VandenBroeck and Keller, Equation (6)

Percentage Accurate: 76.7% → 99.1%

Time: 18.2s

Alternatives: 8

Speedup: 1.0×

• could not determine a ground truth

  1. F = 1.1127160739375956e+167
  2. l = -4224448614853865.5

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, 0.8× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ l_s = \mathsf{copysign}\left(1, \ell\right) \\ l_s \cdot \begin{array}{l} \mathbf{if}\;\pi \cdot l_m \leq 50000000000:\\ \;\;\;\;\pi \cdot l_m - \frac{\frac{\tan \left(\pi \cdot l_m\right)}{F}}{F}\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot l_m\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
l_s = (copysign.f64 1 l)
(FPCore (l_s F l_m)
 :precision binary64
 (*
  l_s
  (if (<= (* PI l_m) 50000000000.0)
    (- (* PI l_m) (/ (/ (tan (* PI l_m)) F) F))
    (* PI l_m))))

C

l_m = fabs(l);
l_s = copysign(1.0, l);
double code(double l_s, double F, double l_m) {
	double tmp;
	if ((((double) M_PI) * l_m) <= 50000000000.0) {
		tmp = (((double) M_PI) * l_m) - ((tan((((double) M_PI) * l_m)) / F) / F);
	} else {
		tmp = ((double) M_PI) * l_m;
	}
	return l_s * tmp;
}

Java

l_m = Math.abs(l);
l_s = Math.copySign(1.0, l);
public static double code(double l_s, double F, double l_m) {
	double tmp;
	if ((Math.PI * l_m) <= 50000000000.0) {
		tmp = (Math.PI * l_m) - ((Math.tan((Math.PI * l_m)) / F) / F);
	} else {
		tmp = Math.PI * l_m;
	}
	return l_s * tmp;
}

Python

l_m = math.fabs(l)
l_s = math.copysign(1.0, l)
def code(l_s, F, l_m):
	tmp = 0
	if (math.pi * l_m) <= 50000000000.0:
		tmp = (math.pi * l_m) - ((math.tan((math.pi * l_m)) / F) / F)
	else:
		tmp = math.pi * l_m
	return l_s * tmp

Julia

l_m = abs(l)
l_s = copysign(1.0, l)
function code(l_s, F, l_m)
	tmp = 0.0
	if (Float64(pi * l_m) <= 50000000000.0)
		tmp = Float64(Float64(pi * l_m) - Float64(Float64(tan(Float64(pi * l_m)) / F) / F));
	else
		tmp = Float64(pi * l_m);
	end
	return Float64(l_s * tmp)
end

MATLAB

l_m = abs(l);
l_s = sign(l) * abs(1.0);
function tmp_2 = code(l_s, F, l_m)
	tmp = 0.0;
	if ((pi * l_m) <= 50000000000.0)
		tmp = (pi * l_m) - ((tan((pi * l_m)) / F) / F);
	else
		tmp = pi * l_m;
	end
	tmp_2 = l_s * tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
l_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[l]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[l$95$s_, F_, l$95$m_] := N[(l$95$s * If[LessEqual[N[(Pi * l$95$m), $MachinePrecision], 50000000000.0], N[(N[(Pi * l$95$m), $MachinePrecision] - N[(N[(N[Tan[N[(Pi * l$95$m), $MachinePrecision]], $MachinePrecision] / F), $MachinePrecision] / F), $MachinePrecision]), $MachinePrecision], N[(Pi * l$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 98.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ l_s = \mathsf{copysign}\left(1, \ell\right) \\ l_s \cdot \begin{array}{l} \mathbf{if}\;\pi \cdot l_m \leq 0.005:\\ \;\;\;\;\pi \cdot l_m - \frac{\pi}{F} \cdot \frac{l_m}{F}\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot l_m\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
l_s = (copysign.f64 1 l)
(FPCore (l_s F l_m)
 :precision binary64
 (*
  l_s
  (if (<= (* PI l_m) 0.005) (- (* PI l_m) (* (/ PI F) (/ l_m F))) (* PI l_m))))

