VandenBroeck and Keller, Equation (6)

Percentage Accurate: 76.2% → 98.8%

Time: 13.6s

Alternatives: 7

Speedup: 2.8×

• could not determine a ground truth

  1. F = 4.4875920202567364e+95
  2. l = -3056710580672685.5

Specification

Math

\[\begin{array}{l} \\ \pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right) \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))

C

double code(double F, double l) {
	return (((double) M_PI) * l) - ((1.0 / (F * F)) * tan((((double) M_PI) * l)));
}

Java

public static double code(double F, double l) {
	return (Math.PI * l) - ((1.0 / (F * F)) * Math.tan((Math.PI * l)));
}

Python

def code(F, l):
	return (math.pi * l) - ((1.0 / (F * F)) * math.tan((math.pi * l)))

Julia

function code(F, l)
	return Float64(Float64(pi * l) - Float64(Float64(1.0 / Float64(F * F)) * tan(Float64(pi * l))))
end

MATLAB

function tmp = code(F, l)
	tmp = (pi * l) - ((1.0 / (F * F)) * tan((pi * l)));
end

Wolfram

code[F_, l_] := N[(N[(Pi * l), $MachinePrecision] - N[(N[(1.0 / N[(F * F), $MachinePrecision]), $MachinePrecision] * N[Tan[N[(Pi * l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right) \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))

C

double code(double F, double l) {
	return (((double) M_PI) * l) - ((1.0 / (F * F)) * tan((((double) M_PI) * l)));
}

Java

public static double code(double F, double l) {
	return (Math.PI * l) - ((1.0 / (F * F)) * Math.tan((Math.PI * l)));
}

Python

def code(F, l):
	return (math.pi * l) - ((1.0 / (F * F)) * math.tan((math.pi * l)))

Julia

function code(F, l)
	return Float64(Float64(pi * l) - Float64(Float64(1.0 / Float64(F * F)) * tan(Float64(pi * l))))
end

MATLAB

function tmp = code(F, l)
	tmp = (pi * l) - ((1.0 / (F * F)) * tan((pi * l)));
end

Wolfram

code[F_, l_] := N[(N[(Pi * l), $MachinePrecision] - N[(N[(1.0 / N[(F * F), $MachinePrecision]), $MachinePrecision] * N[Tan[N[(Pi * l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -5 \cdot 10^{+26} \lor \neg \left(\pi \cdot \ell \leq 5000000000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= (* PI l) -5e+26) (not (<= (* PI l) 5000000000000.0)))
   (* PI l)
   (- (* PI l) (/ (/ (tan (* PI l)) F) F))))

C

double code(double F, double l) {
	double tmp;
	if (((((double) M_PI) * l) <= -5e+26) || !((((double) M_PI) * l) <= 5000000000000.0)) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = (((double) M_PI) * l) - ((tan((((double) M_PI) * l)) / F) / F);
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if (((Math.PI * l) <= -5e+26) || !((Math.PI * l) <= 5000000000000.0)) {
		tmp = Math.PI * l;
	} else {
		tmp = (Math.PI * l) - ((Math.tan((Math.PI * l)) / F) / F);
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if ((math.pi * l) <= -5e+26) or not ((math.pi * l) <= 5000000000000.0):
		tmp = math.pi * l
	else:
		tmp = (math.pi * l) - ((math.tan((math.pi * l)) / F) / F)
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((Float64(pi * l) <= -5e+26) || !(Float64(pi * l) <= 5000000000000.0))
		tmp = Float64(pi * l);
	else
		tmp = Float64(Float64(pi * l) - Float64(Float64(tan(Float64(pi * l)) / F) / F));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if (((pi * l) <= -5e+26) || ~(((pi * l) <= 5000000000000.0)))
		tmp = pi * l;
	else
		tmp = (pi * l) - ((tan((pi * l)) / F) / F);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[N[(Pi * l), $MachinePrecision], -5e+26], N[Not[LessEqual[N[(Pi * l), $MachinePrecision], 5000000000000.0]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(N[(Pi * l), $MachinePrecision] - N[(N[(N[Tan[N[(Pi * l), $MachinePrecision]], $MachinePrecision] / F), $MachinePrecision] / F), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (PI.f64) l) < -5.0000000000000001e26 or 5e12 < (*.f64 (PI.f64) l)

   1. Initial program 62.4%

      \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right) \]
   2. Step-by-step derivation

      1. associate-*l/ 62.4%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{1 \cdot \tan \left(\pi \cdot \ell\right)}{F \cdot F}} \]

      2. *-lft-identity 62.4%

         \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\tan \left(\pi \cdot \ell\right)}}{F \cdot F} \]

