VandenBroeck and Keller, Equation (6)

Percentage Accurate: 76.7% → 99.1%

Time: 12.0s

Alternatives: 6

Speedup: 1.0×

• could not determine a ground truth

  1. F = 8.385577140373355e+151
  2. l = 3873816694660815.5

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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -5 \cdot 10^{+18} \lor \neg \left(\pi \cdot \ell \leq 10000000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= (* PI l) -5e+18) (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+18) || !((((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+18) || !((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+18) 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+18) || !(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+18) || ~(((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+18], 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) < -5e18 or 1e10 < (*.f64 (PI.f64) l)

   1. Initial program 68.1%

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

      1. associate-*l/ 68.1%

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

      2. *-lft-identity 68.1%

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

   3. Simplified 68.1%

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

   4. Taylor expanded in l around 0 52.5%

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

      1. unpow2 52.5%

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

   6. Simplified 52.5%

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

   7. Taylor expanded in F around inf 99.6%

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

   if -5e18 < (*.f64 (PI.f64) l) < 1e10

   1. Initial program 89.3%

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

      1. associate-*l/ 89.5%

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

      2. *-un-lft-identity 89.5%

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

      3. associate-/r* 99.5%

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

   3. Applied egg-rr 99.5%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -5 \cdot 10^{+18} \lor \neg \left(\pi \cdot \ell \leq 10000000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell - \frac{\frac{\tan \left(\pi \cdot \ell\right)}{F}}{F}\\ \end{array} \]

Alternative 2: 98.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -5000000 \lor \neg \left(\pi \cdot \ell \leq 10000000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(\ell - \frac{\frac{\ell}{F}}{F}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= (* PI l) -5000000.0) (not (<= (* PI l) 10000000000.0)))
   (* PI l)
   (* PI (- l (/ (/ l F) F)))))

C

double code(double F, double l) {
	double tmp;
	if (((((double) M_PI) * l) <= -5000000.0) || !((((double) M_PI) * l) <= 10000000000.0)) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = ((double) M_PI) * (l - ((l / F) / F));
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if (((Math.PI * l) <= -5000000.0) || !((Math.PI * l) <= 10000000000.0)) {
		tmp = Math.PI * l;
	} else {
		tmp = Math.PI * (l - ((l / F) / F));
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if ((math.pi * l) <= -5000000.0) or not ((math.pi * l) <= 10000000000.0):
		tmp = math.pi * l
	else:
		tmp = math.pi * (l - ((l / F) / F))
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((Float64(pi * l) <= -5000000.0) || !(Float64(pi * l) <= 10000000000.0))
		tmp = Float64(pi * l);
	else
		tmp = Float64(pi * Float64(l - Float64(Float64(l / F) / F)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if (((pi * l) <= -5000000.0) || ~(((pi * l) <= 10000000000.0)))
		tmp = pi * l;
	else
		tmp = pi * (l - ((l / F) / F));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[N[(Pi * l), $MachinePrecision], -5000000.0], N[Not[LessEqual[N[(Pi * l), $MachinePrecision], 10000000000.0]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(Pi * N[(l - N[(N[(l / F), $MachinePrecision] / F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (PI.f64) l) < -5e6 or 1e10 < (*.f64 (PI.f64) l)

   1. Initial program 69.1%

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

      1. associate-*l/ 69.1%

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

      2. *-lft-identity 69.1%

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

   3. Simplified 69.1%

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

   4. Taylor expanded in l around 0 52.4%

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

      1. unpow2 52.4%

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

   6. Simplified 52.4%

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

   7. Taylor expanded in F around inf 98.2%

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

   if -5e6 < (*.f64 (PI.f64) l) < 1e10

   1. Initial program 88.9%

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

   2. Taylor expanded in l around 0 88.8%

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

      1. associate-/l* 88.8%

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

      2. associate-/r/ 88.9%

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

      3. unpow2 88.9%

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

   4. Simplified 88.9%

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

      1. *-commutative 88.9%

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

      2. distribute-lft-out-- 88.9%

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

      3. associate-/r* 99.2%

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

   6. Applied egg-rr 99.2%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\pi \cdot \ell \leq -5000000 \lor \neg \left(\pi \cdot \ell \leq 10000000000\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(\ell - \frac{\frac{\ell}{F}}{F}\right)\\ \end{array} \]

