VandenBroeck and Keller, Equation (6)

Percentage Accurate: 76.6% → 98.5%

Time: 19.5s

Alternatives: 10

Speedup: 1.5×

• could not determine a ground truth

  1. F = 1.3023869204790456e-308
  2. l = 327411477470871.5

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: 76.6% 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: 98.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -5 \cdot 10^{+23} \lor \neg \left(\pi \cdot \ell \leq 50\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= (* PI l) -5e+23) (not (<= (* PI l) 50.0)))
   (* PI l)
   (- (* PI l) (/ (/ (tan (* PI l)) F) F))))

C

double code(double F, double l) {
	double tmp;
	if (((((double) M_PI) * l) <= -5e+23) || !((((double) M_PI) * l) <= 50.0)) {
		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+23) || !((Math.PI * l) <= 50.0)) {
		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+23) or not ((math.pi * l) <= 50.0):
		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+23) || !(Float64(pi * l) <= 50.0))
		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+23) || ~(((pi * l) <= 50.0)))
		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+23], N[Not[LessEqual[N[(Pi * l), $MachinePrecision], 50.0]], $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) < -4.9999999999999999e23 or 50 < (*.f64 (PI.f64) l)

   1. Initial program 63.5%

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

   2. Taylor expanded in l around 0 46.0%

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

      1. unpow2 46.0%

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

      2. times-frac 46.0%

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

   4. Simplified 46.0%

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

   5. Taylor expanded in F around inf 99.5%

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

   if -4.9999999999999999e23 < (*.f64 (PI.f64) l) < 50

   1. Initial program 86.1%

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

      1. associate-*l/ 86.5%

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

      2. *-un-lft-identity 86.5%

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

      3. associate-/r* 99.5%

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

   3. Applied egg-rr 99.5%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -5 \cdot 10^{+23} \lor \neg \left(\pi \cdot \ell \leq 50\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}\\ \end{array} \]

Alternative 2: 97.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -5 \cdot 10^{+23} \lor \neg \left(\pi \cdot \ell \leq 10^{-13}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\frac{\ell}{F}}{\frac{F}{\pi}}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= (* PI l) -5e+23) (not (<= (* PI l) 1e-13)))
   (* PI l)
   (- (* PI l) (/ (/ l F) (/ F PI)))))

C

double code(double F, double l) {
	double tmp;
	if (((((double) M_PI) * l) <= -5e+23) || !((((double) M_PI) * l) <= 1e-13)) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = (((double) M_PI) * l) - ((l / F) / (F / ((double) M_PI)));
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if (((Math.PI * l) <= -5e+23) || !((Math.PI * l) <= 1e-13)) {
		tmp = Math.PI * l;
	} else {
		tmp = (Math.PI * l) - ((l / F) / (F / Math.PI));
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if ((math.pi * l) <= -5e+23) or not ((math.pi * l) <= 1e-13):
		tmp = math.pi * l
	else:
		tmp = (math.pi * l) - ((l / F) / (F / math.pi))
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((Float64(pi * l) <= -5e+23) || !(Float64(pi * l) <= 1e-13))
		tmp = Float64(pi * l);
	else
		tmp = Float64(Float64(pi * l) - Float64(Float64(l / F) / Float64(F / pi)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if (((pi * l) <= -5e+23) || ~(((pi * l) <= 1e-13)))
		tmp = pi * l;
	else
		tmp = (pi * l) - ((l / F) / (F / pi));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[N[(Pi * l), $MachinePrecision], -5e+23], N[Not[LessEqual[N[(Pi * l), $MachinePrecision], 1e-13]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(N[(Pi * l), $MachinePrecision] - N[(N[(l / F), $MachinePrecision] / N[(F / Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (PI.f64) l) < -4.9999999999999999e23 or 1e-13 < (*.f64 (PI.f64) l)

   1. Initial program 63.8%

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

   2. Taylor expanded in l around 0 45.7%

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

      1. unpow2 45.7%

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

      2. times-frac 45.7%

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

   4. Simplified 45.7%

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

   5. Taylor expanded in F around inf 98.8%

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

   if -4.9999999999999999e23 < (*.f64 (PI.f64) l) < 1e-13

   1. Initial program 86.0%

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

   2. Taylor expanded in l around 0 86.4%

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

      1. unpow2 86.4%

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

      2. times-frac 99.4%

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

   4. Simplified 99.4%

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

      1. clear-num 99.5%

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

      2. un-div-inv 99.6%

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

   6. Applied egg-rr 99.6%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -5 \cdot 10^{+23} \lor \neg \left(\pi \cdot \ell \leq 10^{-13}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\frac{\ell}{F}}{\frac{F}{\pi}}\\ \end{array} \]

Alternative 3: 90.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \ell \cdot \left(\pi - \frac{\pi}{F \cdot F}\right)\\ \mathbf{if}\;\ell \leq -2.65 \cdot 10^{+17}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;\ell \leq -2.8 \cdot 10^{-175}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq -1.55 \cdot 10^{-257}:\\ \;\;\;\;\frac{\pi}{F} \cdot \left(-\frac{\ell}{F}\right)\\ \mathbf{elif}\;\ell \leq 5.5:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (let* ((t_0 (* l (- PI (/ PI (* F F))))))
   (if (<= l -2.65e+17)
     (* PI l)
     (if (<= l -2.8e-175)
       t_0
       (if (<= l -1.55e-257)
         (* (/ PI F) (- (/ l F)))
         (if (<= l 5.5) t_0 (* PI l)))))))

C

double code(double F, double l) {
	double t_0 = l * (((double) M_PI) - (((double) M_PI) / (F * F)));
	double tmp;
	if (l <= -2.65e+17) {
		tmp = ((double) M_PI) * l;
	} else if (l <= -2.8e-175) {
		tmp = t_0;
	} else if (l <= -1.55e-257) {
		tmp = (((double) M_PI) / F) * -(l / F);
	} else if (l <= 5.5) {
		tmp = t_0;
	} else {
		tmp = ((double) M_PI) * l;
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double t_0 = l * (Math.PI - (Math.PI / (F * F)));
	double tmp;
	if (l <= -2.65e+17) {
		tmp = Math.PI * l;
	} else if (l <= -2.8e-175) {
		tmp = t_0;
	} else if (l <= -1.55e-257) {
		tmp = (Math.PI / F) * -(l / F);
	} else if (l <= 5.5) {
		tmp = t_0;
	} else {
		tmp = Math.PI * l;
	}
	return tmp;
}