C

l_m = fabs(l);
l_s = copysign(1.0, l);
double code(double l_s, double F, double l_m) {
	double tmp;
	if ((((double) M_PI) * l_m) <= 0.005) {
		tmp = (((double) M_PI) * l_m) - ((((double) M_PI) / F) * (l_m / F));
	} else {
		tmp = ((double) M_PI) * l_m;
	}
	return l_s * tmp;
}

Java

l_m = Math.abs(l);
l_s = Math.copySign(1.0, l);
public static double code(double l_s, double F, double l_m) {
	double tmp;
	if ((Math.PI * l_m) <= 0.005) {
		tmp = (Math.PI * l_m) - ((Math.PI / F) * (l_m / F));
	} else {
		tmp = Math.PI * l_m;
	}
	return l_s * tmp;
}

Python

l_m = math.fabs(l)
l_s = math.copysign(1.0, l)
def code(l_s, F, l_m):
	tmp = 0
	if (math.pi * l_m) <= 0.005:
		tmp = (math.pi * l_m) - ((math.pi / F) * (l_m / F))
	else:
		tmp = math.pi * l_m
	return l_s * tmp

Julia

l_m = abs(l)
l_s = copysign(1.0, l)
function code(l_s, F, l_m)
	tmp = 0.0
	if (Float64(pi * l_m) <= 0.005)
		tmp = Float64(Float64(pi * l_m) - Float64(Float64(pi / F) * Float64(l_m / F)));
	else
		tmp = Float64(pi * l_m);
	end
	return Float64(l_s * tmp)
end

MATLAB

l_m = abs(l);
l_s = sign(l) * abs(1.0);
function tmp_2 = code(l_s, F, l_m)
	tmp = 0.0;
	if ((pi * l_m) <= 0.005)
		tmp = (pi * l_m) - ((pi / F) * (l_m / F));
	else
		tmp = pi * l_m;
	end
	tmp_2 = l_s * tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
l_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[l]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[l$95$s_, F_, l$95$m_] := N[(l$95$s * If[LessEqual[N[(Pi * l$95$m), $MachinePrecision], 0.005], N[(N[(Pi * l$95$m), $MachinePrecision] - N[(N[(Pi / F), $MachinePrecision] * N[(l$95$m / F), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(Pi * l$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 92.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ l_s = \mathsf{copysign}\left(1, \ell\right) \\ l_s \cdot \begin{array}{l} \mathbf{if}\;\pi \cdot l_m \leq 0.005:\\ \;\;\;\;\left(\pi \cdot l_m\right) \cdot \left(1 - {F}^{-2}\right)\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot l_m\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
l_s = (copysign.f64 1 l)
(FPCore (l_s F l_m)
 :precision binary64
 (*
  l_s
  (if (<= (* PI l_m) 0.005) (* (* PI l_m) (- 1.0 (pow F -2.0))) (* PI l_m))))

C

l_m = fabs(l);
l_s = copysign(1.0, l);
double code(double l_s, double F, double l_m) {
	double tmp;
	if ((((double) M_PI) * l_m) <= 0.005) {
		tmp = (((double) M_PI) * l_m) * (1.0 - pow(F, -2.0));
	} else {
		tmp = ((double) M_PI) * l_m;
	}
	return l_s * tmp;
}

Java

l_m = Math.abs(l);
l_s = Math.copySign(1.0, l);
public static double code(double l_s, double F, double l_m) {
	double tmp;
	if ((Math.PI * l_m) <= 0.005) {
		tmp = (Math.PI * l_m) * (1.0 - Math.pow(F, -2.0));
	} else {
		tmp = Math.PI * l_m;
	}
	return l_s * tmp;
}

Python

l_m = math.fabs(l)
l_s = math.copysign(1.0, l)
def code(l_s, F, l_m):
	tmp = 0
	if (math.pi * l_m) <= 0.005:
		tmp = (math.pi * l_m) * (1.0 - math.pow(F, -2.0))
	else:
		tmp = math.pi * l_m
	return l_s * tmp

