Henrywood and Agarwal, Equation (3)

Percentage Accurate: 73.9% → 96.9%

Time: 13.6s

Alternatives: 16

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: 73.9% 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 74.5%

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

   1. pow1/2 74.5%

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

   2. add-cube-cbrt 74.1%

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

   3. pow3 74.1%

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

   4. pow-pow 74.1%

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

   5. metadata-eval 74.1%

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

4. Applied egg-rr 74.1%

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

   1. cbrt-div 84.6%

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

6. Applied egg-rr 84.6%

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

   1. *-commutative 84.6%

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

   2. cbrt-prod 98.2%

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

8. Applied egg-rr 98.2%

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

Alternative 2: 77.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{if}\;t\_0 \leq 2 \cdot 10^{-298}:\\ \;\;\;\;\frac{c0}{{\left(V \cdot \frac{\ell}{A}\right)}^{0.5}}\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left(\frac{V}{\frac{A}{\ell}}\right)}^{-0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (* c0 (sqrt (/ A (* l V))))))
   (if (<= t_0 2e-298)
     (/ c0 (pow (* V (/ l A)) 0.5))
     (if (<= t_0 2e+307) t_0 (* c0 (pow (/ V (/ A l)) -0.5))))))

C

double code(double c0, double A, double V, double l) {
	double t_0 = c0 * sqrt((A / (l * V)));
	double tmp;
	if (t_0 <= 2e-298) {
		tmp = c0 / pow((V * (l / A)), 0.5);
	} else if (t_0 <= 2e+307) {
		tmp = t_0;
	} else {
		tmp = c0 * pow((V / (A / 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((a / (l * v)))
    if (t_0 <= 2d-298) then
        tmp = c0 / ((v * (l / a)) ** 0.5d0)
    else if (t_0 <= 2d+307) then
        tmp = t_0
    else
        tmp = c0 * ((v / (a / 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((A / (l * V)));
	double tmp;
	if (t_0 <= 2e-298) {
		tmp = c0 / Math.pow((V * (l / A)), 0.5);
	} else if (t_0 <= 2e+307) {
		tmp = t_0;
	} else {
		tmp = c0 * Math.pow((V / (A / l)), -0.5);
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	t_0 = c0 * math.sqrt((A / (l * V)))
	tmp = 0
	if t_0 <= 2e-298:
		tmp = c0 / math.pow((V * (l / A)), 0.5)
	elif t_0 <= 2e+307:
		tmp = t_0
	else:
		tmp = c0 * math.pow((V / (A / l)), -0.5)
	return tmp

Julia

function code(c0, A, V, l)
	t_0 = Float64(c0 * sqrt(Float64(A / Float64(l * V))))
	tmp = 0.0
	if (t_0 <= 2e-298)
		tmp = Float64(c0 / (Float64(V * Float64(l / A)) ^ 0.5));
	elseif (t_0 <= 2e+307)
		tmp = t_0;
	else
		tmp = Float64(c0 * (Float64(V / Float64(A / l)) ^ -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	t_0 = c0 * sqrt((A / (l * V)));
	tmp = 0.0;
	if (t_0 <= 2e-298)
		tmp = c0 / ((V * (l / A)) ^ 0.5);
	elseif (t_0 <= 2e+307)
		tmp = t_0;
	else
		tmp = c0 * ((V / (A / l)) ^ -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := Block[{t$95$0 = N[(c0 * N[Sqrt[N[(A / N[(l * V), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 2e-298], N[(c0 / N[Power[N[(V * N[(l / A), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2e+307], t$95$0, N[(c0 * N[Power[N[(V / N[(A / l), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l)))) < 1.99999999999999982e-298

   1. Initial program 67.8%

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

      1. pow1/2 67.8%

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

      2. add-cube-cbrt 67.4%

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

      3. pow3 67.4%

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

      4. pow-pow 67.4%

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

      5. metadata-eval 67.4%

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

   4. Applied egg-rr 67.4%

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

      1. cbrt-div 80.1%

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

   6. Applied egg-rr 80.1%

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

      1. add-sqr-sqrt 80.1%

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

      2. sqrt-unprod 67.2%

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

      3. pow-prod-up 67.2%

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

      4. metadata-eval 67.2%

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

      5. pow3 67.2%

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

      6. cbrt-undiv 67.4%

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

      7. cbrt-undiv 67.5%

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

      8. cbrt-undiv 67.4%

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

      9. add-cube-cbrt 67.8%

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

      10. sqrt-undiv 38.1%

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

      11. clear-num 38.1%

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

      12. sqrt-div 67.7%

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

      13. associate-*r/ 73.9%

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

   8. Applied egg-rr 73.9%

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

   if 1.99999999999999982e-298 < (*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l)))) < 1.99999999999999997e307

   1. Initial program 96.7%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Add Preprocessing

   if 1.99999999999999997e307 < (*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))

   1. Initial program 59.9%

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

      1. pow1/2 59.9%

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

      2. clear-num 59.9%

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

      3. inv-pow 59.9%

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

      4. pow-pow 60.5%

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

      5. associate-/l* 70.0%

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

      6. metadata-eval 70.0%

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

   4. Applied egg-rr 70.0%

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

      1. clear-num 70.0%

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

      2. un-div-inv 70.0%

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

   6. Applied egg-rr 70.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}} \leq 2 \cdot 10^{-298}:\\ \;\;\;\;\frac{c0}{{\left(V \cdot \frac{\ell}{A}\right)}^{0.5}}\\ \mathbf{elif}\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}} \leq 2 \cdot 10^{+307}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left(\frac{V}{\frac{A}{\ell}}\right)}^{-0.5}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{if}\;t\_0 \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left(\frac{V}{\frac{A}{\ell}}\right)}^{-0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (* c0 (sqrt (/ A (* l V))))))
   (if (<= t_0 0.0)
     (* c0 (sqrt (/ (/ A V) l)))
     (if (<= t_0 2e+307) t_0 (* c0 (pow (/ V (/ A l)) -0.5))))))

C

double code(double c0, double A, double V, double l) {
	double t_0 = c0 * sqrt((A / (l * V)));
	double tmp;
	if (t_0 <= 0.0) {
		tmp = c0 * sqrt(((A / V) / l));
	} else if (t_0 <= 2e+307) {
		tmp = t_0;
	} else {
		tmp = c0 * pow((V / (A / 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((a / (l * v)))
    if (t_0 <= 0.0d0) then
        tmp = c0 * sqrt(((a / v) / l))
    else if (t_0 <= 2d+307) then
        tmp = t_0
    else
        tmp = c0 * ((v / (a / 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((A / (l * V)));
	double tmp;
	if (t_0 <= 0.0) {
		tmp = c0 * Math.sqrt(((A / V) / l));
	} else if (t_0 <= 2e+307) {
		tmp = t_0;
	} else {
		tmp = c0 * Math.pow((V / (A / l)), -0.5);
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	t_0 = c0 * math.sqrt((A / (l * V)))
	tmp = 0
	if t_0 <= 0.0:
		tmp = c0 * math.sqrt(((A / V) / l))
	elif t_0 <= 2e+307:
		tmp = t_0
	else:
		tmp = c0 * math.pow((V / (A / l)), -0.5)
	return tmp

Julia

function code(c0, A, V, l)
	t_0 = Float64(c0 * sqrt(Float64(A / Float64(l * V))))
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = Float64(c0 * sqrt(Float64(Float64(A / V) / l)));
	elseif (t_0 <= 2e+307)
		tmp = t_0;
	else
		tmp = Float64(c0 * (Float64(V / Float64(A / l)) ^ -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	t_0 = c0 * sqrt((A / (l * V)));
	tmp = 0.0;
	if (t_0 <= 0.0)
		tmp = c0 * sqrt(((A / V) / l));
	elseif (t_0 <= 2e+307)
		tmp = t_0;
	else
		tmp = c0 * ((V / (A / l)) ^ -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := Block[{t$95$0 = N[(c0 * N[Sqrt[N[(A / N[(l * V), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.0], N[(c0 * N[Sqrt[N[(N[(A / V), $MachinePrecision] / l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2e+307], t$95$0, N[(c0 * N[Power[N[(V / N[(A / l), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l)))) < 0.0

   1. Initial program 67.2%

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

      1. associate-/r* 72.1%

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

   4. Applied egg-rr 72.1%

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

   if 0.0 < (*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l)))) < 1.99999999999999997e307

   1. Initial program 96.8%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Add Preprocessing

   if 1.99999999999999997e307 < (*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))

   1. Initial program 59.9%

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

      1. pow1/2 59.9%

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

      2. clear-num 59.9%

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

      3. inv-pow 59.9%

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

      4. pow-pow 60.5%

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

      5. associate-/l* 70.0%

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

      6. metadata-eval 70.0%

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

   4. Applied egg-rr 70.0%

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

      1. clear-num 70.0%

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

      2. un-div-inv 70.0%

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

   6. Applied egg-rr 70.0%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}} \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}} \leq 2 \cdot 10^{+307}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left(\frac{V}{\frac{A}{\ell}}\right)}^{-0.5}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{if}\;t\_0 \leq 0 \lor \neg \left(t\_0 \leq 10^{+276}\right):\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (* c0 (sqrt (/ A (* l V))))))
   (if (or (<= t_0 0.0) (not (<= t_0 1e+276)))
     (* c0 (sqrt (/ (/ A V) l)))
     t_0)))

C

double code(double c0, double A, double V, double l) {
	double t_0 = c0 * sqrt((A / (l * V)));
	double tmp;
	if ((t_0 <= 0.0) || !(t_0 <= 1e+276)) {
		tmp = c0 * sqrt(((A / V) / l));
	} else {
		tmp = 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 = c0 * sqrt((a / (l * v)))
    if ((t_0 <= 0.0d0) .or. (.not. (t_0 <= 1d+276))) then
        tmp = c0 * sqrt(((a / v) / l))
    else
        tmp = t_0
    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((A / (l * V)));
	double tmp;
	if ((t_0 <= 0.0) || !(t_0 <= 1e+276)) {
		tmp = c0 * Math.sqrt(((A / V) / l));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	t_0 = c0 * math.sqrt((A / (l * V)))
	tmp = 0
	if (t_0 <= 0.0) or not (t_0 <= 1e+276):
		tmp = c0 * math.sqrt(((A / V) / l))
	else:
		tmp = t_0
	return tmp

Julia

function code(c0, A, V, l)
	t_0 = Float64(c0 * sqrt(Float64(A / Float64(l * V))))
	tmp = 0.0
	if ((t_0 <= 0.0) || !(t_0 <= 1e+276))
		tmp = Float64(c0 * sqrt(Float64(Float64(A / V) / l)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	t_0 = c0 * sqrt((A / (l * V)));
	tmp = 0.0;
	if ((t_0 <= 0.0) || ~((t_0 <= 1e+276)))
		tmp = c0 * sqrt(((A / V) / l));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := Block[{t$95$0 = N[(c0 * N[Sqrt[N[(A / N[(l * V), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 0.0], N[Not[LessEqual[t$95$0, 1e+276]], $MachinePrecision]], N[(c0 * N[Sqrt[N[(N[(A / V), $MachinePrecision] / l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$0]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l)))) < 0.0 or 1.0000000000000001e276 < (*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l))))

