Henrywood and Agarwal, Equation (3)

Percentage Accurate: 73.8% → 89.3%

Time: 7.9s

Alternatives: 9

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: 73.8% 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: 89.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -\infty:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq -4 \cdot 10^{-307}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{-\ell \cdot V}}\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{+291}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot V}} \cdot \sqrt{A}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (if (<= (* l V) (- INFINITY))
   (* c0 (sqrt (/ (/ A V) l)))
   (if (<= (* l V) -4e-307)
     (* c0 (/ (sqrt (- A)) (sqrt (- (* l V)))))
     (if (<= (* l V) 0.0)
       (* c0 (sqrt (/ (/ A l) V)))
       (if (<= (* l V) 2e+291)
         (* (/ c0 (sqrt (* l V))) (sqrt A))
         (/ c0 (sqrt (* l (/ V A)))))))))

C

double code(double c0, double A, double V, double l) {
	double tmp;
	if ((l * V) <= -((double) INFINITY)) {
		tmp = c0 * sqrt(((A / V) / l));
	} else if ((l * V) <= -4e-307) {
		tmp = c0 * (sqrt(-A) / sqrt(-(l * V)));
	} else if ((l * V) <= 0.0) {
		tmp = c0 * sqrt(((A / l) / V));
	} else if ((l * V) <= 2e+291) {
		tmp = (c0 / sqrt((l * V))) * sqrt(A);
	} else {
		tmp = c0 / sqrt((l * (V / A)));
	}
	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 / V) / l));
	} else if ((l * V) <= -4e-307) {
		tmp = c0 * (Math.sqrt(-A) / Math.sqrt(-(l * V)));
	} else if ((l * V) <= 0.0) {
		tmp = c0 * Math.sqrt(((A / l) / V));
	} else if ((l * V) <= 2e+291) {
		tmp = (c0 / Math.sqrt((l * V))) * Math.sqrt(A);
	} else {
		tmp = c0 / Math.sqrt((l * (V / A)));
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	tmp = 0
	if (l * V) <= -math.inf:
		tmp = c0 * math.sqrt(((A / V) / l))
	elif (l * V) <= -4e-307:
		tmp = c0 * (math.sqrt(-A) / math.sqrt(-(l * V)))
	elif (l * V) <= 0.0:
		tmp = c0 * math.sqrt(((A / l) / V))
	elif (l * V) <= 2e+291:
		tmp = (c0 / math.sqrt((l * V))) * math.sqrt(A)
	else:
		tmp = c0 / math.sqrt((l * (V / A)))
	return tmp

Julia

function code(c0, A, V, l)
	tmp = 0.0
	if (Float64(l * V) <= Float64(-Inf))
		tmp = Float64(c0 * sqrt(Float64(Float64(A / V) / l)));
	elseif (Float64(l * V) <= -4e-307)
		tmp = Float64(c0 * Float64(sqrt(Float64(-A)) / sqrt(Float64(-Float64(l * V)))));
	elseif (Float64(l * V) <= 0.0)
		tmp = Float64(c0 * sqrt(Float64(Float64(A / l) / V)));
	elseif (Float64(l * V) <= 2e+291)
		tmp = Float64(Float64(c0 / sqrt(Float64(l * V))) * sqrt(A));
	else
		tmp = Float64(c0 / sqrt(Float64(l * Float64(V / A))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	tmp = 0.0;
	if ((l * V) <= -Inf)
		tmp = c0 * sqrt(((A / V) / l));
	elseif ((l * V) <= -4e-307)
		tmp = c0 * (sqrt(-A) / sqrt(-(l * V)));
	elseif ((l * V) <= 0.0)
		tmp = c0 * sqrt(((A / l) / V));
	elseif ((l * V) <= 2e+291)
		tmp = (c0 / sqrt((l * V))) * sqrt(A);
	else
		tmp = c0 / sqrt((l * (V / A)));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := If[LessEqual[N[(l * V), $MachinePrecision], (-Infinity)], N[(c0 * N[Sqrt[N[(N[(A / V), $MachinePrecision] / l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], -4e-307], N[(c0 * N[(N[Sqrt[(-A)], $MachinePrecision] / N[Sqrt[(-N[(l * V), $MachinePrecision])], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], 0.0], N[(c0 * N[Sqrt[N[(N[(A / l), $MachinePrecision] / V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], 2e+291], N[(N[(c0 / N[Sqrt[N[(l * V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Sqrt[A], $MachinePrecision]), $MachinePrecision], N[(c0 / N[Sqrt[N[(l * N[(V / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 24.0%