Julia

l_m = abs(l)
l_s = copysign(1.0, l)
function code(l_s, F, l_m)
	tmp = 0.0
	if (Float64(pi * l_m) <= 0.005)
		tmp = Float64(Float64(pi * l_m) * Float64(1.0 - (F ^ -2.0)));
	else
		tmp = Float64(pi * l_m);
	end
	return Float64(l_s * tmp)
end

MATLAB

l_m = abs(l);
l_s = sign(l) * abs(1.0);
function tmp_2 = code(l_s, F, l_m)
	tmp = 0.0;
	if ((pi * l_m) <= 0.005)
		tmp = (pi * l_m) * (1.0 - (F ^ -2.0));
	else
		tmp = pi * l_m;
	end
	tmp_2 = l_s * tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
l_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[l]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[l$95$s_, F_, l$95$m_] := N[(l$95$s * If[LessEqual[N[(Pi * l$95$m), $MachinePrecision], 0.005], N[(N[(Pi * l$95$m), $MachinePrecision] * N[(1.0 - N[Power[F, -2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(Pi * l$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 49.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ l_s = \mathsf{copysign}\left(1, \ell\right) \\ l_s \cdot \begin{array}{l} \mathbf{if}\;F \leq 1.95 \cdot 10^{-259}:\\ \;\;\;\;\frac{-1}{F \cdot \frac{F}{\pi \cdot l_m}}\\ \mathbf{elif}\;F \leq 1.3 \cdot 10^{-208}:\\ \;\;\;\;\pi \cdot l_m\\ \mathbf{elif}\;F \leq 1.2 \cdot 10^{-186}:\\ \;\;\;\;\frac{\frac{-l_m}{\frac{F}{\pi}}}{F}\\ \mathbf{elif}\;F \leq 5.5 \cdot 10^{-153} \lor \neg \left(F \leq 4.2 \cdot 10^{-133}\right):\\ \;\;\;\;\pi \cdot l_m\\ \mathbf{else}:\\ \;\;\;\;\frac{-l_m}{\frac{{F}^{2}}{\pi}}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
l_s = (copysign.f64 1 l)
(FPCore (l_s F l_m)
 :precision binary64
 (*
  l_s
  (if (<= F 1.95e-259)
    (/ -1.0 (* F (/ F (* PI l_m))))
    (if (<= F 1.3e-208)
      (* PI l_m)
      (if (<= F 1.2e-186)
        (/ (/ (- l_m) (/ F PI)) F)
        (if (or (<= F 5.5e-153) (not (<= F 4.2e-133)))
          (* PI l_m)
          (/ (- l_m) (/ (pow F 2.0) PI))))))))

C

l_m = fabs(l);
l_s = copysign(1.0, l);
double code(double l_s, double F, double l_m) {
	double tmp;
	if (F <= 1.95e-259) {
		tmp = -1.0 / (F * (F / (((double) M_PI) * l_m)));
	} else if (F <= 1.3e-208) {
		tmp = ((double) M_PI) * l_m;
	} else if (F <= 1.2e-186) {
		tmp = (-l_m / (F / ((double) M_PI))) / F;
	} else if ((F <= 5.5e-153) || !(F <= 4.2e-133)) {
		tmp = ((double) M_PI) * l_m;
	} else {
		tmp = -l_m / (pow(F, 2.0) / ((double) M_PI));
	}
	return l_s * tmp;
}

Java

l_m = Math.abs(l);
l_s = Math.copySign(1.0, l);
public static double code(double l_s, double F, double l_m) {
	double tmp;
	if (F <= 1.95e-259) {
		tmp = -1.0 / (F * (F / (Math.PI * l_m)));
	} else if (F <= 1.3e-208) {
		tmp = Math.PI * l_m;
	} else if (F <= 1.2e-186) {
		tmp = (-l_m / (F / Math.PI)) / F;
	} else if ((F <= 5.5e-153) || !(F <= 4.2e-133)) {
		tmp = Math.PI * l_m;
	} else {
		tmp = -l_m / (Math.pow(F, 2.0) / Math.PI);
	}
	return l_s * tmp;
}

