Henrywood and Agarwal, Equation (3)

Percentage Accurate: 73.3% → 96.9%

Time: 10.9s

Alternatives: 11

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \end{array} \]

FPCore

(FPCore (c0 A V l) :precision binary64 (* c0 (sqrt (/ A (* V l)))))

C

double code(double c0, double A, double V, double l) {
	return c0 * sqrt((A / (V * l)));
}

Fortran

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

Java

public static double code(double c0, double A, double V, double l) {
	return c0 * Math.sqrt((A / (V * l)));
}

Python

def code(c0, A, V, l):
	return c0 * math.sqrt((A / (V * l)))

Julia

function code(c0, A, V, l)
	return Float64(c0 * sqrt(Float64(A / Float64(V * l))))
end

MATLAB

function tmp = code(c0, A, V, l)
	tmp = c0 * sqrt((A / (V * l)));
end

Wolfram

code[c0_, A_, V_, l_] := N[(c0 * N[Sqrt[N[(A / N[(V * l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 73.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \end{array} \]

FPCore

(FPCore (c0 A V l) :precision binary64 (* c0 (sqrt (/ A (* V l)))))

C

double code(double c0, double A, double V, double l) {
	return c0 * sqrt((A / (V * l)));
}

Fortran

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

Java

public static double code(double c0, double A, double V, double l) {
	return c0 * Math.sqrt((A / (V * l)));
}

Python

def code(c0, A, V, l):
	return c0 * math.sqrt((A / (V * l)))

Julia

function code(c0, A, V, l)
	return Float64(c0 * sqrt(Float64(A / Float64(V * l))))
end

MATLAB

function tmp = code(c0, A, V, l)
	tmp = c0 * sqrt((A / (V * l)));
end

Wolfram

code[c0_, A_, V_, l_] := N[(c0 * N[Sqrt[N[(A / N[(V * l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ c0 \cdot {\left(\frac{\sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{V}}\right)}^{1.5} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (* c0 (pow (/ (cbrt A) (* (cbrt l) (cbrt V))) 1.5)))

C

double code(double c0, double A, double V, double l) {
	return c0 * pow((cbrt(A) / (cbrt(l) * cbrt(V))), 1.5);
}

Java

public static double code(double c0, double A, double V, double l) {
	return c0 * Math.pow((Math.cbrt(A) / (Math.cbrt(l) * Math.cbrt(V))), 1.5);
}

Julia

function code(c0, A, V, l)
	return Float64(c0 * (Float64(cbrt(A) / Float64(cbrt(l) * cbrt(V))) ^ 1.5))
end

Wolfram

code[c0_, A_, V_, l_] := N[(c0 * N[Power[N[(N[Power[A, 1/3], $MachinePrecision] / N[(N[Power[l, 1/3], $MachinePrecision] * N[Power[V, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.5], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.7%

   \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
2. Step-by-step derivation

   1. pow1/2 70.7%

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

   2. add-cube-cbrt 70.2%

      \[\leadsto c0 \cdot {\color{blue}{\left(\left(\sqrt[3]{\frac{A}{V \cdot \ell}} \cdot \sqrt[3]{\frac{A}{V \cdot \ell}}\right) \cdot \sqrt[3]{\frac{A}{V \cdot \ell}}\right)}}^{0.5} \]

   3. pow3 70.1%

      \[\leadsto c0 \cdot {\color{blue}{\left({\left(\sqrt[3]{\frac{A}{V \cdot \ell}}\right)}^{3}\right)}}^{0.5} \]

   4. pow-pow 70.1%

      \[\leadsto c0 \cdot \color{blue}{{\left(\sqrt[3]{\frac{A}{V \cdot \ell}}\right)}^{\left(3 \cdot 0.5\right)}} \]

   5. associate-/r* 73.6%

      \[\leadsto c0 \cdot {\left(\sqrt[3]{\color{blue}{\frac{\frac{A}{V}}{\ell}}}\right)}^{\left(3 \cdot 0.5\right)} \]

   6. metadata-eval 73.6%

      \[\leadsto c0 \cdot {\left(\sqrt[3]{\frac{\frac{A}{V}}{\ell}}\right)}^{\color{blue}{1.5}} \]

3. Applied egg-rr 73.6%

   \[\leadsto c0 \cdot \color{blue}{{\left(\sqrt[3]{\frac{\frac{A}{V}}{\ell}}\right)}^{1.5}} \]
4. Step-by-step derivation

   1. associate-/r* 70.1%

      \[\leadsto c0 \cdot {\left(\sqrt[3]{\color{blue}{\frac{A}{V \cdot \ell}}}\right)}^{1.5} \]

   2. cbrt-div 81.3%

      \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\sqrt[3]{A}}{\sqrt[3]{V \cdot \ell}}\right)}}^{1.5} \]

   3. *-commutative 81.3%

      \[\leadsto c0 \cdot {\left(\frac{\sqrt[3]{A}}{\sqrt[3]{\color{blue}{\ell \cdot V}}}\right)}^{1.5} \]

5. Applied egg-rr 81.3%

   \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\sqrt[3]{A}}{\sqrt[3]{\ell \cdot V}}\right)}}^{1.5} \]
6. Step-by-step derivation

   1. cbrt-prod 97.6%

      \[\leadsto c0 \cdot {\left(\frac{\sqrt[3]{A}}{\color{blue}{\sqrt[3]{\ell} \cdot \sqrt[3]{V}}}\right)}^{1.5} \]

7. Applied egg-rr 97.6%

   \[\leadsto c0 \cdot {\left(\frac{\sqrt[3]{A}}{\color{blue}{\sqrt[3]{\ell} \cdot \sqrt[3]{V}}}\right)}^{1.5} \]

8. Final simplification 97.6%

   \[\leadsto c0 \cdot {\left(\frac{\sqrt[3]{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{V}}\right)}^{1.5} \]

Alternative 2: 92.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -1 \cdot 10^{+282}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\frac{-\ell}{A}}}{\sqrt{\frac{-1}{V}}}}\\ \mathbf{elif}\;\ell \cdot V \leq -5 \cdot 10^{-320}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{-318} \lor \neg \left(\ell \cdot V \leq 2 \cdot 10^{+304}\right):\\ \;\;\;\;c0 \cdot {\left(\frac{\sqrt[3]{\frac{A}{V}}}{\sqrt[3]{\ell}}\right)}^{1.5}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\ell \cdot V}}{\sqrt{A}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (if (<= (* l V) -1e+282)
   (/ c0 (/ (sqrt (/ (- l) A)) (sqrt (/ -1.0 V))))
   (if (<= (* l V) -5e-320)
     (* c0 (/ (sqrt (- A)) (sqrt (* V (- l)))))
     (if (or (<= (* l V) 2e-318) (not (<= (* l V) 2e+304)))
       (* c0 (pow (/ (cbrt (/ A V)) (cbrt l)) 1.5))
       (/ c0 (/ (sqrt (* l V)) (sqrt A)))))))

C

double code(double c0, double A, double V, double l) {
	double tmp;
	if ((l * V) <= -1e+282) {
		tmp = c0 / (sqrt((-l / A)) / sqrt((-1.0 / V)));
	} else if ((l * V) <= -5e-320) {
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	} else if (((l * V) <= 2e-318) || !((l * V) <= 2e+304)) {
		tmp = c0 * pow((cbrt((A / V)) / cbrt(l)), 1.5);
	} else {
		tmp = c0 / (sqrt((l * V)) / sqrt(A));
	}
	return tmp;
}

Java

public static double code(double c0, double A, double V, double l) {
	double tmp;
	if ((l * V) <= -1e+282) {
		tmp = c0 / (Math.sqrt((-l / A)) / Math.sqrt((-1.0 / V)));
	} else if ((l * V) <= -5e-320) {
		tmp = c0 * (Math.sqrt(-A) / Math.sqrt((V * -l)));
	} else if (((l * V) <= 2e-318) || !((l * V) <= 2e+304)) {
		tmp = c0 * Math.pow((Math.cbrt((A / V)) / Math.cbrt(l)), 1.5);
	} else {
		tmp = c0 / (Math.sqrt((l * V)) / Math.sqrt(A));
	}
	return tmp;
}

Julia

function code(c0, A, V, l)
	tmp = 0.0
	if (Float64(l * V) <= -1e+282)
		tmp = Float64(c0 / Float64(sqrt(Float64(Float64(-l) / A)) / sqrt(Float64(-1.0 / V))));
	elseif (Float64(l * V) <= -5e-320)
		tmp = Float64(c0 * Float64(sqrt(Float64(-A)) / sqrt(Float64(V * Float64(-l)))));
	elseif ((Float64(l * V) <= 2e-318) || !(Float64(l * V) <= 2e+304))
		tmp = Float64(c0 * (Float64(cbrt(Float64(A / V)) / cbrt(l)) ^ 1.5));
	else
		tmp = Float64(c0 / Float64(sqrt(Float64(l * V)) / sqrt(A)));
	end
	return tmp
end

Wolfram

code[c0_, A_, V_, l_] := If[LessEqual[N[(l * V), $MachinePrecision], -1e+282], N[(c0 / N[(N[Sqrt[N[((-l) / A), $MachinePrecision]], $MachinePrecision] / N[Sqrt[N[(-1.0 / V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], -5e-320], N[(c0 * N[(N[Sqrt[(-A)], $MachinePrecision] / N[Sqrt[N[(V * (-l)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(l * V), $MachinePrecision], 2e-318], N[Not[LessEqual[N[(l * V), $MachinePrecision], 2e+304]], $MachinePrecision]], N[(c0 * N[Power[N[(N[Power[N[(A / V), $MachinePrecision], 1/3], $MachinePrecision] / N[Power[l, 1/3], $MachinePrecision]), $MachinePrecision], 1.5], $MachinePrecision]), $MachinePrecision], N[(c0 / N[(N[Sqrt[N[(l * V), $MachinePrecision]], $MachinePrecision] / N[Sqrt[A], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 V l) < -1.00000000000000003e282