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 70.7

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

   4. Applied egg-rr 70.7%

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

   if -inf.0 < (*.f64 V l) < -3.99999999999999964e-307

   1. Initial program 85.2%

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 81.1

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

   4. Applied egg-rr 81.1%

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

      1. associate-/r* N/A

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

      2. lift-*.f64 N/A

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

      3. frac-2neg N/A

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

      4. sqrt-div N/A

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

      5. lower-/.f64 N/A

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

      6. lower-sqrt.f64 N/A

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

      7. lower-neg.f64 N/A

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

      8. lower-sqrt.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 99.4

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

   6. Applied egg-rr 99.4%

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

   if -3.99999999999999964e-307 < (*.f64 V l) < 0.0

   1. Initial program 41.6%

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 60.3

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

   4. Applied egg-rr 60.3%

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

   if 0.0 < (*.f64 V l) < 1.9999999999999999e291

   1. Initial program 83.9%

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

      1. lift-*.f64 N/A

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

      2. sqrt-div N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-sqrt.f64 N/A

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

      10. lower-sqrt.f64 97.5

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

   4. Applied egg-rr 97.5%

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

   if 1.9999999999999999e291 < (*.f64 V l)

   1. Initial program 46.4%

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

      1. lift-*.f64 N/A

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

      2. div-inv N/A

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

      3. inv-pow N/A

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

      6. pow-pow N/A

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

      7. pow2 N/A

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

      8. remove-double-neg N/A

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

      9. remove-double-neg N/A

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

      10. sqr-neg N/A

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

      11. pow-prod-down N/A

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

      12. pow-prod-up N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval N/A

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

      15. metadata-eval N/A

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

      16. inv-pow N/A

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

      17. div-inv N/A

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

      18. lift-*.f64 N/A

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

      19. distribute-lft-neg-in N/A

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

      20. associate-/r* N/A

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

   4. Applied egg-rr 81.7%

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

   6. Applied egg-rr 46.4%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 82.0

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

   8. Applied egg-rr 82.0%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq -\infty:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq -4 \cdot 10^{-307}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{-\ell \cdot V}}\\ \mathbf{elif}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{+291}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot V}} \cdot \sqrt{A}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 79.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{A}{\ell \cdot V}\\ \mathbf{if}\;t\_0 \leq 4 \cdot 10^{-278}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+269}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{\ell \cdot V}{A}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (/ A (* l V))))
   (if (<= t_0 4e-278)
     (* c0 (sqrt (/ (/ A V) l)))
     (if (<= t_0 2e+269)
       (/ c0 (sqrt (/ (* l V) A)))
       (/ c0 (sqrt (* l (/ V A))))))))

C

double code(double c0, double A, double V, double l) {
	double t_0 = A / (l * V);
	double tmp;
	if (t_0 <= 4e-278) {
		tmp = c0 * sqrt(((A / V) / l));
	} else if (t_0 <= 2e+269) {
		tmp = c0 / sqrt(((l * V) / A));
	} else {
		tmp = c0 / sqrt((l * (V / A)));
	}
	return tmp;
}

Fortran

real(8) function code(c0, a, v, l)
    real(8), intent (in) :: c0
    real(8), intent (in) :: a
    real(8), intent (in) :: v
    real(8), intent (in) :: l
    real(8) :: t_0
    real(8) :: tmp
    t_0 = a / (l * v)
    if (t_0 <= 4d-278) then
        tmp = c0 * sqrt(((a / v) / l))
    else if (t_0 <= 2d+269) then
        tmp = c0 / sqrt(((l * v) / a))
    else
        tmp = c0 / sqrt((l * (v / a)))
    end if
    code = tmp
end function

Java

public static double code(double c0, double A, double V, double l) {
	double t_0 = A / (l * V);
	double tmp;
	if (t_0 <= 4e-278) {
		tmp = c0 * Math.sqrt(((A / V) / l));
	} else if (t_0 <= 2e+269) {
		tmp = c0 / Math.sqrt(((l * V) / A));
	} else {
		tmp = c0 / Math.sqrt((l * (V / A)));
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	t_0 = A / (l * V)
	tmp = 0
	if t_0 <= 4e-278:
		tmp = c0 * math.sqrt(((A / V) / l))
	elif t_0 <= 2e+269:
		tmp = c0 / math.sqrt(((l * V) / A))
	else:
		tmp = c0 / math.sqrt((l * (V / A)))
	return tmp

