VandenBroeck and Keller, Equation (6)

Percentage Accurate: 76.7% → 99.1%

Time: 18.8s

Alternatives: 13

Speedup: 1.5×

• could not determine a ground truth

  1. F = -94372078818.86917
  2. l = 1994047354859783.5

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: 76.7% 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: 99.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -1 \cdot 10^{+18} \lor \neg \left(\pi \cdot \ell \leq 2000000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell + \frac{\tan \left(\pi \cdot \ell\right) \cdot \frac{-1}{F}}{F}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= (* PI l) -1e+18) (not (<= (* PI l) 2000000000.0)))
   (* PI l)
   (+ (* PI l) (/ (* (tan (* PI l)) (/ -1.0 F)) F))))

C

double code(double F, double l) {
	double tmp;
	if (((((double) M_PI) * l) <= -1e+18) || !((((double) M_PI) * l) <= 2000000000.0)) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = (((double) M_PI) * l) + ((tan((((double) M_PI) * l)) * (-1.0 / F)) / F);
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if (((Math.PI * l) <= -1e+18) || !((Math.PI * l) <= 2000000000.0)) {
		tmp = Math.PI * l;
	} else {
		tmp = (Math.PI * l) + ((Math.tan((Math.PI * l)) * (-1.0 / F)) / F);
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if ((math.pi * l) <= -1e+18) or not ((math.pi * l) <= 2000000000.0):
		tmp = math.pi * l
	else:
		tmp = (math.pi * l) + ((math.tan((math.pi * l)) * (-1.0 / F)) / F)
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((Float64(pi * l) <= -1e+18) || !(Float64(pi * l) <= 2000000000.0))
		tmp = Float64(pi * l);
	else
		tmp = Float64(Float64(pi * l) + Float64(Float64(tan(Float64(pi * l)) * Float64(-1.0 / F)) / F));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if (((pi * l) <= -1e+18) || ~(((pi * l) <= 2000000000.0)))
		tmp = pi * l;
	else
		tmp = (pi * l) + ((tan((pi * l)) * (-1.0 / F)) / F);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[N[(Pi * l), $MachinePrecision], -1e+18], N[Not[LessEqual[N[(Pi * l), $MachinePrecision], 2000000000.0]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(N[(Pi * l), $MachinePrecision] + N[(N[(N[Tan[N[(Pi * l), $MachinePrecision]], $MachinePrecision] * N[(-1.0 / F), $MachinePrecision]), $MachinePrecision] / F), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (PI.f64) l) < -1e18 or 2e9 < (*.f64 (PI.f64) l)

   1. Initial program 59.8%

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

      1. associate-*l/ 59.8%

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

      2. *-lft-identity 59.8%

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

   3. Simplified 59.8%

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

   4. Taylor expanded in l around 0 47.6%

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

      1. unpow2 47.6%

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

   6. Simplified 47.6%

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

   7. Taylor expanded in F around inf 99.5%

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

   if -1e18 < (*.f64 (PI.f64) l) < 2e9

   1. Initial program 88.4%

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

      1. associate-/r* 88.5%

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

      2. metadata-eval 88.5%

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

      3. add-sqr-sqrt 46.2%

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

      4. sqrt-prod 69.9%

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

      5. sqrt-div 69.9%

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

      6. associate-*l/ 69.9%

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

      7. sqrt-div 69.9%

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

      8. metadata-eval 69.9%

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

      9. sqrt-prod 51.0%

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

      10. add-sqr-sqrt 98.9%

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

   3. Applied egg-rr 98.9%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -1 \cdot 10^{+18} \lor \neg \left(\pi \cdot \ell \leq 2000000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell + \frac{\tan \left(\pi \cdot \ell\right) \cdot \frac{-1}{F}}{F}\\ \end{array} \]

Alternative 2: 99.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -1 \cdot 10^{+18} \lor \neg \left(\pi \cdot \ell \leq 2000000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell + \frac{-1}{\frac{F}{\frac{\tan \left(\pi \cdot \ell\right)}{F}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= (* PI l) -1e+18) (not (<= (* PI l) 2000000000.0)))
   (* PI l)
   (+ (* PI l) (/ -1.0 (/ F (/ (tan (* PI l)) F))))))

C

double code(double F, double l) {
	double tmp;
	if (((((double) M_PI) * l) <= -1e+18) || !((((double) M_PI) * l) <= 2000000000.0)) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = (((double) M_PI) * l) + (-1.0 / (F / (tan((((double) M_PI) * l)) / F)));
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if (((Math.PI * l) <= -1e+18) || !((Math.PI * l) <= 2000000000.0)) {
		tmp = Math.PI * l;
	} else {
		tmp = (Math.PI * l) + (-1.0 / (F / (Math.tan((Math.PI * l)) / F)));
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if ((math.pi * l) <= -1e+18) or not ((math.pi * l) <= 2000000000.0):
		tmp = math.pi * l
	else:
		tmp = (math.pi * l) + (-1.0 / (F / (math.tan((math.pi * l)) / F)))
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((Float64(pi * l) <= -1e+18) || !(Float64(pi * l) <= 2000000000.0))
		tmp = Float64(pi * l);
	else
		tmp = Float64(Float64(pi * l) + Float64(-1.0 / Float64(F / Float64(tan(Float64(pi * l)) / F))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if (((pi * l) <= -1e+18) || ~(((pi * l) <= 2000000000.0)))
		tmp = pi * l;
	else
		tmp = (pi * l) + (-1.0 / (F / (tan((pi * l)) / F)));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[N[(Pi * l), $MachinePrecision], -1e+18], N[Not[LessEqual[N[(Pi * l), $MachinePrecision], 2000000000.0]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(N[(Pi * l), $MachinePrecision] + N[(-1.0 / N[(F / N[(N[Tan[N[(Pi * l), $MachinePrecision]], $MachinePrecision] / F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (PI.f64) l) < -1e18 or 2e9 < (*.f64 (PI.f64) l)