   3. Simplified 62.4%

      \[\leadsto \color{blue}{\pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right)}{F \cdot F}} \]

   4. Taylor expanded in l around 0 48.4%

      \[\leadsto \color{blue}{\ell \cdot \left(\pi - \frac{\pi}{{F}^{2}}\right)} \]
   5. Step-by-step derivation

      1. unpow2 48.4%

         \[\leadsto \ell \cdot \left(\pi - \frac{\pi}{\color{blue}{F \cdot F}}\right) \]

   6. Simplified 48.4%

      \[\leadsto \color{blue}{\ell \cdot \left(\pi - \frac{\pi}{F \cdot F}\right)} \]

   7. Taylor expanded in F around inf 99.5%

      \[\leadsto \color{blue}{\ell \cdot \pi} \]

   if -5.0000000000000001e26 < (*.f64 (PI.f64) l) < 5e12

   1. Initial program 88.2%

      \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right) \]
   2. Step-by-step derivation

      1. associate-*l/ 89.7%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{1 \cdot \tan \left(\pi \cdot \ell\right)}{F \cdot F}} \]

      2. *-un-lft-identity 89.7%

         \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\tan \left(\pi \cdot \ell\right)}}{F \cdot F} \]

      3. associate-/r* 98.1%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}} \]

   3. Applied egg-rr 98.1%

      \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -5 \cdot 10^{+26} \lor \neg \left(\pi \cdot \ell \leq 5000000000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}\\ \end{array} \]

Alternative 2: 97.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -5 \cdot 10^{+26} \lor \neg \left(\pi \cdot \ell \leq 5000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\pi}{F} \cdot \frac{\ell}{F}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= (* PI l) -5e+26) (not (<= (* PI l) 5000000.0)))
   (* PI l)
   (- (* PI l) (* (/ PI F) (/ l F)))))

C

double code(double F, double l) {
	double tmp;
	if (((((double) M_PI) * l) <= -5e+26) || !((((double) M_PI) * l) <= 5000000.0)) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = (((double) M_PI) * l) - ((((double) M_PI) / F) * (l / F));
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if (((Math.PI * l) <= -5e+26) || !((Math.PI * l) <= 5000000.0)) {
		tmp = Math.PI * l;
	} else {
		tmp = (Math.PI * l) - ((Math.PI / F) * (l / F));
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if ((math.pi * l) <= -5e+26) or not ((math.pi * l) <= 5000000.0):
		tmp = math.pi * l
	else:
		tmp = (math.pi * l) - ((math.pi / F) * (l / F))
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((Float64(pi * l) <= -5e+26) || !(Float64(pi * l) <= 5000000.0))
		tmp = Float64(pi * l);
	else
		tmp = Float64(Float64(pi * l) - Float64(Float64(pi / F) * Float64(l / F)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if (((pi * l) <= -5e+26) || ~(((pi * l) <= 5000000.0)))
		tmp = pi * l;
	else
		tmp = (pi * l) - ((pi / F) * (l / F));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[N[(Pi * l), $MachinePrecision], -5e+26], N[Not[LessEqual[N[(Pi * l), $MachinePrecision], 5000000.0]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(N[(Pi * l), $MachinePrecision] - N[(N[(Pi / F), $MachinePrecision] * N[(l / F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (PI.f64) l) < -5.0000000000000001e26 or 5e6 < (*.f64 (PI.f64) l)

   1. Initial program 62.7%

      \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right) \]
   2. Step-by-step derivation

      1. associate-*l/ 62.7%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{1 \cdot \tan \left(\pi \cdot \ell\right)}{F \cdot F}} \]

      2. *-lft-identity 62.7%

         \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\tan \left(\pi \cdot \ell\right)}}{F \cdot F} \]

   3. Simplified 62.7%

      \[\leadsto \color{blue}{\pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right)}{F \cdot F}} \]

   4. Taylor expanded in l around 0 48.1%

      \[\leadsto \color{blue}{\ell \cdot \left(\pi - \frac{\pi}{{F}^{2}}\right)} \]
   5. Step-by-step derivation

      1. unpow2 48.1%

         \[\leadsto \ell \cdot \left(\pi - \frac{\pi}{\color{blue}{F \cdot F}}\right) \]

   6. Simplified 48.1%

      \[\leadsto \color{blue}{\ell \cdot \left(\pi - \frac{\pi}{F \cdot F}\right)} \]

   7. Taylor expanded in F around inf 97.3%

      \[\leadsto \color{blue}{\ell \cdot \pi} \]

   if -5.0000000000000001e26 < (*.f64 (PI.f64) l) < 5e6

   1. Initial program 88.9%

      \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right) \]
   2. Step-by-step derivation

