VandenBroeck and Keller, Equation (6)

Percentage Accurate: 75.8% → 98.5%

Time: 12.8s

Alternatives: 10

Speedup: 1.5×

• could not determine a ground truth

  1. F = 6.947419798611997e-41
  2. l = -3274080197544203.5

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: 75.8% 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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -5 \cdot 10^{+29} \lor \neg \left(\pi \cdot \ell \leq 10000000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell + \frac{-1}{F \cdot \frac{F}{\tan \left(\pi \cdot \ell\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= (* PI l) -5e+29) (not (<= (* PI l) 10000000000.0)))
   (* PI l)
   (+ (* PI l) (/ -1.0 (* F (/ F (tan (* PI l))))))))

C

double code(double F, double l) {
	double tmp;
	if (((((double) M_PI) * l) <= -5e+29) || !((((double) M_PI) * l) <= 10000000000.0)) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = (((double) M_PI) * l) + (-1.0 / (F * (F / tan((((double) M_PI) * l)))));
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if (((Math.PI * l) <= -5e+29) || !((Math.PI * l) <= 10000000000.0)) {
		tmp = Math.PI * l;
	} else {
		tmp = (Math.PI * l) + (-1.0 / (F * (F / Math.tan((Math.PI * l)))));
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if ((math.pi * l) <= -5e+29) or not ((math.pi * l) <= 10000000000.0):
		tmp = math.pi * l
	else:
		tmp = (math.pi * l) + (-1.0 / (F * (F / math.tan((math.pi * l)))))
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((Float64(pi * l) <= -5e+29) || !(Float64(pi * l) <= 10000000000.0))
		tmp = Float64(pi * l);
	else
		tmp = Float64(Float64(pi * l) + Float64(-1.0 / Float64(F * Float64(F / tan(Float64(pi * l))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if (((pi * l) <= -5e+29) || ~(((pi * l) <= 10000000000.0)))
		tmp = pi * l;
	else
		tmp = (pi * l) + (-1.0 / (F * (F / tan((pi * l)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[N[(Pi * l), $MachinePrecision], -5e+29], N[Not[LessEqual[N[(Pi * l), $MachinePrecision], 10000000000.0]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(N[(Pi * l), $MachinePrecision] + N[(-1.0 / N[(F * N[(F / N[Tan[N[(Pi * l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (PI.f64) l) < -5.0000000000000001e29 or 1e10 < (*.f64 (PI.f64) l)

   1. Initial program 61.9%

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

      1. associate-*l/ 61.9%

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

      2. *-lft-identity 61.9%

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

   3. Simplified 61.9%

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

   4. Taylor expanded in l around 0 46.3%

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

      1. unpow2 46.3%

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

   6. Simplified 46.3%

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

   7. Taylor expanded in F around inf 99.6%

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

   if -5.0000000000000001e29 < (*.f64 (PI.f64) l) < 1e10

   1. Initial program 87.1%

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

      1. associate-*l/ 88.7%

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

      2. *-lft-identity 88.7%

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

   3. Simplified 88.7%

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

      1. associate-/r* 99.0%

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

      2. div-inv 99.0%

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

   5. Applied egg-rr 99.0%

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

      1. clear-num 98.9%

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

      2. frac-times 99.0%

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

      3. metadata-eval 99.0%

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

   7. Applied egg-rr 99.0%

      \[\leadsto \pi \cdot \ell - \color{blue}{\frac{1}{\frac{F}{\tan \left(\pi \cdot \ell\right)} \cdot F}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -5 \cdot 10^{+29} \lor \neg \left(\pi \cdot \ell \leq 10000000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell + \frac{-1}{F \cdot \frac{F}{\tan \left(\pi \cdot \ell\right)}}\\ \end{array} \]

Alternative 2: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -5 \cdot 10^{+29} \lor \neg \left(\pi \cdot \ell \leq 10000000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= (* PI l) -5e+29) (not (<= (* PI l) 10000000000.0)))
   (* PI l)
   (- (* PI l) (/ (/ (tan (* PI l)) F) F))))