Alternative 3: 47.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq 1.35 \cdot 10^{-275} \lor \neg \left(F \leq 3.1 \cdot 10^{-117}\right) \land \left(F \leq 2.15 \cdot 10^{-71} \lor \neg \left(F \leq 3 \cdot 10^{-17}\right) \land F \leq 8.5 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{-\ell}{\frac{F}{\frac{\pi}{F}}}\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (or (<= F 1.35e-275)
         (and (not (<= F 3.1e-117))
              (or (<= F 2.15e-71) (and (not (<= F 3e-17)) (<= F 8.5e-5)))))
   (/ (- l) (/ F (/ PI F)))
   (* PI l)))

C

double code(double F, double l) {
	double tmp;
	if ((F <= 1.35e-275) || (!(F <= 3.1e-117) && ((F <= 2.15e-71) || (!(F <= 3e-17) && (F <= 8.5e-5))))) {
		tmp = -l / (F / (((double) M_PI) / F));
	} else {
		tmp = ((double) M_PI) * l;
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if ((F <= 1.35e-275) || (!(F <= 3.1e-117) && ((F <= 2.15e-71) || (!(F <= 3e-17) && (F <= 8.5e-5))))) {
		tmp = -l / (F / (Math.PI / F));
	} else {
		tmp = Math.PI * l;
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if (F <= 1.35e-275) or (not (F <= 3.1e-117) and ((F <= 2.15e-71) or (not (F <= 3e-17) and (F <= 8.5e-5)))):
		tmp = -l / (F / (math.pi / F))
	else:
		tmp = math.pi * l
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if ((F <= 1.35e-275) || (!(F <= 3.1e-117) && ((F <= 2.15e-71) || (!(F <= 3e-17) && (F <= 8.5e-5)))))
		tmp = Float64(Float64(-l) / Float64(F / Float64(pi / F)));
	else
		tmp = Float64(pi * l);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if ((F <= 1.35e-275) || (~((F <= 3.1e-117)) && ((F <= 2.15e-71) || (~((F <= 3e-17)) && (F <= 8.5e-5)))))
		tmp = -l / (F / (pi / F));
	else
		tmp = pi * l;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[Or[LessEqual[F, 1.35e-275], And[N[Not[LessEqual[F, 3.1e-117]], $MachinePrecision], Or[LessEqual[F, 2.15e-71], And[N[Not[LessEqual[F, 3e-17]], $MachinePrecision], LessEqual[F, 8.5e-5]]]]], N[((-l) / N[(F / N[(Pi / F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(Pi * l), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if F < 1.34999999999999997e-275 or 3.10000000000000011e-117 < F < 2.1499999999999998e-71 or 3.00000000000000006e-17 < F < 8.500000000000001e-5

   1. Initial program 78.8%

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

      1. associate-*l/ 78.8%

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

      2. *-lft-identity 78.8%

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

   3. Simplified 78.8%

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

   4. Taylor expanded in l around 0 72.0%

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

      1. unpow2 72.0%

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

   6. Simplified 72.0%

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

   7. Taylor expanded in F around 0 29.2%

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

      1. mul-1-neg 29.2%

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

      2. unpow2 29.2%

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

      3. associate-/l* 29.3%

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

      4. associate-/l* 29.3%

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

   9. Simplified 29.3%

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

   if 1.34999999999999997e-275 < F < 3.10000000000000011e-117 or 2.1499999999999998e-71 < F < 3.00000000000000006e-17 or 8.500000000000001e-5 < F

   1. Initial program 78.3%

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

      1. associate-*l/ 78.5%

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

      2. *-lft-identity 78.5%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in l around 0 66.8%

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

      1. unpow2 66.8%

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

   6. Simplified 66.8%

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

   7. Taylor expanded in F around inf 85.6%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;F \leq 1.35 \cdot 10^{-275} \lor \neg \left(F \leq 3.1 \cdot 10^{-117}\right) \land \left(F \leq 2.15 \cdot 10^{-71} \lor \neg \left(F \leq 3 \cdot 10^{-17}\right) \land F \leq 8.5 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{-\ell}{\frac{F}{\frac{\pi}{F}}}\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \ell\\ \end{array} \]