   1. Initial program 66.5%

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

      1. associate-/r* 72.1%

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

   4. Applied egg-rr 72.1%

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

   if 0.0 < (*.f64 c0 (sqrt.f64 (/.f64 A (*.f64 V l)))) < 1.0000000000000001e276

   1. Initial program 96.7%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}} \leq 0 \lor \neg \left(c0 \cdot \sqrt{\frac{A}{\ell \cdot V}} \leq 10^{+276}\right):\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := c0 \cdot \frac{\sqrt{-\frac{A}{\ell}}}{\sqrt{-V}}\\ \mathbf{if}\;V \leq -3.5 \cdot 10^{+215}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;V \leq -6 \cdot 10^{-96}:\\ \;\;\;\;c0 \cdot {\left(\frac{\sqrt[3]{A}}{\sqrt[3]{\ell \cdot V}}\right)}^{1.5}\\ \mathbf{elif}\;V \leq -1 \cdot 10^{-310}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell}}}{\sqrt{V}}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (* c0 (/ (sqrt (- (/ A l))) (sqrt (- V))))))
   (if (<= V -3.5e+215)
     t_0
     (if (<= V -6e-96)
       (* c0 (pow (/ (cbrt A) (cbrt (* l V))) 1.5))
       (if (<= V -1e-310) t_0 (/ (* c0 (/ (sqrt A) (sqrt l))) (sqrt V)))))))

C

double code(double c0, double A, double V, double l) {
	double t_0 = c0 * (sqrt(-(A / l)) / sqrt(-V));
	double tmp;
	if (V <= -3.5e+215) {
		tmp = t_0;
	} else if (V <= -6e-96) {
		tmp = c0 * pow((cbrt(A) / cbrt((l * V))), 1.5);
	} else if (V <= -1e-310) {
		tmp = t_0;
	} else {
		tmp = (c0 * (sqrt(A) / sqrt(l))) / sqrt(V);
	}
	return tmp;
}

Java

public static double code(double c0, double A, double V, double l) {
	double t_0 = c0 * (Math.sqrt(-(A / l)) / Math.sqrt(-V));
	double tmp;
	if (V <= -3.5e+215) {
		tmp = t_0;
	} else if (V <= -6e-96) {
		tmp = c0 * Math.pow((Math.cbrt(A) / Math.cbrt((l * V))), 1.5);
	} else if (V <= -1e-310) {
		tmp = t_0;
	} else {
		tmp = (c0 * (Math.sqrt(A) / Math.sqrt(l))) / Math.sqrt(V);
	}
	return tmp;
}

Julia

function code(c0, A, V, l)
	t_0 = Float64(c0 * Float64(sqrt(Float64(-Float64(A / l))) / sqrt(Float64(-V))))
	tmp = 0.0
	if (V <= -3.5e+215)
		tmp = t_0;
	elseif (V <= -6e-96)
		tmp = Float64(c0 * (Float64(cbrt(A) / cbrt(Float64(l * V))) ^ 1.5));
	elseif (V <= -1e-310)
		tmp = t_0;
	else
		tmp = Float64(Float64(c0 * Float64(sqrt(A) / sqrt(l))) / sqrt(V));
	end
	return tmp
end

Wolfram

code[c0_, A_, V_, l_] := Block[{t$95$0 = N[(c0 * N[(N[Sqrt[(-N[(A / l), $MachinePrecision])], $MachinePrecision] / N[Sqrt[(-V)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[V, -3.5e+215], t$95$0, If[LessEqual[V, -6e-96], N[(c0 * N[Power[N[(N[Power[A, 1/3], $MachinePrecision] / N[Power[N[(l * V), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], 1.5], $MachinePrecision]), $MachinePrecision], If[LessEqual[V, -1e-310], t$95$0, N[(N[(c0 * N[(N[Sqrt[A], $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Sqrt[V], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if V < -3.49999999999999977e215 or -6e-96 < V < -9.999999999999969e-311

   1. Initial program 67.4%

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

      1. associate-/r* 60.2%

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

   4. Applied egg-rr 60.2%

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

      1. associate-/r* 67.4%

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

      2. associate-/l/ 70.2%

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

      3. frac-2neg 70.2%

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

      4. sqrt-div 87.9%

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

      5. distribute-neg-frac2 87.9%

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

   6. Applied egg-rr 87.9%

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

   if -3.49999999999999977e215 < V < -6e-96

   1. Initial program 80.3%

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

      1. pow1/2 80.3%

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

      2. add-cube-cbrt 79.6%

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

      3. pow3 79.7%

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

      4. pow-pow 79.7%

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

      5. metadata-eval 79.7%

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

   4. Applied egg-rr 79.7%

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

      1. cbrt-div 90.3%

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

   6. Applied egg-rr 90.3%

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

   if -9.999999999999969e-311 < V

   1. Initial program 74.4%

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

      1. associate-/r* 76.0%

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

   4. Applied egg-rr 76.0%

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

      1. *-commutative 76.0%

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

      2. associate-/r* 74.4%

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

      3. associate-/l/ 74.5%

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

      4. sqrt-div 84.4%

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

      5. associate-*l/ 83.3%

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

      6. pow1/2 83.3%

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

   6. Applied egg-rr 83.3%

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

      1. unpow1/2 83.3%

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

      2. sqrt-div 51.5%

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

   8. Applied egg-rr 51.5%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;V \leq -3.5 \cdot 10^{+215}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-\frac{A}{\ell}}}{\sqrt{-V}}\\ \mathbf{elif}\;V \leq -6 \cdot 10^{-96}:\\ \;\;\;\;c0 \cdot {\left(\frac{\sqrt[3]{A}}{\sqrt[3]{\ell \cdot V}}\right)}^{1.5}\\ \mathbf{elif}\;V \leq -1 \cdot 10^{-310}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-\frac{A}{\ell}}}{\sqrt{-V}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell}}}{\sqrt{V}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -\infty:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-\frac{A}{\ell}}}{\sqrt{-V}}\\ \mathbf{elif}\;\ell \cdot V \leq -2 \cdot 10^{-294}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot {\left(\frac{V}{\frac{A}{\ell}}\right)}^{-0.5}\\ \mathbf{elif}\;\ell \cdot V \leq 10^{+301}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{{\left(V \cdot \frac{\ell}{A}\right)}^{0.5}}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (if (<= (* l V) (- INFINITY))
   (* c0 (/ (sqrt (- (/ A l))) (sqrt (- V))))
   (if (<= (* l V) -2e-294)
     (* c0 (/ (sqrt (- A)) (sqrt (* V (- l)))))
     (if (<= (* l V) 0.0)
       (* c0 (pow (/ V (/ A l)) -0.5))
       (if (<= (* l V) 1e+301)
         (* c0 (/ (sqrt A) (sqrt (* l V))))
         (/ c0 (pow (* V (/ l A)) 0.5)))))))

C

double code(double c0, double A, double V, double l) {
	double tmp;
	if ((l * V) <= -((double) INFINITY)) {
		tmp = c0 * (sqrt(-(A / l)) / sqrt(-V));
	} else if ((l * V) <= -2e-294) {
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	} else if ((l * V) <= 0.0) {
		tmp = c0 * pow((V / (A / l)), -0.5);
	} else if ((l * V) <= 1e+301) {
		tmp = c0 * (sqrt(A) / sqrt((l * V)));
	} else {
		tmp = c0 / pow((V * (l / A)), 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(-(A / l)) / Math.sqrt(-V));
	} else if ((l * V) <= -2e-294) {
		tmp = c0 * (Math.sqrt(-A) / Math.sqrt((V * -l)));
	} else if ((l * V) <= 0.0) {
		tmp = c0 * Math.pow((V / (A / l)), -0.5);
	} else if ((l * V) <= 1e+301) {
		tmp = c0 * (Math.sqrt(A) / Math.sqrt((l * V)));
	} else {
		tmp = c0 / Math.pow((V * (l / A)), 0.5);
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	tmp = 0
	if (l * V) <= -math.inf:
		tmp = c0 * (math.sqrt(-(A / l)) / math.sqrt(-V))
	elif (l * V) <= -2e-294:
		tmp = c0 * (math.sqrt(-A) / math.sqrt((V * -l)))
	elif (l * V) <= 0.0:
		tmp = c0 * math.pow((V / (A / l)), -0.5)
	elif (l * V) <= 1e+301:
		tmp = c0 * (math.sqrt(A) / math.sqrt((l * V)))
	else:
		tmp = c0 / math.pow((V * (l / A)), 0.5)
	return tmp

Julia

function code(c0, A, V, l)
	tmp = 0.0
	if (Float64(l * V) <= Float64(-Inf))
		tmp = Float64(c0 * Float64(sqrt(Float64(-Float64(A / l))) / sqrt(Float64(-V))));
	elseif (Float64(l * V) <= -2e-294)
		tmp = Float64(c0 * Float64(sqrt(Float64(-A)) / sqrt(Float64(V * Float64(-l)))));
	elseif (Float64(l * V) <= 0.0)
		tmp = Float64(c0 * (Float64(V / Float64(A / l)) ^ -0.5));
	elseif (Float64(l * V) <= 1e+301)
		tmp = Float64(c0 * Float64(sqrt(A) / sqrt(Float64(l * V))));
	else
		tmp = Float64(c0 / (Float64(V * Float64(l / A)) ^ 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(-(A / l)) / sqrt(-V));
	elseif ((l * V) <= -2e-294)
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	elseif ((l * V) <= 0.0)
		tmp = c0 * ((V / (A / l)) ^ -0.5);
	elseif ((l * V) <= 1e+301)
		tmp = c0 * (sqrt(A) / sqrt((l * V)));
	else
		tmp = c0 / ((V * (l / A)) ^ 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := If[LessEqual[N[(l * V), $MachinePrecision], (-Infinity)], N[(c0 * N[(N[Sqrt[(-N[(A / l), $MachinePrecision])], $MachinePrecision] / N[Sqrt[(-V)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], -2e-294], N[(c0 * N[(N[Sqrt[(-A)], $MachinePrecision] / N[Sqrt[N[(V * (-l)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], 0.0], N[(c0 * N[Power[N[(V / N[(A / l), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], 1e+301], N[(c0 * N[(N[Sqrt[A], $MachinePrecision] / N[Sqrt[N[(l * V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 / N[Power[N[(V * N[(l / A), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 5.7%