C

double code(double F, double l) {
	double tmp;
	if (((((double) M_PI) * l) <= -5e+29) || !((((double) M_PI) * l) <= 10000000000.0)) {
		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+29) || !((Math.PI * l) <= 10000000000.0)) {
		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+29) or not ((math.pi * l) <= 10000000000.0):
		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+29) || !(Float64(pi * l) <= 10000000000.0))
		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+29) || ~(((pi * l) <= 10000000000.0)))
		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+29], N[Not[LessEqual[N[(Pi * l), $MachinePrecision], 10000000000.0]], $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) < -5.0000000000000001e29 or 1e10 < (*.f64 (PI.f64) l)

   1. Initial program 61.9%

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

      1. associate-*l/ 61.9%

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

      2. *-lft-identity 61.9%

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

   3. Simplified 61.9%

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

   4. Taylor expanded in l around 0 46.3%

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

      1. unpow2 46.3%

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

   6. Simplified 46.3%

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

   7. Taylor expanded in F around inf 99.6%

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

   if -5.0000000000000001e29 < (*.f64 (PI.f64) l) < 1e10

   1. Initial program 87.1%

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

      1. associate-*l/ 88.7%

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

      2. *-un-lft-identity 88.7%

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

      3. associate-/r* 99.0%

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

   3. Applied egg-rr 99.0%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -5 \cdot 10^{+29} \lor \neg \left(\pi \cdot \ell \leq 10000000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}\\ \end{array} \]

Alternative 3: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -2000000 \lor \neg \left(\pi \cdot \ell \leq 5 \cdot 10^{-13}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \pi \cdot \frac{\frac{\ell}{F}}{F}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= (* PI l) -2000000.0) (not (<= (* PI l) 5e-13)))
   (* PI l)
   (- (* PI l) (* PI (/ (/ l F) F)))))

C

double code(double F, double l) {
	double tmp;
	if (((((double) M_PI) * l) <= -2000000.0) || !((((double) M_PI) * l) <= 5e-13)) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = (((double) M_PI) * l) - (((double) M_PI) * ((l / F) / F));
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if (((Math.PI * l) <= -2000000.0) || !((Math.PI * l) <= 5e-13)) {
		tmp = Math.PI * l;
	} else {
		tmp = (Math.PI * l) - (Math.PI * ((l / F) / F));
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if ((math.pi * l) <= -2000000.0) or not ((math.pi * l) <= 5e-13):
		tmp = math.pi * l
	else:
		tmp = (math.pi * l) - (math.pi * ((l / F) / F))
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((Float64(pi * l) <= -2000000.0) || !(Float64(pi * l) <= 5e-13))
		tmp = Float64(pi * l);
	else
		tmp = Float64(Float64(pi * l) - Float64(pi * Float64(Float64(l / F) / F)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if (((pi * l) <= -2000000.0) || ~(((pi * l) <= 5e-13)))
		tmp = pi * l;
	else
		tmp = (pi * l) - (pi * ((l / F) / F));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[N[(Pi * l), $MachinePrecision], -2000000.0], N[Not[LessEqual[N[(Pi * l), $MachinePrecision], 5e-13]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(N[(Pi * l), $MachinePrecision] - N[(Pi * N[(N[(l / F), $MachinePrecision] / F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (PI.f64) l) < -2e6 or 4.9999999999999999e-13 < (*.f64 (PI.f64) l)

   1. Initial program 64.0%

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

      1. associate-*l/ 64.0%

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

      2. *-lft-identity 64.0%

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

   3. Simplified 64.0%

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

   4. Taylor expanded in l around 0 47.0%

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

      1. unpow2 47.0%

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

   6. Simplified 47.0%

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

   7. Taylor expanded in F around inf 96.4%

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

   if -2e6 < (*.f64 (PI.f64) l) < 4.9999999999999999e-13

   1. Initial program 87.0%

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

      1. associate-*l/ 88.6%

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

      2. *-un-lft-identity 88.6%

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

      3. associate-/r* 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in l around 0 99.3%

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

      1. associate-/l* 99.3%

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

      2. associate-/r/ 99.3%

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

   6. Simplified 99.3%

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

      1. associate-/l* 99.3%

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

      2. associate-/r/ 99.3%

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

   8. Applied egg-rr 99.3%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -2000000 \lor \neg \left(\pi \cdot \ell \leq 5 \cdot 10^{-13}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \pi \cdot \frac{\frac{\ell}{F}}{F}\\ \end{array} \]