Alternative 4: 47.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-\ell}{\frac{F}{\frac{\pi}{F}}}\\ \mathbf{if}\;F \leq 4 \cdot 10^{-274}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 10^{-119}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;F \leq 5.2 \cdot 10^{-70}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 3.5 \cdot 10^{-17} \lor \neg \left(F \leq 8.5 \cdot 10^{-5}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\ell \cdot \frac{-\pi}{F \cdot F}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (let* ((t_0 (/ (- l) (/ F (/ PI F)))))
   (if (<= F 4e-274)
     t_0
     (if (<= F 1e-119)
       (* PI l)
       (if (<= F 5.2e-70)
         t_0
         (if (or (<= F 3.5e-17) (not (<= F 8.5e-5)))
           (* PI l)
           (* l (/ (- PI) (* F F)))))))))

C

double code(double F, double l) {
	double t_0 = -l / (F / (((double) M_PI) / F));
	double tmp;
	if (F <= 4e-274) {
		tmp = t_0;
	} else if (F <= 1e-119) {
		tmp = ((double) M_PI) * l;
	} else if (F <= 5.2e-70) {
		tmp = t_0;
	} else if ((F <= 3.5e-17) || !(F <= 8.5e-5)) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = l * (-((double) M_PI) / (F * F));
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double t_0 = -l / (F / (Math.PI / F));
	double tmp;
	if (F <= 4e-274) {
		tmp = t_0;
	} else if (F <= 1e-119) {
		tmp = Math.PI * l;
	} else if (F <= 5.2e-70) {
		tmp = t_0;
	} else if ((F <= 3.5e-17) || !(F <= 8.5e-5)) {
		tmp = Math.PI * l;
	} else {
		tmp = l * (-Math.PI / (F * F));
	}
	return tmp;
}

Python

def code(F, l):
	t_0 = -l / (F / (math.pi / F))
	tmp = 0
	if F <= 4e-274:
		tmp = t_0
	elif F <= 1e-119:
		tmp = math.pi * l
	elif F <= 5.2e-70:
		tmp = t_0
	elif (F <= 3.5e-17) or not (F <= 8.5e-5):
		tmp = math.pi * l
	else:
		tmp = l * (-math.pi / (F * F))
	return tmp

Julia

function code(F, l)
	t_0 = Float64(Float64(-l) / Float64(F / Float64(pi / F)))
	tmp = 0.0
	if (F <= 4e-274)
		tmp = t_0;
	elseif (F <= 1e-119)
		tmp = Float64(pi * l);
	elseif (F <= 5.2e-70)
		tmp = t_0;
	elseif ((F <= 3.5e-17) || !(F <= 8.5e-5))
		tmp = Float64(pi * l);
	else
		tmp = Float64(l * Float64(Float64(-pi) / Float64(F * F)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	t_0 = -l / (F / (pi / F));
	tmp = 0.0;
	if (F <= 4e-274)
		tmp = t_0;
	elseif (F <= 1e-119)
		tmp = pi * l;
	elseif (F <= 5.2e-70)
		tmp = t_0;
	elseif ((F <= 3.5e-17) || ~((F <= 8.5e-5)))
		tmp = pi * l;
	else
		tmp = l * (-pi / (F * F));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := Block[{t$95$0 = N[((-l) / N[(F / N[(Pi / F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, 4e-274], t$95$0, If[LessEqual[F, 1e-119], N[(Pi * l), $MachinePrecision], If[LessEqual[F, 5.2e-70], t$95$0, If[Or[LessEqual[F, 3.5e-17], N[Not[LessEqual[F, 8.5e-5]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(l * N[((-Pi) / N[(F * F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if F < 3.99999999999999986e-274 or 1.00000000000000001e-119 < F < 5.20000000000000004e-70

   1. Initial program 78.3%

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

      1. associate-*l/ 78.3%

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

      2. *-lft-identity 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in l around 0 71.3%

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

      1. unpow2 71.3%

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

   6. Simplified 71.3%

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

   7. Taylor expanded in F around 0 27.3%

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

      1. mul-1-neg 27.3%

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

      2. unpow2 27.3%

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

      3. associate-/l* 27.4%

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

      4. associate-/l* 27.3%

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

   9. Simplified 27.3%

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

   if 3.99999999999999986e-274 < F < 1.00000000000000001e-119 or 5.20000000000000004e-70 < F < 3.5000000000000002e-17 or 8.500000000000001e-5 < F

   1. Initial program 78.3%

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

      1. associate-*l/ 78.5%

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

      2. *-lft-identity 78.5%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in l around 0 66.8%

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

      1. unpow2 66.8%

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

   6. Simplified 66.8%

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

   7. Taylor expanded in F around inf 85.6%

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

   if 3.5000000000000002e-17 < F < 8.500000000000001e-5

   1. Initial program 98.8%

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

      1. associate-*l/ 98.8%

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

      2. *-lft-identity 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in l around 0 99.2%