   1. Initial program 59.8%

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

      1. associate-*l/ 59.8%

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

      2. *-lft-identity 59.8%

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

   3. Simplified 59.8%

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

   4. Taylor expanded in l around 0 47.6%

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

      1. unpow2 47.6%

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

   6. Simplified 47.6%

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

   7. Taylor expanded in F around inf 99.5%

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

   if -1e18 < (*.f64 (PI.f64) l) < 2e9

   1. Initial program 88.4%

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

      1. associate-/r/ 88.5%

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

      2. associate-/l* 98.8%

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

   3. Applied egg-rr 98.8%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -1 \cdot 10^{+18} \lor \neg \left(\pi \cdot \ell \leq 2000000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell + \frac{-1}{\frac{F}{\frac{\tan \left(\pi \cdot \ell\right)}{F}}}\\ \end{array} \]

Alternative 3: 99.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -1 \cdot 10^{+18} \lor \neg \left(\pi \cdot \ell \leq 2000000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= (* PI l) -1e+18) (not (<= (* PI l) 2000000000.0)))
   (* PI l)
   (- (* PI l) (/ (/ (tan (* PI l)) F) F))))

C

double code(double F, double l) {
	double tmp;
	if (((((double) M_PI) * l) <= -1e+18) || !((((double) M_PI) * l) <= 2000000000.0)) {
		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) <= -1e+18) || !((Math.PI * l) <= 2000000000.0)) {
		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) <= -1e+18) or not ((math.pi * l) <= 2000000000.0):
		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) <= -1e+18) || !(Float64(pi * l) <= 2000000000.0))
		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) <= -1e+18) || ~(((pi * l) <= 2000000000.0)))
		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], -1e+18], N[Not[LessEqual[N[(Pi * l), $MachinePrecision], 2000000000.0]], $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) < -1e18 or 2e9 < (*.f64 (PI.f64) l)

   1. Initial program 59.8%

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

      1. associate-*l/ 59.8%

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

      2. *-lft-identity 59.8%

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

   3. Simplified 59.8%

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

   4. Taylor expanded in l around 0 47.6%

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

      1. unpow2 47.6%

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

   6. Simplified 47.6%

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

   7. Taylor expanded in F around inf 99.5%

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

   if -1e18 < (*.f64 (PI.f64) l) < 2e9

   1. Initial program 88.4%

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

      1. associate-*l/ 88.5%

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

      2. *-un-lft-identity 88.5%

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

      3. associate-/r* 98.8%

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

   3. Applied egg-rr 98.8%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -1 \cdot 10^{+18} \lor \neg \left(\pi \cdot \ell \leq 2000000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}\\ \end{array} \]

Alternative 4: 98.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -50000000000 \lor \neg \left(\pi \cdot \ell \leq 500000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\pi}{F \cdot \frac{F}{\ell}}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= (* PI l) -50000000000.0) (not (<= (* PI l) 500000.0)))
   (* PI l)
   (- (* PI l) (/ PI (* F (/ F l))))))

C

double code(double F, double l) {
	double tmp;
	if (((((double) M_PI) * l) <= -50000000000.0) || !((((double) M_PI) * l) <= 500000.0)) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = (((double) M_PI) * l) - (((double) M_PI) / (F * (F / l)));
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if (((Math.PI * l) <= -50000000000.0) || !((Math.PI * l) <= 500000.0)) {
		tmp = Math.PI * l;
	} else {
		tmp = (Math.PI * l) - (Math.PI / (F * (F / l)));
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if ((math.pi * l) <= -50000000000.0) or not ((math.pi * l) <= 500000.0):
		tmp = math.pi * l
	else:
		tmp = (math.pi * l) - (math.pi / (F * (F / l)))
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((Float64(pi * l) <= -50000000000.0) || !(Float64(pi * l) <= 500000.0))
		tmp = Float64(pi * l);
	else
		tmp = Float64(Float64(pi * l) - Float64(pi / Float64(F * Float64(F / l))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if (((pi * l) <= -50000000000.0) || ~(((pi * l) <= 500000.0)))
		tmp = pi * l;
	else
		tmp = (pi * l) - (pi / (F * (F / l)));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[N[(Pi * l), $MachinePrecision], -50000000000.0], N[Not[LessEqual[N[(Pi * l), $MachinePrecision], 500000.0]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(N[(Pi * l), $MachinePrecision] - N[(Pi / N[(F * N[(F / l), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (PI.f64) l) < -5e10 or 5e5 < (*.f64 (PI.f64) l)