Alternative 4: 98.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -380000 \lor \neg \left(\ell \leq 0.038\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\ell}{F} \cdot \frac{\pi}{F}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= l -380000.0) (not (<= l 0.038)))
   (* PI l)
   (- (* PI l) (* (/ l F) (/ PI F)))))

C

double code(double F, double l) {
	double tmp;
	if ((l <= -380000.0) || !(l <= 0.038)) {
		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 <= -380000.0) || !(l <= 0.038)) {
		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 <= -380000.0) or not (l <= 0.038):
		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 <= -380000.0) || !(l <= 0.038))
		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 <= -380000.0) || ~((l <= 0.038)))
		tmp = pi * l;
	else
		tmp = (pi * l) - ((l / F) * (pi / F));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[l, -380000.0], N[Not[LessEqual[l, 0.038]], $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 < -3.8e5 or 0.0379999999999999991 < l

   1. Initial program 64.0%

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

      1. associate-*l/ 64.0%

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

      2. *-lft-identity 64.0%

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

   3. Simplified 64.0%

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

   4. Taylor expanded in l around 0 47.0%

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

      1. unpow2 47.0%

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

   6. Simplified 47.0%

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

   7. Taylor expanded in F around inf 96.4%

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

   if -3.8e5 < l < 0.0379999999999999991

   1. Initial program 87.0%

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

      1. associate-*l/ 88.6%

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

      2. *-lft-identity 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in l around 0 86.7%

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

      1. unpow2 86.7%

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

   6. Simplified 86.7%

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

   7. Taylor expanded in F around 0 88.3%

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

      1. *-commutative 88.3%

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

      2. mul-1-neg 88.3%

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

      3. unsub-neg 88.3%

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

      4. *-commutative 88.3%

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

      5. *-commutative 88.3%

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

      6. unpow2 88.3%

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

      7. times-frac 99.3%

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

   9. Simplified 99.3%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -380000 \lor \neg \left(\ell \leq 0.038\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\ell}{F} \cdot \frac{\pi}{F}\\ \end{array} \]

Alternative 5: 92.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -380000 \lor \neg \left(\ell \leq 0.038\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\ell \cdot \left(\pi - \frac{\pi}{F \cdot F}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= l -380000.0) (not (<= l 0.038)))
   (* PI l)
   (* l (- PI (/ PI (* F F))))))

C

double code(double F, double l) {
	double tmp;
	if ((l <= -380000.0) || !(l <= 0.038)) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = l * (((double) M_PI) - (((double) M_PI) / (F * F)));
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if ((l <= -380000.0) || !(l <= 0.038)) {
		tmp = Math.PI * l;
	} else {
		tmp = l * (Math.PI - (Math.PI / (F * F)));
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if (l <= -380000.0) or not (l <= 0.038):
		tmp = math.pi * l
	else:
		tmp = l * (math.pi - (math.pi / (F * F)))
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((l <= -380000.0) || !(l <= 0.038))
		tmp = Float64(pi * l);
	else
		tmp = Float64(l * Float64(pi - Float64(pi / Float64(F * F))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if ((l <= -380000.0) || ~((l <= 0.038)))
		tmp = pi * l;
	else
		tmp = l * (pi - (pi / (F * F)));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[l, -380000.0], N[Not[LessEqual[l, 0.038]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(l * N[(Pi - N[(Pi / N[(F * F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < -3.8e5 or 0.0379999999999999991 < l

   1. Initial program 64.0%

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

      1. associate-*l/ 64.0%

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

      2. *-lft-identity 64.0%

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

   3. Simplified 64.0%

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

   4. Taylor expanded in l around 0 47.0%

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

      1. unpow2 47.0%

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

   6. Simplified 47.0%

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

   7. Taylor expanded in F around inf 96.4%

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

   if -3.8e5 < l < 0.0379999999999999991

   1. Initial program 87.0%

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

      1. associate-*l/ 88.6%

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

      2. *-lft-identity 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in l around 0 86.7%

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

      1. unpow2 86.7%

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

   6. Simplified 86.7%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -380000 \lor \neg \left(\ell \leq 0.038\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\ell \cdot \left(\pi - \frac{\pi}{F \cdot F}\right)\\ \end{array} \]