Python

l_m = math.fabs(l)
l_s = math.copysign(1.0, l)
def code(l_s, F, l_m):
	tmp = 0
	if F <= 1.95e-259:
		tmp = -1.0 / (F * (F / (math.pi * l_m)))
	elif F <= 1.3e-208:
		tmp = math.pi * l_m
	elif F <= 1.2e-186:
		tmp = (-l_m / (F / math.pi)) / F
	elif (F <= 5.5e-153) or not (F <= 4.2e-133):
		tmp = math.pi * l_m
	else:
		tmp = -l_m / (math.pow(F, 2.0) / math.pi)
	return l_s * tmp

Julia

l_m = abs(l)
l_s = copysign(1.0, l)
function code(l_s, F, l_m)
	tmp = 0.0
	if (F <= 1.95e-259)
		tmp = Float64(-1.0 / Float64(F * Float64(F / Float64(pi * l_m))));
	elseif (F <= 1.3e-208)
		tmp = Float64(pi * l_m);
	elseif (F <= 1.2e-186)
		tmp = Float64(Float64(Float64(-l_m) / Float64(F / pi)) / F);
	elseif ((F <= 5.5e-153) || !(F <= 4.2e-133))
		tmp = Float64(pi * l_m);
	else
		tmp = Float64(Float64(-l_m) / Float64((F ^ 2.0) / pi));
	end
	return Float64(l_s * tmp)
end

MATLAB

l_m = abs(l);
l_s = sign(l) * abs(1.0);
function tmp_2 = code(l_s, F, l_m)
	tmp = 0.0;
	if (F <= 1.95e-259)
		tmp = -1.0 / (F * (F / (pi * l_m)));
	elseif (F <= 1.3e-208)
		tmp = pi * l_m;
	elseif (F <= 1.2e-186)
		tmp = (-l_m / (F / pi)) / F;
	elseif ((F <= 5.5e-153) || ~((F <= 4.2e-133)))
		tmp = pi * l_m;
	else
		tmp = -l_m / ((F ^ 2.0) / pi);
	end
	tmp_2 = l_s * tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
l_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[l]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[l$95$s_, F_, l$95$m_] := N[(l$95$s * If[LessEqual[F, 1.95e-259], N[(-1.0 / N[(F * N[(F / N[(Pi * l$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1.3e-208], N[(Pi * l$95$m), $MachinePrecision], If[LessEqual[F, 1.2e-186], N[(N[((-l$95$m) / N[(F / Pi), $MachinePrecision]), $MachinePrecision] / F), $MachinePrecision], If[Or[LessEqual[F, 5.5e-153], N[Not[LessEqual[F, 4.2e-133]], $MachinePrecision]], N[(Pi * l$95$m), $MachinePrecision], N[((-l$95$m) / N[(N[Power[F, 2.0], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 49.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ l_s = \mathsf{copysign}\left(1, \ell\right) \\ l_s \cdot \begin{array}{l} \mathbf{if}\;F \leq 4.5 \cdot 10^{-259}:\\ \;\;\;\;\frac{-1}{F \cdot \frac{F}{\pi \cdot l_m}}\\ \mathbf{elif}\;F \leq 1.35 \cdot 10^{-208}:\\ \;\;\;\;\pi \cdot l_m\\ \mathbf{elif}\;F \leq 1.7 \cdot 10^{-186}:\\ \;\;\;\;\frac{\frac{-l_m}{\frac{F}{\pi}}}{F}\\ \mathbf{elif}\;F \leq 3.3 \cdot 10^{-156} \lor \neg \left(F \leq 1.9 \cdot 10^{-133}\right):\\ \;\;\;\;\pi \cdot l_m\\ \mathbf{else}:\\ \;\;\;\;\frac{l_m \cdot \left(-\pi\right)}{{F}^{2}}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
l_s = (copysign.f64 1 l)
(FPCore (l_s F l_m)
 :precision binary64
 (*
  l_s
  (if (<= F 4.5e-259)
    (/ -1.0 (* F (/ F (* PI l_m))))
    (if (<= F 1.35e-208)
      (* PI l_m)
      (if (<= F 1.7e-186)
        (/ (/ (- l_m) (/ F PI)) F)
        (if (or (<= F 3.3e-156) (not (<= F 1.9e-133)))
          (* PI l_m)
          (/ (* l_m (- PI)) (pow F 2.0))))))))