   1. Initial program 28.4%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 28.4%

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

      2. clear-num 28.4%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{1}{\frac{V \cdot \ell}{A}}\right)}}^{0.5} \]

      3. inv-pow 28.4%

         \[\leadsto c0 \cdot {\color{blue}{\left({\left(\frac{V \cdot \ell}{A}\right)}^{-1}\right)}}^{0.5} \]

      4. pow-pow 28.4%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V \cdot \ell}{A}\right)}^{\left(-1 \cdot 0.5\right)}} \]

      5. *-commutative 28.4%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{\ell \cdot V}}{A}\right)}^{\left(-1 \cdot 0.5\right)} \]

      6. associate-/l* 48.3%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell}{\frac{A}{V}}\right)}}^{\left(-1 \cdot 0.5\right)} \]

      7. metadata-eval 48.3%

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

   3. Applied egg-rr 48.3%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{\frac{A}{V}}\right)}^{-0.5}} \]
   4. Step-by-step derivation

      1. associate-/r/ 48.3%

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

   5. Simplified 48.3%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{A} \cdot V\right)}^{-0.5}} \]
   6. Step-by-step derivation

      1. associate-/r/ 48.3%

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

      2. metadata-eval 48.3%

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

      3. sqrt-pow2 48.2%

         \[\leadsto c0 \cdot \color{blue}{{\left(\sqrt{\frac{\ell}{\frac{A}{V}}}\right)}^{-1}} \]

      4. inv-pow 48.2%

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

      5. un-div-inv 48.3%

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

      6. associate-/l* 28.4%

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

      7. *-commutative 28.4%

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

      8. associate-*l/ 48.3%

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

      9. *-commutative 48.3%

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

   7. Applied egg-rr 48.3%

      \[\leadsto \color{blue}{\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}} \]
   8. Step-by-step derivation

      1. clear-num 48.3%

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

      2. *-un-lft-identity 48.3%

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

      3. associate-*l/ 48.3%

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

      4. div-inv 48.3%

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

      5. associate-/l/ 48.3%

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

      6. frac-2neg 48.3%

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

      7. sqrt-div 29.2%

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

      8. distribute-neg-frac 29.2%

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

      9. distribute-neg-frac 29.2%

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

      10. metadata-eval 29.2%

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

   9. Applied egg-rr 29.2%

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

   if -1.00000000000000003e282 < (*.f64 V l) < -4.99994e-320

   1. Initial program 87.5%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. frac-2neg 87.5%

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

      2. sqrt-div 98.9%

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

      3. distribute-rgt-neg-in 98.9%

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

   3. Applied egg-rr 98.9%

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

   if -4.99994e-320 < (*.f64 V l) < 2.0000024e-318 or 1.9999999999999999e304 < (*.f64 V l)

   1. Initial program 38.8%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 38.8%

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

      2. add-cube-cbrt 38.8%

         \[\leadsto c0 \cdot {\color{blue}{\left(\left(\sqrt[3]{\frac{A}{V \cdot \ell}} \cdot \sqrt[3]{\frac{A}{V \cdot \ell}}\right) \cdot \sqrt[3]{\frac{A}{V \cdot \ell}}\right)}}^{0.5} \]

      3. pow3 38.8%

         \[\leadsto c0 \cdot {\color{blue}{\left({\left(\sqrt[3]{\frac{A}{V \cdot \ell}}\right)}^{3}\right)}}^{0.5} \]

      4. pow-pow 38.8%

         \[\leadsto c0 \cdot \color{blue}{{\left(\sqrt[3]{\frac{A}{V \cdot \ell}}\right)}^{\left(3 \cdot 0.5\right)}} \]

      5. associate-/r* 76.5%

         \[\leadsto c0 \cdot {\left(\sqrt[3]{\color{blue}{\frac{\frac{A}{V}}{\ell}}}\right)}^{\left(3 \cdot 0.5\right)} \]

      6. metadata-eval 76.5%

         \[\leadsto c0 \cdot {\left(\sqrt[3]{\frac{\frac{A}{V}}{\ell}}\right)}^{\color{blue}{1.5}} \]

   3. Applied egg-rr 76.5%

      \[\leadsto c0 \cdot \color{blue}{{\left(\sqrt[3]{\frac{\frac{A}{V}}{\ell}}\right)}^{1.5}} \]
   4. Step-by-step derivation

      1. cbrt-div 88.6%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\sqrt[3]{\frac{A}{V}}}{\sqrt[3]{\ell}}\right)}}^{1.5} \]

      2. div-inv 88.7%

         \[\leadsto c0 \cdot {\color{blue}{\left(\sqrt[3]{\frac{A}{V}} \cdot \frac{1}{\sqrt[3]{\ell}}\right)}}^{1.5} \]

   5. Applied egg-rr 88.7%

      \[\leadsto c0 \cdot {\color{blue}{\left(\sqrt[3]{\frac{A}{V}} \cdot \frac{1}{\sqrt[3]{\ell}}\right)}}^{1.5} \]
   6. Step-by-step derivation

      1. associate-*r/ 88.6%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\sqrt[3]{\frac{A}{V}} \cdot 1}{\sqrt[3]{\ell}}\right)}}^{1.5} \]

      2. *-rgt-identity 88.6%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{\sqrt[3]{\frac{A}{V}}}}{\sqrt[3]{\ell}}\right)}^{1.5} \]

   7. Simplified 88.6%

      \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\sqrt[3]{\frac{A}{V}}}{\sqrt[3]{\ell}}\right)}}^{1.5} \]

   if 2.0000024e-318 < (*.f64 V l) < 1.9999999999999999e304

   1. Initial program 79.9%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. sqrt-div 99.4%

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

      2. associate-*r/ 94.2%

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

   3. Applied egg-rr 94.2%

      \[\leadsto \color{blue}{\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}} \]
   4. Step-by-step derivation

      1. associate-/l* 99.4%

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

   5. Simplified 99.4%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -1 \cdot 10^{+282}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\frac{-\ell}{A}}}{\sqrt{\frac{-1}{V}}}}\\ \mathbf{elif}\;\ell \cdot V \leq -5 \cdot 10^{-320}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{-318} \lor \neg \left(\ell \cdot V \leq 2 \cdot 10^{+304}\right):\\ \;\;\;\;c0 \cdot {\left(\frac{\sqrt[3]{\frac{A}{V}}}{\sqrt[3]{\ell}}\right)}^{1.5}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\ell \cdot V}}{\sqrt{A}}}\\ \end{array} \]

Alternative 3: 80.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -2 \cdot 10^{+251}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell}} \cdot \sqrt{\frac{A}{V}}\\ \mathbf{elif}\;\ell \cdot V \leq -5 \cdot 10^{-76}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{-318}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\sqrt{A} \cdot \frac{c0}{\sqrt{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (if (<= (* l V) -2e+251)
   (* (/ c0 (sqrt l)) (sqrt (/ A V)))
   (if (<= (* l V) -5e-76)
     (* c0 (sqrt (/ A (* l V))))
     (if (<= (* l V) 2e-318)
       (/ c0 (sqrt (/ V (/ A l))))
       (if (<= (* l V) 2e+304)
         (* (sqrt A) (/ c0 (sqrt (* l V))))
         (* c0 (pow (/ (/ A V) l) 0.5)))))))

C

double code(double c0, double A, double V, double l) {
	double tmp;
	if ((l * V) <= -2e+251) {
		tmp = (c0 / sqrt(l)) * sqrt((A / V));
	} else if ((l * V) <= -5e-76) {
		tmp = c0 * sqrt((A / (l * V)));
	} else if ((l * V) <= 2e-318) {
		tmp = c0 / sqrt((V / (A / l)));
	} else if ((l * V) <= 2e+304) {
		tmp = sqrt(A) * (c0 / sqrt((l * V)));
	} else {
		tmp = c0 * pow(((A / V) / l), 0.5);
	}
	return tmp;
}

Fortran

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 ((l * v) <= (-2d+251)) then
        tmp = (c0 / sqrt(l)) * sqrt((a / v))
    else if ((l * v) <= (-5d-76)) then
        tmp = c0 * sqrt((a / (l * v)))
    else if ((l * v) <= 2d-318) then
        tmp = c0 / sqrt((v / (a / l)))
    else if ((l * v) <= 2d+304) then
        tmp = sqrt(a) * (c0 / sqrt((l * v)))
    else
        tmp = c0 * (((a / v) / l) ** 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double c0, double A, double V, double l) {
	double tmp;
	if ((l * V) <= -2e+251) {
		tmp = (c0 / Math.sqrt(l)) * Math.sqrt((A / V));
	} else if ((l * V) <= -5e-76) {
		tmp = c0 * Math.sqrt((A / (l * V)));
	} else if ((l * V) <= 2e-318) {
		tmp = c0 / Math.sqrt((V / (A / l)));
	} else if ((l * V) <= 2e+304) {
		tmp = Math.sqrt(A) * (c0 / Math.sqrt((l * V)));
	} else {
		tmp = c0 * Math.pow(((A / V) / l), 0.5);
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	tmp = 0
	if (l * V) <= -2e+251:
		tmp = (c0 / math.sqrt(l)) * math.sqrt((A / V))
	elif (l * V) <= -5e-76:
		tmp = c0 * math.sqrt((A / (l * V)))
	elif (l * V) <= 2e-318:
		tmp = c0 / math.sqrt((V / (A / l)))
	elif (l * V) <= 2e+304:
		tmp = math.sqrt(A) * (c0 / math.sqrt((l * V)))
	else:
		tmp = c0 * math.pow(((A / V) / l), 0.5)
	return tmp