Alternative 6: 74.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \cdot F \leq 10^{-292} \lor \neg \left(F \cdot F \leq 5 \cdot 10^{-138}\right) \land F \cdot F \leq 2 \cdot 10^{-80}:\\ \;\;\;\;\frac{\ell}{F} \cdot \frac{-1}{\frac{F}{\pi}}\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= (* F F) 1e-292)
         (and (not (<= (* F F) 5e-138)) (<= (* F F) 2e-80)))
   (* (/ l F) (/ -1.0 (/ F PI)))
   (* PI l)))

C

double code(double F, double l) {
	double tmp;
	if (((F * F) <= 1e-292) || (!((F * F) <= 5e-138) && ((F * F) <= 2e-80))) {
		tmp = (l / F) * (-1.0 / (F / ((double) M_PI)));
	} else {
		tmp = ((double) M_PI) * l;
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if (((F * F) <= 1e-292) || (!((F * F) <= 5e-138) && ((F * F) <= 2e-80))) {
		tmp = (l / F) * (-1.0 / (F / Math.PI));
	} else {
		tmp = Math.PI * l;
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if ((F * F) <= 1e-292) or (not ((F * F) <= 5e-138) and ((F * F) <= 2e-80)):
		tmp = (l / F) * (-1.0 / (F / math.pi))
	else:
		tmp = math.pi * l
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((Float64(F * F) <= 1e-292) || (!(Float64(F * F) <= 5e-138) && (Float64(F * F) <= 2e-80)))
		tmp = Float64(Float64(l / F) * Float64(-1.0 / Float64(F / pi)));
	else
		tmp = Float64(pi * l);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if (((F * F) <= 1e-292) || (~(((F * F) <= 5e-138)) && ((F * F) <= 2e-80)))
		tmp = (l / F) * (-1.0 / (F / pi));
	else
		tmp = pi * l;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[N[(F * F), $MachinePrecision], 1e-292], And[N[Not[LessEqual[N[(F * F), $MachinePrecision], 5e-138]], $MachinePrecision], LessEqual[N[(F * F), $MachinePrecision], 2e-80]]], N[(N[(l / F), $MachinePrecision] * N[(-1.0 / N[(F / Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(Pi * l), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 F F) < 1.0000000000000001e-292 or 4.99999999999999989e-138 < (*.f64 F F) < 1.99999999999999992e-80

   1. Initial program 47.4%

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

      1. associate-*l/ 50.1%

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

      2. *-lft-identity 50.1%

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

   3. Simplified 50.1%

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

   4. Taylor expanded in l around 0 42.1%

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

      1. unpow2 42.1%

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

   6. Simplified 42.1%

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

   7. Taylor expanded in F around 0 44.8%

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

      1. mul-1-neg 44.8%

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

      2. associate-/l* 44.7%

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

      3. distribute-neg-frac 44.7%

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

      4. unpow2 44.7%

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

      5. *-lft-identity 44.7%

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

      6. times-frac 44.7%

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

      7. /-rgt-identity 44.7%

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

   9. Simplified 44.7%

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

       1. neg-mul-1 44.7%

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

       2. *-commutative 44.7%

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

       3. times-frac 63.0%

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

   11. Applied egg-rr 63.0%

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

   if 1.0000000000000001e-292 < (*.f64 F F) < 4.99999999999999989e-138 or 1.99999999999999992e-80 < (*.f64 F F)

   1. Initial program 90.7%

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

      1. associate-*l/ 90.7%

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

      2. *-lft-identity 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in l around 0 81.5%

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

      1. unpow2 81.5%

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

   6. Simplified 81.5%

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

   7. Taylor expanded in F around inf 88.8%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;F \cdot F \leq 10^{-292} \lor \neg \left(F \cdot F \leq 5 \cdot 10^{-138}\right) \land F \cdot F \leq 2 \cdot 10^{-80}:\\ \;\;\;\;\frac{\ell}{F} \cdot \frac{-1}{\frac{F}{\pi}}\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell\\ \end{array} \]