Julia

function code(c0, A, V, l)
	t_0 = Float64(A / Float64(l * V))
	tmp = 0.0
	if (t_0 <= 4e-278)
		tmp = Float64(c0 * sqrt(Float64(Float64(A / V) / l)));
	elseif (t_0 <= 2e+269)
		tmp = Float64(c0 / sqrt(Float64(Float64(l * V) / A)));
	else
		tmp = Float64(c0 / sqrt(Float64(l * Float64(V / A))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	t_0 = A / (l * V);
	tmp = 0.0;
	if (t_0 <= 4e-278)
		tmp = c0 * sqrt(((A / V) / l));
	elseif (t_0 <= 2e+269)
		tmp = c0 / sqrt(((l * V) / A));
	else
		tmp = c0 / sqrt((l * (V / A)));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := Block[{t$95$0 = N[(A / N[(l * V), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 4e-278], N[(c0 * N[Sqrt[N[(N[(A / V), $MachinePrecision] / l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2e+269], N[(c0 / N[Sqrt[N[(N[(l * V), $MachinePrecision] / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(c0 / N[Sqrt[N[(l * N[(V / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 A (*.f64 V l)) < 3.99999999999999975e-278

   1. Initial program 45.3%

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 58.5

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

   4. Applied egg-rr 58.5%

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

   if 3.99999999999999975e-278 < (/.f64 A (*.f64 V l)) < 2.0000000000000001e269

   1. Initial program 99.6%

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

      1. lift-*.f64 N/A

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

      2. sqrt-div N/A

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

      3. clear-num N/A

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

      4. sqrt-div N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-sqrt.f64 N/A

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

      8. lower-/.f64 99.6

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

   4. Applied egg-rr 99.6%

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

   if 2.0000000000000001e269 < (/.f64 A (*.f64 V l))

   1. Initial program 44.5%

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

      1. lift-*.f64 N/A

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

      2. div-inv N/A

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

      3. inv-pow N/A

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

      6. pow-pow N/A

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

      7. pow2 N/A

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

      8. remove-double-neg N/A

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

      9. remove-double-neg N/A

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

      10. sqr-neg N/A

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

      11. pow-prod-down N/A

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

      12. pow-prod-up N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval N/A

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

      15. metadata-eval N/A

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

      16. inv-pow N/A

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

      17. div-inv N/A

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

      18. lift-*.f64 N/A

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

      19. distribute-lft-neg-in N/A

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

      20. associate-/r* N/A

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

   4. Applied egg-rr 55.3%

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

   6. Applied egg-rr 45.6%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 55.4

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

   8. Applied egg-rr 55.4%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{\ell \cdot V} \leq 4 \cdot 10^{-278}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;\frac{A}{\ell \cdot V} \leq 2 \cdot 10^{+269}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{\ell \cdot V}{A}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{A}{\ell \cdot V}\\ \mathbf{if}\;t\_0 \leq 2 \cdot 10^{-273}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+269}:\\ \;\;\;\;c0 \cdot \sqrt{t\_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (/ A (* l V))))
   (if (<= t_0 2e-273)
     (* c0 (sqrt (/ (/ A V) l)))
     (if (<= t_0 2e+269) (* c0 (sqrt t_0)) (/ c0 (sqrt (* l (/ V A))))))))

C

double code(double c0, double A, double V, double l) {
	double t_0 = A / (l * V);
	double tmp;
	if (t_0 <= 2e-273) {
		tmp = c0 * sqrt(((A / V) / l));
	} else if (t_0 <= 2e+269) {
		tmp = c0 * sqrt(t_0);
	} else {
		tmp = c0 / sqrt((l * (V / A)));
	}
	return tmp;
}

Fortran

real(8) function code(c0, a, v, l)
    real(8), intent (in) :: c0
    real(8), intent (in) :: a
    real(8), intent (in) :: v
    real(8), intent (in) :: l
    real(8) :: t_0
    real(8) :: tmp
    t_0 = a / (l * v)
    if (t_0 <= 2d-273) then
        tmp = c0 * sqrt(((a / v) / l))
    else if (t_0 <= 2d+269) then
        tmp = c0 * sqrt(t_0)
    else
        tmp = c0 / sqrt((l * (v / a)))
    end if
    code = tmp
end function