      1. associate-*l/ 90.5%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{1 \cdot \tan \left(\pi \cdot \ell\right)}{F \cdot F}} \]

      2. *-un-lft-identity 90.5%

         \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\tan \left(\pi \cdot \ell\right)}}{F \cdot F} \]

      3. associate-/r* 99.2%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}} \]

   3. Applied egg-rr 99.2%

      \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}} \]

   4. Taylor expanded in l around 0 89.3%

      \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\ell \cdot \pi}{{F}^{2}}} \]
   5. Step-by-step derivation

      1. *-commutative 89.3%

         \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\pi \cdot \ell}}{{F}^{2}} \]

      2. unpow2 89.3%

         \[\leadsto \pi \cdot \ell - \frac{\pi \cdot \ell}{\color{blue}{F \cdot F}} \]

      3. times-frac 98.1%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\pi}{F} \cdot \frac{\ell}{F}} \]

   6. Simplified 98.1%

      \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\pi}{F} \cdot \frac{\ell}{F}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -5 \cdot 10^{+26} \lor \neg \left(\pi \cdot \ell \leq 5000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\pi}{F} \cdot \frac{\ell}{F}\\ \end{array} \]

Alternative 3: 74.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -3500000 \lor \neg \left(\ell \leq -1.4 \cdot 10^{-121} \lor \neg \left(\ell \leq -1.06 \cdot 10^{-195}\right) \land \ell \leq 9 \cdot 10^{-202}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \frac{\frac{-\ell}{F}}{F}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= l -3500000.0)
         (not
          (or (<= l -1.4e-121) (and (not (<= l -1.06e-195)) (<= l 9e-202)))))
   (* PI l)
   (* PI (/ (/ (- l) F) F))))

C

double code(double F, double l) {
	double tmp;
	if ((l <= -3500000.0) || !((l <= -1.4e-121) || (!(l <= -1.06e-195) && (l <= 9e-202)))) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = ((double) M_PI) * ((-l / F) / F);
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if ((l <= -3500000.0) || !((l <= -1.4e-121) || (!(l <= -1.06e-195) && (l <= 9e-202)))) {
		tmp = Math.PI * l;
	} else {
		tmp = Math.PI * ((-l / F) / F);
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if (l <= -3500000.0) or not ((l <= -1.4e-121) or (not (l <= -1.06e-195) and (l <= 9e-202))):
		tmp = math.pi * l
	else:
		tmp = math.pi * ((-l / F) / F)
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((l <= -3500000.0) || !((l <= -1.4e-121) || (!(l <= -1.06e-195) && (l <= 9e-202))))
		tmp = Float64(pi * l);
	else
		tmp = Float64(pi * Float64(Float64(Float64(-l) / F) / F));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if ((l <= -3500000.0) || ~(((l <= -1.4e-121) || (~((l <= -1.06e-195)) && (l <= 9e-202)))))
		tmp = pi * l;
	else
		tmp = pi * ((-l / F) / F);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[l, -3500000.0], N[Not[Or[LessEqual[l, -1.4e-121], And[N[Not[LessEqual[l, -1.06e-195]], $MachinePrecision], LessEqual[l, 9e-202]]]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(Pi * N[(N[((-l) / F), $MachinePrecision] / F), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < -3.5e6 or -1.4000000000000001e-121 < l < -1.06e-195 or 9.00000000000000078e-202 < l

   1. Initial program 71.9%

      \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right) \]
   2. Step-by-step derivation

      1. associate-*l/ 72.6%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{1 \cdot \tan \left(\pi \cdot \ell\right)}{F \cdot F}} \]

      2. *-lft-identity 72.6%

         \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\tan \left(\pi \cdot \ell\right)}}{F \cdot F} \]

   3. Simplified 72.6%

      \[\leadsto \color{blue}{\pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right)}{F \cdot F}} \]

   4. Taylor expanded in l around 0 61.8%

      \[\leadsto \color{blue}{\ell \cdot \left(\pi - \frac{\pi}{{F}^{2}}\right)} \]
   5. Step-by-step derivation

      1. unpow2 61.8%

         \[\leadsto \ell \cdot \left(\pi - \frac{\pi}{\color{blue}{F \cdot F}}\right) \]

   6. Simplified 61.8%

      \[\leadsto \color{blue}{\ell \cdot \left(\pi - \frac{\pi}{F \cdot F}\right)} \]

   7. Taylor expanded in F around inf 88.1%

      \[\leadsto \color{blue}{\ell \cdot \pi} \]

   if -3.5e6 < l < -1.4000000000000001e-121 or -1.06e-195 < l < 9.00000000000000078e-202