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

      1. unpow2 99.2%

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

   6. Simplified 99.2%

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

   7. Taylor expanded in F around 0 98.8%

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

      1. unpow2 98.8%

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

      2. associate-*r/ 98.8%

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

      3. neg-mul-1 98.8%

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

   9. Simplified 98.8%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;F \leq 4 \cdot 10^{-274}:\\ \;\;\;\;\frac{-\ell}{\frac{F}{\frac{\pi}{F}}}\\ \mathbf{elif}\;F \leq 10^{-119}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;F \leq 5.2 \cdot 10^{-70}:\\ \;\;\;\;\frac{-\ell}{\frac{F}{\frac{\pi}{F}}}\\ \mathbf{elif}\;F \leq 3.5 \cdot 10^{-17} \lor \neg \left(F \leq 8.5 \cdot 10^{-5}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\ell \cdot \frac{-\pi}{F \cdot F}\\ \end{array} \]

Alternative 5: 47.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq 1.6 \cdot 10^{-275}:\\ \;\;\;\;\frac{-\ell}{\frac{F}{\frac{\pi}{F}}}\\ \mathbf{elif}\;F \leq 1.14 \cdot 10^{-120}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;F \leq 5 \cdot 10^{-72}:\\ \;\;\;\;\frac{-\ell}{\frac{F \cdot F}{\pi}}\\ \mathbf{elif}\;F \leq 2.8 \cdot 10^{-17} \lor \neg \left(F \leq 8.5 \cdot 10^{-5}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\ell \cdot \frac{-\pi}{F \cdot F}\\ \end{array} \end{array} \]

FPCore

(FPCore (F l)
 :precision binary64
 (if (<= F 1.6e-275)
   (/ (- l) (/ F (/ PI F)))
   (if (<= F 1.14e-120)
     (* PI l)
     (if (<= F 5e-72)
       (/ (- l) (/ (* F F) PI))
       (if (or (<= F 2.8e-17) (not (<= F 8.5e-5)))
         (* PI l)
         (* l (/ (- PI) (* F F))))))))

C

double code(double F, double l) {
	double tmp;
	if (F <= 1.6e-275) {
		tmp = -l / (F / (((double) M_PI) / F));
	} else if (F <= 1.14e-120) {
		tmp = ((double) M_PI) * l;
	} else if (F <= 5e-72) {
		tmp = -l / ((F * F) / ((double) M_PI));
	} else if ((F <= 2.8e-17) || !(F <= 8.5e-5)) {
		tmp = ((double) M_PI) * l;
	} else {
		tmp = l * (-((double) M_PI) / (F * F));
	}
	return tmp;
}

Java

public static double code(double F, double l) {
	double tmp;
	if (F <= 1.6e-275) {
		tmp = -l / (F / (Math.PI / F));
	} else if (F <= 1.14e-120) {
		tmp = Math.PI * l;
	} else if (F <= 5e-72) {
		tmp = -l / ((F * F) / Math.PI);
	} else if ((F <= 2.8e-17) || !(F <= 8.5e-5)) {
		tmp = Math.PI * l;
	} else {
		tmp = l * (-Math.PI / (F * F));
	}
	return tmp;
}

Python

def code(F, l):
	tmp = 0
	if F <= 1.6e-275:
		tmp = -l / (F / (math.pi / F))
	elif F <= 1.14e-120:
		tmp = math.pi * l
	elif F <= 5e-72:
		tmp = -l / ((F * F) / math.pi)
	elif (F <= 2.8e-17) or not (F <= 8.5e-5):
		tmp = math.pi * l
	else:
		tmp = l * (-math.pi / (F * F))
	return tmp