   1. Initial program 60.1%

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

      1. associate-*l/ 60.1%

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

      2. *-lft-identity 60.1%

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

   3. Simplified 60.1%

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

   4. Taylor expanded in l around 0 46.4%

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

      1. unpow2 46.4%

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

   6. Simplified 46.4%

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

   7. Taylor expanded in F around inf 97.2%

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

   if -5e10 < (*.f64 (PI.f64) l) < 5e5

   1. Initial program 88.8%

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

      1. inv-pow 88.8%

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

      2. unpow-prod-down 88.8%

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

      3. pow-prod-up 88.8%

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

      4. pow-to-exp 45.6%

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

      5. metadata-eval 45.6%

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

   3. Applied egg-rr 45.6%

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

   4. Taylor expanded in l around 0 88.4%

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

      1. *-commutative 88.4%

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

      2. unpow2 88.4%

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

      3. times-frac 98.9%

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

   6. Simplified 98.9%

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

      1. *-commutative 98.9%

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

      2. clear-num 98.9%

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

      3. frac-times 99.0%

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

      4. *-un-lft-identity 99.0%

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

   8. Applied egg-rr 99.0%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -50000000000 \lor \neg \left(\pi \cdot \ell \leq 500000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\pi}{F \cdot \frac{F}{\ell}}\\ \end{array} \]

Alternative 5: 98.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -70000000 \lor \neg \left(\ell \leq 260000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\pi}{F} \cdot \frac{\ell}{F}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= l -70000000.0) (not (<= l 260000000.0)))
   (* PI l)
   (- (* PI l) (* (/ PI F) (/ l F)))))

C

double code(double F, double l) {
	double tmp;
	if ((l <= -70000000.0) || !(l <= 260000000.0)) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = (((double) M_PI) * l) - ((((double) M_PI) / F) * (l / F));
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if ((l <= -70000000.0) || !(l <= 260000000.0)) {
		tmp = Math.PI * l;
	} else {
		tmp = (Math.PI * l) - ((Math.PI / F) * (l / F));
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if (l <= -70000000.0) or not (l <= 260000000.0):
		tmp = math.pi * l
	else:
		tmp = (math.pi * l) - ((math.pi / F) * (l / F))
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((l <= -70000000.0) || !(l <= 260000000.0))
		tmp = Float64(pi * l);
	else
		tmp = Float64(Float64(pi * l) - Float64(Float64(pi / F) * Float64(l / F)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if ((l <= -70000000.0) || ~((l <= 260000000.0)))
		tmp = pi * l;
	else
		tmp = (pi * l) - ((pi / F) * (l / F));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[l, -70000000.0], N[Not[LessEqual[l, 260000000.0]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(N[(Pi * l), $MachinePrecision] - N[(N[(Pi / F), $MachinePrecision] * N[(l / F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < -7e7 or 2.6e8 < l

   1. Initial program 60.1%

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

      1. associate-*l/ 60.1%

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

      2. *-lft-identity 60.1%

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

   3. Simplified 60.1%

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

   4. Taylor expanded in l around 0 46.4%

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

      1. unpow2 46.4%

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

   6. Simplified 46.4%

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

   7. Taylor expanded in F around inf 97.2%

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

   if -7e7 < l < 2.6e8

   1. Initial program 88.8%

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

      1. inv-pow 88.8%

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

      2. unpow-prod-down 88.8%

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

      3. pow-prod-up 88.8%

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

      4. pow-to-exp 45.6%

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

      5. metadata-eval 45.6%

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

   3. Applied egg-rr 45.6%

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

   4. Taylor expanded in l around 0 88.4%

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

      1. *-commutative 88.4%

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

      2. unpow2 88.4%

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

      3. times-frac 98.9%

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

   6. Simplified 98.9%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -70000000 \lor \neg \left(\ell \leq 260000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\pi}{F} \cdot \frac{\ell}{F}\\ \end{array} \]

Alternative 6: 92.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -70000000 \lor \neg \left(\ell \leq 260000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\ell \cdot \left(\pi \cdot \left(1 - {F}^{-2}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= l -70000000.0) (not (<= l 260000000.0)))
   (* PI l)
   (* l (* PI (- 1.0 (pow F -2.0))))))

C

double code(double F, double l) {
	double tmp;
	if ((l <= -70000000.0) || !(l <= 260000000.0)) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = l * (((double) M_PI) * (1.0 - pow(F, -2.0)));
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if ((l <= -70000000.0) || !(l <= 260000000.0)) {
		tmp = Math.PI * l;
	} else {
		tmp = l * (Math.PI * (1.0 - Math.pow(F, -2.0)));
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if (l <= -70000000.0) or not (l <= 260000000.0):
		tmp = math.pi * l
	else:
		tmp = l * (math.pi * (1.0 - math.pow(F, -2.0)))
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((l <= -70000000.0) || !(l <= 260000000.0))
		tmp = Float64(pi * l);
	else
		tmp = Float64(l * Float64(pi * Float64(1.0 - (F ^ -2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if ((l <= -70000000.0) || ~((l <= 260000000.0)))
		tmp = pi * l;
	else
		tmp = l * (pi * (1.0 - (F ^ -2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[l, -70000000.0], N[Not[LessEqual[l, 260000000.0]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(l * N[(Pi * N[(1.0 - N[Power[F, -2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < -7e7 or 2.6e8 < l

   1. Initial program 60.1%

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

      1. associate-*l/ 60.1%

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

      2. *-lft-identity 60.1%

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

   3. Simplified 60.1%

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

   4. Taylor expanded in l around 0 46.4%

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

      1. unpow2 46.4%

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

   6. Simplified 46.4%

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

   7. Taylor expanded in F around inf 97.2%

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

   if -7e7 < l < 2.6e8

   1. Initial program 88.8%

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

      1. associate-*l/ 88.8%

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

      2. *-lft-identity 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in l around 0 88.4%