   1. Initial program 85.3%

      \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right) \]
   2. Step-by-step derivation

      1. associate-*l/ 86.4%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{1 \cdot \tan \left(\pi \cdot \ell\right)}{F \cdot F}} \]

      2. *-un-lft-identity 86.4%

         \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\tan \left(\pi \cdot \ell\right)}}{F \cdot F} \]

      3. associate-/r* 98.9%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}} \]

   3. Applied egg-rr 98.9%

      \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}} \]

   4. Taylor expanded in l around 0 84.1%

      \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\ell \cdot \pi}{{F}^{2}}} \]
   5. Step-by-step derivation

      1. *-commutative 84.1%

         \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\pi \cdot \ell}}{{F}^{2}} \]

      2. unpow2 84.1%

         \[\leadsto \pi \cdot \ell - \frac{\pi \cdot \ell}{\color{blue}{F \cdot F}} \]

      3. times-frac 96.8%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\pi}{F} \cdot \frac{\ell}{F}} \]

   6. Simplified 96.8%

      \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\pi}{F} \cdot \frac{\ell}{F}} \]

   7. Taylor expanded in F around 0 50.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{\ell \cdot \pi}{{F}^{2}}} \]
   8. Step-by-step derivation

      1. mul-1-neg 50.4%

         \[\leadsto \color{blue}{-\frac{\ell \cdot \pi}{{F}^{2}}} \]

      2. associate-*l/ 50.5%

         \[\leadsto -\color{blue}{\frac{\ell}{{F}^{2}} \cdot \pi} \]

      3. distribute-lft-neg-in 50.5%

         \[\leadsto \color{blue}{\left(-\frac{\ell}{{F}^{2}}\right) \cdot \pi} \]

      4. unpow2 50.5%

         \[\leadsto \left(-\frac{\ell}{\color{blue}{F \cdot F}}\right) \cdot \pi \]

      5. associate-/r* 63.1%

         \[\leadsto \left(-\color{blue}{\frac{\frac{\ell}{F}}{F}}\right) \cdot \pi \]

      6. associate-/r* 50.5%

         \[\leadsto \left(-\color{blue}{\frac{\ell}{F \cdot F}}\right) \cdot \pi \]

   9. Simplified 50.5%

      \[\leadsto \color{blue}{\left(-\frac{\ell}{F \cdot F}\right) \cdot \pi} \]

   10. Taylor expanded in l around 0 50.4%

       \[\leadsto \color{blue}{-1 \cdot \frac{\ell \cdot \pi}{{F}^{2}}} \]
   11. Step-by-step derivation

       1. mul-1-neg 50.4%

          \[\leadsto \color{blue}{-\frac{\ell \cdot \pi}{{F}^{2}}} \]

       2. associate-/l* 50.5%

          \[\leadsto -\color{blue}{\frac{\ell}{\frac{{F}^{2}}{\pi}}} \]

       3. associate-/r/ 50.5%

          \[\leadsto -\color{blue}{\frac{\ell}{{F}^{2}} \cdot \pi} \]

       4. unpow2 50.5%

          \[\leadsto -\frac{\ell}{\color{blue}{F \cdot F}} \cdot \pi \]

       5. associate-/r* 63.1%

          \[\leadsto -\color{blue}{\frac{\frac{\ell}{F}}{F}} \cdot \pi \]

       6. *-rgt-identity 63.1%

          \[\leadsto -\frac{\color{blue}{\frac{\ell}{F} \cdot 1}}{F} \cdot \pi \]

       7. associate-*r/ 63.1%

          \[\leadsto -\color{blue}{\left(\frac{\ell}{F} \cdot \frac{1}{F}\right)} \cdot \pi \]

       8. *-rgt-identity 63.1%

          \[\leadsto -\left(\frac{\color{blue}{\ell \cdot 1}}{F} \cdot \frac{1}{F}\right) \cdot \pi \]

       9. associate-*r/ 63.1%

          \[\leadsto -\left(\color{blue}{\left(\ell \cdot \frac{1}{F}\right)} \cdot \frac{1}{F}\right) \cdot \pi \]

       10. associate-*r* 49.4%

           \[\leadsto -\color{blue}{\left(\ell \cdot \left(\frac{1}{F} \cdot \frac{1}{F}\right)\right)} \cdot \pi \]

       11. unpow-1 49.4%

           \[\leadsto -\left(\ell \cdot \left(\color{blue}{{F}^{-1}} \cdot \frac{1}{F}\right)\right) \cdot \pi \]