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

      1. associate-/r* 37.7%

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

   4. Applied egg-rr 37.7%

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

      1. associate-/r* 5.7%

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

      2. associate-/l/ 37.1%

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

      3. frac-2neg 37.1%

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

      4. sqrt-div 70.7%

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

      5. distribute-neg-frac2 70.7%

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

   6. Applied egg-rr 70.7%

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

   if -inf.0 < (*.f64 V l) < -2.00000000000000003e-294

   1. Initial program 85.2%

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

      1. associate-/r* 80.1%

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

   4. Applied egg-rr 80.1%

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

      1. associate-/r* 85.2%

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

      2. frac-2neg 85.2%

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

      3. sqrt-div 99.4%

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

      4. neg-sub0 99.4%

         \[\leadsto c0 \cdot \frac{\sqrt{\color{blue}{0 - A}}}{\sqrt{-V \cdot \ell}} \]

      5. distribute-rgt-neg-in 99.4%

         \[\leadsto c0 \cdot \frac{\sqrt{0 - A}}{\sqrt{\color{blue}{V \cdot \left(-\ell\right)}}} \]

   6. Applied egg-rr 99.4%

      \[\leadsto c0 \cdot \color{blue}{\frac{\sqrt{0 - A}}{\sqrt{V \cdot \left(-\ell\right)}}} \]

   if -2.00000000000000003e-294 < (*.f64 V l) < -0.0

   1. Initial program 47.6%

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

      1. pow1/2 47.6%

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

      2. clear-num 47.6%

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

      3. inv-pow 47.6%

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

      4. pow-pow 47.6%

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

      5. associate-/l* 79.3%

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

      6. metadata-eval 79.3%

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

   4. Applied egg-rr 79.3%

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

      1. clear-num 79.3%

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

      2. un-div-inv 79.4%

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

   6. Applied egg-rr 79.4%

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

   if -0.0 < (*.f64 V l) < 1.00000000000000005e301

   1. Initial program 85.2%

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

      1. associate-/r* 70.4%

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

   4. Applied egg-rr 70.4%

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

      1. associate-/r* 85.2%

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

      2. sqrt-div 99.0%

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

   6. Applied egg-rr 99.0%

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

   if 1.00000000000000005e301 < (*.f64 V l)

   1. Initial program 29.8%

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

      1. pow1/2 29.8%

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

      2. add-cube-cbrt 29.8%

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

      3. pow3 29.8%

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

      4. pow-pow 29.8%

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

      5. metadata-eval 29.8%

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

   4. Applied egg-rr 29.8%

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

      1. cbrt-div 29.8%

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

   6. Applied egg-rr 29.8%

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

      1. add-sqr-sqrt 29.8%

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

      2. sqrt-unprod 29.8%

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

      3. pow-prod-up 29.8%

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

      4. metadata-eval 29.8%

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

      5. pow3 29.8%

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

      6. cbrt-undiv 29.8%

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

      7. cbrt-undiv 29.8%

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

      8. cbrt-undiv 29.8%

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

      9. add-cube-cbrt 29.8%

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

      10. sqrt-undiv 29.8%

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

      11. clear-num 29.8%

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

      12. sqrt-div 29.8%

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

      13. associate-*r/ 68.4%

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

   8. Applied egg-rr 68.5%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -\infty:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-\frac{A}{\ell}}}{\sqrt{-V}}\\ \mathbf{elif}\;\ell \cdot V \leq -2 \cdot 10^{-294}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot {\left(\frac{V}{\frac{A}{\ell}}\right)}^{-0.5}\\ \mathbf{elif}\;\ell \cdot V \leq 10^{+301}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{{\left(V \cdot \frac{\ell}{A}\right)}^{0.5}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -5 \cdot 10^{+132}:\\ \;\;\;\;c0 \cdot \frac{{\left(\frac{A}{V}\right)}^{0.5}}{\sqrt{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq -5 \cdot 10^{-206}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot \left({\left(\frac{V}{A}\right)}^{-0.5} \cdot {\ell}^{-0.5}\right)\\ \mathbf{elif}\;\ell \cdot V \leq 10^{+301}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{{\left(V \cdot \frac{\ell}{A}\right)}^{0.5}}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (if (<= (* l V) -5e+132)
   (* c0 (/ (pow (/ A V) 0.5) (sqrt l)))
   (if (<= (* l V) -5e-206)
     (* c0 (sqrt (/ A (* l V))))
     (if (<= (* l V) 0.0)
       (* c0 (* (pow (/ V A) -0.5) (pow l -0.5)))
       (if (<= (* l V) 1e+301)
         (* c0 (/ (sqrt A) (sqrt (* l V))))
         (/ c0 (pow (* V (/ l A)) 0.5)))))))

C

double code(double c0, double A, double V, double l) {
	double tmp;
	if ((l * V) <= -5e+132) {
		tmp = c0 * (pow((A / V), 0.5) / sqrt(l));
	} else if ((l * V) <= -5e-206) {
		tmp = c0 * sqrt((A / (l * V)));
	} else if ((l * V) <= 0.0) {
		tmp = c0 * (pow((V / A), -0.5) * pow(l, -0.5));
	} else if ((l * V) <= 1e+301) {
		tmp = c0 * (sqrt(A) / sqrt((l * V)));
	} else {
		tmp = c0 / pow((V * (l / A)), 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) <= (-5d+132)) then
        tmp = c0 * (((a / v) ** 0.5d0) / sqrt(l))
    else if ((l * v) <= (-5d-206)) then
        tmp = c0 * sqrt((a / (l * v)))
    else if ((l * v) <= 0.0d0) then
        tmp = c0 * (((v / a) ** (-0.5d0)) * (l ** (-0.5d0)))
    else if ((l * v) <= 1d+301) then
        tmp = c0 * (sqrt(a) / sqrt((l * v)))
    else
        tmp = c0 / ((v * (l / a)) ** 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) <= -5e+132) {
		tmp = c0 * (Math.pow((A / V), 0.5) / Math.sqrt(l));
	} else if ((l * V) <= -5e-206) {
		tmp = c0 * Math.sqrt((A / (l * V)));
	} else if ((l * V) <= 0.0) {
		tmp = c0 * (Math.pow((V / A), -0.5) * Math.pow(l, -0.5));
	} else if ((l * V) <= 1e+301) {
		tmp = c0 * (Math.sqrt(A) / Math.sqrt((l * V)));
	} else {
		tmp = c0 / Math.pow((V * (l / A)), 0.5);
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	tmp = 0
	if (l * V) <= -5e+132:
		tmp = c0 * (math.pow((A / V), 0.5) / math.sqrt(l))
	elif (l * V) <= -5e-206:
		tmp = c0 * math.sqrt((A / (l * V)))
	elif (l * V) <= 0.0:
		tmp = c0 * (math.pow((V / A), -0.5) * math.pow(l, -0.5))
	elif (l * V) <= 1e+301:
		tmp = c0 * (math.sqrt(A) / math.sqrt((l * V)))
	else:
		tmp = c0 / math.pow((V * (l / A)), 0.5)
	return tmp

Julia

function code(c0, A, V, l)
	tmp = 0.0
	if (Float64(l * V) <= -5e+132)
		tmp = Float64(c0 * Float64((Float64(A / V) ^ 0.5) / sqrt(l)));
	elseif (Float64(l * V) <= -5e-206)
		tmp = Float64(c0 * sqrt(Float64(A / Float64(l * V))));
	elseif (Float64(l * V) <= 0.0)
		tmp = Float64(c0 * Float64((Float64(V / A) ^ -0.5) * (l ^ -0.5)));
	elseif (Float64(l * V) <= 1e+301)
		tmp = Float64(c0 * Float64(sqrt(A) / sqrt(Float64(l * V))));
	else
		tmp = Float64(c0 / (Float64(V * Float64(l / A)) ^ 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	tmp = 0.0;
	if ((l * V) <= -5e+132)
		tmp = c0 * (((A / V) ^ 0.5) / sqrt(l));
	elseif ((l * V) <= -5e-206)
		tmp = c0 * sqrt((A / (l * V)));
	elseif ((l * V) <= 0.0)
		tmp = c0 * (((V / A) ^ -0.5) * (l ^ -0.5));
	elseif ((l * V) <= 1e+301)
		tmp = c0 * (sqrt(A) / sqrt((l * V)));
	else
		tmp = c0 / ((V * (l / A)) ^ 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := If[LessEqual[N[(l * V), $MachinePrecision], -5e+132], N[(c0 * N[(N[Power[N[(A / V), $MachinePrecision], 0.5], $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], -5e-206], N[(c0 * N[Sqrt[N[(A / N[(l * V), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], 0.0], N[(c0 * N[(N[Power[N[(V / A), $MachinePrecision], -0.5], $MachinePrecision] * N[Power[l, -0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], 1e+301], N[(c0 * N[(N[Sqrt[A], $MachinePrecision] / N[Sqrt[N[(l * V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 / N[Power[N[(V * N[(l / A), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 V l) < -5.0000000000000001e132

   1. Initial program 63.6%

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

      1. associate-/r* 66.6%

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

      2. sqrt-div 48.5%

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

      3. pow1/2 48.5%

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

      4. pow1/2 48.5%

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

   4. Applied egg-rr 48.5%

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

      1. unpow1/2 48.5%

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

   6. Simplified 48.5%

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

   if -5.0000000000000001e132 < (*.f64 V l) < -5e-206

   1. Initial program 93.4%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Add Preprocessing

   if -5e-206 < (*.f64 V l) < -0.0

   1. Initial program 50.6%

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

      1. pow1/2 50.6%

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

      2. clear-num 50.7%

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

      3. inv-pow 50.7%

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

      4. pow-pow 50.7%

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

      5. associate-/l* 75.8%

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

      6. metadata-eval 75.8%

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

   4. Applied egg-rr 75.8%

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

      1. clear-num 75.8%

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

      2. un-div-inv 75.8%

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

   6. Applied egg-rr 75.8%

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

      1. associate-/r/ 75.8%

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

      2. unpow-prod-down 47.9%

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

   8. Applied egg-rr 47.9%

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

   if -0.0 < (*.f64 V l) < 1.00000000000000005e301

   1. Initial program 85.2%

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

      1. associate-/r* 70.4%

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

   4. Applied egg-rr 70.4%

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

      1. associate-/r* 85.2%

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

      2. sqrt-div 99.0%

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

   6. Applied egg-rr 99.0%

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

   if 1.00000000000000005e301 < (*.f64 V l)