Julia

function code(c0, A, V, l)
	tmp = 0.0
	if (Float64(l * V) <= -2e+251)
		tmp = Float64(Float64(c0 / sqrt(l)) * sqrt(Float64(A / V)));
	elseif (Float64(l * V) <= -5e-76)
		tmp = Float64(c0 * sqrt(Float64(A / Float64(l * V))));
	elseif (Float64(l * V) <= 2e-318)
		tmp = Float64(c0 / sqrt(Float64(V / Float64(A / l))));
	elseif (Float64(l * V) <= 2e+304)
		tmp = Float64(sqrt(A) * Float64(c0 / sqrt(Float64(l * V))));
	else
		tmp = Float64(c0 * (Float64(Float64(A / V) / l) ^ 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	tmp = 0.0;
	if ((l * V) <= -2e+251)
		tmp = (c0 / sqrt(l)) * sqrt((A / V));
	elseif ((l * V) <= -5e-76)
		tmp = c0 * sqrt((A / (l * V)));
	elseif ((l * V) <= 2e-318)
		tmp = c0 / sqrt((V / (A / l)));
	elseif ((l * V) <= 2e+304)
		tmp = sqrt(A) * (c0 / sqrt((l * V)));
	else
		tmp = c0 * (((A / V) / l) ^ 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := If[LessEqual[N[(l * V), $MachinePrecision], -2e+251], N[(N[(c0 / N[Sqrt[l], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(A / V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], -5e-76], N[(c0 * N[Sqrt[N[(A / N[(l * V), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], 2e-318], N[(c0 / N[Sqrt[N[(V / N[(A / l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], 2e+304], N[(N[Sqrt[A], $MachinePrecision] * N[(c0 / N[Sqrt[N[(l * V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 * N[Power[N[(N[(A / V), $MachinePrecision] / l), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 V l) < -2.0000000000000001e251

   1. Initial program 30.2%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. sqrt-div 0.0%

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

      2. associate-*r/ 0.0%

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

   3. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}} \]
   4. Step-by-step derivation

      1. associate-/l* 0.0%

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

   5. Simplified 0.0%

      \[\leadsto \color{blue}{\frac{c0}{\frac{\sqrt{V \cdot \ell}}{\sqrt{A}}}} \]
   6. Step-by-step derivation

      1. sqrt-undiv 30.2%

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

      2. *-commutative 30.2%

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

      3. associate-/l* 48.5%

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

      4. sqrt-div 31.4%

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

      5. associate-/r/ 31.4%

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

   7. Applied egg-rr 31.4%

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

   if -2.0000000000000001e251 < (*.f64 V l) < -4.9999999999999998e-76

   1. Initial program 93.6%

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

   if -4.9999999999999998e-76 < (*.f64 V l) < 2.0000024e-318

   1. Initial program 62.1%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 62.1%

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

      2. clear-num 62.1%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{1}{\frac{V \cdot \ell}{A}}\right)}}^{0.5} \]

      3. inv-pow 62.1%

         \[\leadsto c0 \cdot {\color{blue}{\left({\left(\frac{V \cdot \ell}{A}\right)}^{-1}\right)}}^{0.5} \]

      4. pow-pow 63.1%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V \cdot \ell}{A}\right)}^{\left(-1 \cdot 0.5\right)}} \]

      5. *-commutative 63.1%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{\ell \cdot V}}{A}\right)}^{\left(-1 \cdot 0.5\right)} \]

      6. associate-/l* 79.6%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell}{\frac{A}{V}}\right)}}^{\left(-1 \cdot 0.5\right)} \]

      7. metadata-eval 79.6%

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

   3. Applied egg-rr 79.6%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{\frac{A}{V}}\right)}^{-0.5}} \]
   4. Step-by-step derivation

      1. associate-/r/ 78.3%

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

   5. Simplified 78.3%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{A} \cdot V\right)}^{-0.5}} \]
   6. Step-by-step derivation

      1. associate-/r/ 79.6%

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

      2. metadata-eval 79.6%

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

      3. sqrt-pow2 79.6%

         \[\leadsto c0 \cdot \color{blue}{{\left(\sqrt{\frac{\ell}{\frac{A}{V}}}\right)}^{-1}} \]

      4. inv-pow 79.6%

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

      5. un-div-inv 79.7%

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

      6. associate-/l* 63.2%

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

      7. *-commutative 63.2%

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

      8. associate-*l/ 79.7%

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

      9. *-commutative 79.7%

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

   7. Applied egg-rr 79.7%

      \[\leadsto \color{blue}{\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}} \]
   8. Step-by-step derivation

      1. *-commutative 79.7%

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

      2. associate-/r/ 78.5%

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

   9. Simplified 78.5%

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

   if 2.0000024e-318 < (*.f64 V l) < 1.9999999999999999e304

   1. Initial program 79.9%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. sqrt-div 99.4%

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

      2. associate-*r/ 94.2%

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

   3. Applied egg-rr 94.2%

      \[\leadsto \color{blue}{\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}} \]
   4. Step-by-step derivation

      1. associate-/l* 99.4%

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

   5. Simplified 99.4%

      \[\leadsto \color{blue}{\frac{c0}{\frac{\sqrt{V \cdot \ell}}{\sqrt{A}}}} \]
   6. Step-by-step derivation

      1. associate-/r/ 98.4%

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

      2. *-commutative 98.4%

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

   7. Applied egg-rr 98.4%

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

   if 1.9999999999999999e304 < (*.f64 V l)

   1. Initial program 34.0%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 34.0%

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

      2. associate-/r* 76.5%

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

   3. Applied egg-rr 76.5%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.5}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -2 \cdot 10^{+251}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell}} \cdot \sqrt{\frac{A}{V}}\\ \mathbf{elif}\;\ell \cdot V \leq -5 \cdot 10^{-76}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{-318}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\sqrt{A} \cdot \frac{c0}{\sqrt{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.5}\\ \end{array} \]

Alternative 4: 81.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -2 \cdot 10^{+251}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell}} \cdot \sqrt{\frac{A}{V}}\\ \mathbf{elif}\;\ell \cdot V \leq -5 \cdot 10^{-76}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{-318}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{+304}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (if (<= (* l V) -2e+251)
   (* (/ c0 (sqrt l)) (sqrt (/ A V)))
   (if (<= (* l V) -5e-76)
     (* c0 (sqrt (/ A (* l V))))
     (if (<= (* l V) 2e-318)
       (/ c0 (sqrt (/ V (/ A l))))
       (if (<= (* l V) 2e+304)
         (* c0 (/ (sqrt A) (sqrt (* l V))))
         (* c0 (pow (/ (/ A V) l) 0.5)))))))

C

double code(double c0, double A, double V, double l) {
	double tmp;
	if ((l * V) <= -2e+251) {
		tmp = (c0 / sqrt(l)) * sqrt((A / V));
	} else if ((l * V) <= -5e-76) {
		tmp = c0 * sqrt((A / (l * V)));
	} else if ((l * V) <= 2e-318) {
		tmp = c0 / sqrt((V / (A / l)));
	} else if ((l * V) <= 2e+304) {
		tmp = c0 * (sqrt(A) / sqrt((l * V)));
	} else {
		tmp = c0 * pow(((A / V) / l), 0.5);
	}
	return tmp;
}

Fortran

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 ((l * v) <= (-2d+251)) then
        tmp = (c0 / sqrt(l)) * sqrt((a / v))
    else if ((l * v) <= (-5d-76)) then
        tmp = c0 * sqrt((a / (l * v)))
    else if ((l * v) <= 2d-318) then
        tmp = c0 / sqrt((v / (a / l)))
    else if ((l * v) <= 2d+304) then
        tmp = c0 * (sqrt(a) / sqrt((l * v)))
    else
        tmp = c0 * (((a / v) / l) ** 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double c0, double A, double V, double l) {
	double tmp;
	if ((l * V) <= -2e+251) {
		tmp = (c0 / Math.sqrt(l)) * Math.sqrt((A / V));
	} else if ((l * V) <= -5e-76) {
		tmp = c0 * Math.sqrt((A / (l * V)));
	} else if ((l * V) <= 2e-318) {
		tmp = c0 / Math.sqrt((V / (A / l)));
	} else if ((l * V) <= 2e+304) {
		tmp = c0 * (Math.sqrt(A) / Math.sqrt((l * V)));
	} else {
		tmp = c0 * Math.pow(((A / V) / l), 0.5);
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	tmp = 0
	if (l * V) <= -2e+251:
		tmp = (c0 / math.sqrt(l)) * math.sqrt((A / V))
	elif (l * V) <= -5e-76:
		tmp = c0 * math.sqrt((A / (l * V)))
	elif (l * V) <= 2e-318:
		tmp = c0 / math.sqrt((V / (A / l)))
	elif (l * V) <= 2e+304:
		tmp = c0 * (math.sqrt(A) / math.sqrt((l * V)))
	else:
		tmp = c0 * math.pow(((A / V) / l), 0.5)
	return tmp

Julia

function code(c0, A, V, l)
	tmp = 0.0
	if (Float64(l * V) <= -2e+251)
		tmp = Float64(Float64(c0 / sqrt(l)) * sqrt(Float64(A / V)));
	elseif (Float64(l * V) <= -5e-76)
		tmp = Float64(c0 * sqrt(Float64(A / Float64(l * V))));
	elseif (Float64(l * V) <= 2e-318)
		tmp = Float64(c0 / sqrt(Float64(V / Float64(A / l))));
	elseif (Float64(l * V) <= 2e+304)
		tmp = Float64(c0 * Float64(sqrt(A) / sqrt(Float64(l * V))));
	else
		tmp = Float64(c0 * (Float64(Float64(A / V) / l) ^ 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	tmp = 0.0;
	if ((l * V) <= -2e+251)
		tmp = (c0 / sqrt(l)) * sqrt((A / V));
	elseif ((l * V) <= -5e-76)
		tmp = c0 * sqrt((A / (l * V)));
	elseif ((l * V) <= 2e-318)
		tmp = c0 / sqrt((V / (A / l)));
	elseif ((l * V) <= 2e+304)
		tmp = c0 * (sqrt(A) / sqrt((l * V)));
	else
		tmp = c0 * (((A / V) / l) ^ 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := If[LessEqual[N[(l * V), $MachinePrecision], -2e+251], N[(N[(c0 / N[Sqrt[l], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(A / V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], -5e-76], N[(c0 * N[Sqrt[N[(A / N[(l * V), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], 2e-318], N[(c0 / N[Sqrt[N[(V / N[(A / l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], 2e+304], N[(c0 * N[(N[Sqrt[A], $MachinePrecision] / N[Sqrt[N[(l * V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 * N[Power[N[(N[(A / V), $MachinePrecision] / l), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 V l) < -2.0000000000000001e251