       12. unpow-1 49.4%

           \[\leadsto -\left(\ell \cdot \left({F}^{-1} \cdot \color{blue}{{F}^{-1}}\right)\right) \cdot \pi \]

       13. pow-sqr 49.4%

           \[\leadsto -\left(\ell \cdot \color{blue}{{F}^{\left(2 \cdot -1\right)}}\right) \cdot \pi \]

       14. metadata-eval 49.4%

           \[\leadsto -\left(\ell \cdot {F}^{\color{blue}{-2}}\right) \cdot \pi \]

       15. distribute-rgt-neg-in 49.4%

           \[\leadsto \color{blue}{\left(\ell \cdot {F}^{-2}\right) \cdot \left(-\pi\right)} \]

   12. Simplified 63.1%

       \[\leadsto \color{blue}{\frac{\frac{\ell}{F}}{F} \cdot \left(-\pi\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -3500000 \lor \neg \left(\ell \leq -1.4 \cdot 10^{-121} \lor \neg \left(\ell \leq -1.06 \cdot 10^{-195}\right) \land \ell \leq 9 \cdot 10^{-202}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \frac{\frac{-\ell}{F}}{F}\\ \end{array} \]

Alternative 4: 92.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -2.9 \cdot 10^{+24} \lor \neg \left(\ell \leq 3600000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(\ell - \frac{\ell}{F \cdot F}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= l -2.9e+24) (not (<= l 3600000.0)))
   (* PI l)
   (* PI (- l (/ l (* F F))))))

C

double code(double F, double l) {
	double tmp;
	if ((l <= -2.9e+24) || !(l <= 3600000.0)) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = ((double) M_PI) * (l - (l / (F * F)));
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if ((l <= -2.9e+24) || !(l <= 3600000.0)) {
		tmp = Math.PI * l;
	} else {
		tmp = Math.PI * (l - (l / (F * F)));
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if (l <= -2.9e+24) or not (l <= 3600000.0):
		tmp = math.pi * l
	else:
		tmp = math.pi * (l - (l / (F * F)))
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((l <= -2.9e+24) || !(l <= 3600000.0))
		tmp = Float64(pi * l);
	else
		tmp = Float64(pi * Float64(l - Float64(l / Float64(F * F))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if ((l <= -2.9e+24) || ~((l <= 3600000.0)))
		tmp = pi * l;
	else
		tmp = pi * (l - (l / (F * F)));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[l, -2.9e+24], N[Not[LessEqual[l, 3600000.0]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(Pi * N[(l - N[(l / N[(F * F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < -2.89999999999999979e24 or 3.6e6 < l

   1. Initial program 62.7%

      \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right) \]
   2. Step-by-step derivation

      1. associate-*l/ 62.7%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{1 \cdot \tan \left(\pi \cdot \ell\right)}{F \cdot F}} \]

      2. *-lft-identity 62.7%

         \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\tan \left(\pi \cdot \ell\right)}}{F \cdot F} \]

   3. Simplified 62.7%

      \[\leadsto \color{blue}{\pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right)}{F \cdot F}} \]

   4. Taylor expanded in l around 0 48.1%

      \[\leadsto \color{blue}{\ell \cdot \left(\pi - \frac{\pi}{{F}^{2}}\right)} \]
   5. Step-by-step derivation

      1. unpow2 48.1%

         \[\leadsto \ell \cdot \left(\pi - \frac{\pi}{\color{blue}{F \cdot F}}\right) \]

   6. Simplified 48.1%

      \[\leadsto \color{blue}{\ell \cdot \left(\pi - \frac{\pi}{F \cdot F}\right)} \]

   7. Taylor expanded in F around inf 97.3%

      \[\leadsto \color{blue}{\ell \cdot \pi} \]

   if -2.89999999999999979e24 < l < 3.6e6

   1. Initial program 88.9%

      \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right) \]
   2. Step-by-step derivation

      1. associate-*l/ 90.5%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{1 \cdot \tan \left(\pi \cdot \ell\right)}{F \cdot F}} \]

      2. *-un-lft-identity 90.5%

         \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\tan \left(\pi \cdot \ell\right)}}{F \cdot F} \]

      3. associate-/r* 99.2%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}} \]

   3. Applied egg-rr 99.2%

      \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}} \]

   4. Taylor expanded in l around 0 89.3%

      \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\ell \cdot \pi}{{F}^{2}}} \]
   5. Step-by-step derivation

      1. *-commutative 89.3%

         \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\pi \cdot \ell}}{{F}^{2}} \]

      2. unpow2 89.3%

         \[\leadsto \pi \cdot \ell - \frac{\pi \cdot \ell}{\color{blue}{F \cdot F}} \]

