Henrywood and Agarwal, Equation (3)

Average Error: 19.4 → 5.9

Time: 5.0s

Precision: binary64

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

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -1 \cdot 10^{+290}:\\ \;\;\;\;\frac{{\ell}^{-0.5} \cdot c0}{\sqrt{\frac{V}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq -5 \cdot 10^{-236}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+307}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \frac{1}{\sqrt{V \cdot \ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{1}{\ell}}{\frac{V}{A}}}\\ \end{array} \]

FPCore

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

↓

(FPCore (c0 A V l)
 :precision binary64
 (if (<= (* V l) -1e+290)
   (/ (* (pow l -0.5) c0) (sqrt (/ V A)))
   (if (<= (* V l) -5e-236)
     (* c0 (/ (sqrt (- A)) (sqrt (* V (- l)))))
     (if (<= (* V l) 0.0)
       (* c0 (/ (sqrt (/ A V)) (sqrt l)))
       (if (<= (* V l) 2e+307)
         (* c0 (* (sqrt A) (/ 1.0 (sqrt (* V l)))))
         (* c0 (sqrt (/ (/ 1.0 l) (/ V A)))))))))

C

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

↓

double code(double c0, double A, double V, double l) {
	double tmp;
	if ((V * l) <= -1e+290) {
		tmp = (pow(l, -0.5) * c0) / sqrt((V / A));
	} else if ((V * l) <= -5e-236) {
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	} else if ((V * l) <= 0.0) {
		tmp = c0 * (sqrt((A / V)) / sqrt(l));
	} else if ((V * l) <= 2e+307) {
		tmp = c0 * (sqrt(A) * (1.0 / sqrt((V * l))));
	} else {
		tmp = c0 * sqrt(((1.0 / 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
    code = c0 * sqrt((a / (v * l)))
end function

↓

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 ((v * l) <= (-1d+290)) then
        tmp = ((l ** (-0.5d0)) * c0) / sqrt((v / a))
    else if ((v * l) <= (-5d-236)) then
        tmp = c0 * (sqrt(-a) / sqrt((v * -l)))
    else if ((v * l) <= 0.0d0) then
        tmp = c0 * (sqrt((a / v)) / sqrt(l))
    else if ((v * l) <= 2d+307) then
        tmp = c0 * (sqrt(a) * (1.0d0 / sqrt((v * l))))
    else
        tmp = c0 * sqrt(((1.0d0 / l) / (v / a)))
    end if
    code = tmp
end function

Java

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

↓

public static double code(double c0, double A, double V, double l) {
	double tmp;
	if ((V * l) <= -1e+290) {
		tmp = (Math.pow(l, -0.5) * c0) / Math.sqrt((V / A));
	} else if ((V * l) <= -5e-236) {
		tmp = c0 * (Math.sqrt(-A) / Math.sqrt((V * -l)));
	} else if ((V * l) <= 0.0) {
		tmp = c0 * (Math.sqrt((A / V)) / Math.sqrt(l));
	} else if ((V * l) <= 2e+307) {
		tmp = c0 * (Math.sqrt(A) * (1.0 / Math.sqrt((V * l))));
	} else {
		tmp = c0 * Math.sqrt(((1.0 / l) / (V / A)));
	}
	return tmp;
}

Python

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

↓

def code(c0, A, V, l):
	tmp = 0
	if (V * l) <= -1e+290:
		tmp = (math.pow(l, -0.5) * c0) / math.sqrt((V / A))
	elif (V * l) <= -5e-236:
		tmp = c0 * (math.sqrt(-A) / math.sqrt((V * -l)))
	elif (V * l) <= 0.0:
		tmp = c0 * (math.sqrt((A / V)) / math.sqrt(l))
	elif (V * l) <= 2e+307:
		tmp = c0 * (math.sqrt(A) * (1.0 / math.sqrt((V * l))))
	else:
		tmp = c0 * math.sqrt(((1.0 / l) / (V / A)))
	return tmp