Python

def code(F, l):
	t_0 = l * (math.pi - (math.pi / (F * F)))
	tmp = 0
	if l <= -2.65e+17:
		tmp = math.pi * l
	elif l <= -2.8e-175:
		tmp = t_0
	elif l <= -1.55e-257:
		tmp = (math.pi / F) * -(l / F)
	elif l <= 5.5:
		tmp = t_0
	else:
		tmp = math.pi * l
	return tmp

Julia

function code(F, l)
	t_0 = Float64(l * Float64(pi - Float64(pi / Float64(F * F))))
	tmp = 0.0
	if (l <= -2.65e+17)
		tmp = Float64(pi * l);
	elseif (l <= -2.8e-175)
		tmp = t_0;
	elseif (l <= -1.55e-257)
		tmp = Float64(Float64(pi / F) * Float64(-Float64(l / F)));
	elseif (l <= 5.5)
		tmp = t_0;
	else
		tmp = Float64(pi * l);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	t_0 = l * (pi - (pi / (F * F)));
	tmp = 0.0;
	if (l <= -2.65e+17)
		tmp = pi * l;
	elseif (l <= -2.8e-175)
		tmp = t_0;
	elseif (l <= -1.55e-257)
		tmp = (pi / F) * -(l / F);
	elseif (l <= 5.5)
		tmp = t_0;
	else
		tmp = pi * l;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := Block[{t$95$0 = N[(l * N[(Pi - N[(Pi / N[(F * F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[l, -2.65e+17], N[(Pi * l), $MachinePrecision], If[LessEqual[l, -2.8e-175], t$95$0, If[LessEqual[l, -1.55e-257], N[(N[(Pi / F), $MachinePrecision] * (-N[(l / F), $MachinePrecision])), $MachinePrecision], If[LessEqual[l, 5.5], t$95$0, N[(Pi * l), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if l < -2.65e17 or 5.5 < l

   1. Initial program 63.8%

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

   2. Taylor expanded in l around 0 45.7%

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

      1. unpow2 45.7%

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

      2. times-frac 45.7%

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

   4. Simplified 45.7%

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

   5. Taylor expanded in F around inf 98.8%

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

   if -2.65e17 < l < -2.8e-175 or -1.55000000000000004e-257 < l < 5.5

   1. Initial program 91.4%

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

   2. Taylor expanded in l around 0 91.4%

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

      1. unpow2 91.4%

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

      2. times-frac 99.4%

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

   4. Simplified 99.4%

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

   5. Taylor expanded in l around 0 91.3%

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

      1. unpow2 91.3%

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

   7. Simplified 91.3%

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

   if -2.8e-175 < l < -1.55000000000000004e-257

   1. Initial program 49.7%

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

   2. Taylor expanded in l around 0 52.4%

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

      1. unpow2 52.4%

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

      2. times-frac 99.5%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in F around 0 33.6%

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

      1. unpow2 33.6%

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

      2. associate-*r/ 33.6%

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

      3. mul-1-neg 33.6%

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

      4. distribute-rgt-neg-out 33.6%

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

   7. Simplified 33.6%

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

      1. associate-/l* 33.1%

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

      2. associate-/r/ 33.5%

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

      3. associate-/l/ 80.7%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 1.8%

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

      6. sqr-neg 1.8%

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

      7. sqrt-unprod 1.8%

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

      8. add-sqr-sqrt 1.8%

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

      9. associate-/r/ 1.8%

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

      10. frac-2neg 1.8%

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

      11. div-inv 1.8%

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

      12. distribute-neg-frac 1.8%

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

      13. distribute-neg-frac 1.8%

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

      14. add-sqr-sqrt 1.8%

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

      15. sqrt-unprod 1.8%

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

      16. sqr-neg 1.8%

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

      17. sqrt-unprod 0.0%

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

      18. add-sqr-sqrt 80.8%

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

      19. frac-2neg 80.8%

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

      20. clear-num 80.7%

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

      21. remove-double-div 80.7%

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

   9. Applied egg-rr 80.7%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -2.65 \cdot 10^{+17}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;\ell \leq -2.8 \cdot 10^{-175}:\\ \;\;\;\;\ell \cdot \left(\pi - \frac{\pi}{F \cdot F}\right)\\ \mathbf{elif}\;\ell \leq -1.55 \cdot 10^{-257}:\\ \;\;\;\;\frac{\pi}{F} \cdot \left(-\frac{\ell}{F}\right)\\ \mathbf{elif}\;\ell \leq 5.5:\\ \;\;\;\;\ell \cdot \left(\pi - \frac{\pi}{F \cdot F}\right)\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell\\ \end{array} \]

Alternative 4: 90.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -2.65 \cdot 10^{+17}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;\ell \leq -6 \cdot 10^{-174}:\\ \;\;\;\;\pi \cdot \left(\ell - \ell \cdot {F}^{-2}\right)\\ \mathbf{elif}\;\ell \leq -2.25 \cdot 10^{-263}:\\ \;\;\;\;\frac{\pi}{F} \cdot \left(-\frac{\ell}{F}\right)\\ \mathbf{elif}\;\ell \leq 5.5:\\ \;\;\;\;\ell \cdot \left(\pi - \frac{\pi}{F \cdot F}\right)\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (<= l -2.65e+17)
   (* PI l)
   (if (<= l -6e-174)
     (* PI (- l (* l (pow F -2.0))))
     (if (<= l -2.25e-263)
       (* (/ PI F) (- (/ l F)))
       (if (<= l 5.5) (* l (- PI (/ PI (* F F)))) (* PI l))))))