   1. Initial program 29.8%

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

      1. pow1/2 29.8%

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

      2. add-cube-cbrt 29.8%

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

      3. pow3 29.8%

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

      4. pow-pow 29.8%

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

      5. metadata-eval 29.8%

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

   4. Applied egg-rr 29.8%

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

      1. cbrt-div 29.8%

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

   6. Applied egg-rr 29.8%

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

      1. add-sqr-sqrt 29.8%

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

      2. sqrt-unprod 29.8%

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

      3. pow-prod-up 29.8%

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

      4. metadata-eval 29.8%

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

      5. pow3 29.8%

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

      6. cbrt-undiv 29.8%

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

      7. cbrt-undiv 29.8%

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

      8. cbrt-undiv 29.8%

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

      9. add-cube-cbrt 29.8%

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

      10. sqrt-undiv 29.8%

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

      11. clear-num 29.8%

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

      12. sqrt-div 29.8%

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

      13. associate-*r/ 68.4%

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

   8. Applied egg-rr 68.5%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -5 \cdot 10^{+132}:\\ \;\;\;\;c0 \cdot \frac{{\left(\frac{A}{V}\right)}^{0.5}}{\sqrt{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq -5 \cdot 10^{-206}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot \left({\left(\frac{V}{A}\right)}^{-0.5} \cdot {\ell}^{-0.5}\right)\\ \mathbf{elif}\;\ell \cdot V \leq 10^{+301}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{{\left(V \cdot \frac{\ell}{A}\right)}^{0.5}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -5 \cdot 10^{+132}:\\ \;\;\;\;c0 \cdot \frac{{\left(\frac{A}{V}\right)}^{0.5}}{\sqrt{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq -5 \cdot 10^{-206}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot \left({\ell}^{-0.5} \cdot \sqrt{\frac{A}{V}}\right)\\ \mathbf{elif}\;\ell \cdot V \leq 10^{+301}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{{\left(V \cdot \frac{\ell}{A}\right)}^{0.5}}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (if (<= (* l V) -5e+132)
   (* c0 (/ (pow (/ A V) 0.5) (sqrt l)))
   (if (<= (* l V) -5e-206)
     (* c0 (sqrt (/ A (* l V))))
     (if (<= (* l V) 0.0)
       (* c0 (* (pow l -0.5) (sqrt (/ A V))))
       (if (<= (* l V) 1e+301)
         (* c0 (/ (sqrt A) (sqrt (* l V))))
         (/ c0 (pow (* V (/ l A)) 0.5)))))))

C

double code(double c0, double A, double V, double l) {
	double tmp;
	if ((l * V) <= -5e+132) {
		tmp = c0 * (pow((A / V), 0.5) / sqrt(l));
	} else if ((l * V) <= -5e-206) {
		tmp = c0 * sqrt((A / (l * V)));
	} else if ((l * V) <= 0.0) {
		tmp = c0 * (pow(l, -0.5) * sqrt((A / V)));
	} else if ((l * V) <= 1e+301) {
		tmp = c0 * (sqrt(A) / sqrt((l * V)));
	} else {
		tmp = c0 / pow((V * (l / A)), 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) <= (-5d+132)) then
        tmp = c0 * (((a / v) ** 0.5d0) / sqrt(l))
    else if ((l * v) <= (-5d-206)) then
        tmp = c0 * sqrt((a / (l * v)))
    else if ((l * v) <= 0.0d0) then
        tmp = c0 * ((l ** (-0.5d0)) * sqrt((a / v)))
    else if ((l * v) <= 1d+301) then
        tmp = c0 * (sqrt(a) / sqrt((l * v)))
    else
        tmp = c0 / ((v * (l / a)) ** 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) <= -5e+132) {
		tmp = c0 * (Math.pow((A / V), 0.5) / Math.sqrt(l));
	} else if ((l * V) <= -5e-206) {
		tmp = c0 * Math.sqrt((A / (l * V)));
	} else if ((l * V) <= 0.0) {
		tmp = c0 * (Math.pow(l, -0.5) * Math.sqrt((A / V)));
	} else if ((l * V) <= 1e+301) {
		tmp = c0 * (Math.sqrt(A) / Math.sqrt((l * V)));
	} else {
		tmp = c0 / Math.pow((V * (l / A)), 0.5);
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	tmp = 0
	if (l * V) <= -5e+132:
		tmp = c0 * (math.pow((A / V), 0.5) / math.sqrt(l))
	elif (l * V) <= -5e-206:
		tmp = c0 * math.sqrt((A / (l * V)))
	elif (l * V) <= 0.0:
		tmp = c0 * (math.pow(l, -0.5) * math.sqrt((A / V)))
	elif (l * V) <= 1e+301:
		tmp = c0 * (math.sqrt(A) / math.sqrt((l * V)))
	else:
		tmp = c0 / math.pow((V * (l / A)), 0.5)
	return tmp

Julia

function code(c0, A, V, l)
	tmp = 0.0
	if (Float64(l * V) <= -5e+132)
		tmp = Float64(c0 * Float64((Float64(A / V) ^ 0.5) / sqrt(l)));
	elseif (Float64(l * V) <= -5e-206)
		tmp = Float64(c0 * sqrt(Float64(A / Float64(l * V))));
	elseif (Float64(l * V) <= 0.0)
		tmp = Float64(c0 * Float64((l ^ -0.5) * sqrt(Float64(A / V))));
	elseif (Float64(l * V) <= 1e+301)
		tmp = Float64(c0 * Float64(sqrt(A) / sqrt(Float64(l * V))));
	else
		tmp = Float64(c0 / (Float64(V * Float64(l / A)) ^ 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	tmp = 0.0;
	if ((l * V) <= -5e+132)
		tmp = c0 * (((A / V) ^ 0.5) / sqrt(l));
	elseif ((l * V) <= -5e-206)
		tmp = c0 * sqrt((A / (l * V)));
	elseif ((l * V) <= 0.0)
		tmp = c0 * ((l ^ -0.5) * sqrt((A / V)));
	elseif ((l * V) <= 1e+301)
		tmp = c0 * (sqrt(A) / sqrt((l * V)));
	else
		tmp = c0 / ((V * (l / A)) ^ 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := If[LessEqual[N[(l * V), $MachinePrecision], -5e+132], N[(c0 * N[(N[Power[N[(A / V), $MachinePrecision], 0.5], $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], -5e-206], N[(c0 * N[Sqrt[N[(A / N[(l * V), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], 0.0], N[(c0 * N[(N[Power[l, -0.5], $MachinePrecision] * N[Sqrt[N[(A / V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], 1e+301], N[(c0 * N[(N[Sqrt[A], $MachinePrecision] / N[Sqrt[N[(l * V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 / N[Power[N[(V * N[(l / A), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 V l) < -5.0000000000000001e132

   1. Initial program 63.6%

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

      1. associate-/r* 66.6%

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

      2. sqrt-div 48.5%

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

      3. pow1/2 48.5%

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

      4. pow1/2 48.5%

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

   4. Applied egg-rr 48.5%

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

      1. unpow1/2 48.5%

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

   6. Simplified 48.5%

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

   if -5.0000000000000001e132 < (*.f64 V l) < -5e-206

   1. Initial program 93.4%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Add Preprocessing

   if -5e-206 < (*.f64 V l) < -0.0

   1. Initial program 50.6%

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

      1. pow1/2 50.6%

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

      2. clear-num 50.7%

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

      3. inv-pow 50.7%

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

      4. pow-pow 50.7%

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

      5. associate-/l* 75.8%

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

      6. metadata-eval 75.8%

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

   4. Applied egg-rr 75.8%

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

      1. clear-num 75.8%

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

      2. un-div-inv 75.8%

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

   6. Applied egg-rr 75.8%

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

      1. add-sqr-sqrt 75.6%

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

      2. sqrt-unprod 74.4%

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

      3. pow-prod-up 74.4%

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

      4. metadata-eval 74.4%

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

      5. inv-pow 74.4%

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

      6. associate-/r/ 74.3%

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

      7. associate-/l/ 74.3%

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

      8. div-inv 74.3%

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

      9. sqrt-prod 47.9%

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

      10. inv-pow 47.9%

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

      11. sqrt-pow1 47.9%

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

      12. metadata-eval 47.9%

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

      13. clear-num 47.8%

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

   8. Applied egg-rr 47.8%

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

   if -0.0 < (*.f64 V l) < 1.00000000000000005e301

   1. Initial program 85.2%

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

      1. associate-/r* 70.4%

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

   4. Applied egg-rr 70.4%

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

      1. associate-/r* 85.2%

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

      2. sqrt-div 99.0%

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

   6. Applied egg-rr 99.0%

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

   if 1.00000000000000005e301 < (*.f64 V l)

   1. Initial program 29.8%

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

      1. pow1/2 29.8%

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

      2. add-cube-cbrt 29.8%

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

      3. pow3 29.8%

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

      4. pow-pow 29.8%

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

      5. metadata-eval 29.8%

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

   4. Applied egg-rr 29.8%

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

      1. cbrt-div 29.8%

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

   6. Applied egg-rr 29.8%

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

      1. add-sqr-sqrt 29.8%

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

      2. sqrt-unprod 29.8%

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

      3. pow-prod-up 29.8%

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

      4. metadata-eval 29.8%

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

      5. pow3 29.8%

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

      6. cbrt-undiv 29.8%

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

      7. cbrt-undiv 29.8%

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

      8. cbrt-undiv 29.8%

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

      9. add-cube-cbrt 29.8%

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

      10. sqrt-undiv 29.8%

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

      11. clear-num 29.8%

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

      12. sqrt-div 29.8%

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

      13. associate-*r/ 68.4%

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

   8. Applied egg-rr 68.5%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -5 \cdot 10^{+132}:\\ \;\;\;\;c0 \cdot \frac{{\left(\frac{A}{V}\right)}^{0.5}}{\sqrt{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq -5 \cdot 10^{-206}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot \left({\ell}^{-0.5} \cdot \sqrt{\frac{A}{V}}\right)\\ \mathbf{elif}\;\ell \cdot V \leq 10^{+301}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{{\left(V \cdot \frac{\ell}{A}\right)}^{0.5}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := c0 \cdot \left({\ell}^{-0.5} \cdot \sqrt{\frac{A}{V}}\right)\\ \mathbf{if}\;\ell \cdot V \leq -5 \cdot 10^{+132}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;\ell \cdot V \leq -5 \cdot 10^{-206}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;\ell \cdot V \leq 10^{+301}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{{\left(V \cdot \frac{\ell}{A}\right)}^{0.5}}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (* c0 (* (pow l -0.5) (sqrt (/ A V))))))
   (if (<= (* l V) -5e+132)
     t_0
     (if (<= (* l V) -5e-206)
       (* c0 (sqrt (/ A (* l V))))
       (if (<= (* l V) 0.0)
         t_0
         (if (<= (* l V) 1e+301)
           (* c0 (/ (sqrt A) (sqrt (* l V))))
           (/ c0 (pow (* V (/ l A)) 0.5))))))))