      3. times-frac 98.1%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\pi}{F} \cdot \frac{\ell}{F}} \]

   6. Simplified 98.1%

      \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\pi}{F} \cdot \frac{\ell}{F}} \]

   7. Taylor expanded in l around 0 87.8%

      \[\leadsto \color{blue}{\ell \cdot \left(\pi - \frac{\pi}{{F}^{2}}\right)} \]
   8. Step-by-step derivation

      1. distribute-rgt-out-- 87.8%

         \[\leadsto \color{blue}{\pi \cdot \ell - \frac{\pi}{{F}^{2}} \cdot \ell} \]

      2. associate-*l/ 89.3%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\pi \cdot \ell}{{F}^{2}}} \]

      3. *-commutative 89.3%

         \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\ell \cdot \pi}}{{F}^{2}} \]

      4. associate-*l/ 89.3%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\ell}{{F}^{2}} \cdot \pi} \]

      5. unpow2 89.3%

         \[\leadsto \pi \cdot \ell - \frac{\ell}{\color{blue}{F \cdot F}} \cdot \pi \]

      6. associate-/r* 98.2%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\frac{\ell}{F}}{F}} \cdot \pi \]

      7. *-commutative 98.2%

         \[\leadsto \color{blue}{\ell \cdot \pi} - \frac{\frac{\ell}{F}}{F} \cdot \pi \]

      8. distribute-rgt-out-- 98.2%

         \[\leadsto \color{blue}{\pi \cdot \left(\ell - \frac{\frac{\ell}{F}}{F}\right)} \]

      9. associate-/r* 89.3%

         \[\leadsto \pi \cdot \left(\ell - \color{blue}{\frac{\ell}{F \cdot F}}\right) \]

   9. Simplified 89.3%

      \[\leadsto \color{blue}{\pi \cdot \left(\ell - \frac{\ell}{F \cdot F}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -2.9 \cdot 10^{+24} \lor \neg \left(\ell \leq 3600000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(\ell - \frac{\ell}{F \cdot F}\right)\\ \end{array} \]

Alternative 5: 73.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -3500000 \lor \neg \left(\ell \leq -1.42 \cdot 10^{-117}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi}{F \cdot F} \cdot \left(-\ell\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= l -3500000.0) (not (<= l -1.42e-117)))
   (* PI l)
   (* (/ PI (* F F)) (- l))))

C

double code(double F, double l) {
	double tmp;
	if ((l <= -3500000.0) || !(l <= -1.42e-117)) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = (((double) M_PI) / (F * F)) * -l;
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if ((l <= -3500000.0) || !(l <= -1.42e-117)) {
		tmp = Math.PI * l;
	} else {
		tmp = (Math.PI / (F * F)) * -l;
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if (l <= -3500000.0) or not (l <= -1.42e-117):
		tmp = math.pi * l
	else:
		tmp = (math.pi / (F * F)) * -l
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((l <= -3500000.0) || !(l <= -1.42e-117))
		tmp = Float64(pi * l);
	else
		tmp = Float64(Float64(pi / Float64(F * F)) * Float64(-l));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if ((l <= -3500000.0) || ~((l <= -1.42e-117)))
		tmp = pi * l;
	else
		tmp = (pi / (F * F)) * -l;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[l, -3500000.0], N[Not[LessEqual[l, -1.42e-117]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(N[(Pi / N[(F * F), $MachinePrecision]), $MachinePrecision] * (-l)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < -3.5e6 or -1.42000000000000001e-117 < l

   1. Initial program 74.1%

      \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right) \]
   2. Step-by-step derivation

      1. associate-*l/ 74.7%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{1 \cdot \tan \left(\pi \cdot \ell\right)}{F \cdot F}} \]

      2. *-lft-identity 74.7%

         \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\tan \left(\pi \cdot \ell\right)}}{F \cdot F} \]

   3. Simplified 74.7%

      \[\leadsto \color{blue}{\pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right)}{F \cdot F}} \]

   4. Taylor expanded in l around 0 65.8%

      \[\leadsto \color{blue}{\ell \cdot \left(\pi - \frac{\pi}{{F}^{2}}\right)} \]
   5. Step-by-step derivation

      1. unpow2 65.8%

         \[\leadsto \ell \cdot \left(\pi - \frac{\pi}{\color{blue}{F \cdot F}}\right) \]

   6. Simplified 65.8%

      \[\leadsto \color{blue}{\ell \cdot \left(\pi - \frac{\pi}{F \cdot F}\right)} \]