C

double code(double F, double l) {
	double tmp;
	if (l <= -2.65e+17) {
		tmp = ((double) M_PI) * l;
	} else if (l <= -6e-174) {
		tmp = ((double) M_PI) * (l - (l * pow(F, -2.0)));
	} else if (l <= -2.25e-263) {
		tmp = (((double) M_PI) / F) * -(l / F);
	} else if (l <= 5.5) {
		tmp = l * (((double) M_PI) - (((double) M_PI) / (F * F)));
	} else {
		tmp = ((double) M_PI) * l;
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if (l <= -2.65e+17) {
		tmp = Math.PI * l;
	} else if (l <= -6e-174) {
		tmp = Math.PI * (l - (l * Math.pow(F, -2.0)));
	} else if (l <= -2.25e-263) {
		tmp = (Math.PI / F) * -(l / F);
	} else if (l <= 5.5) {
		tmp = l * (Math.PI - (Math.PI / (F * F)));
	} else {
		tmp = Math.PI * l;
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if l <= -2.65e+17:
		tmp = math.pi * l
	elif l <= -6e-174:
		tmp = math.pi * (l - (l * math.pow(F, -2.0)))
	elif l <= -2.25e-263:
		tmp = (math.pi / F) * -(l / F)
	elif l <= 5.5:
		tmp = l * (math.pi - (math.pi / (F * F)))
	else:
		tmp = math.pi * l
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if (l <= -2.65e+17)
		tmp = Float64(pi * l);
	elseif (l <= -6e-174)
		tmp = Float64(pi * Float64(l - Float64(l * (F ^ -2.0))));
	elseif (l <= -2.25e-263)
		tmp = Float64(Float64(pi / F) * Float64(-Float64(l / F)));
	elseif (l <= 5.5)
		tmp = Float64(l * Float64(pi - Float64(pi / Float64(F * F))));
	else
		tmp = Float64(pi * l);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if (l <= -2.65e+17)
		tmp = pi * l;
	elseif (l <= -6e-174)
		tmp = pi * (l - (l * (F ^ -2.0)));
	elseif (l <= -2.25e-263)
		tmp = (pi / F) * -(l / F);
	elseif (l <= 5.5)
		tmp = l * (pi - (pi / (F * F)));
	else
		tmp = pi * l;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[LessEqual[l, -2.65e+17], N[(Pi * l), $MachinePrecision], If[LessEqual[l, -6e-174], N[(Pi * N[(l - N[(l * N[Power[F, -2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[l, -2.25e-263], N[(N[(Pi / F), $MachinePrecision] * (-N[(l / F), $MachinePrecision])), $MachinePrecision], If[LessEqual[l, 5.5], N[(l * N[(Pi - N[(Pi / N[(F * F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(Pi * l), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if l < -2.65e17 or 5.5 < l

   1. Initial program 63.8%

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

   2. Taylor expanded in l around 0 45.7%

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

      1. unpow2 45.7%

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

      2. times-frac 45.7%

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

   4. Simplified 45.7%

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

   5. Taylor expanded in F around inf 98.8%

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

   if -2.65e17 < l < -6.00000000000000042e-174

   1. Initial program 91.9%

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

   2. Taylor expanded in l around 0 91.9%

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

      1. unpow2 91.9%

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

      2. times-frac 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in l around 0 91.9%

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

      1. sub-neg 91.9%

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

      2. mul-1-neg 91.9%

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

      3. distribute-rgt-in 91.9%

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

      4. mul-1-neg 91.9%

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

      5. distribute-lft-neg-in 91.9%

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

      6. unpow2 91.9%

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

      7. associate-*l/ 91.9%

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

      8. *-commutative 91.9%

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

      9. unpow2 91.9%

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

      10. unsub-neg 91.9%

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

      11. unpow2 91.9%

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

      12. *-commutative 91.9%

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

      13. *-lft-identity 91.9%

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

      14. associate-*l/ 91.9%

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

   7. Simplified 92.0%

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

   if -6.00000000000000042e-174 < l < -2.2499999999999999e-263

   1. Initial program 49.7%

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

   2. Taylor expanded in l around 0 52.4%

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

      1. unpow2 52.4%

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

      2. times-frac 99.5%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in F around 0 33.6%

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

      1. unpow2 33.6%

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

      2. associate-*r/ 33.6%

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

      3. mul-1-neg 33.6%

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

      4. distribute-rgt-neg-out 33.6%

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

   7. Simplified 33.6%

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

      1. associate-/l* 33.1%

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

      2. associate-/r/ 33.5%

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

      3. associate-/l/ 80.7%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 1.8%

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

      6. sqr-neg 1.8%

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

      7. sqrt-unprod 1.8%

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

      8. add-sqr-sqrt 1.8%

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

      9. associate-/r/ 1.8%

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

      10. frac-2neg 1.8%

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

      11. div-inv 1.8%

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

      12. distribute-neg-frac 1.8%

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

      13. distribute-neg-frac 1.8%

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

      14. add-sqr-sqrt 1.8%

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

      15. sqrt-unprod 1.8%

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

      16. sqr-neg 1.8%

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

      17. sqrt-unprod 0.0%

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

      18. add-sqr-sqrt 80.8%

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

      19. frac-2neg 80.8%

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

      20. clear-num 80.7%

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

      21. remove-double-div 80.7%

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

   9. Applied egg-rr 80.7%

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

   if -2.2499999999999999e-263 < l < 5.5

   1. Initial program 91.1%

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

   2. Taylor expanded in l around 0 91.1%

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

      1. unpow2 91.1%

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

      2. times-frac 99.5%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in l around 0 91.0%

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

      1. unpow2 91.0%

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

   7. Simplified 91.0%

      \[\leadsto \color{blue}{\ell \cdot \left(\pi - \frac{\pi}{F \cdot F}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -2.65 \cdot 10^{+17}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;\ell \leq -6 \cdot 10^{-174}:\\ \;\;\;\;\pi \cdot \left(\ell - \ell \cdot {F}^{-2}\right)\\ \mathbf{elif}\;\ell \leq -2.25 \cdot 10^{-263}:\\ \;\;\;\;\frac{\pi}{F} \cdot \left(-\frac{\ell}{F}\right)\\ \mathbf{elif}\;\ell \leq 5.5:\\ \;\;\;\;\ell \cdot \left(\pi - \frac{\pi}{F \cdot F}\right)\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell\\ \end{array} \]