   1. Initial program 30.2%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. sqrt-div 0.0%

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

      2. associate-*r/ 0.0%

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

   3. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}} \]
   4. Step-by-step derivation

      1. associate-/l* 0.0%

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

   5. Simplified 0.0%

      \[\leadsto \color{blue}{\frac{c0}{\frac{\sqrt{V \cdot \ell}}{\sqrt{A}}}} \]
   6. Step-by-step derivation

      1. sqrt-undiv 30.2%

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

      2. *-commutative 30.2%

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

      3. associate-/l* 48.5%

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

      4. sqrt-div 31.4%

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

      5. associate-/r/ 31.4%

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

   7. Applied egg-rr 31.4%

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

   if -2.0000000000000001e251 < (*.f64 V l) < -4.9999999999999998e-76

   1. Initial program 93.6%

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

   if -4.9999999999999998e-76 < (*.f64 V l) < 2.0000024e-318

   1. Initial program 62.1%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 62.1%

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

      2. clear-num 62.1%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{1}{\frac{V \cdot \ell}{A}}\right)}}^{0.5} \]

      3. inv-pow 62.1%

         \[\leadsto c0 \cdot {\color{blue}{\left({\left(\frac{V \cdot \ell}{A}\right)}^{-1}\right)}}^{0.5} \]

      4. pow-pow 63.1%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V \cdot \ell}{A}\right)}^{\left(-1 \cdot 0.5\right)}} \]

      5. *-commutative 63.1%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{\ell \cdot V}}{A}\right)}^{\left(-1 \cdot 0.5\right)} \]

      6. associate-/l* 79.6%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell}{\frac{A}{V}}\right)}}^{\left(-1 \cdot 0.5\right)} \]

      7. metadata-eval 79.6%

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

   3. Applied egg-rr 79.6%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{\frac{A}{V}}\right)}^{-0.5}} \]
   4. Step-by-step derivation

      1. associate-/r/ 78.3%

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

   5. Simplified 78.3%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{A} \cdot V\right)}^{-0.5}} \]
   6. Step-by-step derivation

      1. associate-/r/ 79.6%

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

      2. metadata-eval 79.6%

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

      3. sqrt-pow2 79.6%

         \[\leadsto c0 \cdot \color{blue}{{\left(\sqrt{\frac{\ell}{\frac{A}{V}}}\right)}^{-1}} \]

      4. inv-pow 79.6%

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

      5. un-div-inv 79.7%

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

      6. associate-/l* 63.2%

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

      7. *-commutative 63.2%

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

      8. associate-*l/ 79.7%

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

      9. *-commutative 79.7%

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

   7. Applied egg-rr 79.7%

      \[\leadsto \color{blue}{\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}} \]
   8. Step-by-step derivation

      1. *-commutative 79.7%

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

      2. associate-/r/ 78.5%

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

   9. Simplified 78.5%

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

   if 2.0000024e-318 < (*.f64 V l) < 1.9999999999999999e304

   1. Initial program 79.9%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. sqrt-div 99.4%

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

      2. associate-*r/ 94.2%

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

   3. Applied egg-rr 94.2%

      \[\leadsto \color{blue}{\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}} \]
   4. Step-by-step derivation

      1. *-commutative 94.2%

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

      2. associate-/l* 98.3%

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

      3. associate-/r/ 99.4%

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

   5. Simplified 99.4%

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

   if 1.9999999999999999e304 < (*.f64 V l)

   1. Initial program 34.0%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 34.0%

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

      2. associate-/r* 76.5%

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

   3. Applied egg-rr 76.5%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.5}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -2 \cdot 10^{+251}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell}} \cdot \sqrt{\frac{A}{V}}\\ \mathbf{elif}\;\ell \cdot V \leq -5 \cdot 10^{-76}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{-318}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{+304}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.5}\\ \end{array} \]

Alternative 5: 81.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -2 \cdot 10^{+251}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell}} \cdot \sqrt{\frac{A}{V}}\\ \mathbf{elif}\;\ell \cdot V \leq -5 \cdot 10^{-76}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{-318}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\ell \cdot V}}{\sqrt{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (if (<= (* l V) -2e+251)
   (* (/ c0 (sqrt l)) (sqrt (/ A V)))
   (if (<= (* l V) -5e-76)
     (* c0 (sqrt (/ A (* l V))))
     (if (<= (* l V) 2e-318)
       (/ c0 (sqrt (/ V (/ A l))))
       (if (<= (* l V) 2e+304)
         (/ c0 (/ (sqrt (* l V)) (sqrt A)))
         (* c0 (pow (/ (/ A V) l) 0.5)))))))

C

double code(double c0, double A, double V, double l) {
	double tmp;
	if ((l * V) <= -2e+251) {
		tmp = (c0 / sqrt(l)) * sqrt((A / V));
	} else if ((l * V) <= -5e-76) {
		tmp = c0 * sqrt((A / (l * V)));
	} else if ((l * V) <= 2e-318) {
		tmp = c0 / sqrt((V / (A / l)));
	} else if ((l * V) <= 2e+304) {
		tmp = c0 / (sqrt((l * V)) / sqrt(A));
	} else {
		tmp = c0 * pow(((A / V) / l), 0.5);
	}
	return tmp;
}

Fortran

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 ((l * v) <= (-2d+251)) then
        tmp = (c0 / sqrt(l)) * sqrt((a / v))
    else if ((l * v) <= (-5d-76)) then
        tmp = c0 * sqrt((a / (l * v)))
    else if ((l * v) <= 2d-318) then
        tmp = c0 / sqrt((v / (a / l)))
    else if ((l * v) <= 2d+304) then
        tmp = c0 / (sqrt((l * v)) / sqrt(a))
    else
        tmp = c0 * (((a / v) / l) ** 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double c0, double A, double V, double l) {
	double tmp;
	if ((l * V) <= -2e+251) {
		tmp = (c0 / Math.sqrt(l)) * Math.sqrt((A / V));
	} else if ((l * V) <= -5e-76) {
		tmp = c0 * Math.sqrt((A / (l * V)));
	} else if ((l * V) <= 2e-318) {
		tmp = c0 / Math.sqrt((V / (A / l)));
	} else if ((l * V) <= 2e+304) {
		tmp = c0 / (Math.sqrt((l * V)) / Math.sqrt(A));
	} else {
		tmp = c0 * Math.pow(((A / V) / l), 0.5);
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	tmp = 0
	if (l * V) <= -2e+251:
		tmp = (c0 / math.sqrt(l)) * math.sqrt((A / V))
	elif (l * V) <= -5e-76:
		tmp = c0 * math.sqrt((A / (l * V)))
	elif (l * V) <= 2e-318:
		tmp = c0 / math.sqrt((V / (A / l)))
	elif (l * V) <= 2e+304:
		tmp = c0 / (math.sqrt((l * V)) / math.sqrt(A))
	else:
		tmp = c0 * math.pow(((A / V) / l), 0.5)
	return tmp

Julia

function code(c0, A, V, l)
	tmp = 0.0
	if (Float64(l * V) <= -2e+251)
		tmp = Float64(Float64(c0 / sqrt(l)) * sqrt(Float64(A / V)));
	elseif (Float64(l * V) <= -5e-76)
		tmp = Float64(c0 * sqrt(Float64(A / Float64(l * V))));
	elseif (Float64(l * V) <= 2e-318)
		tmp = Float64(c0 / sqrt(Float64(V / Float64(A / l))));
	elseif (Float64(l * V) <= 2e+304)
		tmp = Float64(c0 / Float64(sqrt(Float64(l * V)) / sqrt(A)));
	else
		tmp = Float64(c0 * (Float64(Float64(A / V) / l) ^ 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	tmp = 0.0;
	if ((l * V) <= -2e+251)
		tmp = (c0 / sqrt(l)) * sqrt((A / V));
	elseif ((l * V) <= -5e-76)
		tmp = c0 * sqrt((A / (l * V)));
	elseif ((l * V) <= 2e-318)
		tmp = c0 / sqrt((V / (A / l)));
	elseif ((l * V) <= 2e+304)
		tmp = c0 / (sqrt((l * V)) / sqrt(A));
	else
		tmp = c0 * (((A / V) / l) ^ 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := If[LessEqual[N[(l * V), $MachinePrecision], -2e+251], N[(N[(c0 / N[Sqrt[l], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(A / V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], -5e-76], N[(c0 * N[Sqrt[N[(A / N[(l * V), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], 2e-318], N[(c0 / N[Sqrt[N[(V / N[(A / l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], 2e+304], N[(c0 / N[(N[Sqrt[N[(l * V), $MachinePrecision]], $MachinePrecision] / N[Sqrt[A], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 * N[Power[N[(N[(A / V), $MachinePrecision] / l), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 V l) < -2.0000000000000001e251

   1. Initial program 30.2%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. sqrt-div 0.0%

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

      2. associate-*r/ 0.0%

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

   3. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}} \]
   4. Step-by-step derivation

      1. associate-/l* 0.0%

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

   5. Simplified 0.0%

      \[\leadsto \color{blue}{\frac{c0}{\frac{\sqrt{V \cdot \ell}}{\sqrt{A}}}} \]
   6. Step-by-step derivation

      1. sqrt-undiv 30.2%

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

      2. *-commutative 30.2%

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

      3. associate-/l* 48.5%

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

      4. sqrt-div 31.4%

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

      5. associate-/r/ 31.4%

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

   7. Applied egg-rr 31.4%

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

   if -2.0000000000000001e251 < (*.f64 V l) < -4.9999999999999998e-76

   1. Initial program 93.6%

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

   if -4.9999999999999998e-76 < (*.f64 V l) < 2.0000024e-318

   1. Initial program 62.1%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 62.1%

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

      2. clear-num 62.1%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{1}{\frac{V \cdot \ell}{A}}\right)}}^{0.5} \]