C

l_m = fabs(l);
l_s = copysign(1.0, l);
double code(double l_s, double F, double l_m) {
	double tmp;
	if (F <= 4.5e-259) {
		tmp = -1.0 / (F * (F / (((double) M_PI) * l_m)));
	} else if (F <= 1.35e-208) {
		tmp = ((double) M_PI) * l_m;
	} else if (F <= 1.7e-186) {
		tmp = (-l_m / (F / ((double) M_PI))) / F;
	} else if ((F <= 3.3e-156) || !(F <= 1.9e-133)) {
		tmp = ((double) M_PI) * l_m;
	} else {
		tmp = (l_m * -((double) M_PI)) / pow(F, 2.0);
	}
	return l_s * tmp;
}

Java

l_m = Math.abs(l);
l_s = Math.copySign(1.0, l);
public static double code(double l_s, double F, double l_m) {
	double tmp;
	if (F <= 4.5e-259) {
		tmp = -1.0 / (F * (F / (Math.PI * l_m)));
	} else if (F <= 1.35e-208) {
		tmp = Math.PI * l_m;
	} else if (F <= 1.7e-186) {
		tmp = (-l_m / (F / Math.PI)) / F;
	} else if ((F <= 3.3e-156) || !(F <= 1.9e-133)) {
		tmp = Math.PI * l_m;
	} else {
		tmp = (l_m * -Math.PI) / Math.pow(F, 2.0);
	}
	return l_s * tmp;
}

Python

l_m = math.fabs(l)
l_s = math.copysign(1.0, l)
def code(l_s, F, l_m):
	tmp = 0
	if F <= 4.5e-259:
		tmp = -1.0 / (F * (F / (math.pi * l_m)))
	elif F <= 1.35e-208:
		tmp = math.pi * l_m
	elif F <= 1.7e-186:
		tmp = (-l_m / (F / math.pi)) / F
	elif (F <= 3.3e-156) or not (F <= 1.9e-133):
		tmp = math.pi * l_m
	else:
		tmp = (l_m * -math.pi) / math.pow(F, 2.0)
	return l_s * tmp

Julia

l_m = abs(l)
l_s = copysign(1.0, l)
function code(l_s, F, l_m)
	tmp = 0.0
	if (F <= 4.5e-259)
		tmp = Float64(-1.0 / Float64(F * Float64(F / Float64(pi * l_m))));
	elseif (F <= 1.35e-208)
		tmp = Float64(pi * l_m);
	elseif (F <= 1.7e-186)
		tmp = Float64(Float64(Float64(-l_m) / Float64(F / pi)) / F);
	elseif ((F <= 3.3e-156) || !(F <= 1.9e-133))
		tmp = Float64(pi * l_m);
	else
		tmp = Float64(Float64(l_m * Float64(-pi)) / (F ^ 2.0));
	end
	return Float64(l_s * tmp)
end