Alternative 5: 73.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -5.1 \cdot 10^{-45}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;\ell \leq 2.85 \cdot 10^{-303}:\\ \;\;\;\;\pi \cdot \frac{\frac{\ell}{F}}{-F}\\ \mathbf{elif}\;\ell \leq 2.7 \cdot 10^{-196}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;\ell \leq 9 \cdot 10^{-175}:\\ \;\;\;\;\left(\pi \cdot \ell\right) \cdot \left(-{F}^{-2}\right)\\ \mathbf{elif}\;\ell \leq 2 \cdot 10^{-98} \lor \neg \left(\ell \leq 5 \cdot 10^{-5}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi \cdot \left(-\ell\right)}{F \cdot F}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (<= l -5.1e-45)
   (* PI l)
   (if (<= l 2.85e-303)
     (* PI (/ (/ l F) (- F)))
     (if (<= l 2.7e-196)
       (* PI l)
       (if (<= l 9e-175)
         (* (* PI l) (- (pow F -2.0)))
         (if (or (<= l 2e-98) (not (<= l 5e-5)))
           (* PI l)
           (/ (* PI (- l)) (* F F))))))))

C

double code(double F, double l) {
	double tmp;
	if (l <= -5.1e-45) {
		tmp = ((double) M_PI) * l;
	} else if (l <= 2.85e-303) {
		tmp = ((double) M_PI) * ((l / F) / -F);
	} else if (l <= 2.7e-196) {
		tmp = ((double) M_PI) * l;
	} else if (l <= 9e-175) {
		tmp = (((double) M_PI) * l) * -pow(F, -2.0);
	} else if ((l <= 2e-98) || !(l <= 5e-5)) {
		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 <= -5.1e-45) {
		tmp = Math.PI * l;
	} else if (l <= 2.85e-303) {
		tmp = Math.PI * ((l / F) / -F);
	} else if (l <= 2.7e-196) {
		tmp = Math.PI * l;
	} else if (l <= 9e-175) {
		tmp = (Math.PI * l) * -Math.pow(F, -2.0);
	} else if ((l <= 2e-98) || !(l <= 5e-5)) {
		tmp = Math.PI * l;
	} else {
		tmp = (Math.PI * -l) / (F * F);
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if l <= -5.1e-45:
		tmp = math.pi * l
	elif l <= 2.85e-303:
		tmp = math.pi * ((l / F) / -F)
	elif l <= 2.7e-196:
		tmp = math.pi * l
	elif l <= 9e-175:
		tmp = (math.pi * l) * -math.pow(F, -2.0)
	elif (l <= 2e-98) or not (l <= 5e-5):
		tmp = math.pi * l
	else:
		tmp = (math.pi * -l) / (F * F)
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if (l <= -5.1e-45)
		tmp = Float64(pi * l);
	elseif (l <= 2.85e-303)
		tmp = Float64(pi * Float64(Float64(l / F) / Float64(-F)));
	elseif (l <= 2.7e-196)
		tmp = Float64(pi * l);
	elseif (l <= 9e-175)
		tmp = Float64(Float64(pi * l) * Float64(-(F ^ -2.0)));
	elseif ((l <= 2e-98) || !(l <= 5e-5))
		tmp = Float64(pi * l);
	else
		tmp = Float64(Float64(pi * Float64(-l)) / Float64(F * F));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if (l <= -5.1e-45)
		tmp = pi * l;
	elseif (l <= 2.85e-303)
		tmp = pi * ((l / F) / -F);
	elseif (l <= 2.7e-196)
		tmp = pi * l;
	elseif (l <= 9e-175)
		tmp = (pi * l) * -(F ^ -2.0);
	elseif ((l <= 2e-98) || ~((l <= 5e-5)))
		tmp = pi * l;
	else
		tmp = (pi * -l) / (F * F);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[LessEqual[l, -5.1e-45], N[(Pi * l), $MachinePrecision], If[LessEqual[l, 2.85e-303], N[(Pi * N[(N[(l / F), $MachinePrecision] / (-F)), $MachinePrecision]), $MachinePrecision], If[LessEqual[l, 2.7e-196], N[(Pi * l), $MachinePrecision], If[LessEqual[l, 9e-175], N[(N[(Pi * l), $MachinePrecision] * (-N[Power[F, -2.0], $MachinePrecision])), $MachinePrecision], If[Or[LessEqual[l, 2e-98], N[Not[LessEqual[l, 5e-5]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(N[(Pi * (-l)), $MachinePrecision] / N[(F * F), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if l < -5.0999999999999997e-45 or 2.84999999999999991e-303 < l < 2.69999999999999982e-196 or 8.99999999999999996e-175 < l < 1.99999999999999988e-98 or 5.00000000000000024e-5 < l

   1. Initial program 71.0%

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

   2. Taylor expanded in l around 0 57.5%

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

      1. unpow2 57.5%

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

      2. times-frac 59.5%

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

   4. Simplified 59.5%

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

   5. Taylor expanded in F around inf 92.3%

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

   if -5.0999999999999997e-45 < l < 2.84999999999999991e-303

   1. Initial program 74.8%

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

   2. Taylor expanded in l around 0 75.6%

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

      1. unpow2 75.6%

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

      2. times-frac 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in F around 0 39.8%