C

double code(double c0, double A, double V, double l) {
	double t_0 = c0 * (pow(l, -0.5) * sqrt((A / V)));
	double tmp;
	if ((l * V) <= -5e+132) {
		tmp = t_0;
	} else if ((l * V) <= -5e-206) {
		tmp = c0 * sqrt((A / (l * V)));
	} else if ((l * V) <= 0.0) {
		tmp = t_0;
	} else if ((l * V) <= 1e+301) {
		tmp = c0 * (sqrt(A) / sqrt((l * V)));
	} else {
		tmp = c0 / pow((V * (l / A)), 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 * ((l ** (-0.5d0)) * sqrt((a / v)))
    if ((l * v) <= (-5d+132)) then
        tmp = t_0
    else if ((l * v) <= (-5d-206)) then
        tmp = c0 * sqrt((a / (l * v)))
    else if ((l * v) <= 0.0d0) then
        tmp = t_0
    else if ((l * v) <= 1d+301) then
        tmp = c0 * (sqrt(a) / sqrt((l * v)))
    else
        tmp = c0 / ((v * (l / a)) ** 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.pow(l, -0.5) * Math.sqrt((A / V)));
	double tmp;
	if ((l * V) <= -5e+132) {
		tmp = t_0;
	} else if ((l * V) <= -5e-206) {
		tmp = c0 * Math.sqrt((A / (l * V)));
	} else if ((l * V) <= 0.0) {
		tmp = t_0;
	} else if ((l * V) <= 1e+301) {
		tmp = c0 * (Math.sqrt(A) / Math.sqrt((l * V)));
	} else {
		tmp = c0 / Math.pow((V * (l / A)), 0.5);
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	t_0 = c0 * (math.pow(l, -0.5) * math.sqrt((A / V)))
	tmp = 0
	if (l * V) <= -5e+132:
		tmp = t_0
	elif (l * V) <= -5e-206:
		tmp = c0 * math.sqrt((A / (l * V)))
	elif (l * V) <= 0.0:
		tmp = t_0
	elif (l * V) <= 1e+301:
		tmp = c0 * (math.sqrt(A) / math.sqrt((l * V)))
	else:
		tmp = c0 / math.pow((V * (l / A)), 0.5)
	return tmp

Julia

function code(c0, A, V, l)
	t_0 = Float64(c0 * Float64((l ^ -0.5) * sqrt(Float64(A / V))))
	tmp = 0.0
	if (Float64(l * V) <= -5e+132)
		tmp = t_0;
	elseif (Float64(l * V) <= -5e-206)
		tmp = Float64(c0 * sqrt(Float64(A / Float64(l * V))));
	elseif (Float64(l * V) <= 0.0)
		tmp = t_0;
	elseif (Float64(l * V) <= 1e+301)
		tmp = Float64(c0 * Float64(sqrt(A) / sqrt(Float64(l * V))));
	else
		tmp = Float64(c0 / (Float64(V * Float64(l / A)) ^ 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	t_0 = c0 * ((l ^ -0.5) * sqrt((A / V)));
	tmp = 0.0;
	if ((l * V) <= -5e+132)
		tmp = t_0;
	elseif ((l * V) <= -5e-206)
		tmp = c0 * sqrt((A / (l * V)));
	elseif ((l * V) <= 0.0)
		tmp = t_0;
	elseif ((l * V) <= 1e+301)
		tmp = c0 * (sqrt(A) / sqrt((l * V)));
	else
		tmp = c0 / ((V * (l / A)) ^ 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := Block[{t$95$0 = N[(c0 * N[(N[Power[l, -0.5], $MachinePrecision] * N[Sqrt[N[(A / V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(l * V), $MachinePrecision], -5e+132], t$95$0, If[LessEqual[N[(l * V), $MachinePrecision], -5e-206], N[(c0 * N[Sqrt[N[(A / N[(l * V), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], 0.0], t$95$0, If[LessEqual[N[(l * V), $MachinePrecision], 1e+301], N[(c0 * N[(N[Sqrt[A], $MachinePrecision] / N[Sqrt[N[(l * V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 / N[Power[N[(V * N[(l / A), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 V l) < -5.0000000000000001e132 or -5e-206 < (*.f64 V l) < -0.0

   1. Initial program 55.9%

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

      1. pow1/2 55.9%

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

      2. clear-num 55.4%

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

      3. inv-pow 55.4%

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

      4. pow-pow 55.4%

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

      5. associate-/l* 72.6%

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

      6. metadata-eval 72.6%

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

   4. Applied egg-rr 72.6%

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

      1. clear-num 72.6%

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

      2. un-div-inv 72.6%

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

   6. Applied egg-rr 72.6%

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

      1. add-sqr-sqrt 72.4%

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

      2. sqrt-unprod 71.8%

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

      3. pow-prod-up 71.7%

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

      4. metadata-eval 71.7%

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

      5. inv-pow 71.7%

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

      6. associate-/r/ 70.5%

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

      7. associate-/l/ 71.1%

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

      8. div-inv 71.1%

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

      9. sqrt-prod 48.1%

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

      10. inv-pow 48.1%

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

      11. sqrt-pow1 48.1%

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

      12. metadata-eval 48.1%

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

      13. clear-num 48.0%

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

   8. Applied egg-rr 48.0%

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

   if -5.0000000000000001e132 < (*.f64 V l) < -5e-206

   1. Initial program 93.4%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Add Preprocessing

   if -0.0 < (*.f64 V l) < 1.00000000000000005e301

   1. Initial program 85.2%

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

      1. associate-/r* 70.4%

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

   4. Applied egg-rr 70.4%

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

      1. associate-/r* 85.2%

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

      2. sqrt-div 99.0%

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

   6. Applied egg-rr 99.0%

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

   if 1.00000000000000005e301 < (*.f64 V l)

   1. Initial program 29.8%

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

      1. pow1/2 29.8%

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

      2. add-cube-cbrt 29.8%

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

      3. pow3 29.8%

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

      4. pow-pow 29.8%

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

      5. metadata-eval 29.8%

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

   4. Applied egg-rr 29.8%

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

      1. cbrt-div 29.8%

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

   6. Applied egg-rr 29.8%

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

      1. add-sqr-sqrt 29.8%

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

      2. sqrt-unprod 29.8%

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

      3. pow-prod-up 29.8%

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

      4. metadata-eval 29.8%

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

      5. pow3 29.8%

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

      6. cbrt-undiv 29.8%

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

      7. cbrt-undiv 29.8%

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

      8. cbrt-undiv 29.8%

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

      9. add-cube-cbrt 29.8%

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

      10. sqrt-undiv 29.8%

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

      11. clear-num 29.8%

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

      12. sqrt-div 29.8%

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

      13. associate-*r/ 68.4%

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

   8. Applied egg-rr 68.5%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -5 \cdot 10^{+132}:\\ \;\;\;\;c0 \cdot \left({\ell}^{-0.5} \cdot \sqrt{\frac{A}{V}}\right)\\ \mathbf{elif}\;\ell \cdot V \leq -5 \cdot 10^{-206}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot \left({\ell}^{-0.5} \cdot \sqrt{\frac{A}{V}}\right)\\ \mathbf{elif}\;\ell \cdot V \leq 10^{+301}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{{\left(V \cdot \frac{\ell}{A}\right)}^{0.5}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{\frac{A}{V}} \cdot \frac{c0}{\sqrt{\ell}}\\ \mathbf{if}\;\ell \cdot V \leq -5 \cdot 10^{+132}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;\ell \cdot V \leq -5 \cdot 10^{-206}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;\ell \cdot V \leq 10^{+301}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{{\left(V \cdot \frac{\ell}{A}\right)}^{0.5}}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (* (sqrt (/ A V)) (/ c0 (sqrt l)))))
   (if (<= (* l V) -5e+132)
     t_0
     (if (<= (* l V) -5e-206)
       (* c0 (sqrt (/ A (* l V))))
       (if (<= (* l V) 0.0)
         t_0
         (if (<= (* l V) 1e+301)
           (* c0 (/ (sqrt A) (sqrt (* l V))))
           (/ c0 (pow (* V (/ l A)) 0.5))))))))

C

double code(double c0, double A, double V, double l) {
	double t_0 = sqrt((A / V)) * (c0 / sqrt(l));
	double tmp;
	if ((l * V) <= -5e+132) {
		tmp = t_0;
	} else if ((l * V) <= -5e-206) {
		tmp = c0 * sqrt((A / (l * V)));
	} else if ((l * V) <= 0.0) {
		tmp = t_0;
	} else if ((l * V) <= 1e+301) {
		tmp = c0 * (sqrt(A) / sqrt((l * V)));
	} else {
		tmp = c0 / pow((V * (l / A)), 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 = sqrt((a / v)) * (c0 / sqrt(l))
    if ((l * v) <= (-5d+132)) then
        tmp = t_0
    else if ((l * v) <= (-5d-206)) then
        tmp = c0 * sqrt((a / (l * v)))
    else if ((l * v) <= 0.0d0) then
        tmp = t_0
    else if ((l * v) <= 1d+301) then
        tmp = c0 * (sqrt(a) / sqrt((l * v)))
    else
        tmp = c0 / ((v * (l / a)) ** 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double c0, double A, double V, double l) {
	double t_0 = Math.sqrt((A / V)) * (c0 / Math.sqrt(l));
	double tmp;
	if ((l * V) <= -5e+132) {
		tmp = t_0;
	} else if ((l * V) <= -5e-206) {
		tmp = c0 * Math.sqrt((A / (l * V)));
	} else if ((l * V) <= 0.0) {
		tmp = t_0;
	} else if ((l * V) <= 1e+301) {
		tmp = c0 * (Math.sqrt(A) / Math.sqrt((l * V)));
	} else {
		tmp = c0 / Math.pow((V * (l / A)), 0.5);
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	t_0 = math.sqrt((A / V)) * (c0 / math.sqrt(l))
	tmp = 0
	if (l * V) <= -5e+132:
		tmp = t_0
	elif (l * V) <= -5e-206:
		tmp = c0 * math.sqrt((A / (l * V)))
	elif (l * V) <= 0.0:
		tmp = t_0
	elif (l * V) <= 1e+301:
		tmp = c0 * (math.sqrt(A) / math.sqrt((l * V)))
	else:
		tmp = c0 / math.pow((V * (l / A)), 0.5)
	return tmp