Java

public static double code(double c0, double A, double V, double l) {
	double t_0 = A / (l * V);
	double tmp;
	if (t_0 <= 2e-273) {
		tmp = c0 * Math.sqrt(((A / V) / l));
	} else if (t_0 <= 2e+269) {
		tmp = c0 * Math.sqrt(t_0);
	} else {
		tmp = c0 / Math.sqrt((l * (V / A)));
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	t_0 = A / (l * V)
	tmp = 0
	if t_0 <= 2e-273:
		tmp = c0 * math.sqrt(((A / V) / l))
	elif t_0 <= 2e+269:
		tmp = c0 * math.sqrt(t_0)
	else:
		tmp = c0 / math.sqrt((l * (V / A)))
	return tmp

Julia

function code(c0, A, V, l)
	t_0 = Float64(A / Float64(l * V))
	tmp = 0.0
	if (t_0 <= 2e-273)
		tmp = Float64(c0 * sqrt(Float64(Float64(A / V) / l)));
	elseif (t_0 <= 2e+269)
		tmp = Float64(c0 * sqrt(t_0));
	else
		tmp = Float64(c0 / sqrt(Float64(l * Float64(V / A))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	t_0 = A / (l * V);
	tmp = 0.0;
	if (t_0 <= 2e-273)
		tmp = c0 * sqrt(((A / V) / l));
	elseif (t_0 <= 2e+269)
		tmp = c0 * sqrt(t_0);
	else
		tmp = c0 / sqrt((l * (V / A)));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := Block[{t$95$0 = N[(A / N[(l * V), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 2e-273], N[(c0 * N[Sqrt[N[(N[(A / V), $MachinePrecision] / l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2e+269], N[(c0 * N[Sqrt[t$95$0], $MachinePrecision]), $MachinePrecision], N[(c0 / N[Sqrt[N[(l * N[(V / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 A (*.f64 V l)) < 2e-273

   1. Initial program 47.1%

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 59.8

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

   4. Applied egg-rr 59.8%

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

   if 2e-273 < (/.f64 A (*.f64 V l)) < 2.0000000000000001e269

   1. Initial program 99.6%

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

   if 2.0000000000000001e269 < (/.f64 A (*.f64 V l))

   1. Initial program 44.5%

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

      1. lift-*.f64 N/A

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

      2. div-inv N/A

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

      3. inv-pow N/A

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

      6. pow-pow N/A

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

      7. pow2 N/A

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

      8. remove-double-neg N/A

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

      9. remove-double-neg N/A

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

      10. sqr-neg N/A

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

      11. pow-prod-down N/A

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

      12. pow-prod-up N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval N/A

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

      15. metadata-eval N/A

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

      16. inv-pow N/A

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

      17. div-inv N/A

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

      18. lift-*.f64 N/A

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

      19. distribute-lft-neg-in N/A

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

      20. associate-/r* N/A

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

   4. Applied egg-rr 55.3%

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

   6. Applied egg-rr 45.6%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 55.4

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

   8. Applied egg-rr 55.4%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{\ell \cdot V} \leq 2 \cdot 10^{-273}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;\frac{A}{\ell \cdot V} \leq 2 \cdot 10^{+269}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{A}{\ell \cdot V}\\ \mathbf{if}\;t\_0 \leq 2 \cdot 10^{-273}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;t\_0 \leq 10^{+225}:\\ \;\;\;\;c0 \cdot \sqrt{t\_0}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (/ A (* l V))))
   (if (<= t_0 2e-273)
     (* c0 (sqrt (/ (/ A V) l)))
     (if (<= t_0 1e+225) (* 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 <= 2e-273) {
		tmp = c0 * sqrt(((A / V) / l));
	} else if (t_0 <= 1e+225) {
		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 <= 2d-273) then
        tmp = c0 * sqrt(((a / v) / l))
    else if (t_0 <= 1d+225) 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 <= 2e-273) {
		tmp = c0 * Math.sqrt(((A / V) / l));
	} else if (t_0 <= 1e+225) {
		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 <= 2e-273:
		tmp = c0 * math.sqrt(((A / V) / l))
	elif t_0 <= 1e+225:
		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 <= 2e-273)
		tmp = Float64(c0 * sqrt(Float64(Float64(A / V) / l)));
	elseif (t_0 <= 1e+225)
		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 <= 2e-273)
		tmp = c0 * sqrt(((A / V) / l));
	elseif (t_0 <= 1e+225)
		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, 2e-273], N[(c0 * N[Sqrt[N[(N[(A / V), $MachinePrecision] / l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1e+225], 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)) < 2e-273