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

      1. unpow2 39.8%

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

      2. associate-*r/ 39.8%

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

      3. mul-1-neg 39.8%

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

      4. distribute-rgt-neg-out 39.8%

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

   7. Simplified 39.8%

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

      1. associate-/l* 39.6%

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

      2. associate-/r/ 39.8%

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

      3. associate-/l/ 63.7%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 3.0%

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

      6. sqr-neg 3.0%

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

      7. sqrt-unprod 3.0%

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

      8. add-sqr-sqrt 3.0%

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

      9. associate-/r/ 3.0%

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

      10. frac-2neg 3.0%

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

      11. associate-/r/ 3.0%

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

      12. add-sqr-sqrt 0.0%

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

      13. sqrt-unprod 63.7%

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

      14. sqr-neg 63.7%

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

      15. sqrt-unprod 63.2%

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

      16. add-sqr-sqrt 63.7%

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

   9. Applied egg-rr 63.7%

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

   if 2.69999999999999982e-196 < l < 8.99999999999999996e-175

   1. Initial program 99.8%

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

   2. Taylor expanded in l around 0 100.0%

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

      1. unpow2 100.0%

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

      2. times-frac 99.6%

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

   4. Simplified 99.6%

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

   5. Taylor expanded in F around 0 84.1%

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

      1. mul-1-neg 84.1%

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

      2. unpow2 84.1%

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

      3. *-commutative 84.1%

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

      4. times-frac 83.9%

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

      5. distribute-rgt-neg-in 83.9%

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

      6. distribute-frac-neg 83.9%

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

      7. *-commutative 83.9%

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

      8. distribute-frac-neg 83.9%

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

      9. distribute-lft-neg-in 83.9%

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

      10. *-rgt-identity 83.9%

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

      11. associate-*r/ 83.4%

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

      12. associate-*r* 83.3%

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

      13. associate-*l/ 84.1%

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

      14. associate-*r/ 83.9%

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

      15. *-rgt-identity 83.9%

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

      16. associate-*r/ 83.5%

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

      17. associate-*r* 83.8%

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

      18. *-commutative 83.8%

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

      19. associate-*r* 83.7%

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

      20. unpow-1 83.7%

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

      21. unpow-1 83.7%

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

   7. Simplified 84.1%

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

   if 1.99999999999999988e-98 < l < 5.00000000000000024e-5

   1. Initial program 99.6%

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

   2. Taylor expanded in l around 0 99.8%

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

      1. unpow2 99.8%

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

      2. times-frac 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in F around 0 70.0%

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

      1. unpow2 70.0%

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

      2. associate-*r/ 70.0%

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

      3. mul-1-neg 70.0%

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

      4. distribute-rgt-neg-out 70.0%

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

   7. Simplified 70.0%

      \[\leadsto \color{blue}{\frac{\ell \cdot \left(-\pi\right)}{F \cdot F}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -5.1 \cdot 10^{-45}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;\ell \leq 2.85 \cdot 10^{-303}:\\ \;\;\;\;\pi \cdot \frac{\frac{\ell}{F}}{-F}\\ \mathbf{elif}\;\ell \leq 2.7 \cdot 10^{-196}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;\ell \leq 9 \cdot 10^{-175}:\\ \;\;\;\;\left(\pi \cdot \ell\right) \cdot \left(-{F}^{-2}\right)\\ \mathbf{elif}\;\ell \leq 2 \cdot 10^{-98} \lor \neg \left(\ell \leq 5 \cdot 10^{-5}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi \cdot \left(-\ell\right)}{F \cdot F}\\ \end{array} \]

Alternative 6: 98.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -2.65 \cdot 10^{+17} \lor \neg \left(\ell \leq 5.5\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\ell}{F} \cdot \frac{\pi}{F}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= l -2.65e+17) (not (<= l 5.5)))
   (* PI l)
   (- (* PI l) (* (/ l F) (/ PI F)))))

C

double code(double F, double l) {
	double tmp;
	if ((l <= -2.65e+17) || !(l <= 5.5)) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = (((double) M_PI) * l) - ((l / F) * (((double) M_PI) / F));
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if ((l <= -2.65e+17) || !(l <= 5.5)) {
		tmp = Math.PI * l;
	} else {
		tmp = (Math.PI * l) - ((l / F) * (Math.PI / F));
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if (l <= -2.65e+17) or not (l <= 5.5):
		tmp = math.pi * l
	else:
		tmp = (math.pi * l) - ((l / F) * (math.pi / F))
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((l <= -2.65e+17) || !(l <= 5.5))
		tmp = Float64(pi * l);
	else
		tmp = Float64(Float64(pi * l) - Float64(Float64(l / F) * Float64(pi / F)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if ((l <= -2.65e+17) || ~((l <= 5.5)))
		tmp = pi * l;
	else
		tmp = (pi * l) - ((l / F) * (pi / F));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[l, -2.65e+17], N[Not[LessEqual[l, 5.5]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(N[(Pi * l), $MachinePrecision] - N[(N[(l / F), $MachinePrecision] * N[(Pi / F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < -2.65e17 or 5.5 < l

   1. Initial program 63.8%

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

   2. Taylor expanded in l around 0 45.7%

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

      1. unpow2 45.7%

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

      2. times-frac 45.7%

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

   4. Simplified 45.7%

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

   5. Taylor expanded in F around inf 98.8%

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

   if -2.65e17 < l < 5.5

   1. Initial program 86.0%

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

   2. Taylor expanded in l around 0 86.4%

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

      1. unpow2 86.4%

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

      2. times-frac 99.4%

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

   4. Simplified 99.4%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -2.65 \cdot 10^{+17} \lor \neg \left(\ell \leq 5.5\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\ell}{F} \cdot \frac{\pi}{F}\\ \end{array} \]

Alternative 7: 74.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -4.2 \cdot 10^{-45} \lor \neg \left(\ell \leq 2.1 \cdot 10^{-303} \lor \neg \left(\ell \leq 2.1 \cdot 10^{-196}\right) \land \left(\ell \leq 3 \cdot 10^{-175} \lor \neg \left(\ell \leq 7 \cdot 10^{-101}\right) \land \ell \leq 1.8 \cdot 10^{-13}\right)\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi}{F} \cdot \left(-\frac{\ell}{F}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= l -4.2e-45)
         (not
          (or (<= l 2.1e-303)
              (and (not (<= l 2.1e-196))
                   (or (<= l 3e-175)
                       (and (not (<= l 7e-101)) (<= l 1.8e-13)))))))
   (* PI l)
   (* (/ PI F) (- (/ l F)))))