Julia

function code(c0, A, V, l)
	t_0 = Float64(sqrt(Float64(A / V)) * Float64(c0 / sqrt(l)))
	tmp = 0.0
	if (Float64(l * V) <= -5e+132)
		tmp = t_0;
	elseif (Float64(l * V) <= -5e-206)
		tmp = Float64(c0 * sqrt(Float64(A / Float64(l * V))));
	elseif (Float64(l * V) <= 0.0)
		tmp = t_0;
	elseif (Float64(l * V) <= 1e+301)
		tmp = Float64(c0 * Float64(sqrt(A) / sqrt(Float64(l * V))));
	else
		tmp = Float64(c0 / (Float64(V * Float64(l / A)) ^ 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	t_0 = sqrt((A / V)) * (c0 / sqrt(l));
	tmp = 0.0;
	if ((l * V) <= -5e+132)
		tmp = t_0;
	elseif ((l * V) <= -5e-206)
		tmp = c0 * sqrt((A / (l * V)));
	elseif ((l * V) <= 0.0)
		tmp = t_0;
	elseif ((l * V) <= 1e+301)
		tmp = c0 * (sqrt(A) / sqrt((l * V)));
	else
		tmp = c0 / ((V * (l / A)) ^ 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := Block[{t$95$0 = N[(N[Sqrt[N[(A / V), $MachinePrecision]], $MachinePrecision] * N[(c0 / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(l * V), $MachinePrecision], -5e+132], t$95$0, If[LessEqual[N[(l * V), $MachinePrecision], -5e-206], N[(c0 * N[Sqrt[N[(A / N[(l * V), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], 0.0], t$95$0, If[LessEqual[N[(l * V), $MachinePrecision], 1e+301], N[(c0 * N[(N[Sqrt[A], $MachinePrecision] / N[Sqrt[N[(l * V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 / N[Power[N[(V * N[(l / A), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 V l) < -5.0000000000000001e132 or -5e-206 < (*.f64 V l) < -0.0

   1. Initial program 55.9%

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

      1. associate-/r* 71.2%

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

   4. Applied egg-rr 71.2%

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

      1. sqrt-div 48.0%

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

      2. associate-*r/ 44.6%

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

      3. pow1/2 44.6%

         \[\leadsto \frac{c0 \cdot \sqrt{\frac{A}{V}}}{\color{blue}{{\ell}^{0.5}}} \]

   6. Applied egg-rr 44.6%

      \[\leadsto \color{blue}{\frac{c0 \cdot \sqrt{\frac{A}{V}}}{{\ell}^{0.5}}} \]
   7. Step-by-step derivation

      1. *-commutative 44.6%

         \[\leadsto \frac{\color{blue}{\sqrt{\frac{A}{V}} \cdot c0}}{{\ell}^{0.5}} \]

      2. associate-/l* 48.0%

         \[\leadsto \color{blue}{\sqrt{\frac{A}{V}} \cdot \frac{c0}{{\ell}^{0.5}}} \]

   8. Simplified 48.0%

      \[\leadsto \color{blue}{\sqrt{\frac{A}{V}} \cdot \frac{c0}{{\ell}^{0.5}}} \]
   9. Step-by-step derivation

      1. *-un-lft-identity 48.0%

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

      2. *-commutative 48.0%

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

   10. Applied egg-rr 48.0%

       \[\leadsto \sqrt{\frac{A}{V}} \cdot \color{blue}{\left(\frac{c0}{{\ell}^{0.5}} \cdot 1\right)} \]
   11. Step-by-step derivation

       1. *-rgt-identity 48.0%

          \[\leadsto \sqrt{\frac{A}{V}} \cdot \color{blue}{\frac{c0}{{\ell}^{0.5}}} \]

       2. unpow1/2 48.0%

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

   12. Simplified 48.0%

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

   if -5.0000000000000001e132 < (*.f64 V l) < -5e-206

   1. Initial program 93.4%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Add Preprocessing

   if -0.0 < (*.f64 V l) < 1.00000000000000005e301

   1. Initial program 85.2%

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

      1. associate-/r* 70.4%

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

   4. Applied egg-rr 70.4%

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

      1. associate-/r* 85.2%

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

      2. sqrt-div 99.0%

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

   6. Applied egg-rr 99.0%

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

   if 1.00000000000000005e301 < (*.f64 V l)

   1. Initial program 29.8%

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

      1. pow1/2 29.8%

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

      2. add-cube-cbrt 29.8%

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

      3. pow3 29.8%

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

      4. pow-pow 29.8%

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

      5. metadata-eval 29.8%

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

   4. Applied egg-rr 29.8%

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

      1. cbrt-div 29.8%

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

   6. Applied egg-rr 29.8%

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

      1. add-sqr-sqrt 29.8%

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

      2. sqrt-unprod 29.8%

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

      3. pow-prod-up 29.8%

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

      4. metadata-eval 29.8%

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

      5. pow3 29.8%

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

      6. cbrt-undiv 29.8%

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

      7. cbrt-undiv 29.8%

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

      8. cbrt-undiv 29.8%

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

      9. add-cube-cbrt 29.8%

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

      10. sqrt-undiv 29.8%

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

      11. clear-num 29.8%

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

      12. sqrt-div 29.8%

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

      13. associate-*r/ 68.4%

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

   8. Applied egg-rr 68.5%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -5 \cdot 10^{+132}:\\ \;\;\;\;\sqrt{\frac{A}{V}} \cdot \frac{c0}{\sqrt{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq -5 \cdot 10^{-206}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;\sqrt{\frac{A}{V}} \cdot \frac{c0}{\sqrt{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq 10^{+301}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{{\left(V \cdot \frac{\ell}{A}\right)}^{0.5}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -5.6 \cdot 10^{-220}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-\frac{A}{\ell}}}{\sqrt{-V}}\\ \mathbf{elif}\;\ell \leq -2 \cdot 10^{-310}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{-V}}}{\sqrt{-\ell}}\\ \mathbf{elif}\;\ell \leq 2 \cdot 10^{+42}:\\ \;\;\;\;c0 \cdot \left({\left(\frac{V}{A}\right)}^{-0.5} \cdot {\ell}^{-0.5}\right)\\ \mathbf{elif}\;\ell \leq 3.3 \cdot 10^{+130}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left({\ell}^{-0.5} \cdot \sqrt{\frac{A}{V}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (if (<= l -5.6e-220)
   (* c0 (/ (sqrt (- (/ A l))) (sqrt (- V))))
   (if (<= l -2e-310)
     (* c0 (/ (sqrt (/ A (- V))) (sqrt (- l))))
     (if (<= l 2e+42)
       (* c0 (* (pow (/ V A) -0.5) (pow l -0.5)))
       (if (<= l 3.3e+130)
         (* c0 (sqrt (/ A (* l V))))
         (* c0 (* (pow l -0.5) (sqrt (/ A V)))))))))

C

double code(double c0, double A, double V, double l) {
	double tmp;
	if (l <= -5.6e-220) {
		tmp = c0 * (sqrt(-(A / l)) / sqrt(-V));
	} else if (l <= -2e-310) {
		tmp = c0 * (sqrt((A / -V)) / sqrt(-l));
	} else if (l <= 2e+42) {
		tmp = c0 * (pow((V / A), -0.5) * pow(l, -0.5));
	} else if (l <= 3.3e+130) {
		tmp = c0 * sqrt((A / (l * V)));
	} else {
		tmp = c0 * (pow(l, -0.5) * sqrt((A / V)));
	}
	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 <= (-5.6d-220)) then
        tmp = c0 * (sqrt(-(a / l)) / sqrt(-v))
    else if (l <= (-2d-310)) then
        tmp = c0 * (sqrt((a / -v)) / sqrt(-l))
    else if (l <= 2d+42) then
        tmp = c0 * (((v / a) ** (-0.5d0)) * (l ** (-0.5d0)))
    else if (l <= 3.3d+130) then
        tmp = c0 * sqrt((a / (l * v)))
    else
        tmp = c0 * ((l ** (-0.5d0)) * sqrt((a / v)))
    end if
    code = tmp
end function

Java

public static double code(double c0, double A, double V, double l) {
	double tmp;
	if (l <= -5.6e-220) {
		tmp = c0 * (Math.sqrt(-(A / l)) / Math.sqrt(-V));
	} else if (l <= -2e-310) {
		tmp = c0 * (Math.sqrt((A / -V)) / Math.sqrt(-l));
	} else if (l <= 2e+42) {
		tmp = c0 * (Math.pow((V / A), -0.5) * Math.pow(l, -0.5));
	} else if (l <= 3.3e+130) {
		tmp = c0 * Math.sqrt((A / (l * V)));
	} else {
		tmp = c0 * (Math.pow(l, -0.5) * Math.sqrt((A / V)));
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	tmp = 0
	if l <= -5.6e-220:
		tmp = c0 * (math.sqrt(-(A / l)) / math.sqrt(-V))
	elif l <= -2e-310:
		tmp = c0 * (math.sqrt((A / -V)) / math.sqrt(-l))
	elif l <= 2e+42:
		tmp = c0 * (math.pow((V / A), -0.5) * math.pow(l, -0.5))
	elif l <= 3.3e+130:
		tmp = c0 * math.sqrt((A / (l * V)))
	else:
		tmp = c0 * (math.pow(l, -0.5) * math.sqrt((A / V)))
	return tmp

Julia

function code(c0, A, V, l)
	tmp = 0.0
	if (l <= -5.6e-220)
		tmp = Float64(c0 * Float64(sqrt(Float64(-Float64(A / l))) / sqrt(Float64(-V))));
	elseif (l <= -2e-310)
		tmp = Float64(c0 * Float64(sqrt(Float64(A / Float64(-V))) / sqrt(Float64(-l))));
	elseif (l <= 2e+42)
		tmp = Float64(c0 * Float64((Float64(V / A) ^ -0.5) * (l ^ -0.5)));
	elseif (l <= 3.3e+130)
		tmp = Float64(c0 * sqrt(Float64(A / Float64(l * V))));
	else
		tmp = Float64(c0 * Float64((l ^ -0.5) * sqrt(Float64(A / V))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	tmp = 0.0;
	if (l <= -5.6e-220)
		tmp = c0 * (sqrt(-(A / l)) / sqrt(-V));
	elseif (l <= -2e-310)
		tmp = c0 * (sqrt((A / -V)) / sqrt(-l));
	elseif (l <= 2e+42)
		tmp = c0 * (((V / A) ^ -0.5) * (l ^ -0.5));
	elseif (l <= 3.3e+130)
		tmp = c0 * sqrt((A / (l * V)));
	else
		tmp = c0 * ((l ^ -0.5) * sqrt((A / V)));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := If[LessEqual[l, -5.6e-220], N[(c0 * N[(N[Sqrt[(-N[(A / l), $MachinePrecision])], $MachinePrecision] / N[Sqrt[(-V)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[l, -2e-310], N[(c0 * N[(N[Sqrt[N[(A / (-V)), $MachinePrecision]], $MachinePrecision] / N[Sqrt[(-l)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[l, 2e+42], N[(c0 * N[(N[Power[N[(V / A), $MachinePrecision], -0.5], $MachinePrecision] * N[Power[l, -0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[l, 3.3e+130], N[(c0 * N[Sqrt[N[(A / N[(l * V), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(c0 * N[(N[Power[l, -0.5], $MachinePrecision] * N[Sqrt[N[(A / V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if l < -5.5999999999999998e-220