MATLAB

l_m = abs(l);
l_s = sign(l) * abs(1.0);
function tmp_2 = code(l_s, F, l_m)
	tmp = 0.0;
	if (F <= 4.5e-259)
		tmp = -1.0 / (F * (F / (pi * l_m)));
	elseif (F <= 1.35e-208)
		tmp = pi * l_m;
	elseif (F <= 1.7e-186)
		tmp = (-l_m / (F / pi)) / F;
	elseif ((F <= 3.3e-156) || ~((F <= 1.9e-133)))
		tmp = pi * l_m;
	else
		tmp = (l_m * -pi) / (F ^ 2.0);
	end
	tmp_2 = l_s * tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
l_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[l]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[l$95$s_, F_, l$95$m_] := N[(l$95$s * If[LessEqual[F, 4.5e-259], N[(-1.0 / N[(F * N[(F / N[(Pi * l$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1.35e-208], N[(Pi * l$95$m), $MachinePrecision], If[LessEqual[F, 1.7e-186], N[(N[((-l$95$m) / N[(F / Pi), $MachinePrecision]), $MachinePrecision] / F), $MachinePrecision], If[Or[LessEqual[F, 3.3e-156], N[Not[LessEqual[F, 1.9e-133]], $MachinePrecision]], N[(Pi * l$95$m), $MachinePrecision], N[(N[(l$95$m * (-Pi)), $MachinePrecision] / N[Power[F, 2.0], $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 49.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ l_s = \mathsf{copysign}\left(1, \ell\right) \\ l_s \cdot \begin{array}{l} \mathbf{if}\;F \leq 4.6 \cdot 10^{-259} \lor \neg \left(F \leq 4.4 \cdot 10^{-209}\right) \land \left(F \leq 1.12 \cdot 10^{-185} \lor \neg \left(F \leq 3.1 \cdot 10^{-152}\right) \land F \leq 1.5 \cdot 10^{-133}\right):\\ \;\;\;\;\frac{-1}{F \cdot \frac{F}{\pi \cdot l_m}}\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot l_m\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
l_s = (copysign.f64 1 l)
(FPCore (l_s F l_m)
 :precision binary64
 (*
  l_s
  (if (or (<= F 4.6e-259)
          (and (not (<= F 4.4e-209))
               (or (<= F 1.12e-185)
                   (and (not (<= F 3.1e-152)) (<= F 1.5e-133)))))
    (/ -1.0 (* F (/ F (* PI l_m))))
    (* PI l_m))))

C

l_m = fabs(l);
l_s = copysign(1.0, l);
double code(double l_s, double F, double l_m) {
	double tmp;
	if ((F <= 4.6e-259) || (!(F <= 4.4e-209) && ((F <= 1.12e-185) || (!(F <= 3.1e-152) && (F <= 1.5e-133))))) {
		tmp = -1.0 / (F * (F / (((double) M_PI) * l_m)));
	} else {
		tmp = ((double) M_PI) * l_m;
	}
	return l_s * tmp;
}

Java

l_m = Math.abs(l);
l_s = Math.copySign(1.0, l);
public static double code(double l_s, double F, double l_m) {
	double tmp;
	if ((F <= 4.6e-259) || (!(F <= 4.4e-209) && ((F <= 1.12e-185) || (!(F <= 3.1e-152) && (F <= 1.5e-133))))) {
		tmp = -1.0 / (F * (F / (Math.PI * l_m)));
	} else {
		tmp = Math.PI * l_m;
	}
	return l_s * tmp;
}

Python

l_m = math.fabs(l)
l_s = math.copysign(1.0, l)
def code(l_s, F, l_m):
	tmp = 0
	if (F <= 4.6e-259) or (not (F <= 4.4e-209) and ((F <= 1.12e-185) or (not (F <= 3.1e-152) and (F <= 1.5e-133)))):
		tmp = -1.0 / (F * (F / (math.pi * l_m)))
	else:
		tmp = math.pi * l_m
	return l_s * tmp

Julia

l_m = abs(l)
l_s = copysign(1.0, l)
function code(l_s, F, l_m)
	tmp = 0.0
	if ((F <= 4.6e-259) || (!(F <= 4.4e-209) && ((F <= 1.12e-185) || (!(F <= 3.1e-152) && (F <= 1.5e-133)))))
		tmp = Float64(-1.0 / Float64(F * Float64(F / Float64(pi * l_m))));
	else
		tmp = Float64(pi * l_m);
	end
	return Float64(l_s * tmp)
end