   7. Taylor expanded in F around inf 80.1%

      \[\leadsto \color{blue}{\ell \cdot \pi} \]

   if -3.5e6 < l < -1.42000000000000001e-117

   1. Initial program 85.9%

      \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right) \]
   2. Step-by-step derivation

      1. associate-*l/ 88.4%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{1 \cdot \tan \left(\pi \cdot \ell\right)}{F \cdot F}} \]

      2. *-lft-identity 88.4%

         \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\tan \left(\pi \cdot \ell\right)}}{F \cdot F} \]

   3. Simplified 88.4%

      \[\leadsto \color{blue}{\pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right)}{F \cdot F}} \]

   4. Taylor expanded in l around 0 80.9%

      \[\leadsto \color{blue}{\ell \cdot \left(\pi - \frac{\pi}{{F}^{2}}\right)} \]
   5. Step-by-step derivation

      1. unpow2 80.9%

         \[\leadsto \ell \cdot \left(\pi - \frac{\pi}{\color{blue}{F \cdot F}}\right) \]

   6. Simplified 80.9%

      \[\leadsto \color{blue}{\ell \cdot \left(\pi - \frac{\pi}{F \cdot F}\right)} \]

   7. Taylor expanded in F around 0 54.2%

      \[\leadsto \ell \cdot \color{blue}{\left(-1 \cdot \frac{\pi}{{F}^{2}}\right)} \]
   8. Step-by-step derivation

      1. associate-*r/ 54.2%

         \[\leadsto \ell \cdot \color{blue}{\frac{-1 \cdot \pi}{{F}^{2}}} \]

      2. neg-mul-1 54.2%

         \[\leadsto \ell \cdot \frac{\color{blue}{-\pi}}{{F}^{2}} \]

      3. unpow2 54.2%

         \[\leadsto \ell \cdot \frac{-\pi}{\color{blue}{F \cdot F}} \]

   9. Simplified 54.2%

      \[\leadsto \ell \cdot \color{blue}{\frac{-\pi}{F \cdot F}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -3500000 \lor \neg \left(\ell \leq -1.42 \cdot 10^{-117}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi}{F \cdot F} \cdot \left(-\ell\right)\\ \end{array} \]

Alternative 6: 73.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -3500000 \lor \neg \left(\ell \leq -1.85 \cdot 10^{-116}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \frac{-\ell}{F \cdot F}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= l -3500000.0) (not (<= l -1.85e-116)))
   (* PI l)
   (* PI (/ (- l) (* F F)))))

C

double code(double F, double l) {
	double tmp;
	if ((l <= -3500000.0) || !(l <= -1.85e-116)) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = ((double) M_PI) * (-l / (F * F));
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if ((l <= -3500000.0) || !(l <= -1.85e-116)) {
		tmp = Math.PI * l;
	} else {
		tmp = Math.PI * (-l / (F * F));
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if (l <= -3500000.0) or not (l <= -1.85e-116):
		tmp = math.pi * l
	else:
		tmp = math.pi * (-l / (F * F))
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((l <= -3500000.0) || !(l <= -1.85e-116))
		tmp = Float64(pi * l);
	else
		tmp = Float64(pi * Float64(Float64(-l) / Float64(F * F)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if ((l <= -3500000.0) || ~((l <= -1.85e-116)))
		tmp = pi * l;
	else
		tmp = pi * (-l / (F * F));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[l, -3500000.0], N[Not[LessEqual[l, -1.85e-116]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(Pi * N[((-l) / N[(F * F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < -3.5e6 or -1.8500000000000001e-116 < l

   1. Initial program 74.1%

      \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right) \]
   2. Step-by-step derivation

      1. associate-*l/ 74.7%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{1 \cdot \tan \left(\pi \cdot \ell\right)}{F \cdot F}} \]

      2. *-lft-identity 74.7%

         \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\tan \left(\pi \cdot \ell\right)}}{F \cdot F} \]

   3. Simplified 74.7%

      \[\leadsto \color{blue}{\pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right)}{F \cdot F}} \]

   4. Taylor expanded in l around 0 65.8%

      \[\leadsto \color{blue}{\ell \cdot \left(\pi - \frac{\pi}{{F}^{2}}\right)} \]
   5. Step-by-step derivation

      1. unpow2 65.8%

         \[\leadsto \ell \cdot \left(\pi - \frac{\pi}{\color{blue}{F \cdot F}}\right) \]

   6. Simplified 65.8%

      \[\leadsto \color{blue}{\ell \cdot \left(\pi - \frac{\pi}{F \cdot F}\right)} \]