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

      1. unpow2 88.4%

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

   6. Simplified 88.4%

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

   7. Taylor expanded in l around 0 88.4%

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

      1. *-lft-identity 88.4%

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

      2. *-lft-identity 88.4%

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

      3. unpow2 88.4%

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

      4. times-frac 88.3%

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

      5. *-lft-identity 88.3%

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

      6. associate-*l/ 88.3%

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

      7. associate-*l* 88.3%

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

      8. unpow-1 88.3%

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

      9. unpow-1 88.3%

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

      10. pow-sqr 88.4%

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

      11. metadata-eval 88.4%

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

      12. distribute-rgt-out-- 88.4%

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

   9. Simplified 88.4%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -70000000 \lor \neg \left(\ell \leq 260000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\ell \cdot \left(\pi \cdot \left(1 - {F}^{-2}\right)\right)\\ \end{array} \]

Alternative 7: 92.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -70000000 \lor \neg \left(\ell \leq 260000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\ell \cdot \left(\pi - \frac{\pi}{F \cdot F}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= l -70000000.0) (not (<= l 260000000.0)))
   (* PI l)
   (* l (- PI (/ PI (* F F))))))

C

double code(double F, double l) {
	double tmp;
	if ((l <= -70000000.0) || !(l <= 260000000.0)) {
		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 <= -70000000.0) || !(l <= 260000000.0)) {
		tmp = Math.PI * l;
	} else {
		tmp = l * (Math.PI - (Math.PI / (F * F)));
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if (l <= -70000000.0) or not (l <= 260000000.0):
		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 <= -70000000.0) || !(l <= 260000000.0))
		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 <= -70000000.0) || ~((l <= 260000000.0)))
		tmp = pi * l;
	else
		tmp = l * (pi - (pi / (F * F)));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[l, -70000000.0], N[Not[LessEqual[l, 260000000.0]], $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 < -7e7 or 2.6e8 < l

   1. Initial program 60.1%

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

      1. associate-*l/ 60.1%

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

      2. *-lft-identity 60.1%

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

   3. Simplified 60.1%

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

   4. Taylor expanded in l around 0 46.4%

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

      1. unpow2 46.4%

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

   6. Simplified 46.4%

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

   7. Taylor expanded in F around inf 97.2%

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

   if -7e7 < l < 2.6e8

   1. Initial program 88.8%

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

      1. associate-*l/ 88.8%

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

      2. *-lft-identity 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in l around 0 88.4%

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

      1. unpow2 88.4%

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

   6. Simplified 88.4%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -70000000 \lor \neg \left(\ell \leq 260000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\ell \cdot \left(\pi - \frac{\pi}{F \cdot F}\right)\\ \end{array} \]

Alternative 8: 92.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -70000000 \lor \neg \left(\ell \leq 260000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(\ell - \ell \cdot {F}^{-2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= l -70000000.0) (not (<= l 260000000.0)))
   (* PI l)
   (* PI (- l (* l (pow F -2.0))))))

C

double code(double F, double l) {
	double tmp;
	if ((l <= -70000000.0) || !(l <= 260000000.0)) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = ((double) M_PI) * (l - (l * pow(F, -2.0)));
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if ((l <= -70000000.0) || !(l <= 260000000.0)) {
		tmp = Math.PI * l;
	} else {
		tmp = Math.PI * (l - (l * Math.pow(F, -2.0)));
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if (l <= -70000000.0) or not (l <= 260000000.0):
		tmp = math.pi * l
	else:
		tmp = math.pi * (l - (l * math.pow(F, -2.0)))
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((l <= -70000000.0) || !(l <= 260000000.0))
		tmp = Float64(pi * l);
	else
		tmp = Float64(pi * Float64(l - Float64(l * (F ^ -2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if ((l <= -70000000.0) || ~((l <= 260000000.0)))
		tmp = pi * l;
	else
		tmp = pi * (l - (l * (F ^ -2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[l, -70000000.0], N[Not[LessEqual[l, 260000000.0]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(Pi * N[(l - N[(l * N[Power[F, -2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < -7e7 or 2.6e8 < l

   1. Initial program 60.1%

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

      1. associate-*l/ 60.1%

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

      2. *-lft-identity 60.1%

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

   3. Simplified 60.1%

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

   4. Taylor expanded in l around 0 46.4%

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

      1. unpow2 46.4%

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

   6. Simplified 46.4%

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

   7. Taylor expanded in F around inf 97.2%

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

   if -7e7 < l < 2.6e8

   1. Initial program 88.8%

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

      1. associate-/r* 88.8%

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

      2. metadata-eval 88.8%

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

      3. add-sqr-sqrt 46.5%

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

      4. sqrt-prod 70.7%

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

      5. sqrt-div 70.7%

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

      6. associate-*l/ 70.7%

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

      7. sqrt-div 70.7%

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

      8. metadata-eval 70.7%

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

      9. sqrt-prod 51.4%

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

      10. add-sqr-sqrt 99.5%

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

   3. Applied egg-rr 99.5%

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

   4. Taylor expanded in l around 0 99.0%

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

      1. associate-/l* 98.9%

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

      2. associate-/r/ 98.9%

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

   6. Simplified 98.9%

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

      1. sub-neg 98.9%

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

      2. associate-*l/ 99.0%

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

      3. associate-/r* 88.4%

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

      4. div-inv 88.3%

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

      5. *-commutative 88.3%

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

      6. distribute-rgt-neg-in 88.3%

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

      7. pow2 88.3%

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

      8. pow-flip 88.4%

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

      9. metadata-eval 88.4%

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

   8. Applied egg-rr 88.4%

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

      1. distribute-rgt-neg-out 88.4%

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

      2. associate-*r* 88.4%

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

      3. sub-neg 88.4%

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

      4. distribute-lft-out-- 88.4%

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

   10. Simplified 88.4%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -70000000 \lor \neg \left(\ell \leq 260000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(\ell - \ell \cdot {F}^{-2}\right)\\ \end{array} \]