MATLAB

l_m = abs(l);
l_s = sign(l) * abs(1.0);
function tmp_2 = code(l_s, F, l_m)
	tmp = 0.0;
	if ((F <= 4.6e-259) || (~((F <= 4.4e-209)) && ((F <= 1.12e-185) || (~((F <= 3.1e-152)) && (F <= 1.5e-133)))))
		tmp = -1.0 / (F * (F / (pi * l_m)));
	else
		tmp = pi * l_m;
	end
	tmp_2 = l_s * tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
l_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[l]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[l$95$s_, F_, l$95$m_] := N[(l$95$s * If[Or[LessEqual[F, 4.6e-259], And[N[Not[LessEqual[F, 4.4e-209]], $MachinePrecision], Or[LessEqual[F, 1.12e-185], And[N[Not[LessEqual[F, 3.1e-152]], $MachinePrecision], LessEqual[F, 1.5e-133]]]]], N[(-1.0 / N[(F * N[(F / N[(Pi * l$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(Pi * l$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 49.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ l_s = \mathsf{copysign}\left(1, \ell\right) \\ \begin{array}{l} t_0 := \frac{-1}{F \cdot \frac{F}{\pi \cdot l_m}}\\ l_s \cdot \begin{array}{l} \mathbf{if}\;F \leq 2.9 \cdot 10^{-258}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 1.3 \cdot 10^{-208}:\\ \;\;\;\;\pi \cdot l_m\\ \mathbf{elif}\;F \leq 3.7 \cdot 10^{-187}:\\ \;\;\;\;\frac{\frac{-l_m}{\frac{F}{\pi}}}{F}\\ \mathbf{elif}\;F \leq 8.5 \cdot 10^{-155} \lor \neg \left(F \leq 5.5 \cdot 10^{-132}\right):\\ \;\;\;\;\pi \cdot l_m\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
l_s = (copysign.f64 1 l)
(FPCore (l_s F l_m)
 :precision binary64
 (let* ((t_0 (/ -1.0 (* F (/ F (* PI l_m))))))
   (*
    l_s
    (if (<= F 2.9e-258)
      t_0
      (if (<= F 1.3e-208)
        (* PI l_m)
        (if (<= F 3.7e-187)
          (/ (/ (- l_m) (/ F PI)) F)
          (if (or (<= F 8.5e-155) (not (<= F 5.5e-132))) (* PI l_m) t_0)))))))

C

l_m = fabs(l);
l_s = copysign(1.0, l);
double code(double l_s, double F, double l_m) {
	double t_0 = -1.0 / (F * (F / (((double) M_PI) * l_m)));
	double tmp;
	if (F <= 2.9e-258) {
		tmp = t_0;
	} else if (F <= 1.3e-208) {
		tmp = ((double) M_PI) * l_m;
	} else if (F <= 3.7e-187) {
		tmp = (-l_m / (F / ((double) M_PI))) / F;
	} else if ((F <= 8.5e-155) || !(F <= 5.5e-132)) {
		tmp = ((double) M_PI) * l_m;
	} else {
		tmp = t_0;
	}
	return l_s * tmp;
}

Java

l_m = Math.abs(l);
l_s = Math.copySign(1.0, l);
public static double code(double l_s, double F, double l_m) {
	double t_0 = -1.0 / (F * (F / (Math.PI * l_m)));
	double tmp;
	if (F <= 2.9e-258) {
		tmp = t_0;
	} else if (F <= 1.3e-208) {
		tmp = Math.PI * l_m;
	} else if (F <= 3.7e-187) {
		tmp = (-l_m / (F / Math.PI)) / F;
	} else if ((F <= 8.5e-155) || !(F <= 5.5e-132)) {
		tmp = Math.PI * l_m;
	} else {
		tmp = t_0;
	}
	return l_s * tmp;
}