Julia

function code(F, l)
	tmp = 0.0
	if (F <= 1.6e-275)
		tmp = Float64(Float64(-l) / Float64(F / Float64(pi / F)));
	elseif (F <= 1.14e-120)
		tmp = Float64(pi * l);
	elseif (F <= 5e-72)
		tmp = Float64(Float64(-l) / Float64(Float64(F * F) / pi));
	elseif ((F <= 2.8e-17) || !(F <= 8.5e-5))
		tmp = Float64(pi * l);
	else
		tmp = Float64(l * Float64(Float64(-pi) / Float64(F * F)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, l)
	tmp = 0.0;
	if (F <= 1.6e-275)
		tmp = -l / (F / (pi / F));
	elseif (F <= 1.14e-120)
		tmp = pi * l;
	elseif (F <= 5e-72)
		tmp = -l / ((F * F) / pi);
	elseif ((F <= 2.8e-17) || ~((F <= 8.5e-5)))
		tmp = pi * l;
	else
		tmp = l * (-pi / (F * F));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, l_] := If[LessEqual[F, 1.6e-275], N[((-l) / N[(F / N[(Pi / F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1.14e-120], N[(Pi * l), $MachinePrecision], If[LessEqual[F, 5e-72], N[((-l) / N[(N[(F * F), $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[F, 2.8e-17], N[Not[LessEqual[F, 8.5e-5]], $MachinePrecision]], N[(Pi * l), $MachinePrecision], N[(l * N[((-Pi) / N[(F * F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if F < 1.6e-275

   1. Initial program 78.8%

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

      1. associate-*l/ 78.8%

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

      2. *-lft-identity 78.8%

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

   3. Simplified 78.8%

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

   4. Taylor expanded in l around 0 71.7%

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

      1. unpow2 71.7%

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

   6. Simplified 71.7%

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

   7. Taylor expanded in F around 0 24.5%

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

      1. mul-1-neg 24.5%

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

      2. unpow2 24.5%

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

      3. associate-/l* 24.5%

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

      4. associate-/l* 24.5%

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

   9. Simplified 24.5%

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

   if 1.6e-275 < F < 1.14000000000000003e-120 or 4.9999999999999996e-72 < F < 2.7999999999999999e-17 or 8.500000000000001e-5 < F

   1. Initial program 78.3%

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

      1. associate-*l/ 78.5%

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

      2. *-lft-identity 78.5%

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

   3. Simplified 78.5%

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

   4. Taylor expanded in l around 0 66.8%

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

      1. unpow2 66.8%

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

   6. Simplified 66.8%

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

   7. Taylor expanded in F around inf 85.6%

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

   if 1.14000000000000003e-120 < F < 4.9999999999999996e-72

   1. Initial program 70.8%

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

      1. associate-*l/ 70.4%

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

      2. *-lft-identity 70.4%

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

   3. Simplified 70.4%

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

   4. Taylor expanded in l around 0 65.9%

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

      1. unpow2 65.9%

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

   6. Simplified 65.9%

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

   7. Taylor expanded in F around 0 65.4%

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

      1. mul-1-neg 65.4%

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

      2. unpow2 65.4%

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

      3. associate-/l* 65.9%

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

      4. distribute-neg-frac 65.9%

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

   9. Simplified 65.9%

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

   if 2.7999999999999999e-17 < F < 8.500000000000001e-5

   1. Initial program 98.8%

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

      1. associate-*l/ 98.8%

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

      2. *-lft-identity 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in l around 0 99.2%

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

      1. unpow2 99.2%

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

   6. Simplified 99.2%

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

   7. Taylor expanded in F around 0 98.8%

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

      1. unpow2 98.8%

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

      2. associate-*r/ 98.8%

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

      3. neg-mul-1 98.8%

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

   9. Simplified 98.8%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;F \leq 1.6 \cdot 10^{-275}:\\ \;\;\;\;\frac{-\ell}{\frac{F}{\frac{\pi}{F}}}\\ \mathbf{elif}\;F \leq 1.14 \cdot 10^{-120}:\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{elif}\;F \leq 5 \cdot 10^{-72}:\\ \;\;\;\;\frac{-\ell}{\frac{F \cdot F}{\pi}}\\ \mathbf{elif}\;F \leq 2.8 \cdot 10^{-17} \lor \neg \left(F \leq 8.5 \cdot 10^{-5}\right):\\ \;\;\;\;\pi \cdot \ell\\ \mathbf{else}:\\ \;\;\;\;\ell \cdot \frac{-\pi}{F \cdot F}\\ \end{array} \]

Alternative 6: 73.2% 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 78.6%

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

   1. associate-*l/ 78.7%

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

   2. *-lft-identity 78.7%

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

3. Simplified 78.7%

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

4. Taylor expanded in l around 0 69.8%

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

   1. unpow2 69.8%

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

6. Simplified 69.8%

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

7. Taylor expanded in F around inf 74.4%

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

8. Final simplification 74.4%

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

Reproduce

herbie shell --seed 2023230 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  :precision binary64
  (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))