   1. Initial program 47.1%

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 59.8

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

   4. Applied egg-rr 59.8%

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

   if 2e-273 < (/.f64 A (*.f64 V l)) < 9.99999999999999928e224

   1. Initial program 99.6%

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

   if 9.99999999999999928e224 < (/.f64 A (*.f64 V l))

   1. Initial program 49.4%

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

      1. associate-/l/ N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 59.3

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

   4. Applied egg-rr 59.3%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{\ell \cdot V} \leq 2 \cdot 10^{-273}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;\frac{A}{\ell \cdot V} \leq 10^{+225}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{A}{\ell \cdot V}\\ t_1 := c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{if}\;t\_0 \leq 2 \cdot 10^{-273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+269}:\\ \;\;\;\;c0 \cdot \sqrt{t\_0}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (let* ((t_0 (/ A (* l V))) (t_1 (* c0 (sqrt (/ (/ A V) l)))))
   (if (<= t_0 2e-273) t_1 (if (<= t_0 2e+269) (* c0 (sqrt t_0)) t_1))))

C

double code(double c0, double A, double V, double l) {
	double t_0 = A / (l * V);
	double t_1 = c0 * sqrt(((A / V) / l));
	double tmp;
	if (t_0 <= 2e-273) {
		tmp = t_1;
	} else if (t_0 <= 2e+269) {
		tmp = c0 * sqrt(t_0);
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = a / (l * v)
    t_1 = c0 * sqrt(((a / v) / l))
    if (t_0 <= 2d-273) then
        tmp = t_1
    else if (t_0 <= 2d+269) then
        tmp = c0 * sqrt(t_0)
    else
        tmp = t_1
    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 t_1 = c0 * Math.sqrt(((A / V) / l));
	double tmp;
	if (t_0 <= 2e-273) {
		tmp = t_1;
	} else if (t_0 <= 2e+269) {
		tmp = c0 * Math.sqrt(t_0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	t_0 = A / (l * V)
	t_1 = c0 * math.sqrt(((A / V) / l))
	tmp = 0
	if t_0 <= 2e-273:
		tmp = t_1
	elif t_0 <= 2e+269:
		tmp = c0 * math.sqrt(t_0)
	else:
		tmp = t_1
	return tmp

Julia

function code(c0, A, V, l)
	t_0 = Float64(A / Float64(l * V))
	t_1 = Float64(c0 * sqrt(Float64(Float64(A / V) / l)))
	tmp = 0.0
	if (t_0 <= 2e-273)
		tmp = t_1;
	elseif (t_0 <= 2e+269)
		tmp = Float64(c0 * sqrt(t_0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	t_0 = A / (l * V);
	t_1 = c0 * sqrt(((A / V) / l));
	tmp = 0.0;
	if (t_0 <= 2e-273)
		tmp = t_1;
	elseif (t_0 <= 2e+269)
		tmp = c0 * sqrt(t_0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := Block[{t$95$0 = N[(A / N[(l * V), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(c0 * N[Sqrt[N[(N[(A / V), $MachinePrecision] / l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 2e-273], t$95$1, If[LessEqual[t$95$0, 2e+269], N[(c0 * N[Sqrt[t$95$0], $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 A (*.f64 V l)) < 2e-273 or 2.0000000000000001e269 < (/.f64 A (*.f64 V l))

   1. Initial program 45.8%

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 57.6

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

   4. Applied egg-rr 57.6%

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

   if 2e-273 < (/.f64 A (*.f64 V l)) < 2.0000000000000001e269

   1. Initial program 99.6%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{\ell \cdot V} \leq 2 \cdot 10^{-273}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;\frac{A}{\ell \cdot V} \leq 2 \cdot 10^{+269}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{+291}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot V}} \cdot \sqrt{A}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (if (<= (* l V) 0.0)
   (* c0 (/ (sqrt (/ A V)) (sqrt l)))
   (if (<= (* l V) 2e+291)
     (* (/ c0 (sqrt (* l V))) (sqrt A))
     (/ c0 (sqrt (* l (/ V A)))))))