Python

l_m = math.fabs(l)
l_s = math.copysign(1.0, l)
def code(l_s, F, l_m):
	t_0 = -1.0 / (F * (F / (math.pi * l_m)))
	tmp = 0
	if F <= 2.9e-258:
		tmp = t_0
	elif F <= 1.3e-208:
		tmp = math.pi * l_m
	elif F <= 3.7e-187:
		tmp = (-l_m / (F / math.pi)) / F
	elif (F <= 8.5e-155) or not (F <= 5.5e-132):
		tmp = math.pi * l_m
	else:
		tmp = t_0
	return l_s * tmp

Julia

l_m = abs(l)
l_s = copysign(1.0, l)
function code(l_s, F, l_m)
	t_0 = Float64(-1.0 / Float64(F * Float64(F / Float64(pi * l_m))))
	tmp = 0.0
	if (F <= 2.9e-258)
		tmp = t_0;
	elseif (F <= 1.3e-208)
		tmp = Float64(pi * l_m);
	elseif (F <= 3.7e-187)
		tmp = Float64(Float64(Float64(-l_m) / Float64(F / pi)) / F);
	elseif ((F <= 8.5e-155) || !(F <= 5.5e-132))
		tmp = Float64(pi * l_m);
	else
		tmp = t_0;
	end
	return Float64(l_s * tmp)
end

MATLAB

l_m = abs(l);
l_s = sign(l) * abs(1.0);
function tmp_2 = code(l_s, F, l_m)
	t_0 = -1.0 / (F * (F / (pi * l_m)));
	tmp = 0.0;
	if (F <= 2.9e-258)
		tmp = t_0;
	elseif (F <= 1.3e-208)
		tmp = pi * l_m;
	elseif (F <= 3.7e-187)
		tmp = (-l_m / (F / pi)) / F;
	elseif ((F <= 8.5e-155) || ~((F <= 5.5e-132)))
		tmp = pi * l_m;
	else
		tmp = t_0;
	end
	tmp_2 = l_s * tmp;
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
l_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[l]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[l$95$s_, F_, l$95$m_] := Block[{t$95$0 = N[(-1.0 / N[(F * N[(F / N[(Pi * l$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(l$95$s * If[LessEqual[F, 2.9e-258], t$95$0, If[LessEqual[F, 1.3e-208], N[(Pi * l$95$m), $MachinePrecision], If[LessEqual[F, 3.7e-187], N[(N[((-l$95$m) / N[(F / Pi), $MachinePrecision]), $MachinePrecision] / F), $MachinePrecision], If[Or[LessEqual[F, 8.5e-155], N[Not[LessEqual[F, 5.5e-132]], $MachinePrecision]], N[(Pi * l$95$m), $MachinePrecision], t$95$0]]]]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 73.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ l_s = \mathsf{copysign}\left(1, \ell\right) \\ l_s \cdot \left(\pi \cdot l_m\right) \end{array} \]

FPCore

l_m = (fabs.f64 l)
l_s = (copysign.f64 1 l)
(FPCore (l_s F l_m) :precision binary64 (* l_s (* PI l_m)))

C

l_m = fabs(l);
l_s = copysign(1.0, l);
double code(double l_s, double F, double l_m) {
	return l_s * (((double) M_PI) * l_m);
}

Java

l_m = Math.abs(l);
l_s = Math.copySign(1.0, l);
public static double code(double l_s, double F, double l_m) {
	return l_s * (Math.PI * l_m);
}

Python

l_m = math.fabs(l)
l_s = math.copysign(1.0, l)
def code(l_s, F, l_m):
	return l_s * (math.pi * l_m)

Julia

l_m = abs(l)
l_s = copysign(1.0, l)
function code(l_s, F, l_m)
	return Float64(l_s * Float64(pi * l_m))
end

MATLAB

l_m = abs(l);
l_s = sign(l) * abs(1.0);
function tmp = code(l_s, F, l_m)
	tmp = l_s * (pi * l_m);
end

Wolfram

l_m = N[Abs[l], $MachinePrecision]
l_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[l]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[l$95$s_, F_, l$95$m_] := N[(l$95$s * N[(Pi * l$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2023348 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  :precision binary64
  (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))