Alternative 9: 73.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \cdot F \leq 2.25 \cdot 10^{-304} \lor \neg \left(F \cdot F \leq 1.08 \cdot 10^{-197} \lor \neg \left(F \cdot F \leq 3.5 \cdot 10^{-133}\right) \land F \cdot F \leq 9.5 \cdot 10^{-52}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \frac{-\ell}{F \cdot F}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= (* F F) 2.25e-304)
         (not
          (or (<= (* F F) 1.08e-197)
              (and (not (<= (* F F) 3.5e-133)) (<= (* F F) 9.5e-52)))))
   (* PI l)
   (* PI (/ (- l) (* F F)))))

C

double code(double F, double l) {
	double tmp;
	if (((F * F) <= 2.25e-304) || !(((F * F) <= 1.08e-197) || (!((F * F) <= 3.5e-133) && ((F * F) <= 9.5e-52)))) {
		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) <= 2.25e-304) || !(((F * F) <= 1.08e-197) || (!((F * F) <= 3.5e-133) && ((F * F) <= 9.5e-52)))) {
		tmp = Math.PI * l;
	} else {
		tmp = Math.PI * (-l / (F * F));
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if ((F * F) <= 2.25e-304) or not (((F * F) <= 1.08e-197) or (not ((F * F) <= 3.5e-133) and ((F * F) <= 9.5e-52))):
		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) <= 2.25e-304) || !((Float64(F * F) <= 1.08e-197) || (!(Float64(F * F) <= 3.5e-133) && (Float64(F * F) <= 9.5e-52))))
		tmp = Float64(pi * l);
	else
		tmp = Float64(pi * Float64(Float64(-l) / Float64(F * F)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if (((F * F) <= 2.25e-304) || ~((((F * F) <= 1.08e-197) || (~(((F * F) <= 3.5e-133)) && ((F * F) <= 9.5e-52)))))
		tmp = pi * l;
	else
		tmp = pi * (-l / (F * F));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[N[(F * F), $MachinePrecision], 2.25e-304], N[Not[Or[LessEqual[N[(F * F), $MachinePrecision], 1.08e-197], And[N[Not[LessEqual[N[(F * F), $MachinePrecision], 3.5e-133]], $MachinePrecision], LessEqual[N[(F * F), $MachinePrecision], 9.5e-52]]]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(Pi * N[((-l) / N[(F * F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 F F) < 2.2499999999999999e-304 or 1.0800000000000001e-197 < (*.f64 F F) < 3.50000000000000003e-133 or 9.50000000000000007e-52 < (*.f64 F F)

   1. Initial program 73.6%

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

      1. associate-*l/ 73.6%

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

      2. *-lft-identity 73.6%

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

   3. Simplified 73.6%

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

   4. Taylor expanded in l around 0 67.5%

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

      1. unpow2 67.5%

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

   6. Simplified 67.5%

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

   7. Taylor expanded in F around inf 78.9%

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

   if 2.2499999999999999e-304 < (*.f64 F F) < 1.0800000000000001e-197 or 3.50000000000000003e-133 < (*.f64 F F) < 9.50000000000000007e-52

   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/ 85.7%

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

      2. *-lft-identity 85.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in l around 0 73.4%

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

      1. unpow2 73.4%

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

   6. Simplified 73.4%

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

   7. Taylor expanded in F around 0 73.3%

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

      1. mul-1-neg 73.3%

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

      2. unpow2 73.3%

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

   9. Simplified 73.3%

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

       1. associate-/l* 73.2%

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

       2. associate-/r/ 73.4%

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

   11. Applied egg-rr 73.4%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;F \cdot F \leq 2.25 \cdot 10^{-304} \lor \neg \left(F \cdot F \leq 1.08 \cdot 10^{-197} \lor \neg \left(F \cdot F \leq 3.5 \cdot 10^{-133}\right) \land F \cdot F \leq 9.5 \cdot 10^{-52}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \frac{-\ell}{F \cdot F}\\ \end{array} \]

Alternative 10: 73.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -1.9 \cdot 10^{-48} \lor \neg \left(\ell \leq -1.25 \cdot 10^{-199} \lor \neg \left(\ell \leq -2.95 \cdot 10^{-232}\right) \land \left(\ell \leq 4.3 \cdot 10^{-276} \lor \neg \left(\ell \leq 9.5 \cdot 10^{-258}\right) \land \ell \leq 1.75 \cdot 10^{-124}\right)\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi}{F} \cdot \left(-\frac{\ell}{F}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= l -1.9e-48)
         (not
          (or (<= l -1.25e-199)
              (and (not (<= l -2.95e-232))
                   (or (<= l 4.3e-276)
                       (and (not (<= l 9.5e-258)) (<= l 1.75e-124)))))))
   (* PI l)
   (* (/ PI F) (- (/ l F)))))