Julia

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

↓

function code(c0, A, V, l)
	tmp = 0.0
	if (Float64(V * l) <= -1e+290)
		tmp = Float64(Float64((l ^ -0.5) * c0) / sqrt(Float64(V / A)));
	elseif (Float64(V * l) <= -5e-236)
		tmp = Float64(c0 * Float64(sqrt(Float64(-A)) / sqrt(Float64(V * Float64(-l)))));
	elseif (Float64(V * l) <= 0.0)
		tmp = Float64(c0 * Float64(sqrt(Float64(A / V)) / sqrt(l)));
	elseif (Float64(V * l) <= 2e+307)
		tmp = Float64(c0 * Float64(sqrt(A) * Float64(1.0 / sqrt(Float64(V * l)))));
	else
		tmp = Float64(c0 * sqrt(Float64(Float64(1.0 / l) / Float64(V / A))));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(c0, A, V, l)
	tmp = 0.0;
	if ((V * l) <= -1e+290)
		tmp = ((l ^ -0.5) * c0) / sqrt((V / A));
	elseif ((V * l) <= -5e-236)
		tmp = c0 * (sqrt(-A) / sqrt((V * -l)));
	elseif ((V * l) <= 0.0)
		tmp = c0 * (sqrt((A / V)) / sqrt(l));
	elseif ((V * l) <= 2e+307)
		tmp = c0 * (sqrt(A) * (1.0 / sqrt((V * l))));
	else
		tmp = c0 * sqrt(((1.0 / l) / (V / A)));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[c0_, A_, V_, l_] := If[LessEqual[N[(V * l), $MachinePrecision], -1e+290], N[(N[(N[Power[l, -0.5], $MachinePrecision] * c0), $MachinePrecision] / N[Sqrt[N[(V / A), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], -5e-236], N[(c0 * N[(N[Sqrt[(-A)], $MachinePrecision] / N[Sqrt[N[(V * (-l)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], 0.0], N[(c0 * N[(N[Sqrt[N[(A / V), $MachinePrecision]], $MachinePrecision] / N[Sqrt[l], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(V * l), $MachinePrecision], 2e+307], N[(c0 * N[(N[Sqrt[A], $MachinePrecision] * N[(1.0 / N[Sqrt[N[(V * l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c0 * N[Sqrt[N[(N[(1.0 / l), $MachinePrecision] / N[(V / A), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 V l) < -1.00000000000000006e290

   1. Initial program 39.3

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

   2. Applied egg-rr 23.2

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

   3. Applied egg-rr 23.2

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

   4. Applied egg-rr 10.3

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

   if -1.00000000000000006e290 < (*.f64 V l) < -4.9999999999999998e-236

   1. Initial program 8.9

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

   2. Applied egg-rr 0.4

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

   if -4.9999999999999998e-236 < (*.f64 V l) < -0.0

   1. Initial program 53.2

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

   2. Applied egg-rr 24.7

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

   if -0.0 < (*.f64 V l) < 1.99999999999999997e307

   1. Initial program 10.3

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

   2. Applied egg-rr 0.8

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

   if 1.99999999999999997e307 < (*.f64 V l)

   1. Initial program 41.9

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

   2. Applied egg-rr 23.3

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

   3. Applied egg-rr 23.4

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\frac{1}{\ell}}{\frac{V}{A}}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 5.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -1 \cdot 10^{+290}:\\ \;\;\;\;\frac{{\ell}^{-0.5} \cdot c0}{\sqrt{\frac{V}{A}}}\\ \mathbf{elif}\;V \cdot \ell \leq -5 \cdot 10^{-236}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{-A}}{\sqrt{V \cdot \left(-\ell\right)}}\\ \mathbf{elif}\;V \cdot \ell \leq 0:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 2 \cdot 10^{+307}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \frac{1}{\sqrt{V \cdot \ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{1}{\ell}}{\frac{V}{A}}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022185 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))