C

double code(double F, double l) {
	double tmp;
	if ((l <= -4.2e-45) || !((l <= 2.1e-303) || (!(l <= 2.1e-196) && ((l <= 3e-175) || (!(l <= 7e-101) && (l <= 1.8e-13)))))) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = (((double) M_PI) / F) * -(l / F);
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if ((l <= -4.2e-45) || !((l <= 2.1e-303) || (!(l <= 2.1e-196) && ((l <= 3e-175) || (!(l <= 7e-101) && (l <= 1.8e-13)))))) {
		tmp = Math.PI * l;
	} else {
		tmp = (Math.PI / F) * -(l / F);
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if (l <= -4.2e-45) or not ((l <= 2.1e-303) or (not (l <= 2.1e-196) and ((l <= 3e-175) or (not (l <= 7e-101) and (l <= 1.8e-13))))):
		tmp = math.pi * l
	else:
		tmp = (math.pi / F) * -(l / F)
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((l <= -4.2e-45) || !((l <= 2.1e-303) || (!(l <= 2.1e-196) && ((l <= 3e-175) || (!(l <= 7e-101) && (l <= 1.8e-13))))))
		tmp = Float64(pi * l);
	else
		tmp = Float64(Float64(pi / F) * Float64(-Float64(l / F)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if ((l <= -4.2e-45) || ~(((l <= 2.1e-303) || (~((l <= 2.1e-196)) && ((l <= 3e-175) || (~((l <= 7e-101)) && (l <= 1.8e-13)))))))
		tmp = pi * l;
	else
		tmp = (pi / F) * -(l / F);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[l, -4.2e-45], N[Not[Or[LessEqual[l, 2.1e-303], And[N[Not[LessEqual[l, 2.1e-196]], $MachinePrecision], Or[LessEqual[l, 3e-175], And[N[Not[LessEqual[l, 7e-101]], $MachinePrecision], LessEqual[l, 1.8e-13]]]]]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(N[(Pi / F), $MachinePrecision] * (-N[(l / F), $MachinePrecision])), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < -4.1999999999999999e-45 or 2.1e-303 < l < 2.09999999999999988e-196 or 3e-175 < l < 6.99999999999999989e-101 or 1.7999999999999999e-13 < l

   1. Initial program 71.0%

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

   2. Taylor expanded in l around 0 57.5%

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

      1. unpow2 57.5%

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

      2. times-frac 59.5%

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

   4. Simplified 59.5%

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

   5. Taylor expanded in F around inf 92.3%

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

   if -4.1999999999999999e-45 < l < 2.1e-303 or 2.09999999999999988e-196 < l < 3e-175 or 6.99999999999999989e-101 < l < 1.7999999999999999e-13

   1. Initial program 82.0%

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

   2. Taylor expanded in l around 0 82.6%

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

      1. unpow2 82.6%

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

      2. times-frac 99.4%

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

   4. Simplified 99.4%

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

   5. Taylor expanded in F around 0 50.0%

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

      1. unpow2 50.0%

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

      2. associate-*r/ 50.0%

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

      3. mul-1-neg 50.0%

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

      4. distribute-rgt-neg-out 50.0%

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

   7. Simplified 50.0%

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

      1. associate-/l* 49.8%

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

      2. associate-/r/ 49.9%

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

      3. associate-/l/ 66.9%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 2.7%

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

      6. sqr-neg 2.7%

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

      7. sqrt-unprod 2.7%

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

      8. add-sqr-sqrt 2.7%

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

      9. associate-/r/ 2.7%

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

      10. frac-2neg 2.7%

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

      11. div-inv 2.7%

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

      12. distribute-neg-frac 2.7%

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

      13. distribute-neg-frac 2.7%

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

      14. add-sqr-sqrt 2.7%

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

      15. sqrt-unprod 2.7%

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

      16. sqr-neg 2.7%

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

      17. sqrt-unprod 0.0%

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

      18. add-sqr-sqrt 66.8%

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

      19. frac-2neg 66.8%

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

      20. clear-num 66.7%

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

      21. remove-double-div 66.7%

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

   9. Applied egg-rr 66.7%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -4.2 \cdot 10^{-45} \lor \neg \left(\ell \leq 2.1 \cdot 10^{-303} \lor \neg \left(\ell \leq 2.1 \cdot 10^{-196}\right) \land \left(\ell \leq 3 \cdot 10^{-175} \lor \neg \left(\ell \leq 7 \cdot 10^{-101}\right) \land \ell \leq 1.8 \cdot 10^{-13}\right)\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi}{F} \cdot \left(-\frac{\ell}{F}\right)\\ \end{array} \]

Alternative 8: 73.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -6.4 \cdot 10^{-45}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;\ell \leq 7 \cdot 10^{-304}:\\ \;\;\;\;\pi \cdot \frac{\frac{\ell}{F}}{-F}\\ \mathbf{elif}\;\ell \leq 3.5 \cdot 10^{-197} \lor \neg \left(\ell \leq 1.4 \cdot 10^{-174} \lor \neg \left(\ell \leq 4.5 \cdot 10^{-100}\right) \land \ell \leq 2.7 \cdot 10^{-7}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi \cdot \left(-\ell\right)}{F \cdot F}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (<= l -6.4e-45)
   (* PI l)
   (if (<= l 7e-304)
     (* PI (/ (/ l F) (- F)))
     (if (or (<= l 3.5e-197)
             (not
              (or (<= l 1.4e-174) (and (not (<= l 4.5e-100)) (<= l 2.7e-7)))))
       (* PI l)
       (/ (* PI (- l)) (* F F))))))

C

double code(double F, double l) {
	double tmp;
	if (l <= -6.4e-45) {
		tmp = ((double) M_PI) * l;
	} else if (l <= 7e-304) {
		tmp = ((double) M_PI) * ((l / F) / -F);
	} else if ((l <= 3.5e-197) || !((l <= 1.4e-174) || (!(l <= 4.5e-100) && (l <= 2.7e-7)))) {
		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 <= -6.4e-45) {
		tmp = Math.PI * l;
	} else if (l <= 7e-304) {
		tmp = Math.PI * ((l / F) / -F);
	} else if ((l <= 3.5e-197) || !((l <= 1.4e-174) || (!(l <= 4.5e-100) && (l <= 2.7e-7)))) {
		tmp = Math.PI * l;
	} else {
		tmp = (Math.PI * -l) / (F * F);
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if l <= -6.4e-45:
		tmp = math.pi * l
	elif l <= 7e-304:
		tmp = math.pi * ((l / F) / -F)
	elif (l <= 3.5e-197) or not ((l <= 1.4e-174) or (not (l <= 4.5e-100) and (l <= 2.7e-7))):
		tmp = math.pi * l
	else:
		tmp = (math.pi * -l) / (F * F)
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if (l <= -6.4e-45)
		tmp = Float64(pi * l);
	elseif (l <= 7e-304)
		tmp = Float64(pi * Float64(Float64(l / F) / Float64(-F)));
	elseif ((l <= 3.5e-197) || !((l <= 1.4e-174) || (!(l <= 4.5e-100) && (l <= 2.7e-7))))
		tmp = Float64(pi * l);
	else
		tmp = Float64(Float64(pi * Float64(-l)) / Float64(F * F));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if (l <= -6.4e-45)
		tmp = pi * l;
	elseif (l <= 7e-304)
		tmp = pi * ((l / F) / -F);
	elseif ((l <= 3.5e-197) || ~(((l <= 1.4e-174) || (~((l <= 4.5e-100)) && (l <= 2.7e-7)))))
		tmp = pi * l;
	else
		tmp = (pi * -l) / (F * F);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[LessEqual[l, -6.4e-45], N[(Pi * l), $MachinePrecision], If[LessEqual[l, 7e-304], N[(Pi * N[(N[(l / F), $MachinePrecision] / (-F)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[l, 3.5e-197], N[Not[Or[LessEqual[l, 1.4e-174], And[N[Not[LessEqual[l, 4.5e-100]], $MachinePrecision], LessEqual[l, 2.7e-7]]]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(N[(Pi * (-l)), $MachinePrecision] / N[(F * F), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if l < -6.40000000000000015e-45 or 7e-304 < l < 3.4999999999999998e-197 or 1.39999999999999999e-174 < l < 4.5000000000000001e-100 or 2.70000000000000009e-7 < l