      3. inv-pow 62.1%

         \[\leadsto c0 \cdot {\color{blue}{\left({\left(\frac{V \cdot \ell}{A}\right)}^{-1}\right)}}^{0.5} \]

      4. pow-pow 63.1%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V \cdot \ell}{A}\right)}^{\left(-1 \cdot 0.5\right)}} \]

      5. *-commutative 63.1%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{\ell \cdot V}}{A}\right)}^{\left(-1 \cdot 0.5\right)} \]

      6. associate-/l* 79.6%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell}{\frac{A}{V}}\right)}}^{\left(-1 \cdot 0.5\right)} \]

      7. metadata-eval 79.6%

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

   3. Applied egg-rr 79.6%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{\frac{A}{V}}\right)}^{-0.5}} \]
   4. Step-by-step derivation

      1. associate-/r/ 78.3%

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

   5. Simplified 78.3%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{A} \cdot V\right)}^{-0.5}} \]
   6. Step-by-step derivation

      1. associate-/r/ 79.6%

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

      2. metadata-eval 79.6%

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

      3. sqrt-pow2 79.6%

         \[\leadsto c0 \cdot \color{blue}{{\left(\sqrt{\frac{\ell}{\frac{A}{V}}}\right)}^{-1}} \]

      4. inv-pow 79.6%

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

      5. un-div-inv 79.7%

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

      6. associate-/l* 63.2%

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

      7. *-commutative 63.2%

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

      8. associate-*l/ 79.7%

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

      9. *-commutative 79.7%

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

   7. Applied egg-rr 79.7%

      \[\leadsto \color{blue}{\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}} \]
   8. Step-by-step derivation

      1. *-commutative 79.7%

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

      2. associate-/r/ 78.5%

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

   9. Simplified 78.5%

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

   if 2.0000024e-318 < (*.f64 V l) < 1.9999999999999999e304

   1. Initial program 79.9%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. sqrt-div 99.4%

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

      2. associate-*r/ 94.2%

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

   3. Applied egg-rr 94.2%

      \[\leadsto \color{blue}{\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}} \]
   4. Step-by-step derivation

      1. associate-/l* 99.4%

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

   5. Simplified 99.4%

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

   if 1.9999999999999999e304 < (*.f64 V l)

   1. Initial program 34.0%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 34.0%

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

      2. associate-/r* 76.5%

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

   3. Applied egg-rr 76.5%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.5}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -2 \cdot 10^{+251}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell}} \cdot \sqrt{\frac{A}{V}}\\ \mathbf{elif}\;\ell \cdot V \leq -5 \cdot 10^{-76}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{-318}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\ell \cdot V}}{\sqrt{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.5}\\ \end{array} \]

Alternative 6: 88.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -\infty:\\ \;\;\;\;\frac{c0}{\sqrt{\ell}} \cdot \sqrt{\frac{A}{V}}\\ \mathbf{elif}\;\ell \cdot V \leq -5 \cdot 10^{-320}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{-318}:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\ell \cdot V}}{\sqrt{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (if (<= (* l V) (- INFINITY))
   (* (/ c0 (sqrt l)) (sqrt (/ A V)))
   (if (<= (* l V) -5e-320)
     (* c0 (/ (sqrt (- A)) (sqrt (* V (- l)))))
     (if (<= (* l V) 2e-318)
       (/ c0 (sqrt (* V (/ l A))))
       (if (<= (* l V) 2e+304)
         (/ c0 (/ (sqrt (* l V)) (sqrt A)))
         (* c0 (pow (/ (/ A V) l) 0.5)))))))

C

double code(double c0, double A, double V, double l) {
	double tmp;
	if ((l * V) <= -((double) INFINITY)) {
		tmp = (c0 / sqrt(l)) * sqrt((A / V));
	} else if ((l * V) <= -5e-320) {
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	} else if ((l * V) <= 2e-318) {
		tmp = c0 / sqrt((V * (l / A)));
	} else if ((l * V) <= 2e+304) {
		tmp = c0 / (sqrt((l * V)) / sqrt(A));
	} else {
		tmp = c0 * pow(((A / V) / l), 0.5);
	}
	return tmp;
}

Java

public static double code(double c0, double A, double V, double l) {
	double tmp;
	if ((l * V) <= -Double.POSITIVE_INFINITY) {
		tmp = (c0 / Math.sqrt(l)) * Math.sqrt((A / V));
	} else if ((l * V) <= -5e-320) {
		tmp = c0 * (Math.sqrt(-A) / Math.sqrt((V * -l)));
	} else if ((l * V) <= 2e-318) {
		tmp = c0 / Math.sqrt((V * (l / A)));
	} else if ((l * V) <= 2e+304) {
		tmp = c0 / (Math.sqrt((l * V)) / Math.sqrt(A));
	} else {
		tmp = c0 * Math.pow(((A / V) / l), 0.5);
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	tmp = 0
	if (l * V) <= -math.inf:
		tmp = (c0 / math.sqrt(l)) * math.sqrt((A / V))
	elif (l * V) <= -5e-320:
		tmp = c0 * (math.sqrt(-A) / math.sqrt((V * -l)))
	elif (l * V) <= 2e-318:
		tmp = c0 / math.sqrt((V * (l / A)))
	elif (l * V) <= 2e+304:
		tmp = c0 / (math.sqrt((l * V)) / math.sqrt(A))
	else:
		tmp = c0 * math.pow(((A / V) / l), 0.5)
	return tmp

Julia

function code(c0, A, V, l)
	tmp = 0.0
	if (Float64(l * V) <= Float64(-Inf))
		tmp = Float64(Float64(c0 / sqrt(l)) * sqrt(Float64(A / V)));
	elseif (Float64(l * V) <= -5e-320)
		tmp = Float64(c0 * Float64(sqrt(Float64(-A)) / sqrt(Float64(V * Float64(-l)))));
	elseif (Float64(l * V) <= 2e-318)
		tmp = Float64(c0 / sqrt(Float64(V * Float64(l / A))));
	elseif (Float64(l * V) <= 2e+304)
		tmp = Float64(c0 / Float64(sqrt(Float64(l * V)) / sqrt(A)));
	else
		tmp = Float64(c0 * (Float64(Float64(A / V) / l) ^ 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	tmp = 0.0;
	if ((l * V) <= -Inf)
		tmp = (c0 / sqrt(l)) * sqrt((A / V));
	elseif ((l * V) <= -5e-320)
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	elseif ((l * V) <= 2e-318)
		tmp = c0 / sqrt((V * (l / A)));
	elseif ((l * V) <= 2e+304)
		tmp = c0 / (sqrt((l * V)) / sqrt(A));
	else
		tmp = c0 * (((A / V) / l) ^ 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := If[LessEqual[N[(l * V), $MachinePrecision], (-Infinity)], N[(N[(c0 / N[Sqrt[l], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(A / V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], -5e-320], N[(c0 * N[(N[Sqrt[(-A)], $MachinePrecision] / N[Sqrt[N[(V * (-l)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], 2e-318], N[(c0 / N[Sqrt[N[(V * N[(l / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], 2e+304], N[(c0 / N[(N[Sqrt[N[(l * V), $MachinePrecision]], $MachinePrecision] / N[Sqrt[A], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 * N[Power[N[(N[(A / V), $MachinePrecision] / l), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 26.2%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. sqrt-div 0.0%

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

      2. associate-*r/ 0.0%

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

   3. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}} \]
   4. Step-by-step derivation

      1. associate-/l* 0.0%

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

   5. Simplified 0.0%

      \[\leadsto \color{blue}{\frac{c0}{\frac{\sqrt{V \cdot \ell}}{\sqrt{A}}}} \]
   6. Step-by-step derivation

      1. sqrt-undiv 26.2%

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

      2. *-commutative 26.2%

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

      3. associate-/l* 47.9%

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

      4. sqrt-div 23.6%

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

      5. associate-/r/ 23.6%

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

   7. Applied egg-rr 23.6%

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

   if -inf.0 < (*.f64 V l) < -4.99994e-320

   1. Initial program 86.8%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. frac-2neg 86.8%

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

      2. sqrt-div 98.9%

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

      3. distribute-rgt-neg-in 98.9%

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

   3. Applied egg-rr 98.9%

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

   if -4.99994e-320 < (*.f64 V l) < 2.0000024e-318

   1. Initial program 40.7%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 40.7%

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

      2. clear-num 40.7%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{1}{\frac{V \cdot \ell}{A}}\right)}}^{0.5} \]

      3. inv-pow 40.7%

         \[\leadsto c0 \cdot {\color{blue}{\left({\left(\frac{V \cdot \ell}{A}\right)}^{-1}\right)}}^{0.5} \]

      4. pow-pow 40.7%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V \cdot \ell}{A}\right)}^{\left(-1 \cdot 0.5\right)}} \]

      5. *-commutative 40.7%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{\ell \cdot V}}{A}\right)}^{\left(-1 \cdot 0.5\right)} \]

      6. associate-/l* 76.7%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell}{\frac{A}{V}}\right)}}^{\left(-1 \cdot 0.5\right)} \]

      7. metadata-eval 76.7%

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

   3. Applied egg-rr 76.7%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{\frac{A}{V}}\right)}^{-0.5}} \]
   4. Step-by-step derivation

      1. associate-/r/ 76.7%

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

   5. Simplified 76.7%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{A} \cdot V\right)}^{-0.5}} \]
   6. Step-by-step derivation

      1. associate-/r/ 76.7%

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

      2. metadata-eval 76.7%

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

      3. sqrt-pow2 76.7%

         \[\leadsto c0 \cdot \color{blue}{{\left(\sqrt{\frac{\ell}{\frac{A}{V}}}\right)}^{-1}} \]