   1. Initial program 76.1%

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

      1. associate-/r* 72.3%

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

   4. Applied egg-rr 72.3%

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

      1. associate-/r* 76.1%

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

      2. associate-/l/ 77.1%

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

      3. frac-2neg 77.1%

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

      4. sqrt-div 50.9%

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

      5. distribute-neg-frac2 50.9%

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

   6. Applied egg-rr 50.9%

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

   if -5.5999999999999998e-220 < l < -1.999999999999994e-310

   1. Initial program 67.1%

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

      1. associate-/r* 79.1%

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

   4. Applied egg-rr 79.1%

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

      1. frac-2neg 79.1%

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

      2. sqrt-div 91.2%

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

      3. distribute-neg-frac2 91.2%

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

   6. Applied egg-rr 91.2%

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

   if -1.999999999999994e-310 < l < 2.00000000000000009e42

   1. Initial program 78.0%

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

      1. pow1/2 78.0%

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

      2. clear-num 77.4%

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

      3. inv-pow 77.4%

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

      4. pow-pow 77.6%

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

      5. associate-/l* 80.4%

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

      6. metadata-eval 80.4%

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

   4. Applied egg-rr 80.4%

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

      1. clear-num 79.9%

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

      2. un-div-inv 79.9%

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

   6. Applied egg-rr 79.9%

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

      1. associate-/r/ 75.3%

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

      2. unpow-prod-down 87.2%

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

   8. Applied egg-rr 87.2%

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

   if 2.00000000000000009e42 < l < 3.3e130

   1. Initial program 81.9%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Add Preprocessing

   if 3.3e130 < l

   1. Initial program 63.7%

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

      1. pow1/2 63.7%

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

      2. clear-num 63.0%

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

      3. inv-pow 63.0%

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

      4. pow-pow 63.0%

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

      5. associate-/l* 68.3%

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

      6. metadata-eval 68.3%

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

   4. Applied egg-rr 68.3%

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

      1. clear-num 68.3%

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

      2. un-div-inv 68.9%

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

   6. Applied egg-rr 68.9%

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

      1. add-sqr-sqrt 68.5%

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

      2. sqrt-unprod 68.9%

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

      3. pow-prod-up 68.8%

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

      4. metadata-eval 68.8%

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

      5. inv-pow 68.8%

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

      6. associate-/r/ 70.8%

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

      7. associate-/l/ 71.5%

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

      8. div-inv 71.6%

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

      9. sqrt-prod 89.0%

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

      10. inv-pow 89.0%

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

      11. sqrt-pow1 89.1%

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

      12. metadata-eval 89.1%

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

      13. clear-num 91.7%

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

   8. Applied egg-rr 91.7%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -5.6 \cdot 10^{-220}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-\frac{A}{\ell}}}{\sqrt{-V}}\\ \mathbf{elif}\;\ell \leq -2 \cdot 10^{-310}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{-V}}}{\sqrt{-\ell}}\\ \mathbf{elif}\;\ell \leq 2 \cdot 10^{+42}:\\ \;\;\;\;c0 \cdot \left({\left(\frac{V}{A}\right)}^{-0.5} \cdot {\ell}^{-0.5}\right)\\ \mathbf{elif}\;\ell \leq 3.3 \cdot 10^{+130}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left({\ell}^{-0.5} \cdot \sqrt{\frac{A}{V}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 82.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot {\left(\frac{V}{\frac{A}{\ell}}\right)}^{-0.5}\\ \mathbf{elif}\;\ell \cdot V \leq 10^{+301}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{{\left(V \cdot \frac{\ell}{A}\right)}^{0.5}}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (if (<= (* l V) 0.0)
   (* c0 (pow (/ V (/ A l)) -0.5))
   (if (<= (* l V) 1e+301)
     (* c0 (/ (sqrt A) (sqrt (* l V))))
     (/ c0 (pow (* V (/ l A)) 0.5)))))

C

double code(double c0, double A, double V, double l) {
	double tmp;
	if ((l * V) <= 0.0) {
		tmp = c0 * pow((V / (A / l)), -0.5);
	} else if ((l * V) <= 1e+301) {
		tmp = c0 * (sqrt(A) / sqrt((l * V)));
	} else {
		tmp = c0 / pow((V * (l / A)), 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) <= 0.0d0) then
        tmp = c0 * ((v / (a / l)) ** (-0.5d0))
    else if ((l * v) <= 1d+301) then
        tmp = c0 * (sqrt(a) / sqrt((l * v)))
    else
        tmp = c0 / ((v * (l / a)) ** 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) <= 0.0) {
		tmp = c0 * Math.pow((V / (A / l)), -0.5);
	} else if ((l * V) <= 1e+301) {
		tmp = c0 * (Math.sqrt(A) / Math.sqrt((l * V)));
	} else {
		tmp = c0 / Math.pow((V * (l / A)), 0.5);
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	tmp = 0
	if (l * V) <= 0.0:
		tmp = c0 * math.pow((V / (A / l)), -0.5)
	elif (l * V) <= 1e+301:
		tmp = c0 * (math.sqrt(A) / math.sqrt((l * V)))
	else:
		tmp = c0 / math.pow((V * (l / A)), 0.5)
	return tmp

Julia

function code(c0, A, V, l)
	tmp = 0.0
	if (Float64(l * V) <= 0.0)
		tmp = Float64(c0 * (Float64(V / Float64(A / l)) ^ -0.5));
	elseif (Float64(l * V) <= 1e+301)
		tmp = Float64(c0 * Float64(sqrt(A) / sqrt(Float64(l * V))));
	else
		tmp = Float64(c0 / (Float64(V * Float64(l / A)) ^ 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	tmp = 0.0;
	if ((l * V) <= 0.0)
		tmp = c0 * ((V / (A / l)) ^ -0.5);
	elseif ((l * V) <= 1e+301)
		tmp = c0 * (sqrt(A) / sqrt((l * V)));
	else
		tmp = c0 / ((V * (l / A)) ^ 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := If[LessEqual[N[(l * V), $MachinePrecision], 0.0], N[(c0 * N[Power[N[(V / N[(A / l), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], 1e+301], N[(c0 * N[(N[Sqrt[A], $MachinePrecision] / N[Sqrt[N[(l * V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 / N[Power[N[(V * N[(l / A), $MachinePrecision]), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 71.3%

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

      1. pow1/2 71.3%

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

      2. clear-num 70.7%

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

      3. inv-pow 70.7%

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

      4. pow-pow 70.7%

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

      5. associate-/l* 75.1%

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

      6. metadata-eval 75.1%

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

   4. Applied egg-rr 75.1%

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

      1. clear-num 74.6%

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

      2. un-div-inv 74.7%

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

   6. Applied egg-rr 74.7%

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

   if -0.0 < (*.f64 V l) < 1.00000000000000005e301

   1. Initial program 85.2%

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

      1. associate-/r* 70.4%

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

   4. Applied egg-rr 70.4%

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

      1. associate-/r* 85.2%

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

      2. sqrt-div 99.0%

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

   6. Applied egg-rr 99.0%

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

   if 1.00000000000000005e301 < (*.f64 V l)

   1. Initial program 29.8%

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

      1. pow1/2 29.8%

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

      2. add-cube-cbrt 29.8%

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

      3. pow3 29.8%

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

      4. pow-pow 29.8%

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

      5. metadata-eval 29.8%

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

   4. Applied egg-rr 29.8%

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

      1. cbrt-div 29.8%

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

   6. Applied egg-rr 29.8%

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

      1. add-sqr-sqrt 29.8%

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

      2. sqrt-unprod 29.8%

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

      3. pow-prod-up 29.8%

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

      4. metadata-eval 29.8%

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

      5. pow3 29.8%

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

      6. cbrt-undiv 29.8%

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

      7. cbrt-undiv 29.8%

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

      8. cbrt-undiv 29.8%

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

      9. add-cube-cbrt 29.8%

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

      10. sqrt-undiv 29.8%

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

      11. clear-num 29.8%

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

      12. sqrt-div 29.8%

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

      13. associate-*r/ 68.4%

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

   8. Applied egg-rr 68.5%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot {\left(\frac{V}{\frac{A}{\ell}}\right)}^{-0.5}\\ \mathbf{elif}\;\ell \cdot V \leq 10^{+301}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{{\left(V \cdot \frac{\ell}{A}\right)}^{0.5}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 78.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{A}{\ell \cdot V}\\ \mathbf{if}\;t\_0 \leq 2 \cdot 10^{-318}:\\ \;\;\;\;\sqrt{c0 \cdot \frac{\frac{c0 \cdot A}{\ell}}{V}}\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+261}:\\ \;\;\;\;\frac{c0}{{\left(\frac{\ell \cdot V}{A}\right)}^{0.5}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left(\frac{V}{\frac{A}{\ell}}\right)}^{-0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (/ A (* l V))))
   (if (<= t_0 2e-318)
     (sqrt (* c0 (/ (/ (* c0 A) l) V)))
     (if (<= t_0 5e+261)
       (/ c0 (pow (/ (* l V) A) 0.5))
       (* c0 (pow (/ V (/ A l)) -0.5))))))

C

double code(double c0, double A, double V, double l) {
	double t_0 = A / (l * V);
	double tmp;
	if (t_0 <= 2e-318) {
		tmp = sqrt((c0 * (((c0 * A) / l) / V)));
	} else if (t_0 <= 5e+261) {
		tmp = c0 / pow(((l * V) / A), 0.5);
	} else {
		tmp = c0 * pow((V / (A / 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 = a / (l * v)
    if (t_0 <= 2d-318) then
        tmp = sqrt((c0 * (((c0 * a) / l) / v)))
    else if (t_0 <= 5d+261) then
        tmp = c0 / (((l * v) / a) ** 0.5d0)
    else
        tmp = c0 * ((v / (a / 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 = A / (l * V);
	double tmp;
	if (t_0 <= 2e-318) {
		tmp = Math.sqrt((c0 * (((c0 * A) / l) / V)));
	} else if (t_0 <= 5e+261) {
		tmp = c0 / Math.pow(((l * V) / A), 0.5);
	} else {
		tmp = c0 * Math.pow((V / (A / l)), -0.5);
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	t_0 = A / (l * V)
	tmp = 0
	if t_0 <= 2e-318:
		tmp = math.sqrt((c0 * (((c0 * A) / l) / V)))
	elif t_0 <= 5e+261:
		tmp = c0 / math.pow(((l * V) / A), 0.5)
	else:
		tmp = c0 * math.pow((V / (A / l)), -0.5)
	return tmp