   1. Initial program 71.0%

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

   2. Taylor expanded in l around 0 57.5%

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

      1. unpow2 57.5%

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

      2. times-frac 59.5%

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

   4. Simplified 59.5%

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

   5. Taylor expanded in F around inf 92.3%

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

   if -6.40000000000000015e-45 < l < 7e-304

   1. Initial program 74.8%

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

   2. Taylor expanded in l around 0 75.6%

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

      1. unpow2 75.6%

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

      2. times-frac 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in F around 0 39.8%

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

      1. unpow2 39.8%

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

      2. associate-*r/ 39.8%

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

      3. mul-1-neg 39.8%

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

      4. distribute-rgt-neg-out 39.8%

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

   7. Simplified 39.8%

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

      1. associate-/l* 39.6%

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

      2. associate-/r/ 39.8%

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

      3. associate-/l/ 63.7%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 3.0%

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

      6. sqr-neg 3.0%

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

      7. sqrt-unprod 3.0%

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

      8. add-sqr-sqrt 3.0%

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

      9. associate-/r/ 3.0%

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

      10. frac-2neg 3.0%

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

      11. associate-/r/ 3.0%

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

      12. add-sqr-sqrt 0.0%

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

      13. sqrt-unprod 63.7%

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

      14. sqr-neg 63.7%

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

      15. sqrt-unprod 63.2%

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

      16. add-sqr-sqrt 63.7%

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

   9. Applied egg-rr 63.7%

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

   if 3.4999999999999998e-197 < l < 1.39999999999999999e-174 or 4.5000000000000001e-100 < l < 2.70000000000000009e-7

   1. Initial program 99.7%

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

   2. Taylor expanded in l around 0 99.8%

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

      1. unpow2 99.8%

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

      2. times-frac 99.4%

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

   4. Simplified 99.4%

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

   5. Taylor expanded in F around 0 74.9%

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

      1. unpow2 74.9%

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

      2. associate-*r/ 74.9%

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

      3. mul-1-neg 74.9%

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

      4. distribute-rgt-neg-out 74.9%

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

   7. Simplified 74.9%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -6.4 \cdot 10^{-45}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;\ell \leq 7 \cdot 10^{-304}:\\ \;\;\;\;\pi \cdot \frac{\frac{\ell}{F}}{-F}\\ \mathbf{elif}\;\ell \leq 3.5 \cdot 10^{-197} \lor \neg \left(\ell \leq 1.4 \cdot 10^{-174} \lor \neg \left(\ell \leq 4.5 \cdot 10^{-100}\right) \land \ell \leq 2.7 \cdot 10^{-7}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi \cdot \left(-\ell\right)}{F \cdot F}\\ \end{array} \]

Alternative 9: 74.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \pi \cdot \frac{\frac{\ell}{F}}{-F}\\ \mathbf{if}\;\ell \leq -9 \cdot 10^{-45}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;\ell \leq 1.8 \cdot 10^{-303}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq 3 \cdot 10^{-195}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;\ell \leq 3.4 \cdot 10^{-175}:\\ \;\;\;\;\frac{\pi}{F} \cdot \left(-\frac{\ell}{F}\right)\\ \mathbf{elif}\;\ell \leq 6.8 \cdot 10^{-99} \lor \neg \left(\ell \leq 6.4 \cdot 10^{-9}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (let* ((t_0 (* PI (/ (/ l F) (- F)))))
   (if (<= l -9e-45)
     (* PI l)
     (if (<= l 1.8e-303)
       t_0
       (if (<= l 3e-195)
         (* PI l)
         (if (<= l 3.4e-175)
           (* (/ PI F) (- (/ l F)))
           (if (or (<= l 6.8e-99) (not (<= l 6.4e-9))) (* PI l) t_0)))))))

C

double code(double F, double l) {
	double t_0 = ((double) M_PI) * ((l / F) / -F);
	double tmp;
	if (l <= -9e-45) {
		tmp = ((double) M_PI) * l;
	} else if (l <= 1.8e-303) {
		tmp = t_0;
	} else if (l <= 3e-195) {
		tmp = ((double) M_PI) * l;
	} else if (l <= 3.4e-175) {
		tmp = (((double) M_PI) / F) * -(l / F);
	} else if ((l <= 6.8e-99) || !(l <= 6.4e-9)) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double t_0 = Math.PI * ((l / F) / -F);
	double tmp;
	if (l <= -9e-45) {
		tmp = Math.PI * l;
	} else if (l <= 1.8e-303) {
		tmp = t_0;
	} else if (l <= 3e-195) {
		tmp = Math.PI * l;
	} else if (l <= 3.4e-175) {
		tmp = (Math.PI / F) * -(l / F);
	} else if ((l <= 6.8e-99) || !(l <= 6.4e-9)) {
		tmp = Math.PI * l;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(F, l):
	t_0 = math.pi * ((l / F) / -F)
	tmp = 0
	if l <= -9e-45:
		tmp = math.pi * l
	elif l <= 1.8e-303:
		tmp = t_0
	elif l <= 3e-195:
		tmp = math.pi * l
	elif l <= 3.4e-175:
		tmp = (math.pi / F) * -(l / F)
	elif (l <= 6.8e-99) or not (l <= 6.4e-9):
		tmp = math.pi * l
	else:
		tmp = t_0
	return tmp

