ((V * l) <= -1e-275) {
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	} else if ((V * l) <= 1e-317) {
		tmp = c0 * (sqrt((A / V)) / sqrt(l));
	} else if ((V * l) <= 2e+303) {
		tmp = c0 * (sqrt(A) / sqrt((V * l)));
	} else {
		tmp = c0 / sqrt((V * (l / A)));
	}
	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 tmp;
	if ((V * l) <= -Double.POSITIVE_INFINITY) {
		tmp = c0 / Math.sqrt((l / (A / V)));
	} else if ((V * l) <= -1e-275) {
		tmp = c0 * (Math.sqrt(-A) / Math.sqrt((V * -l)));
	} else if ((V * l) <= 1e-317) {
		tmp = c0 * (Math.sqrt((A / V)) / Math.sqrt(l));
	} else if ((V * l) <= 2e+303) {
		tmp = c0 * (Math.sqrt(A) / Math.sqrt((V * l)));
	} else {
		tmp = c0 / Math.sqrt((V * (l / A)));
	}
	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) <= -math.inf:
		tmp = c0 / math.sqrt((l / (A / V)))
	elif (V * l) <= -1e-275:
		tmp = c0 * (math.sqrt(-A) / math.sqrt((V * -l)))
	elif (V * l) <= 1e-317:
		tmp = c0 * (math.sqrt((A / V)) / math.sqrt(l))
	elif (V * l) <= 2e+303:
		tmp = c0 * (math.sqrt(A) / math.sqrt((V * l)))
	else:
		tmp = c0 / math.sqrt((V * (l / A)))
	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) <= Float64(-Inf))
		tmp = Float64(c0 / sqrt(Float64(l / Float64(A / V))));
	elseif (Float64(V * l) <= -1e-275)
		tmp = Float64(c0 * Float64(sqrt(Float64(-A)) / sqrt(Float64(V * Float64(-l)))));
	elseif (Float64(V * l) <= 1e-317)
		tmp = Float64(c0 * Float64(sqrt(Float64(A / V)) / sqrt(l)));
	elseif (Float64(V * l) <= 2e+303)
		tmp = Float64(c0 * Float64(sqrt(A) / sqrt(Float64(V * l))));
	else
		tmp = Float64(c0 / sqrt(Float64(V * Float64(l / A))));
	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) <= -Inf)
		tmp = c0 / sqrt((l / (A / V)));
	elseif ((V * l) <= -1e-275)
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	elseif ((V * l) <= 1e-317)
		tmp = c0 * (sqrt((A / V)) / sqrt(l));
	elseif ((V * l) <= 2e+303)
		tmp = c0 * (sqrt(A) / sqrt((V * l)));
	else
		tmp = c0 / sqrt((V * (l / A)));
	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], (-Infinity)], N[(c0 / N[Sqrt[N[(l / N[(A / V), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], -1e-275], N[(c0 * N[(N[Sqrt[(-A)], $MachinePrecision] / N[Sqrt[N[(V * (-l)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], 1e-317], N[(c0 * N[(N[Sqrt[N[(A / V), $MachinePrecision]], $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], 2e+303], N[(c0 * N[(N[Sqrt[A], $MachinePrecision] / N[Sqrt[N[(V * l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 / N[Sqrt[N[(V * N[(l / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

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

\mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-275}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\

\mathbf{elif}\;V \cdot \ell \leq 10^{-317}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\

\mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+303}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\

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


\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 5 regimes

  2. if (*.f64 V l) < -inf.0

    1. Initial program 40.5

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

    2. Applied egg-rr23.3

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

    3. Applied egg-rr23.8

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

    4. Applied egg-rr23.8

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

    5. Taylor expanded in V around 0 40.5

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

    6. Simplified23.8

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

    if -inf.0 < (*.f64 V l) < -9.99999999999999934e-276

    1. Initial program 9.4

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

    2. Applied egg-rr0.4

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

    if -9.99999999999999934e-276 < (*.f64 V l) < 1.00000023e-317

    1. Initial program 57.6

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

    2. Applied egg-rr25.8

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

    if 1.00000023e-317 < (*.f64 V l) < 2e303

    1. Initial program 9.9

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

    2. Applied egg-rr0.5

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

    if 2e303 < (*.f64 V l)

    1. Initial program 39.2

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

    2. Applied egg-rr22.5

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

    3. Applied egg-rr23.1

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

    4. Applied egg-rr23.1

      \[\leadsto \color{blue}{\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}} \]
  3. Recombined 5 regimes into one program.

  4. Final simplification6.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{\ell}{\frac{A}{V}}}}\\ \mathbf{elif}\;V \cdot \ell \leq -1 \cdot 10^{-275}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 10^{-317}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+303}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022171 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))