Julia

function code(c0, A, V, l)
	t_0 = Float64(A / Float64(l * V))
	tmp = 0.0
	if (t_0 <= 2e-318)
		tmp = sqrt(Float64(c0 * Float64(Float64(Float64(c0 * A) / l) / V)));
	elseif (t_0 <= 5e+261)
		tmp = Float64(c0 / (Float64(Float64(l * V) / A) ^ 0.5));
	else
		tmp = Float64(c0 * (Float64(V / Float64(A / l)) ^ -0.5));
	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-318)
		tmp = sqrt((c0 * (((c0 * A) / l) / V)));
	elseif (t_0 <= 5e+261)
		tmp = c0 / (((l * V) / A) ^ 0.5);
	else
		tmp = c0 * ((V / (A / l)) ^ -0.5);
	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-318], N[Sqrt[N[(c0 * N[(N[(N[(c0 * A), $MachinePrecision] / l), $MachinePrecision] / V), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[t$95$0, 5e+261], N[(c0 / N[Power[N[(N[(l * V), $MachinePrecision] / A), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision], N[(c0 * N[Power[N[(V / N[(A / l), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 A (*.f64 V l)) < 2.0000024e-318

   1. Initial program 30.2%

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

      1. pow1/2 30.2%

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

      2. add-cube-cbrt 30.2%

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

      3. pow3 30.2%

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

      4. pow-pow 30.2%

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

      5. metadata-eval 30.2%

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

   4. Applied egg-rr 30.2%

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

      1. cbrt-div 63.4%

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

   6. Applied egg-rr 63.4%

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

      1. *-commutative 63.4%

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

      2. cbrt-prod 96.7%

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

   8. Applied egg-rr 96.7%

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

      1. add-sqr-sqrt 61.8%

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

      2. sqrt-unprod 50.8%

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

      3. *-commutative 50.8%

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

      4. *-commutative 50.8%

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

      5. swap-sqr 33.0%

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

   10. Applied egg-rr 33.2%

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

       1. associate-*r* 38.0%

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

       2. *-commutative 38.0%

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

       3. associate-*l/ 44.7%

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

       4. associate-*l/ 38.2%

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

   12. Simplified 38.2%

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

   if 2.0000024e-318 < (/.f64 A (*.f64 V l)) < 5.0000000000000001e261

   1. Initial program 99.5%

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

      1. pow1/2 99.5%

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

      2. add-cube-cbrt 98.8%

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

      3. pow3 98.8%

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

      4. pow-pow 98.8%

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

      5. metadata-eval 98.8%

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

   4. Applied egg-rr 98.8%

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

      1. cbrt-div 98.5%

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

   6. Applied egg-rr 98.5%

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

      1. add-sqr-sqrt 98.4%

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

      2. sqrt-unprod 98.5%

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

      3. pow-prod-up 98.4%

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

      4. metadata-eval 98.4%

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

      5. pow3 98.4%

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

      6. cbrt-undiv 98.8%

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

      7. cbrt-undiv 99.0%

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

      8. cbrt-undiv 98.8%

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

      9. add-cube-cbrt 99.5%

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

      10. sqrt-undiv 53.0%

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

      11. clear-num 53.0%

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

      12. sqrt-div 99.5%

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

      13. associate-*r/ 91.9%

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

   8. Applied egg-rr 91.9%

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

      1. associate-*r/ 99.6%

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

   10. Simplified 99.6%

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

   if 5.0000000000000001e261 < (/.f64 A (*.f64 V l))

   1. Initial program 45.6%

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

      1. pow1/2 45.6%

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

      2. clear-num 45.6%

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

      3. inv-pow 45.6%

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

      4. pow-pow 45.9%

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

      5. associate-/l* 59.1%

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

      6. metadata-eval 59.1%

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

   4. Applied egg-rr 59.1%

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

      1. clear-num 59.2%

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

      2. un-div-inv 59.2%

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

   6. Applied egg-rr 59.2%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{\ell \cdot V} \leq 2 \cdot 10^{-318}:\\ \;\;\;\;\sqrt{c0 \cdot \frac{\frac{c0 \cdot A}{\ell}}{V}}\\ \mathbf{elif}\;\frac{A}{\ell \cdot V} \leq 5 \cdot 10^{+261}:\\ \;\;\;\;\frac{c0}{{\left(\frac{\ell \cdot V}{A}\right)}^{0.5}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left(\frac{V}{\frac{A}{\ell}}\right)}^{-0.5}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 80.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{A}{\ell \cdot V}\\ \mathbf{if}\;t\_0 \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;t\_0 \leq 10^{+263}:\\ \;\;\;\;c0 \cdot \sqrt{t\_0}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left(V \cdot \frac{\ell}{A}\right)}^{-0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (/ A (* l V))))
   (if (<= t_0 0.0)
     (* c0 (sqrt (/ (/ A V) l)))
     (if (<= t_0 1e+263) (* c0 (sqrt t_0)) (* c0 (pow (* V (/ l A)) -0.5))))))

C

double code(double c0, double A, double V, double l) {
	double t_0 = A / (l * V);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = c0 * sqrt(((A / V) / l));
	} else if (t_0 <= 1e+263) {
		tmp = c0 * sqrt(t_0);
	} else {
		tmp = c0 * pow((V * (l / A)), -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 = a / (l * v)
    if (t_0 <= 0.0d0) then
        tmp = c0 * sqrt(((a / v) / l))
    else if (t_0 <= 1d+263) then
        tmp = c0 * sqrt(t_0)
    else
        tmp = c0 * ((v * (l / a)) ** (-0.5d0))
    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) {
		tmp = c0 * Math.sqrt(((A / V) / l));
	} else if (t_0 <= 1e+263) {
		tmp = c0 * Math.sqrt(t_0);
	} else {
		tmp = c0 * Math.pow((V * (l / A)), -0.5);
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	t_0 = A / (l * V)
	tmp = 0
	if t_0 <= 0.0:
		tmp = c0 * math.sqrt(((A / V) / l))
	elif t_0 <= 1e+263:
		tmp = c0 * math.sqrt(t_0)
	else:
		tmp = c0 * math.pow((V * (l / A)), -0.5)
	return tmp

Julia

function code(c0, A, V, l)
	t_0 = Float64(A / Float64(l * V))
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = Float64(c0 * sqrt(Float64(Float64(A / V) / l)));
	elseif (t_0 <= 1e+263)
		tmp = Float64(c0 * sqrt(t_0));
	else
		tmp = Float64(c0 * (Float64(V * Float64(l / A)) ^ -0.5));
	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)
		tmp = c0 * sqrt(((A / V) / l));
	elseif (t_0 <= 1e+263)
		tmp = c0 * sqrt(t_0);
	else
		tmp = c0 * ((V * (l / A)) ^ -0.5);
	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, 0.0], N[(c0 * N[Sqrt[N[(N[(A / V), $MachinePrecision] / l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1e+263], N[(c0 * N[Sqrt[t$95$0], $MachinePrecision]), $MachinePrecision], N[(c0 * N[Power[N[(V * N[(l / A), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 27.8%

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

      1. associate-/r* 46.6%

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

   4. Applied egg-rr 46.6%

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

   if 0.0 < (/.f64 A (*.f64 V l)) < 1.00000000000000002e263

   1. Initial program 98.4%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Add Preprocessing

   if 1.00000000000000002e263 < (/.f64 A (*.f64 V l))

   1. Initial program 44.7%

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

      1. pow1/2 44.7%

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

      2. clear-num 44.7%

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

      3. inv-pow 44.7%

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

      4. pow-pow 45.0%

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

      5. associate-/l* 58.5%

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

      6. metadata-eval 58.5%

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

   4. Applied egg-rr 58.5%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{\ell \cdot V} \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;\frac{A}{\ell \cdot V} \leq 10^{+263}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot {\left(V \cdot \frac{\ell}{A}\right)}^{-0.5}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 80.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{A}{\ell \cdot V}\\ \mathbf{if}\;t\_0 \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;t\_0 \leq 4 \cdot 10^{+282}:\\ \;\;\;\;c0 \cdot \sqrt{t\_0}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (/ A (* l V))))
   (if (<= t_0 0.0)
     (* c0 (sqrt (/ (/ A V) l)))
     (if (<= t_0 4e+282) (* c0 (sqrt t_0)) (* c0 (sqrt (/ (/ A l) V)))))))

C

double code(double c0, double A, double V, double l) {
	double t_0 = A / (l * V);
	double tmp;
	if (t_0 <= 0.0) {
		tmp = c0 * sqrt(((A / V) / l));
	} else if (t_0 <= 4e+282) {
		tmp = c0 * sqrt(t_0);
	} else {
		tmp = c0 * sqrt(((A / l) / V));
	}
	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) then
        tmp = c0 * sqrt(((a / v) / l))
    else if (t_0 <= 4d+282) then
        tmp = c0 * sqrt(t_0)
    else
        tmp = c0 * sqrt(((a / l) / v))
    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) {
		tmp = c0 * Math.sqrt(((A / V) / l));
	} else if (t_0 <= 4e+282) {
		tmp = c0 * Math.sqrt(t_0);
	} else {
		tmp = c0 * Math.sqrt(((A / l) / V));
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	t_0 = A / (l * V)
	tmp = 0
	if t_0 <= 0.0:
		tmp = c0 * math.sqrt(((A / V) / l))
	elif t_0 <= 4e+282:
		tmp = c0 * math.sqrt(t_0)
	else:
		tmp = c0 * math.sqrt(((A / l) / V))
	return tmp

Julia

function code(c0, A, V, l)
	t_0 = Float64(A / Float64(l * V))
	tmp = 0.0
	if (t_0 <= 0.0)
		tmp = Float64(c0 * sqrt(Float64(Float64(A / V) / l)));
	elseif (t_0 <= 4e+282)
		tmp = Float64(c0 * sqrt(t_0));
	else
		tmp = Float64(c0 * sqrt(Float64(Float64(A / l) / V)));
	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)
		tmp = c0 * sqrt(((A / V) / l));
	elseif (t_0 <= 4e+282)
		tmp = c0 * sqrt(t_0);
	else
		tmp = c0 * sqrt(((A / l) / V));
	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, 0.0], N[(c0 * N[Sqrt[N[(N[(A / V), $MachinePrecision] / l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 4e+282], N[(c0 * N[Sqrt[t$95$0], $MachinePrecision]), $MachinePrecision], N[(c0 * N[Sqrt[N[(N[(A / l), $MachinePrecision] / V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 27.8%

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

      1. associate-/r* 46.6%

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

   4. Applied egg-rr 46.6%

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

   if 0.0 < (/.f64 A (*.f64 V l)) < 4.00000000000000013e282

   1. Initial program 98.4%

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
   2. Add Preprocessing

   if 4.00000000000000013e282 < (/.f64 A (*.f64 V l))

   1. Initial program 43.8%

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

      1. *-commutative 43.8%

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

      2. associate-/r* 58.2%

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

   4. Applied egg-rr 58.2%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{\ell \cdot V} \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;\frac{A}{\ell \cdot V} \leq 4 \cdot 10^{+282}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 73.9% 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 74.5%

   \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
2. Add Preprocessing

3. Final simplification 74.5%

   \[\leadsto c0 \cdot \sqrt{\frac{A}{\ell \cdot V}} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024098 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))