Alternative 7: 74.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \cdot F \leq 10^{-292}:\\ \;\;\;\;\frac{-1}{F} \cdot \frac{\ell}{\frac{F}{\pi}}\\ \mathbf{elif}\;F \cdot F \leq 5 \cdot 10^{-138} \lor \neg \left(F \cdot F \leq 2 \cdot 10^{-80}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi \cdot \left(-\ell\right)}{F \cdot F}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (<= (* F F) 1e-292)
   (* (/ -1.0 F) (/ l (/ F PI)))
   (if (or (<= (* F F) 5e-138) (not (<= (* F F) 2e-80)))
     (* PI l)
     (/ (* PI (- l)) (* F F)))))

C

double code(double F, double l) {
	double tmp;
	if ((F * F) <= 1e-292) {
		tmp = (-1.0 / F) * (l / (F / ((double) M_PI)));
	} else if (((F * F) <= 5e-138) || !((F * F) <= 2e-80)) {
		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 ((F * F) <= 1e-292) {
		tmp = (-1.0 / F) * (l / (F / Math.PI));
	} else if (((F * F) <= 5e-138) || !((F * F) <= 2e-80)) {
		tmp = Math.PI * l;
	} else {
		tmp = (Math.PI * -l) / (F * F);
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if (F * F) <= 1e-292:
		tmp = (-1.0 / F) * (l / (F / math.pi))
	elif ((F * F) <= 5e-138) or not ((F * F) <= 2e-80):
		tmp = math.pi * l
	else:
		tmp = (math.pi * -l) / (F * F)
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if (Float64(F * F) <= 1e-292)
		tmp = Float64(Float64(-1.0 / F) * Float64(l / Float64(F / pi)));
	elseif ((Float64(F * F) <= 5e-138) || !(Float64(F * F) <= 2e-80))
		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 ((F * F) <= 1e-292)
		tmp = (-1.0 / F) * (l / (F / pi));
	elseif (((F * F) <= 5e-138) || ~(((F * F) <= 2e-80)))
		tmp = pi * l;
	else
		tmp = (pi * -l) / (F * F);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[LessEqual[N[(F * F), $MachinePrecision], 1e-292], N[(N[(-1.0 / F), $MachinePrecision] * N[(l / N[(F / Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(F * F), $MachinePrecision], 5e-138], N[Not[LessEqual[N[(F * F), $MachinePrecision], 2e-80]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(N[(Pi * (-l)), $MachinePrecision] / N[(F * F), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 F F) < 1.0000000000000001e-292

   1. Initial program 38.5%

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

      1. associate-*l/ 41.8%

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

      2. *-lft-identity 41.8%

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

   3. Simplified 41.8%

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

   4. Taylor expanded in l around 0 35.8%

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

      1. unpow2 35.8%

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

   6. Simplified 35.8%

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

   7. Taylor expanded in F around 0 39.1%

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

      1. mul-1-neg 39.1%

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

      2. associate-/l* 39.1%

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

      3. distribute-neg-frac 39.1%

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

      4. unpow2 39.1%

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

      5. *-lft-identity 39.1%

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

      6. times-frac 39.1%

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

      7. /-rgt-identity 39.1%

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

   9. Simplified 39.1%

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

       1. neg-mul-1 39.1%

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

       2. times-frac 61.7%

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

   11. Applied egg-rr 61.7%

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

   if 1.0000000000000001e-292 < (*.f64 F F) < 4.99999999999999989e-138 or 1.99999999999999992e-80 < (*.f64 F F)

   1. Initial program 90.7%

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

      1. associate-*l/ 90.7%

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

      2. *-lft-identity 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in l around 0 81.5%

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

      1. unpow2 81.5%

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

   6. Simplified 81.5%

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

   7. Taylor expanded in F around inf 88.8%

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

   if 4.99999999999999989e-138 < (*.f64 F F) < 1.99999999999999992e-80

   1. Initial program 85.2%

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

      1. associate-*l/ 85.5%

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

      2. *-lft-identity 85.5%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in l around 0 68.8%

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

      1. unpow2 68.8%

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

   6. Simplified 68.8%

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

   7. Taylor expanded in F around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. unpow2 68.8%

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

   9. Simplified 68.8%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;F \cdot F \leq 10^{-292}:\\ \;\;\;\;\frac{-1}{F} \cdot \frac{\ell}{\frac{F}{\pi}}\\ \mathbf{elif}\;F \cdot F \leq 5 \cdot 10^{-138} \lor \neg \left(F \cdot F \leq 2 \cdot 10^{-80}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi \cdot \left(-\ell\right)}{F \cdot F}\\ \end{array} \]

