Henrywood and Agarwal, Equation (3)

Average Error: 19.3 → 5.6

Time: 4.2s

Precision: binary64

\[ \begin{array}{c}[V, l] = \mathsf{sort}([V, l])\\ \end{array} \]

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;\frac{c0 \cdot \sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq -2 \cdot 10^{-310}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{\ell \cdot \left(-V\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;c0 \cdot \frac{1}{\sqrt{\ell} \cdot \sqrt{\frac{V}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+300}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \end{array} \]

FPCore

(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 (/ A V))) (sqrt l))
   (if (<= (* V l) -2e-310)
     (* c0 (/ (sqrt (- A)) (sqrt (* l (- V)))))
     (if (<= (* V l) 0.0)
       (* c0 (/ 1.0 (* (sqrt l) (sqrt (/ V A)))))
       (if (<= (* V l) 2e+300)
         (* c0 (/ (sqrt A) (sqrt (* V l))))
         (* c0 (sqrt (/ (/ A V) l))))))))

C

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((A / V))) / sqrt(l);
	} else if ((V * l) <= -2e-310) {
		tmp = c0 * (sqrt(-A) / sqrt((l * -V)));
	} else if ((V * l) <= 0.0) {
		tmp = c0 * (1.0 / (sqrt(l) * sqrt((V / A))));
	} else if ((V * l) <= 2e+300) {
		tmp = c0 * (sqrt(A) / sqrt((V * l)));
	} else {
		tmp = c0 * sqrt(((A / V) / l));
	}
	return tmp;
}

Java

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((A / V))) / Math.sqrt(l);
	} else if ((V * l) <= -2e-310) {
		tmp = c0 * (Math.sqrt(-A) / Math.sqrt((l * -V)));
	} else if ((V * l) <= 0.0) {
		tmp = c0 * (1.0 / (Math.sqrt(l) * Math.sqrt((V / A))));
	} else if ((V * l) <= 2e+300) {
		tmp = c0 * (Math.sqrt(A) / Math.sqrt((V * l)));
	} else {
		tmp = c0 * Math.sqrt(((A / V) / l));
	}
	return tmp;
}

Python

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((A / V))) / math.sqrt(l)
	elif (V * l) <= -2e-310:
		tmp = c0 * (math.sqrt(-A) / math.sqrt((l * -V)))
	elif (V * l) <= 0.0:
		tmp = c0 * (1.0 / (math.sqrt(l) * math.sqrt((V / A))))
	elif (V * l) <= 2e+300:
		tmp = c0 * (math.sqrt(A) / math.sqrt((V * l)))
	else:
		tmp = c0 * math.sqrt(((A / V) / l))
	return tmp

Julia

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(Float64(c0 * sqrt(Float64(A / V))) / sqrt(l));
	elseif (Float64(V * l) <= -2e-310)
		tmp = Float64(c0 * Float64(sqrt(Float64(-A)) / sqrt(Float64(l * Float64(-V)))));
	elseif (Float64(V * l) <= 0.0)
		tmp = Float64(c0 * Float64(1.0 / Float64(sqrt(l) * sqrt(Float64(V / A)))));
	elseif (Float64(V * l) <= 2e+300)
		tmp = Float64(c0 * Float64(sqrt(A) / sqrt(Float64(V * l))));
	else
		tmp = Float64(c0 * sqrt(Float64(Float64(A / V) / l)));
	end
	return tmp
end

MATLAB

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((A / V))) / sqrt(l);
	elseif ((V * l) <= -2e-310)
		tmp = c0 * (sqrt(-A) / sqrt((l * -V)));
	elseif ((V * l) <= 0.0)
		tmp = c0 * (1.0 / (sqrt(l) * sqrt((V / A))));
	elseif ((V * l) <= 2e+300)
		tmp = c0 * (sqrt(A) / sqrt((V * l)));
	else
		tmp = c0 * sqrt(((A / V) / l));
	end
	tmp_2 = tmp;
end

Wolfram

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[(N[(c0 * N[Sqrt[N[(A / V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], -2e-310], N[(c0 * N[(N[Sqrt[(-A)], $MachinePrecision] / N[Sqrt[N[(l * (-V)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], 0.0], N[(c0 * N[(1.0 / N[(N[Sqrt[l], $MachinePrecision] * N[Sqrt[N[(V / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], 2e+300], N[(c0 * N[(N[Sqrt[A], $MachinePrecision] / N[Sqrt[N[(V * l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 * N[Sqrt[N[(N[(A / V), $MachinePrecision] / l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 42.4

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

   2. Applied egg-rr 26.0

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

   3. Taylor expanded in c0 around 0 42.4

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

   4. Simplified 25.4

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

   5. Applied egg-rr 12.7

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

   if -inf.0 < (*.f64 V l) < -1.999999999999994e-310

   1. Initial program 9.5

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

   2. Applied egg-rr 0.4

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

   if -1.999999999999994e-310 < (*.f64 V l) < 0.0

   1. Initial program 62.8

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

   2. Applied egg-rr 37.2

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

   3. Applied egg-rr 28.1

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

   if 0.0 < (*.f64 V l) < 2.0000000000000001e300

   1. Initial program 10.6

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

   2. Applied egg-rr 0.7

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

   if 2.0000000000000001e300 < (*.f64 V l)

   1. Initial program 41.8

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

   2. Applied egg-rr 24.9

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

   3. Taylor expanded in c0 around 0 41.8

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

   4. Simplified 24.3

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

4. Final simplification 5.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -\infty:\\ \;\;\;\;\frac{c0 \cdot \sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq -2 \cdot 10^{-310}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{\ell \cdot \left(-V\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;c0 \cdot \frac{1}{\sqrt{\ell} \cdot \sqrt{\frac{V}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+300}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022212 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))