C

double code(double F, double l) {
	double tmp;
	if ((l <= -1.9e-48) || !((l <= -1.25e-199) || (!(l <= -2.95e-232) && ((l <= 4.3e-276) || (!(l <= 9.5e-258) && (l <= 1.75e-124)))))) {
		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 <= -1.9e-48) || !((l <= -1.25e-199) || (!(l <= -2.95e-232) && ((l <= 4.3e-276) || (!(l <= 9.5e-258) && (l <= 1.75e-124)))))) {
		tmp = Math.PI * l;
	} else {
		tmp = (Math.PI / F) * -(l / F);
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if (l <= -1.9e-48) or not ((l <= -1.25e-199) or (not (l <= -2.95e-232) and ((l <= 4.3e-276) or (not (l <= 9.5e-258) and (l <= 1.75e-124))))):
		tmp = math.pi * l
	else:
		tmp = (math.pi / F) * -(l / F)
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((l <= -1.9e-48) || !((l <= -1.25e-199) || (!(l <= -2.95e-232) && ((l <= 4.3e-276) || (!(l <= 9.5e-258) && (l <= 1.75e-124))))))
		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 <= -1.9e-48) || ~(((l <= -1.25e-199) || (~((l <= -2.95e-232)) && ((l <= 4.3e-276) || (~((l <= 9.5e-258)) && (l <= 1.75e-124)))))))
		tmp = pi * l;
	else
		tmp = (pi / F) * -(l / F);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[l, -1.9e-48], N[Not[Or[LessEqual[l, -1.25e-199], And[N[Not[LessEqual[l, -2.95e-232]], $MachinePrecision], Or[LessEqual[l, 4.3e-276], And[N[Not[LessEqual[l, 9.5e-258]], $MachinePrecision], LessEqual[l, 1.75e-124]]]]]], $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 < -1.90000000000000001e-48 or -1.2499999999999999e-199 < l < -2.95000000000000008e-232 or 4.2999999999999996e-276 < l < 9.5000000000000009e-258 or 1.7499999999999999e-124 < l

   1. Initial program 72.1%

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

      1. associate-*l/ 72.1%

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

      2. *-lft-identity 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in l around 0 62.5%

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

      1. unpow2 62.5%

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

   6. Simplified 62.5%

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

   7. Taylor expanded in F around inf 88.4%

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

   if -1.90000000000000001e-48 < l < -1.2499999999999999e-199 or -2.95000000000000008e-232 < l < 4.2999999999999996e-276 or 9.5000000000000009e-258 < l < 1.7499999999999999e-124

   1. Initial program 82.0%

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

      1. associate-*l/ 82.0%

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

      2. *-lft-identity 82.0%

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

   3. Simplified 82.0%

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

   4. Taylor expanded in l around 0 82.1%

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

      1. unpow2 82.1%

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

   6. Simplified 82.1%

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

   7. Taylor expanded in F around 0 50.4%

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

      1. mul-1-neg 50.4%

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

      2. unpow2 50.4%

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

   9. Simplified 50.4%

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

       1. *-commutative 50.4%

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

       2. times-frac 67.9%

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

   11. Applied egg-rr 67.9%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -1.9 \cdot 10^{-48} \lor \neg \left(\ell \leq -1.25 \cdot 10^{-199} \lor \neg \left(\ell \leq -2.95 \cdot 10^{-232}\right) \land \left(\ell \leq 4.3 \cdot 10^{-276} \lor \neg \left(\ell \leq 9.5 \cdot 10^{-258}\right) \land \ell \leq 1.75 \cdot 10^{-124}\right)\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi}{F} \cdot \left(-\frac{\ell}{F}\right)\\ \end{array} \]

Alternative 11: 73.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\ell \leq -1.75 \cdot 10^{-48} \lor \neg \left(\ell \leq -6 \cdot 10^{-203}\right) \land \left(\ell \leq -2.35 \cdot 10^{-232} \lor \neg \left(\ell \leq 5.2 \cdot 10^{-276}\right) \land \left(\ell \leq 1.65 \cdot 10^{-255} \lor \neg \left(\ell \leq 7 \cdot 10^{-125}\right)\right)\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-\pi}{\frac{F}{\ell}}}{F}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= l -1.75e-48)
         (and (not (<= l -6e-203))
              (or (<= l -2.35e-232)
                  (and (not (<= l 5.2e-276))
                       (or (<= l 1.65e-255) (not (<= l 7e-125)))))))
   (* PI l)
   (/ (/ (- PI) (/ F l)) F)))