Julia

function code(F, l)
	t_0 = Float64(pi * Float64(Float64(l / F) / Float64(-F)))
	tmp = 0.0
	if (l <= -9e-45)
		tmp = Float64(pi * l);
	elseif (l <= 1.8e-303)
		tmp = t_0;
	elseif (l <= 3e-195)
		tmp = Float64(pi * l);
	elseif (l <= 3.4e-175)
		tmp = Float64(Float64(pi / F) * Float64(-Float64(l / F)));
	elseif ((l <= 6.8e-99) || !(l <= 6.4e-9))
		tmp = Float64(pi * l);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	t_0 = pi * ((l / F) / -F);
	tmp = 0.0;
	if (l <= -9e-45)
		tmp = pi * l;
	elseif (l <= 1.8e-303)
		tmp = t_0;
	elseif (l <= 3e-195)
		tmp = pi * l;
	elseif (l <= 3.4e-175)
		tmp = (pi / F) * -(l / F);
	elseif ((l <= 6.8e-99) || ~((l <= 6.4e-9)))
		tmp = pi * l;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := Block[{t$95$0 = N[(Pi * N[(N[(l / F), $MachinePrecision] / (-F)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[l, -9e-45], N[(Pi * l), $MachinePrecision], If[LessEqual[l, 1.8e-303], t$95$0, If[LessEqual[l, 3e-195], N[(Pi * l), $MachinePrecision], If[LessEqual[l, 3.4e-175], N[(N[(Pi / F), $MachinePrecision] * (-N[(l / F), $MachinePrecision])), $MachinePrecision], If[Or[LessEqual[l, 6.8e-99], N[Not[LessEqual[l, 6.4e-9]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if l < -8.9999999999999997e-45 or 1.7999999999999999e-303 < l < 3e-195 or 3.4e-175 < l < 6.80000000000000014e-99 or 6.40000000000000023e-9 < l

   1. Initial program 71.0%

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

   2. Taylor expanded in l around 0 57.5%

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

      1. unpow2 57.5%

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

      2. times-frac 59.5%

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

   4. Simplified 59.5%

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

   5. Taylor expanded in F around inf 92.3%

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

   if -8.9999999999999997e-45 < l < 1.7999999999999999e-303 or 6.80000000000000014e-99 < l < 6.40000000000000023e-9

   1. Initial program 80.0%

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

   2. Taylor expanded in l around 0 80.7%

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

      1. unpow2 80.7%

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

      2. times-frac 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in F around 0 46.1%

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

      1. unpow2 46.1%

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

      2. associate-*r/ 46.1%

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

      3. mul-1-neg 46.1%

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

      4. distribute-rgt-neg-out 46.1%

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

   7. Simplified 46.1%

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

      1. associate-/l* 46.0%

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

      2. associate-/r/ 46.1%

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

      3. associate-/l/ 64.9%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 2.8%

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

      6. sqr-neg 2.8%

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

      7. sqrt-unprod 2.8%

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

      8. add-sqr-sqrt 2.8%

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

      9. associate-/r/ 2.8%

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

      10. frac-2neg 2.8%

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

      11. associate-/r/ 2.8%

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

      12. add-sqr-sqrt 0.0%

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

      13. sqrt-unprod 64.9%

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

      14. sqr-neg 64.9%

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

      15. sqrt-unprod 64.5%

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

      16. add-sqr-sqrt 64.9%

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

   9. Applied egg-rr 64.9%

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

   if 3e-195 < l < 3.4e-175

   1. Initial program 99.8%

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

   2. Taylor expanded in l around 0 100.0%

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

      1. unpow2 100.0%

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

      2. times-frac 99.6%

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

   4. Simplified 99.6%

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

   5. Taylor expanded in F around 0 84.1%

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

      1. unpow2 84.1%

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

      2. associate-*r/ 84.1%

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

      3. mul-1-neg 84.1%

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

      4. distribute-rgt-neg-out 84.1%

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

   7. Simplified 84.1%

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

      1. associate-/l* 83.8%

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

      2. associate-/r/ 83.7%

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

      3. associate-/l/ 83.9%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 2.5%

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

      6. sqr-neg 2.5%

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

      7. sqrt-unprod 2.5%

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

      8. add-sqr-sqrt 2.5%

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

      9. associate-/r/ 2.5%

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

      10. frac-2neg 2.5%

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

      11. div-inv 2.5%

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

      12. distribute-neg-frac 2.5%

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

      13. distribute-neg-frac 2.5%

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

      14. add-sqr-sqrt 2.5%

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

      15. sqrt-unprod 2.5%

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

      16. sqr-neg 2.5%

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

      17. sqrt-unprod 0.0%

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

      18. add-sqr-sqrt 83.9%

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

      19. frac-2neg 83.9%

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

      20. clear-num 83.9%

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

      21. remove-double-div 83.9%

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

   9. Applied egg-rr 83.9%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -9 \cdot 10^{-45}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;\ell \leq 1.8 \cdot 10^{-303}:\\ \;\;\;\;\pi \cdot \frac{\frac{\ell}{F}}{-F}\\ \mathbf{elif}\;\ell \leq 3 \cdot 10^{-195}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;\ell \leq 3.4 \cdot 10^{-175}:\\ \;\;\;\;\frac{\pi}{F} \cdot \left(-\frac{\ell}{F}\right)\\ \mathbf{elif}\;\ell \leq 6.8 \cdot 10^{-99} \lor \neg \left(\ell \leq 6.4 \cdot 10^{-9}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \frac{\frac{\ell}{F}}{-F}\\ \end{array} \]

Alternative 10: 74.0% 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 74.0%

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

2. Taylor expanded in l around 0 64.3%

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

   1. unpow2 64.3%

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

   2. times-frac 70.2%

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

4. Simplified 70.2%

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

5. Taylor expanded in F around inf 76.7%

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

6. Final simplification 76.7%

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

Reproduce

herbie shell --seed 2023274 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  :precision binary64
  (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))