Alternative 8: 73.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -1.35 \cdot 10^{-24} \lor \neg \left(\ell \leq -7 \cdot 10^{-155} \lor \neg \left(\ell \leq 1.1 \cdot 10^{-145}\right) \land \ell \leq 1.5 \cdot 10^{-79}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi \cdot \left(-\ell\right)}{F \cdot F}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= l -1.35e-24)
         (not (or (<= l -7e-155) (and (not (<= l 1.1e-145)) (<= l 1.5e-79)))))
   (* PI l)
   (/ (* PI (- l)) (* F F))))

C

double code(double F, double l) {
	double tmp;
	if ((l <= -1.35e-24) || !((l <= -7e-155) || (!(l <= 1.1e-145) && (l <= 1.5e-79)))) {
		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 <= -1.35e-24) || !((l <= -7e-155) || (!(l <= 1.1e-145) && (l <= 1.5e-79)))) {
		tmp = Math.PI * l;
	} else {
		tmp = (Math.PI * -l) / (F * F);
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if (l <= -1.35e-24) or not ((l <= -7e-155) or (not (l <= 1.1e-145) and (l <= 1.5e-79))):
		tmp = math.pi * l
	else:
		tmp = (math.pi * -l) / (F * F)
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((l <= -1.35e-24) || !((l <= -7e-155) || (!(l <= 1.1e-145) && (l <= 1.5e-79))))
		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 <= -1.35e-24) || ~(((l <= -7e-155) || (~((l <= 1.1e-145)) && (l <= 1.5e-79)))))
		tmp = pi * l;
	else
		tmp = (pi * -l) / (F * F);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[l, -1.35e-24], N[Not[Or[LessEqual[l, -7e-155], And[N[Not[LessEqual[l, 1.1e-145]], $MachinePrecision], LessEqual[l, 1.5e-79]]]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(N[(Pi * (-l)), $MachinePrecision] / N[(F * F), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < -1.35000000000000003e-24 or -7.00000000000000031e-155 < l < 1.1e-145 or 1.5e-79 < 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 64.4%

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

      1. unpow2 64.4%

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

   6. Simplified 64.4%

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

   7. Taylor expanded in F around inf 80.5%

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

   if -1.35000000000000003e-24 < l < -7.00000000000000031e-155 or 1.1e-145 < l < 1.5e-79

   1. Initial program 87.5%

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

      1. associate-*l/ 89.4%

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

      2. *-lft-identity 89.4%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in l around 0 87.6%

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

      1. unpow2 87.6%

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

   6. Simplified 87.6%

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

   7. Taylor expanded in F around 0 62.1%

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

      1. mul-1-neg 62.1%

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

      2. unpow2 62.1%

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

   9. Simplified 62.1%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -1.35 \cdot 10^{-24} \lor \neg \left(\ell \leq -7 \cdot 10^{-155} \lor \neg \left(\ell \leq 1.1 \cdot 10^{-145}\right) \land \ell \leq 1.5 \cdot 10^{-79}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi \cdot \left(-\ell\right)}{F \cdot F}\\ \end{array} \]

Alternative 9: 73.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -5.5 \cdot 10^{-23}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;\ell \leq -9.6 \cdot 10^{-155}:\\ \;\;\;\;\frac{\pi \cdot \left(-\ell\right)}{F \cdot F}\\ \mathbf{elif}\;\ell \leq 3.8 \cdot 10^{-142} \lor \neg \left(\ell \leq 6.7 \cdot 10^{-80}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\frac{-\ell}{F \cdot \frac{F}{\pi}}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (<= l -5.5e-23)
   (* PI l)
   (if (<= l -9.6e-155)
     (/ (* PI (- l)) (* F F))
     (if (or (<= l 3.8e-142) (not (<= l 6.7e-80)))
       (* PI l)
       (/ (- l) (* F (/ F PI)))))))