C

double code(double F, double l) {
	double tmp;
	if ((l <= -1.75e-48) || (!(l <= -6e-203) && ((l <= -2.35e-232) || (!(l <= 5.2e-276) && ((l <= 1.65e-255) || !(l <= 7e-125)))))) {
		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 <= -1.75e-48) || (!(l <= -6e-203) && ((l <= -2.35e-232) || (!(l <= 5.2e-276) && ((l <= 1.65e-255) || !(l <= 7e-125)))))) {
		tmp = Math.PI * l;
	} else {
		tmp = (-Math.PI / (F / l)) / F;
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if (l <= -1.75e-48) or (not (l <= -6e-203) and ((l <= -2.35e-232) or (not (l <= 5.2e-276) and ((l <= 1.65e-255) or not (l <= 7e-125))))):
		tmp = math.pi * l
	else:
		tmp = (-math.pi / (F / l)) / F
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((l <= -1.75e-48) || (!(l <= -6e-203) && ((l <= -2.35e-232) || (!(l <= 5.2e-276) && ((l <= 1.65e-255) || !(l <= 7e-125))))))
		tmp = Float64(pi * l);
	else
		tmp = Float64(Float64(Float64(-pi) / Float64(F / l)) / F);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if ((l <= -1.75e-48) || (~((l <= -6e-203)) && ((l <= -2.35e-232) || (~((l <= 5.2e-276)) && ((l <= 1.65e-255) || ~((l <= 7e-125)))))))
		tmp = pi * l;
	else
		tmp = (-pi / (F / l)) / F;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[l, -1.75e-48], And[N[Not[LessEqual[l, -6e-203]], $MachinePrecision], Or[LessEqual[l, -2.35e-232], And[N[Not[LessEqual[l, 5.2e-276]], $MachinePrecision], Or[LessEqual[l, 1.65e-255], N[Not[LessEqual[l, 7e-125]], $MachinePrecision]]]]]], N[(Pi * l), $MachinePrecision], N[(N[((-Pi) / N[(F / l), $MachinePrecision]), $MachinePrecision] / F), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if l < -1.74999999999999996e-48 or -6.0000000000000002e-203 < l < -2.35000000000000017e-232 or 5.19999999999999969e-276 < l < 1.64999999999999994e-255 or 6.99999999999999995e-125 < l

   1. Initial program 72.1%

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

      1. associate-*l/ 72.1%

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

      2. *-lft-identity 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in l around 0 62.5%

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

      1. unpow2 62.5%

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

   6. Simplified 62.5%

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

   7. Taylor expanded in F around inf 88.4%

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

   if -1.74999999999999996e-48 < l < -6.0000000000000002e-203 or -2.35000000000000017e-232 < l < 5.19999999999999969e-276 or 1.64999999999999994e-255 < l < 6.99999999999999995e-125

   1. Initial program 82.0%

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

      1. associate-*l/ 82.0%

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

      2. *-lft-identity 82.0%

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

   3. Simplified 82.0%

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

   4. Taylor expanded in l around 0 82.1%

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

      1. unpow2 82.1%

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

   6. Simplified 82.1%

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

   7. Taylor expanded in F around 0 50.4%

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

      1. mul-1-neg 50.4%

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

      2. unpow2 50.4%

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

   9. Simplified 50.4%

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

   10. Taylor expanded in l around 0 50.4%

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

       1. *-commutative 50.4%

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

       2. unpow2 50.4%

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

       3. associate-/r* 68.0%

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

       4. associate-/l* 68.0%

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

   12. Simplified 68.0%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -1.75 \cdot 10^{-48} \lor \neg \left(\ell \leq -6 \cdot 10^{-203}\right) \land \left(\ell \leq -2.35 \cdot 10^{-232} \lor \neg \left(\ell \leq 5.2 \cdot 10^{-276}\right) \land \left(\ell \leq 1.65 \cdot 10^{-255} \lor \neg \left(\ell \leq 7 \cdot 10^{-125}\right)\right)\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-\pi}{\frac{F}{\ell}}}{F}\\ \end{array} \]

Alternative 12: 73.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\frac{-\pi}{\frac{F}{\ell}}}{F}\\ \mathbf{if}\;\ell \leq -2.15 \cdot 10^{-48}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;\ell \leq -4.6 \cdot 10^{-201}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq -3.15 \cdot 10^{-232}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;\ell \leq 4.8 \cdot 10^{-276}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\ell \leq 2.9 \cdot 10^{-258} \lor \neg \left(\ell \leq 1.75 \cdot 10^{-124}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(-\frac{\frac{\ell}{F}}{F}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (let* ((t_0 (/ (/ (- PI) (/ F l)) F)))
   (if (<= l -2.15e-48)
     (* PI l)
     (if (<= l -4.6e-201)
       t_0
       (if (<= l -3.15e-232)
         (* PI l)
         (if (<= l 4.8e-276)
           t_0
           (if (or (<= l 2.9e-258) (not (<= l 1.75e-124)))
             (* PI l)
             (* PI (- (/ (/ l F) F))))))))))

C

double code(double F, double l) {
	double t_0 = (-((double) M_PI) / (F / l)) / F;
	double tmp;
	if (l <= -2.15e-48) {
		tmp = ((double) M_PI) * l;
	} else if (l <= -4.6e-201) {
		tmp = t_0;
	} else if (l <= -3.15e-232) {
		tmp = ((double) M_PI) * l;
	} else if (l <= 4.8e-276) {
		tmp = t_0;
	} else if ((l <= 2.9e-258) || !(l <= 1.75e-124)) {
		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 t_0 = (-Math.PI / (F / l)) / F;
	double tmp;
	if (l <= -2.15e-48) {
		tmp = Math.PI * l;
	} else if (l <= -4.6e-201) {
		tmp = t_0;
	} else if (l <= -3.15e-232) {
		tmp = Math.PI * l;
	} else if (l <= 4.8e-276) {
		tmp = t_0;
	} else if ((l <= 2.9e-258) || !(l <= 1.75e-124)) {
		tmp = Math.PI * l;
	} else {
		tmp = Math.PI * -((l / F) / F);
	}
	return tmp;
}

Python

def code(F, l):
	t_0 = (-math.pi / (F / l)) / F
	tmp = 0
	if l <= -2.15e-48:
		tmp = math.pi * l
	elif l <= -4.6e-201:
		tmp = t_0
	elif l <= -3.15e-232:
		tmp = math.pi * l
	elif l <= 4.8e-276:
		tmp = t_0
	elif (l <= 2.9e-258) or not (l <= 1.75e-124):
		tmp = math.pi * l
	else:
		tmp = math.pi * -((l / F) / F)
	return tmp