C

double code(double c0, double A, double V, double l) {
	double tmp;
	if ((l * V) <= 0.0) {
		tmp = c0 * (sqrt((A / V)) / sqrt(l));
	} else if ((l * V) <= 2e+291) {
		tmp = (c0 / sqrt((l * V))) * sqrt(A);
	} else {
		tmp = c0 / sqrt((l * (V / A)));
	}
	return tmp;
}

Fortran

real(8) function code(c0, a, v, l)
    real(8), intent (in) :: c0
    real(8), intent (in) :: a
    real(8), intent (in) :: v
    real(8), intent (in) :: l
    real(8) :: tmp
    if ((l * v) <= 0.0d0) then
        tmp = c0 * (sqrt((a / v)) / sqrt(l))
    else if ((l * v) <= 2d+291) then
        tmp = (c0 / sqrt((l * v))) * sqrt(a)
    else
        tmp = c0 / sqrt((l * (v / a)))
    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.sqrt((A / V)) / Math.sqrt(l));
	} else if ((l * V) <= 2e+291) {
		tmp = (c0 / Math.sqrt((l * V))) * Math.sqrt(A);
	} else {
		tmp = c0 / Math.sqrt((l * (V / A)));
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	tmp = 0
	if (l * V) <= 0.0:
		tmp = c0 * (math.sqrt((A / V)) / math.sqrt(l))
	elif (l * V) <= 2e+291:
		tmp = (c0 / math.sqrt((l * V))) * math.sqrt(A)
	else:
		tmp = c0 / math.sqrt((l * (V / A)))
	return tmp

Julia

function code(c0, A, V, l)
	tmp = 0.0
	if (Float64(l * V) <= 0.0)
		tmp = Float64(c0 * Float64(sqrt(Float64(A / V)) / sqrt(l)));
	elseif (Float64(l * V) <= 2e+291)
		tmp = Float64(Float64(c0 / sqrt(Float64(l * V))) * sqrt(A));
	else
		tmp = Float64(c0 / sqrt(Float64(l * Float64(V / A))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	tmp = 0.0;
	if ((l * V) <= 0.0)
		tmp = c0 * (sqrt((A / V)) / sqrt(l));
	elseif ((l * V) <= 2e+291)
		tmp = (c0 / sqrt((l * V))) * sqrt(A);
	else
		tmp = c0 / sqrt((l * (V / A)));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := If[LessEqual[N[(l * V), $MachinePrecision], 0.0], N[(c0 * N[(N[Sqrt[N[(A / V), $MachinePrecision]], $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], 2e+291], N[(N[(c0 / N[Sqrt[N[(l * V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Sqrt[A], $MachinePrecision]), $MachinePrecision], N[(c0 / N[Sqrt[N[(l * N[(V / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 69.7%

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

      1. associate-/r* N/A

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

      2. sqrt-div N/A

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

      3. lower-/.f64 N/A

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

      4. lower-sqrt.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-sqrt.f64 51.5

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

   4. Applied egg-rr 51.5%

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

   if 0.0 < (*.f64 V l) < 1.9999999999999999e291

   1. Initial program 83.9%

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

      1. lift-*.f64 N/A

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

      2. sqrt-div N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-sqrt.f64 N/A

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

      10. lower-sqrt.f64 97.5

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

   4. Applied egg-rr 97.5%

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

   if 1.9999999999999999e291 < (*.f64 V l)

   1. Initial program 46.4%

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

      1. lift-*.f64 N/A

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

      2. div-inv N/A

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

      3. inv-pow N/A

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

      6. pow-pow N/A

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

      7. pow2 N/A

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

      8. remove-double-neg N/A

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

      9. remove-double-neg N/A

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

      10. sqr-neg N/A

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

      11. pow-prod-down N/A

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

      12. pow-prod-up N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval N/A

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

      15. metadata-eval N/A

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

      16. inv-pow N/A

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

      17. div-inv N/A

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

      18. lift-*.f64 N/A

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

      19. distribute-lft-neg-in N/A

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

      20. associate-/r* N/A

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

   4. Applied egg-rr 81.7%

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

   6. Applied egg-rr 46.4%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 82.0

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

   8. Applied egg-rr 82.0%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{+291}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot V}} \cdot \sqrt{A}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{+291}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot V}} \cdot \sqrt{A}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (if (<= (* l V) 0.0)
   (* c0 (sqrt (/ (/ A V) l)))
   (if (<= (* l V) 2e+291)
     (* (/ c0 (sqrt (* l V))) (sqrt A))
     (/ c0 (sqrt (* l (/ V A)))))))