   7. Taylor expanded in F around inf 80.1%

      \[\leadsto \color{blue}{\ell \cdot \pi} \]

   if -3.5e6 < l < -1.8500000000000001e-116

   1. Initial program 85.9%

      \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right) \]
   2. Step-by-step derivation

      1. associate-*l/ 88.4%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{1 \cdot \tan \left(\pi \cdot \ell\right)}{F \cdot F}} \]

      2. *-un-lft-identity 88.4%

         \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\tan \left(\pi \cdot \ell\right)}}{F \cdot F} \]

      3. associate-/r* 98.4%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}} \]

   3. Applied egg-rr 98.4%

      \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}} \]

   4. Taylor expanded in l around 0 83.2%

      \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\ell \cdot \pi}{{F}^{2}}} \]
   5. Step-by-step derivation

      1. *-commutative 83.2%

         \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\pi \cdot \ell}}{{F}^{2}} \]

      2. unpow2 83.2%

         \[\leadsto \pi \cdot \ell - \frac{\pi \cdot \ell}{\color{blue}{F \cdot F}} \]

      3. times-frac 93.3%

         \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\pi}{F} \cdot \frac{\ell}{F}} \]

   6. Simplified 93.3%

      \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\pi}{F} \cdot \frac{\ell}{F}} \]

   7. Taylor expanded in F around 0 56.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{\ell \cdot \pi}{{F}^{2}}} \]
   8. Step-by-step derivation

      1. mul-1-neg 56.5%

         \[\leadsto \color{blue}{-\frac{\ell \cdot \pi}{{F}^{2}}} \]

      2. associate-*l/ 56.5%

         \[\leadsto -\color{blue}{\frac{\ell}{{F}^{2}} \cdot \pi} \]

      3. distribute-lft-neg-in 56.5%

         \[\leadsto \color{blue}{\left(-\frac{\ell}{{F}^{2}}\right) \cdot \pi} \]

      4. unpow2 56.5%

         \[\leadsto \left(-\frac{\ell}{\color{blue}{F \cdot F}}\right) \cdot \pi \]

      5. associate-/r* 66.7%

         \[\leadsto \left(-\color{blue}{\frac{\frac{\ell}{F}}{F}}\right) \cdot \pi \]

      6. associate-/r* 56.5%

         \[\leadsto \left(-\color{blue}{\frac{\ell}{F \cdot F}}\right) \cdot \pi \]

   9. Simplified 56.5%

      \[\leadsto \color{blue}{\left(-\frac{\ell}{F \cdot F}\right) \cdot \pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -3500000 \lor \neg \left(\ell \leq -1.85 \cdot 10^{-116}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \frac{-\ell}{F \cdot F}\\ \end{array} \]

Alternative 7: 73.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \pi \cdot \ell \end{array} \]

FPCore

(FPCore (F l) :precision binary64 (* PI l))

C

double code(double F, double l) {
	return ((double) M_PI) * l;
}

Java

public static double code(double F, double l) {
	return Math.PI * l;
}

Python

def code(F, l):
	return math.pi * l

Julia

function code(F, l)
	return Float64(pi * l)
end

MATLAB

function tmp = code(F, l)
	tmp = pi * l;
end

Wolfram

code[F_, l_] := N[(Pi * l), $MachinePrecision]

Derivation

1. Initial program 75.5%

   \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right) \]
2. Step-by-step derivation

   1. associate-*l/ 76.2%

      \[\leadsto \pi \cdot \ell - \color{blue}{\frac{1 \cdot \tan \left(\pi \cdot \ell\right)}{F \cdot F}} \]

   2. *-lft-identity 76.2%

      \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\tan \left(\pi \cdot \ell\right)}}{F \cdot F} \]

3. Simplified 76.2%

   \[\leadsto \color{blue}{\pi \cdot \ell - \frac{\tan \left(\pi \cdot \ell\right)}{F \cdot F}} \]

4. Taylor expanded in l around 0 67.5%

   \[\leadsto \color{blue}{\ell \cdot \left(\pi - \frac{\pi}{{F}^{2}}\right)} \]
5. Step-by-step derivation

   1. unpow2 67.5%

      \[\leadsto \ell \cdot \left(\pi - \frac{\pi}{\color{blue}{F \cdot F}}\right) \]

6. Simplified 67.5%

   \[\leadsto \color{blue}{\ell \cdot \left(\pi - \frac{\pi}{F \cdot F}\right)} \]

7. Taylor expanded in F around inf 74.2%

   \[\leadsto \color{blue}{\ell \cdot \pi} \]

8. Final simplification 74.2%

   \[\leadsto \pi \cdot \ell \]

Reproduce

herbie shell --seed 2023250 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  :precision binary64
  (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))