C

double code(double F, double l) {
	double tmp;
	if (l <= -5.5e-23) {
		tmp = ((double) M_PI) * l;
	} else if (l <= -9.6e-155) {
		tmp = (((double) M_PI) * -l) / (F * F);
	} else if ((l <= 3.8e-142) || !(l <= 6.7e-80)) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = -l / (F * (F / ((double) M_PI)));
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if (l <= -5.5e-23) {
		tmp = Math.PI * l;
	} else if (l <= -9.6e-155) {
		tmp = (Math.PI * -l) / (F * F);
	} else if ((l <= 3.8e-142) || !(l <= 6.7e-80)) {
		tmp = Math.PI * l;
	} else {
		tmp = -l / (F * (F / Math.PI));
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if l <= -5.5e-23:
		tmp = math.pi * l
	elif l <= -9.6e-155:
		tmp = (math.pi * -l) / (F * F)
	elif (l <= 3.8e-142) or not (l <= 6.7e-80):
		tmp = math.pi * l
	else:
		tmp = -l / (F * (F / math.pi))
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if (l <= -5.5e-23)
		tmp = Float64(pi * l);
	elseif (l <= -9.6e-155)
		tmp = Float64(Float64(pi * Float64(-l)) / Float64(F * F));
	elseif ((l <= 3.8e-142) || !(l <= 6.7e-80))
		tmp = Float64(pi * l);
	else
		tmp = Float64(Float64(-l) / Float64(F * Float64(F / pi)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if (l <= -5.5e-23)
		tmp = pi * l;
	elseif (l <= -9.6e-155)
		tmp = (pi * -l) / (F * F);
	elseif ((l <= 3.8e-142) || ~((l <= 6.7e-80)))
		tmp = pi * l;
	else
		tmp = -l / (F * (F / pi));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[LessEqual[l, -5.5e-23], N[(Pi * l), $MachinePrecision], If[LessEqual[l, -9.6e-155], N[(N[(Pi * (-l)), $MachinePrecision] / N[(F * F), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[l, 3.8e-142], N[Not[LessEqual[l, 6.7e-80]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[((-l) / N[(F * N[(F / Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if l < -5.5000000000000001e-23 or -9.600000000000001e-155 < l < 3.79999999999999972e-142 or 6.70000000000000002e-80 < 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 64.4%

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

      1. unpow2 64.4%

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

   6. Simplified 64.4%

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

   7. Taylor expanded in F around inf 80.5%

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

   if -5.5000000000000001e-23 < l < -9.600000000000001e-155

   1. Initial program 89.0%

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

      1. associate-*l/ 89.2%

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

      2. *-lft-identity 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in l around 0 89.2%

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

      1. unpow2 89.2%

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

   6. Simplified 89.2%

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

   7. Taylor expanded in F around 0 63.0%

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

      1. mul-1-neg 63.0%

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

      2. unpow2 63.0%

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

   9. Simplified 63.0%

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

   if 3.79999999999999972e-142 < l < 6.70000000000000002e-80

   1. Initial program 85.5%

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

      1. associate-*l/ 89.8%

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

      2. *-lft-identity 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in l around 0 85.5%

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

      1. unpow2 85.5%

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

   6. Simplified 85.5%

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

   7. Taylor expanded in F around 0 61.0%

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

      1. mul-1-neg 61.0%

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

      2. associate-/l* 60.7%

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

      3. distribute-neg-frac 60.7%

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

      4. unpow2 60.7%

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

      5. *-lft-identity 60.7%

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

      6. times-frac 61.1%

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

      7. /-rgt-identity 61.1%

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

   9. Simplified 61.1%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -5.5 \cdot 10^{-23}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;\ell \leq -9.6 \cdot 10^{-155}:\\ \;\;\;\;\frac{\pi \cdot \left(-\ell\right)}{F \cdot F}\\ \mathbf{elif}\;\ell \leq 3.8 \cdot 10^{-142} \lor \neg \left(\ell \leq 6.7 \cdot 10^{-80}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\frac{-\ell}{F \cdot \frac{F}{\pi}}\\ \end{array} \]

Alternative 10: 73.4% 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 76.5%

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

   1. associate-*l/ 77.4%

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

   2. *-lft-identity 77.4%

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

3. Simplified 77.4%

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

4. Taylor expanded in l around 0 68.6%

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

   1. unpow2 68.6%

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

6. Simplified 68.6%

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

7. Taylor expanded in F around inf 71.3%

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

8. Final simplification 71.3%

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

Reproduce

herbie shell --seed 2023192 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  :precision binary64
  (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))