      4. inv-pow 76.7%

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

      5. un-div-inv 76.8%

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

      6. associate-/l* 40.7%

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

      7. *-commutative 40.7%

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

      8. associate-*l/ 76.8%

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

      9. *-commutative 76.8%

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

   7. Applied egg-rr 76.8%

      \[\leadsto \color{blue}{\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 40.7%

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

      2. associate-*l/ 76.8%

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

      3. *-commutative 76.8%

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

   9. Simplified 76.8%

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

   if 2.0000024e-318 < (*.f64 V l) < 1.9999999999999999e304

   1. Initial program 79.9%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. sqrt-div 99.4%

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

      2. associate-*r/ 94.2%

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

   3. Applied egg-rr 94.2%

      \[\leadsto \color{blue}{\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}} \]
   4. Step-by-step derivation

      1. associate-/l* 99.4%

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

   5. Simplified 99.4%

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

   if 1.9999999999999999e304 < (*.f64 V l)

   1. Initial program 34.0%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 34.0%

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

      2. associate-/r* 76.5%

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

   3. Applied egg-rr 76.5%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.5}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -\infty:\\ \;\;\;\;\frac{c0}{\sqrt{\ell}} \cdot \sqrt{\frac{A}{V}}\\ \mathbf{elif}\;\ell \cdot V \leq -5 \cdot 10^{-320}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{-318}:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\ell \cdot V}}{\sqrt{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.5}\\ \end{array} \]

Alternative 7: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c0}{\frac{\sqrt{\frac{-\ell}{A}}}{\sqrt{\frac{-1}{V}}}}\\ \mathbf{if}\;\ell \cdot V \leq -1 \cdot 10^{+282}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \cdot V \leq -5 \cdot 10^{-299}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{-318}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\ell \cdot V}}{\sqrt{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (/ c0 (/ (sqrt (/ (- l) A)) (sqrt (/ -1.0 V))))))
   (if (<= (* l V) -1e+282)
     t_0
     (if (<= (* l V) -5e-299)
       (* c0 (/ (sqrt (- A)) (sqrt (* V (- l)))))
       (if (<= (* l V) 2e-318)
         t_0
         (if (<= (* l V) 2e+304)
           (/ c0 (/ (sqrt (* l V)) (sqrt A)))
           (* c0 (pow (/ (/ A V) l) 0.5))))))))

C

double code(double c0, double A, double V, double l) {
	double t_0 = c0 / (sqrt((-l / A)) / sqrt((-1.0 / V)));
	double tmp;
	if ((l * V) <= -1e+282) {
		tmp = t_0;
	} else if ((l * V) <= -5e-299) {
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	} else if ((l * V) <= 2e-318) {
		tmp = t_0;
	} else if ((l * V) <= 2e+304) {
		tmp = c0 / (sqrt((l * V)) / sqrt(A));
	} else {
		tmp = c0 * pow(((A / V) / l), 0.5);
	}
	return tmp;
}

Fortran

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 = c0 / (sqrt((-l / a)) / sqrt(((-1.0d0) / v)))
    if ((l * v) <= (-1d+282)) then
        tmp = t_0
    else if ((l * v) <= (-5d-299)) then
        tmp = c0 * (sqrt(-a) / sqrt((v * -l)))
    else if ((l * v) <= 2d-318) then
        tmp = t_0
    else if ((l * v) <= 2d+304) then
        tmp = c0 / (sqrt((l * v)) / sqrt(a))
    else
        tmp = c0 * (((a / v) / l) ** 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double c0, double A, double V, double l) {
	double t_0 = c0 / (Math.sqrt((-l / A)) / Math.sqrt((-1.0 / V)));
	double tmp;
	if ((l * V) <= -1e+282) {
		tmp = t_0;
	} else if ((l * V) <= -5e-299) {
		tmp = c0 * (Math.sqrt(-A) / Math.sqrt((V * -l)));
	} else if ((l * V) <= 2e-318) {
		tmp = t_0;
	} else if ((l * V) <= 2e+304) {
		tmp = c0 / (Math.sqrt((l * V)) / Math.sqrt(A));
	} else {
		tmp = c0 * Math.pow(((A / V) / l), 0.5);
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	t_0 = c0 / (math.sqrt((-l / A)) / math.sqrt((-1.0 / V)))
	tmp = 0
	if (l * V) <= -1e+282:
		tmp = t_0
	elif (l * V) <= -5e-299:
		tmp = c0 * (math.sqrt(-A) / math.sqrt((V * -l)))
	elif (l * V) <= 2e-318:
		tmp = t_0
	elif (l * V) <= 2e+304:
		tmp = c0 / (math.sqrt((l * V)) / math.sqrt(A))
	else:
		tmp = c0 * math.pow(((A / V) / l), 0.5)
	return tmp

Julia

function code(c0, A, V, l)
	t_0 = Float64(c0 / Float64(sqrt(Float64(Float64(-l) / A)) / sqrt(Float64(-1.0 / V))))
	tmp = 0.0
	if (Float64(l * V) <= -1e+282)
		tmp = t_0;
	elseif (Float64(l * V) <= -5e-299)
		tmp = Float64(c0 * Float64(sqrt(Float64(-A)) / sqrt(Float64(V * Float64(-l)))));
	elseif (Float64(l * V) <= 2e-318)
		tmp = t_0;
	elseif (Float64(l * V) <= 2e+304)
		tmp = Float64(c0 / Float64(sqrt(Float64(l * V)) / sqrt(A)));
	else
		tmp = Float64(c0 * (Float64(Float64(A / V) / l) ^ 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	t_0 = c0 / (sqrt((-l / A)) / sqrt((-1.0 / V)));
	tmp = 0.0;
	if ((l * V) <= -1e+282)
		tmp = t_0;
	elseif ((l * V) <= -5e-299)
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	elseif ((l * V) <= 2e-318)
		tmp = t_0;
	elseif ((l * V) <= 2e+304)
		tmp = c0 / (sqrt((l * V)) / sqrt(A));
	else
		tmp = c0 * (((A / V) / l) ^ 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := Block[{t$95$0 = N[(c0 / N[(N[Sqrt[N[((-l) / A), $MachinePrecision]], $MachinePrecision] / N[Sqrt[N[(-1.0 / V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(l * V), $MachinePrecision], -1e+282], t$95$0, If[LessEqual[N[(l * V), $MachinePrecision], -5e-299], N[(c0 * N[(N[Sqrt[(-A)], $MachinePrecision] / N[Sqrt[N[(V * (-l)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], 2e-318], t$95$0, If[LessEqual[N[(l * V), $MachinePrecision], 2e+304], N[(c0 / N[(N[Sqrt[N[(l * V), $MachinePrecision]], $MachinePrecision] / N[Sqrt[A], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 * N[Power[N[(N[(A / V), $MachinePrecision] / l), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 V l) < -1.00000000000000003e282 or -4.99999999999999956e-299 < (*.f64 V l) < 2.0000024e-318

   1. Initial program 38.2%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 38.2%

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

      2. clear-num 38.2%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{1}{\frac{V \cdot \ell}{A}}\right)}}^{0.5} \]

      3. inv-pow 38.2%

         \[\leadsto c0 \cdot {\color{blue}{\left({\left(\frac{V \cdot \ell}{A}\right)}^{-1}\right)}}^{0.5} \]

      4. pow-pow 38.2%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V \cdot \ell}{A}\right)}^{\left(-1 \cdot 0.5\right)}} \]

      5. *-commutative 38.2%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{\ell \cdot V}}{A}\right)}^{\left(-1 \cdot 0.5\right)} \]

      6. associate-/l* 65.5%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell}{\frac{A}{V}}\right)}}^{\left(-1 \cdot 0.5\right)} \]

      7. metadata-eval 65.5%

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

   3. Applied egg-rr 65.5%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{\frac{A}{V}}\right)}^{-0.5}} \]
   4. Step-by-step derivation

      1. associate-/r/ 65.5%

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

   5. Simplified 65.5%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{A} \cdot V\right)}^{-0.5}} \]
   6. Step-by-step derivation

      1. associate-/r/ 65.5%

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

      2. metadata-eval 65.5%

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

      3. sqrt-pow2 65.5%

         \[\leadsto c0 \cdot \color{blue}{{\left(\sqrt{\frac{\ell}{\frac{A}{V}}}\right)}^{-1}} \]

      4. inv-pow 65.5%

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

      5. un-div-inv 65.5%

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

      6. associate-/l* 38.2%

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

      7. *-commutative 38.2%

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

      8. associate-*l/ 65.5%

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

      9. *-commutative 65.5%

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

   7. Applied egg-rr 65.5%

      \[\leadsto \color{blue}{\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}} \]
   8. Step-by-step derivation

      1. clear-num 65.5%

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

      2. *-un-lft-identity 65.5%

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

      3. associate-*l/ 65.5%

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

      4. div-inv 65.5%

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

      5. associate-/l/ 65.6%

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

      6. frac-2neg 65.6%

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

      7. sqrt-div 47.4%

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

      8. distribute-neg-frac 47.4%

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

      9. distribute-neg-frac 47.4%

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

      10. metadata-eval 47.4%

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

   9. Applied egg-rr 47.4%

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

   if -1.00000000000000003e282 < (*.f64 V l) < -4.99999999999999956e-299

   1. Initial program 88.0%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. frac-2neg 88.0%

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

      2. sqrt-div 99.5%

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

      3. distribute-rgt-neg-in 99.5%

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

   3. Applied egg-rr 99.5%

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

   if 2.0000024e-318 < (*.f64 V l) < 1.9999999999999999e304

   1. Initial program 79.9%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. sqrt-div 99.4%

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

      2. associate-*r/ 94.2%

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

   3. Applied egg-rr 94.2%

      \[\leadsto \color{blue}{\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}} \]
   4. Step-by-step derivation

      1. associate-/l* 99.4%

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

   5. Simplified 99.4%

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

   if 1.9999999999999999e304 < (*.f64 V l)