C

double code(double c0, double A, double V, double l) {
	double tmp;
	if ((l * V) <= 0.0) {
		tmp = c0 * sqrt(((A / V) / l));
	} else if ((l * V) <= 2e+291) {
		tmp = (c0 / sqrt((l * V))) * sqrt(A);
	} else {
		tmp = c0 / sqrt((l * (V / A)));
	}
	return tmp;
}

Fortran

real(8) function code(c0, a, v, l)
    real(8), intent (in) :: c0
    real(8), intent (in) :: a
    real(8), intent (in) :: v
    real(8), intent (in) :: l
    real(8) :: tmp
    if ((l * v) <= 0.0d0) then
        tmp = c0 * sqrt(((a / v) / l))
    else if ((l * v) <= 2d+291) then
        tmp = (c0 / sqrt((l * v))) * sqrt(a)
    else
        tmp = c0 / sqrt((l * (v / a)))
    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.sqrt(((A / V) / l));
	} else if ((l * V) <= 2e+291) {
		tmp = (c0 / Math.sqrt((l * V))) * Math.sqrt(A);
	} else {
		tmp = c0 / Math.sqrt((l * (V / A)));
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	tmp = 0
	if (l * V) <= 0.0:
		tmp = c0 * math.sqrt(((A / V) / l))
	elif (l * V) <= 2e+291:
		tmp = (c0 / math.sqrt((l * V))) * math.sqrt(A)
	else:
		tmp = c0 / math.sqrt((l * (V / A)))
	return tmp

Julia

function code(c0, A, V, l)
	tmp = 0.0
	if (Float64(l * V) <= 0.0)
		tmp = Float64(c0 * sqrt(Float64(Float64(A / V) / l)));
	elseif (Float64(l * V) <= 2e+291)
		tmp = Float64(Float64(c0 / sqrt(Float64(l * V))) * sqrt(A));
	else
		tmp = Float64(c0 / sqrt(Float64(l * Float64(V / A))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	tmp = 0.0;
	if ((l * V) <= 0.0)
		tmp = c0 * sqrt(((A / V) / l));
	elseif ((l * V) <= 2e+291)
		tmp = (c0 / sqrt((l * V))) * sqrt(A);
	else
		tmp = c0 / sqrt((l * (V / A)));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := If[LessEqual[N[(l * V), $MachinePrecision], 0.0], N[(c0 * N[Sqrt[N[(N[(A / V), $MachinePrecision] / l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(l * V), $MachinePrecision], 2e+291], N[(N[(c0 / N[Sqrt[N[(l * V), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Sqrt[A], $MachinePrecision]), $MachinePrecision], N[(c0 / N[Sqrt[N[(l * N[(V / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 69.7%

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 75.0

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

   4. Applied egg-rr 75.0%

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

   if 0.0 < (*.f64 V l) < 1.9999999999999999e291

   1. Initial program 83.9%

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

      1. lift-*.f64 N/A

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

      2. sqrt-div N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower-sqrt.f64 N/A

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

      10. lower-sqrt.f64 97.5

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

   4. Applied egg-rr 97.5%

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

   if 1.9999999999999999e291 < (*.f64 V l)

   1. Initial program 46.4%

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

      1. lift-*.f64 N/A

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

      2. div-inv N/A

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

      3. inv-pow N/A

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

      6. pow-pow N/A

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

      7. pow2 N/A

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

      8. remove-double-neg N/A

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

      9. remove-double-neg N/A

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

      10. sqr-neg N/A

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

      11. pow-prod-down N/A

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

      12. pow-prod-up N/A

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

      13. metadata-eval N/A

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

      14. metadata-eval N/A

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

      15. metadata-eval N/A

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

      16. inv-pow N/A

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

      17. div-inv N/A

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

      18. lift-*.f64 N/A

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

      19. distribute-lft-neg-in N/A

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

      20. associate-/r* N/A

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

   4. Applied egg-rr 81.7%

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

   6. Applied egg-rr 46.4%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 82.0

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

   8. Applied egg-rr 82.0%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \cdot V \leq 0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;\ell \cdot V \leq 2 \cdot 10^{+291}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot V}} \cdot \sqrt{A}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{\sqrt{\ell \cdot \frac{V}{A}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq 3.1 \cdot 10^{-298}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{-\ell}}}{\sqrt{-V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \end{array} \end{array} \]