Julia

function code(F, l)
	t_0 = Float64(Float64(Float64(-pi) / Float64(F / l)) / F)
	tmp = 0.0
	if (l <= -2.15e-48)
		tmp = Float64(pi * l);
	elseif (l <= -4.6e-201)
		tmp = t_0;
	elseif (l <= -3.15e-232)
		tmp = Float64(pi * l);
	elseif (l <= 4.8e-276)
		tmp = t_0;
	elseif ((l <= 2.9e-258) || !(l <= 1.75e-124))
		tmp = Float64(pi * l);
	else
		tmp = Float64(pi * Float64(-Float64(Float64(l / F) / F)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	t_0 = (-pi / (F / l)) / F;
	tmp = 0.0;
	if (l <= -2.15e-48)
		tmp = pi * l;
	elseif (l <= -4.6e-201)
		tmp = t_0;
	elseif (l <= -3.15e-232)
		tmp = pi * l;
	elseif (l <= 4.8e-276)
		tmp = t_0;
	elseif ((l <= 2.9e-258) || ~((l <= 1.75e-124)))
		tmp = pi * l;
	else
		tmp = pi * -((l / F) / F);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := Block[{t$95$0 = N[(N[((-Pi) / N[(F / l), $MachinePrecision]), $MachinePrecision] / F), $MachinePrecision]}, If[LessEqual[l, -2.15e-48], N[(Pi * l), $MachinePrecision], If[LessEqual[l, -4.6e-201], t$95$0, If[LessEqual[l, -3.15e-232], N[(Pi * l), $MachinePrecision], If[LessEqual[l, 4.8e-276], t$95$0, If[Or[LessEqual[l, 2.9e-258], N[Not[LessEqual[l, 1.75e-124]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(Pi * (-N[(N[(l / F), $MachinePrecision] / F), $MachinePrecision])), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if l < -2.15e-48 or -4.59999999999999971e-201 < l < -3.15000000000000005e-232 or 4.79999999999999965e-276 < l < 2.9e-258 or 1.7499999999999999e-124 < l

   1. Initial program 72.1%

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

      1. associate-*l/ 72.1%

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

      2. *-lft-identity 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in l around 0 62.5%

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

      1. unpow2 62.5%

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

   6. Simplified 62.5%

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

   7. Taylor expanded in F around inf 88.4%

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

   if -2.15e-48 < l < -4.59999999999999971e-201 or -3.15000000000000005e-232 < l < 4.79999999999999965e-276

   1. Initial program 82.1%

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

      1. associate-*l/ 82.1%

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

      2. *-lft-identity 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in l around 0 82.2%

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

      1. unpow2 82.2%

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

   6. Simplified 82.2%

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

   7. Taylor expanded in F around 0 50.4%

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

      1. mul-1-neg 50.4%

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

      2. unpow2 50.4%

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

   9. Simplified 50.4%

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

   10. Taylor expanded in l around 0 50.4%

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

       1. *-commutative 50.4%

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

       2. unpow2 50.4%

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

       3. associate-/r* 68.0%

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

       4. associate-/l* 67.9%

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

   12. Simplified 67.9%

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

   if 2.9e-258 < l < 1.7499999999999999e-124

   1. Initial program 81.6%

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

      1. associate-/r* 81.8%

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

      2. metadata-eval 81.8%

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

      3. add-sqr-sqrt 48.1%

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

      4. sqrt-prod 58.0%

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

      5. sqrt-div 57.9%

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

      6. associate-*l/ 57.9%

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

      7. sqrt-div 58.0%

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

      8. metadata-eval 58.0%

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

      9. sqrt-prod 61.4%

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

      10. add-sqr-sqrt 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in l around 0 99.6%

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

      1. associate-/l* 99.6%

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

      2. associate-/r/ 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in F around 0 50.3%

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

      1. mul-1-neg 50.3%

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

      2. unpow2 50.3%

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

      3. associate-*l/ 50.4%

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

      4. *-commutative 50.4%

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

      5. distribute-rgt-neg-in 50.4%

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

      6. associate-/r* 68.3%

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

   9. Simplified 68.3%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\ell \leq -2.15 \cdot 10^{-48}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;\ell \leq -4.6 \cdot 10^{-201}:\\ \;\;\;\;\frac{\frac{-\pi}{\frac{F}{\ell}}}{F}\\ \mathbf{elif}\;\ell \leq -3.15 \cdot 10^{-232}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;\ell \leq 4.8 \cdot 10^{-276}:\\ \;\;\;\;\frac{\frac{-\pi}{\frac{F}{\ell}}}{F}\\ \mathbf{elif}\;\ell \leq 2.9 \cdot 10^{-258} \lor \neg \left(\ell \leq 1.75 \cdot 10^{-124}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(-\frac{\frac{\ell}{F}}{F}\right)\\ \end{array} \]

Alternative 13: 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 75.0%

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

   1. associate-*l/ 75.0%

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

   2. *-lft-identity 75.0%

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

3. Simplified 75.0%

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

4. Taylor expanded in l around 0 68.2%

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

   1. unpow2 68.2%

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

6. Simplified 68.2%

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

7. Taylor expanded in F around inf 72.6%

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

8. Final simplification 72.6%

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

Reproduce

herbie shell --seed 2023174 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  :precision binary64
  (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))