   1. Initial program 34.0%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 34.0%

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

      2. associate-/r* 76.5%

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

   3. Applied egg-rr 76.5%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -1 \cdot 10^{+282}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\frac{-\ell}{A}}}{\sqrt{\frac{-1}{V}}}}\\ \mathbf{elif}\;\ell \cdot V \leq -5 \cdot 10^{-299}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{-318}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\frac{-\ell}{A}}}{\sqrt{\frac{-1}{V}}}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\frac{c0}{\frac{\sqrt{\ell \cdot V}}{\sqrt{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.5}\\ \end{array} \]

Alternative 8: 77.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -5 \cdot 10^{-310}:\\ \;\;\;\;c0 \cdot {\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.5}\\ \mathbf{elif}\;\ell \leq 4.3 \cdot 10^{+217}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (if (<= l -5e-310)
   (* c0 (pow (/ (/ A V) l) 0.5))
   (if (<= l 4.3e+217)
     (* c0 (/ (sqrt (/ A V)) (sqrt l)))
     (/ c0 (sqrt (/ V (/ A l)))))))

C

double code(double c0, double A, double V, double l) {
	double tmp;
	if (l <= -5e-310) {
		tmp = c0 * pow(((A / V) / l), 0.5);
	} else if (l <= 4.3e+217) {
		tmp = c0 * (sqrt((A / V)) / sqrt(l));
	} else {
		tmp = c0 / sqrt((V / (A / l)));
	}
	return tmp;
}

Fortran

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 (l <= (-5d-310)) then
        tmp = c0 * (((a / v) / l) ** 0.5d0)
    else if (l <= 4.3d+217) then
        tmp = c0 * (sqrt((a / v)) / sqrt(l))
    else
        tmp = c0 / sqrt((v / (a / l)))
    end if
    code = tmp
end function

Java

public static double code(double c0, double A, double V, double l) {
	double tmp;
	if (l <= -5e-310) {
		tmp = c0 * Math.pow(((A / V) / l), 0.5);
	} else if (l <= 4.3e+217) {
		tmp = c0 * (Math.sqrt((A / V)) / Math.sqrt(l));
	} else {
		tmp = c0 / Math.sqrt((V / (A / l)));
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	tmp = 0
	if l <= -5e-310:
		tmp = c0 * math.pow(((A / V) / l), 0.5)
	elif l <= 4.3e+217:
		tmp = c0 * (math.sqrt((A / V)) / math.sqrt(l))
	else:
		tmp = c0 / math.sqrt((V / (A / l)))
	return tmp

Julia

function code(c0, A, V, l)
	tmp = 0.0
	if (l <= -5e-310)
		tmp = Float64(c0 * (Float64(Float64(A / V) / l) ^ 0.5));
	elseif (l <= 4.3e+217)
		tmp = Float64(c0 * Float64(sqrt(Float64(A / V)) / sqrt(l)));
	else
		tmp = Float64(c0 / sqrt(Float64(V / Float64(A / l))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	tmp = 0.0;
	if (l <= -5e-310)
		tmp = c0 * (((A / V) / l) ^ 0.5);
	elseif (l <= 4.3e+217)
		tmp = c0 * (sqrt((A / V)) / sqrt(l));
	else
		tmp = c0 / sqrt((V / (A / l)));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := If[LessEqual[l, -5e-310], N[(c0 * N[Power[N[(N[(A / V), $MachinePrecision] / l), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision], If[LessEqual[l, 4.3e+217], N[(c0 * N[(N[Sqrt[N[(A / V), $MachinePrecision]], $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 / N[Sqrt[N[(V / N[(A / l), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if l < -4.999999999999985e-310

   1. Initial program 65.6%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 65.6%

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

      2. associate-/r* 71.1%

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

   3. Applied egg-rr 71.1%

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

   if -4.999999999999985e-310 < l < 4.3000000000000001e217

   1. Initial program 77.0%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. associate-/r* 81.8%

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

      2. sqrt-div 88.4%

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

   3. Applied egg-rr 88.4%

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

   if 4.3000000000000001e217 < l

   1. Initial program 76.3%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 76.3%

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

      2. clear-num 74.9%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{1}{\frac{V \cdot \ell}{A}}\right)}}^{0.5} \]

      3. inv-pow 74.9%

         \[\leadsto c0 \cdot {\color{blue}{\left({\left(\frac{V \cdot \ell}{A}\right)}^{-1}\right)}}^{0.5} \]

      4. pow-pow 74.9%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V \cdot \ell}{A}\right)}^{\left(-1 \cdot 0.5\right)}} \]

      5. *-commutative 74.9%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{\ell \cdot V}}{A}\right)}^{\left(-1 \cdot 0.5\right)} \]

      6. associate-/l* 54.7%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell}{\frac{A}{V}}\right)}}^{\left(-1 \cdot 0.5\right)} \]

      7. metadata-eval 54.7%

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

   3. Applied egg-rr 54.7%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{\frac{A}{V}}\right)}^{-0.5}} \]
   4. Step-by-step derivation

      1. associate-/r/ 79.9%

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

   5. Simplified 79.9%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{A} \cdot V\right)}^{-0.5}} \]
   6. Step-by-step derivation

      1. associate-/r/ 54.7%

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

      2. metadata-eval 54.7%

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

      3. sqrt-pow2 54.7%

         \[\leadsto c0 \cdot \color{blue}{{\left(\sqrt{\frac{\ell}{\frac{A}{V}}}\right)}^{-1}} \]

      4. inv-pow 54.7%

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

      5. un-div-inv 54.7%

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

      6. associate-/l* 75.0%

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

      7. *-commutative 75.0%

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

      8. associate-*l/ 58.6%

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

      9. *-commutative 58.6%

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

   7. Applied egg-rr 58.6%

      \[\leadsto \color{blue}{\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}} \]
   8. Step-by-step derivation

      1. *-commutative 58.6%

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

      2. associate-/r/ 79.7%

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

   9. Simplified 79.7%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -5 \cdot 10^{-310}:\\ \;\;\;\;c0 \cdot {\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.5}\\ \mathbf{elif}\;\ell \leq 4.3 \cdot 10^{+217}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \end{array} \]

Alternative 9: 79.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{A}{\ell \cdot V}\\ \mathbf{if}\;t_0 \leq 0 \lor \neg \left(t_0 \leq 2 \cdot 10^{+301}\right):\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{t_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (/ A (* l V))))
   (if (or (<= t_0 0.0) (not (<= t_0 2e+301)))
     (/ c0 (sqrt (* V (/ l A))))
     (* c0 (sqrt t_0)))))

C

double code(double c0, double A, double V, double l) {
	double t_0 = A / (l * V);
	double tmp;
	if ((t_0 <= 0.0) || !(t_0 <= 2e+301)) {
		tmp = c0 / sqrt((V * (l / A)));
	} else {
		tmp = c0 * sqrt(t_0);
	}
	return tmp;
}

Fortran

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 = a / (l * v)
    if ((t_0 <= 0.0d0) .or. (.not. (t_0 <= 2d+301))) then
        tmp = c0 / sqrt((v * (l / a)))
    else
        tmp = c0 * sqrt(t_0)
    end if
    code = tmp
end function

Java

public static double code(double c0, double A, double V, double l) {
	double t_0 = A / (l * V);
	double tmp;
	if ((t_0 <= 0.0) || !(t_0 <= 2e+301)) {
		tmp = c0 / Math.sqrt((V * (l / A)));
	} else {
		tmp = c0 * Math.sqrt(t_0);
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	t_0 = A / (l * V)
	tmp = 0
	if (t_0 <= 0.0) or not (t_0 <= 2e+301):
		tmp = c0 / math.sqrt((V * (l / A)))
	else:
		tmp = c0 * math.sqrt(t_0)
	return tmp

Julia

function code(c0, A, V, l)
	t_0 = Float64(A / Float64(l * V))
	tmp = 0.0
	if ((t_0 <= 0.0) || !(t_0 <= 2e+301))
		tmp = Float64(c0 / sqrt(Float64(V * Float64(l / A))));
	else
		tmp = Float64(c0 * sqrt(t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	t_0 = A / (l * V);
	tmp = 0.0;
	if ((t_0 <= 0.0) || ~((t_0 <= 2e+301)))
		tmp = c0 / sqrt((V * (l / A)));
	else
		tmp = c0 * sqrt(t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := Block[{t$95$0 = N[(A / N[(l * V), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 0.0], N[Not[LessEqual[t$95$0, 2e+301]], $MachinePrecision]], N[(c0 / N[Sqrt[N[(V * N[(l / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(c0 * N[Sqrt[t$95$0], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 A (*.f64 V l)) < 0.0 or 2.00000000000000011e301 < (/.f64 A (*.f64 V l))

   1. Initial program 32.7%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 32.7%

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

      2. clear-num 32.7%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{1}{\frac{V \cdot \ell}{A}}\right)}}^{0.5} \]

      3. inv-pow 32.7%

         \[\leadsto c0 \cdot {\color{blue}{\left({\left(\frac{V \cdot \ell}{A}\right)}^{-1}\right)}}^{0.5} \]

      4. pow-pow 33.4%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V \cdot \ell}{A}\right)}^{\left(-1 \cdot 0.5\right)}} \]

      5. *-commutative 33.4%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{\ell \cdot V}}{A}\right)}^{\left(-1 \cdot 0.5\right)} \]

      6. associate-/l* 52.6%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell}{\frac{A}{V}}\right)}}^{\left(-1 \cdot 0.5\right)} \]

      7. metadata-eval 52.6%

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

   3. Applied egg-rr 52.6%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{\frac{A}{V}}\right)}^{-0.5}} \]
   4. Step-by-step derivation

      1. associate-/r/ 51.7%

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

   5. Simplified 51.7%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{A} \cdot V\right)}^{-0.5}} \]
   6. Step-by-step derivation

      1. associate-/r/ 52.6%

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

      2. metadata-eval 52.6%

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

      3. sqrt-pow2 52.6%

         \[\leadsto c0 \cdot \color{blue}{{\left(\sqrt{\frac{\ell}{\frac{A}{V}}}\right)}^{-1}} \]