FPCore

(FPCore (c0 A V l)
 :precision binary64
 (if (<= l 3.1e-298)
   (* c0 (/ (sqrt (/ A (- l))) (sqrt (- V))))
   (* c0 (/ (sqrt (/ A V)) (sqrt l)))))

C

double code(double c0, double A, double V, double l) {
	double tmp;
	if (l <= 3.1e-298) {
		tmp = c0 * (sqrt((A / -l)) / sqrt(-V));
	} else {
		tmp = c0 * (sqrt((A / V)) / sqrt(l));
	}
	return tmp;
}

Fortran

real(8) function code(c0, a, v, l)
    real(8), intent (in) :: c0
    real(8), intent (in) :: a
    real(8), intent (in) :: v
    real(8), intent (in) :: l
    real(8) :: tmp
    if (l <= 3.1d-298) then
        tmp = c0 * (sqrt((a / -l)) / sqrt(-v))
    else
        tmp = c0 * (sqrt((a / v)) / sqrt(l))
    end if
    code = tmp
end function

Java

public static double code(double c0, double A, double V, double l) {
	double tmp;
	if (l <= 3.1e-298) {
		tmp = c0 * (Math.sqrt((A / -l)) / Math.sqrt(-V));
	} else {
		tmp = c0 * (Math.sqrt((A / V)) / Math.sqrt(l));
	}
	return tmp;
}

Python

def code(c0, A, V, l):
	tmp = 0
	if l <= 3.1e-298:
		tmp = c0 * (math.sqrt((A / -l)) / math.sqrt(-V))
	else:
		tmp = c0 * (math.sqrt((A / V)) / math.sqrt(l))
	return tmp

Julia

function code(c0, A, V, l)
	tmp = 0.0
	if (l <= 3.1e-298)
		tmp = Float64(c0 * Float64(sqrt(Float64(A / Float64(-l))) / sqrt(Float64(-V))));
	else
		tmp = Float64(c0 * Float64(sqrt(Float64(A / V)) / sqrt(l)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c0, A, V, l)
	tmp = 0.0;
	if (l <= 3.1e-298)
		tmp = c0 * (sqrt((A / -l)) / sqrt(-V));
	else
		tmp = c0 * (sqrt((A / V)) / sqrt(l));
	end
	tmp_2 = tmp;
end

Wolfram

code[c0_, A_, V_, l_] := If[LessEqual[l, 3.1e-298], N[(c0 * N[(N[Sqrt[N[(A / (-l)), $MachinePrecision]], $MachinePrecision] / N[Sqrt[(-V)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 * N[(N[Sqrt[N[(A / V), $MachinePrecision]], $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < 3.1000000000000002e-298

   1. Initial program 70.5%

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 71.5

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

   4. Applied egg-rr 71.5%

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

      1. lift-/.f64 N/A

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

      2. div-inv N/A

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

      3. lift-/.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. frac-2neg N/A

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

      6. associate-*l/ N/A

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

      7. sqrt-div N/A

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

      8. lower-/.f64 N/A

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

      9. lower-sqrt.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. div-inv N/A

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

      12. distribute-frac-neg N/A

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

      13. distribute-frac-neg2 N/A

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

      14. lower-/.f64 N/A

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

      15. lower-neg.f64 N/A

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

      16. lower-sqrt.f64 N/A

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

      17. lower-neg.f64 48.5

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

   6. Applied egg-rr 48.5%

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

   if 3.1000000000000002e-298 < l

   1. Initial program 76.5%

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

      1. associate-/r* N/A

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

      2. sqrt-div N/A

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

      3. lower-/.f64 N/A

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

      4. lower-sqrt.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-sqrt.f64 85.5

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

   4. Applied egg-rr 85.5%

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

Alternative 9: 73.8% 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 73.7%

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

3. Final simplification 73.7%

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

Reproduce

herbie shell --seed 2024207 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))