      4. inv-pow 52.6%

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

      5. un-div-inv 52.6%

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

      6. associate-/l* 33.4%

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

      7. *-commutative 33.4%

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

      8. associate-*l/ 52.6%

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

      9. *-commutative 52.6%

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

   7. Applied egg-rr 52.6%

      \[\leadsto \color{blue}{\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 33.4%

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

      2. associate-*l/ 51.8%

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

      3. *-commutative 51.8%

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

   9. Simplified 51.8%

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

   if 0.0 < (/.f64 A (*.f64 V l)) < 2.00000000000000011e301

   1. Initial program 98.8%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{\ell \cdot V} \leq 0 \lor \neg \left(\frac{A}{\ell \cdot V} \leq 2 \cdot 10^{+301}\right):\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \end{array} \]

Alternative 10: 79.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{A}{\ell \cdot V}\\ \mathbf{if}\;t_0 \leq 2 \cdot 10^{-282}:\\ \;\;\;\;c0 \cdot {\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.5}\\ \mathbf{elif}\;t_0 \leq 2 \cdot 10^{+301}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{\ell \cdot V}{A}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (/ A (* l V))))
   (if (<= t_0 2e-282)
     (* c0 (pow (/ (/ A V) l) 0.5))
     (if (<= t_0 2e+301)
       (/ c0 (sqrt (/ (* l V) A)))
       (/ c0 (sqrt (* V (/ l A))))))))

C

double code(double c0, double A, double V, double l) {
	double t_0 = A / (l * V);
	double tmp;
	if (t_0 <= 2e-282) {
		tmp = c0 * pow(((A / V) / l), 0.5);
	} else if (t_0 <= 2e+301) {
		tmp = c0 / sqrt(((l * V) / A));
	} else {
		tmp = c0 / sqrt((V * (l / A)));
	}
	return tmp;
}

Fortran

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 = a / (l * v)
    if (t_0 <= 2d-282) then
        tmp = c0 * (((a / v) / l) ** 0.5d0)
    else if (t_0 <= 2d+301) then
        tmp = c0 / sqrt(((l * v) / a))
    else
        tmp = c0 / sqrt((v * (l / a)))
    end if
    code = tmp
end function

Java

public static double code(double c0, double A, double V, double l) {
	double t_0 = A / (l * V);
	double tmp;
	if (t_0 <= 2e-282) {
		tmp = c0 * Math.pow(((A / V) / l), 0.5);
	} else if (t_0 <= 2e+301) {
		tmp = c0 / Math.sqrt(((l * V) / A));
	} else {
		tmp = c0 / Math.sqrt((V * (l / A)));
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	t_0 = A / (l * V)
	tmp = 0
	if t_0 <= 2e-282:
		tmp = c0 * math.pow(((A / V) / l), 0.5)
	elif t_0 <= 2e+301:
		tmp = c0 / math.sqrt(((l * V) / A))
	else:
		tmp = c0 / math.sqrt((V * (l / A)))
	return tmp

Julia

function code(c0, A, V, l)
	t_0 = Float64(A / Float64(l * V))
	tmp = 0.0
	if (t_0 <= 2e-282)
		tmp = Float64(c0 * (Float64(Float64(A / V) / l) ^ 0.5));
	elseif (t_0 <= 2e+301)
		tmp = Float64(c0 / sqrt(Float64(Float64(l * V) / A)));
	else
		tmp = Float64(c0 / sqrt(Float64(V * Float64(l / A))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	t_0 = A / (l * V);
	tmp = 0.0;
	if (t_0 <= 2e-282)
		tmp = c0 * (((A / V) / l) ^ 0.5);
	elseif (t_0 <= 2e+301)
		tmp = c0 / sqrt(((l * V) / A));
	else
		tmp = c0 / sqrt((V * (l / A)));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := Block[{t$95$0 = N[(A / N[(l * V), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 2e-282], N[(c0 * N[Power[N[(N[(A / V), $MachinePrecision] / l), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2e+301], N[(c0 / N[Sqrt[N[(N[(l * V), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(c0 / N[Sqrt[N[(V * N[(l / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 A (*.f64 V l)) < 2e-282

   1. Initial program 30.0%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 30.0%

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

      2. associate-/r* 49.4%

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

   3. Applied egg-rr 49.4%

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

   if 2e-282 < (/.f64 A (*.f64 V l)) < 2.00000000000000011e301

   1. Initial program 99.3%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 99.3%

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

      2. clear-num 99.2%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{1}{\frac{V \cdot \ell}{A}}\right)}}^{0.5} \]

      3. inv-pow 99.2%

         \[\leadsto c0 \cdot {\color{blue}{\left({\left(\frac{V \cdot \ell}{A}\right)}^{-1}\right)}}^{0.5} \]

      4. pow-pow 99.3%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V \cdot \ell}{A}\right)}^{\left(-1 \cdot 0.5\right)}} \]

      5. *-commutative 99.3%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{\ell \cdot V}}{A}\right)}^{\left(-1 \cdot 0.5\right)} \]

      6. associate-/l* 89.5%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell}{\frac{A}{V}}\right)}}^{\left(-1 \cdot 0.5\right)} \]

      7. metadata-eval 89.5%

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

   3. Applied egg-rr 89.5%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{\frac{A}{V}}\right)}^{-0.5}} \]
   4. Step-by-step derivation

      1. associate-/r/ 87.2%

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

   5. Simplified 87.2%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{A} \cdot V\right)}^{-0.5}} \]
   6. Step-by-step derivation

      1. associate-/r/ 89.5%

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

      2. metadata-eval 89.5%

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

      3. sqrt-pow2 89.4%

         \[\leadsto c0 \cdot \color{blue}{{\left(\sqrt{\frac{\ell}{\frac{A}{V}}}\right)}^{-1}} \]

      4. inv-pow 89.4%

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

      5. un-div-inv 89.5%

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

      6. associate-/l* 99.3%

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

      7. *-commutative 99.3%

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

      8. associate-*l/ 88.8%

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

      9. *-commutative 88.8%

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

   7. Applied egg-rr 88.8%

      \[\leadsto \color{blue}{\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 99.3%

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

   9. Applied egg-rr 99.3%

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

   if 2.00000000000000011e301 < (/.f64 A (*.f64 V l))

   1. Initial program 39.2%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Step-by-step derivation

      1. pow1/2 39.2%

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

      2. clear-num 39.2%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{1}{\frac{V \cdot \ell}{A}}\right)}}^{0.5} \]

      3. inv-pow 39.2%

         \[\leadsto c0 \cdot {\color{blue}{\left({\left(\frac{V \cdot \ell}{A}\right)}^{-1}\right)}}^{0.5} \]

      4. pow-pow 40.6%

         \[\leadsto c0 \cdot \color{blue}{{\left(\frac{V \cdot \ell}{A}\right)}^{\left(-1 \cdot 0.5\right)}} \]

      5. *-commutative 40.6%

         \[\leadsto c0 \cdot {\left(\frac{\color{blue}{\ell \cdot V}}{A}\right)}^{\left(-1 \cdot 0.5\right)} \]

      6. associate-/l* 61.3%

         \[\leadsto c0 \cdot {\color{blue}{\left(\frac{\ell}{\frac{A}{V}}\right)}}^{\left(-1 \cdot 0.5\right)} \]

      7. metadata-eval 61.3%

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

   3. Applied egg-rr 61.3%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{\frac{A}{V}}\right)}^{-0.5}} \]
   4. Step-by-step derivation

      1. associate-/r/ 59.6%

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

   5. Simplified 59.6%

      \[\leadsto c0 \cdot \color{blue}{{\left(\frac{\ell}{A} \cdot V\right)}^{-0.5}} \]
   6. Step-by-step derivation

      1. associate-/r/ 61.3%

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

      2. metadata-eval 61.3%

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

      3. sqrt-pow2 61.3%

         \[\leadsto c0 \cdot \color{blue}{{\left(\sqrt{\frac{\ell}{\frac{A}{V}}}\right)}^{-1}} \]

      4. inv-pow 61.3%

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

      5. un-div-inv 61.4%

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

      6. associate-/l* 40.6%

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

      7. *-commutative 40.6%

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

      8. associate-*l/ 61.4%

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

      9. *-commutative 61.4%

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

   7. Applied egg-rr 61.4%

      \[\leadsto \color{blue}{\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 40.6%

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

      2. associate-*l/ 59.7%

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

      3. *-commutative 59.7%

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

   9. Simplified 59.7%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{\ell \cdot V} \leq 2 \cdot 10^{-282}:\\ \;\;\;\;c0 \cdot {\left(\frac{\frac{A}{V}}{\ell}\right)}^{0.5}\\ \mathbf{elif}\;\frac{A}{\ell \cdot V} \leq 2 \cdot 10^{+301}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{\ell \cdot V}{A}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{V \cdot \frac{\ell}{A}}}\\ \end{array} \]

Alternative 11: 73.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ c0 \cdot \sqrt{\frac{A}{\ell \cdot V}} \end{array} \]

FPCore

(FPCore (c0 A V l) :precision binary64 (* c0 (sqrt (/ A (* l V)))))

C

double code(double c0, double A, double V, double l) {
	return c0 * sqrt((A / (l * V)));
}

Fortran

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 / (l * v)))
end function

Java

public static double code(double c0, double A, double V, double l) {
	return c0 * Math.sqrt((A / (l * V)));
}

Python

def code(c0, A, V, l):
	return c0 * math.sqrt((A / (l * V)))

Julia

function code(c0, A, V, l)
	return Float64(c0 * sqrt(Float64(A / Float64(l * V))))
end

MATLAB

function tmp = code(c0, A, V, l)
	tmp = c0 * sqrt((A / (l * V)));
end

Wolfram

code[c0_, A_, V_, l_] := N[(c0 * N[Sqrt[N[(A / N[(l * V), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.7%

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

2. Final simplification 70.7%

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

Reproduce

herbie shell --seed 2023305 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))