VandenBroeck and Keller, Equation (6)

Percentage Accurate: 75.8% → 99.3%

Time: 15.5s

Alternatives: 8

Speedup: 1.5×

• could not determine a ground truth

  1. F = -8.627823758941014e-34
  2. l = 2903625612996762.5

Specification

Math

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

FPCore

(FPCore (F l)
 :precision binary64
 (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))

C

double code(double F, double l) {
	return (((double) M_PI) * l) - ((1.0 / (F * F)) * tan((((double) M_PI) * l)));
}

Java

public static double code(double F, double l) {
	return (Math.PI * l) - ((1.0 / (F * F)) * Math.tan((Math.PI * l)));
}

Python

def code(F, l):
	return (math.pi * l) - ((1.0 / (F * F)) * math.tan((math.pi * l)))

Julia

function code(F, l)
	return Float64(Float64(pi * l) - Float64(Float64(1.0 / Float64(F * F)) * tan(Float64(pi * l))))
end

MATLAB

function tmp = code(F, l)
	tmp = (pi * l) - ((1.0 / (F * F)) * tan((pi * l)));
end

Wolfram

code[F_, l_] := N[(N[(Pi * l), $MachinePrecision] - N[(N[(1.0 / N[(F * F), $MachinePrecision]), $MachinePrecision] * N[Tan[N[(Pi * l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 75.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (F l)
 :precision binary64
 (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))

C

double code(double F, double l) {
	return (((double) M_PI) * l) - ((1.0 / (F * F)) * tan((((double) M_PI) * l)));
}

Java

public static double code(double F, double l) {
	return (Math.PI * l) - ((1.0 / (F * F)) * Math.tan((Math.PI * l)));
}

Python

def code(F, l):
	return (math.pi * l) - ((1.0 / (F * F)) * math.tan((math.pi * l)))

Julia

function code(F, l)
	return Float64(Float64(pi * l) - Float64(Float64(1.0 / Float64(F * F)) * tan(Float64(pi * l))))
end

MATLAB

function tmp = code(F, l)
	tmp = (pi * l) - ((1.0 / (F * F)) * tan((pi * l)));
end

Wolfram

code[F_, l_] := N[(N[(Pi * l), $MachinePrecision] - N[(N[(1.0 / N[(F * F), $MachinePrecision]), $MachinePrecision] * N[Tan[N[(Pi * l), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ l_s = \mathsf{copysign}\left(1, \ell\right) \\ l_s \cdot \begin{array}{l} \mathbf{if}\;\pi \cdot l_m \leq 10^{+15}:\\ \;\;\;\;\pi \cdot l_m - \frac{\frac{\sin \left(\pi \cdot l_m\right)}{F \cdot \cos \left(\pi \cdot l_m\right)}}{F}\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot l_m\\ \end{array} \end{array} \]

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) 1e+15)
    (- (* PI l_m) (/ (/ (sin (* PI l_m)) (* F (cos (* PI 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) <= 1e+15) {
		tmp = (((double) M_PI) * l_m) - ((sin((((double) M_PI) * l_m)) / (F * cos((((double) M_PI) * 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) <= 1e+15) {
		tmp = (Math.PI * l_m) - ((Math.sin((Math.PI * l_m)) / (F * Math.cos((Math.PI * 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) <= 1e+15:
		tmp = (math.pi * l_m) - ((math.sin((math.pi * l_m)) / (F * math.cos((math.pi * 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) <= 1e+15)
		tmp = Float64(Float64(pi * l_m) - Float64(Float64(sin(Float64(pi * l_m)) / Float64(F * cos(Float64(pi * 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) <= 1e+15)
		tmp = (pi * l_m) - ((sin((pi * l_m)) / (F * cos((pi * 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], 1e+15], N[(N[(Pi * l$95$m), $MachinePrecision] - N[(N[(N[Sin[N[(Pi * l$95$m), $MachinePrecision]], $MachinePrecision] / N[(F * N[Cos[N[(Pi * l$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / F), $MachinePrecision]), $MachinePrecision], N[(Pi * l$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 2: 99.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ l_s = \mathsf{copysign}\left(1, \ell\right) \\ l_s \cdot \begin{array}{l} \mathbf{if}\;\pi \cdot l_m \leq 10^{+15}:\\ \;\;\;\;\pi \cdot l_m - \frac{\frac{\tan \left(\pi \cdot l_m\right)}{F}}{F}\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot l_m\\ \end{array} \end{array} \]

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) 1e+15)
    (- (* 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) <= 1e+15) {
		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) <= 1e+15) {
		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) <= 1e+15:
		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) <= 1e+15)
		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) <= 1e+15)
		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], 1e+15], 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 3: 98.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ l_s = \mathsf{copysign}\left(1, \ell\right) \\ l_s \cdot \begin{array}{l} \mathbf{if}\;\pi \cdot l_m \leq 10^{+15}:\\ \;\;\;\;\pi \cdot l_m - \frac{\pi}{F \cdot \frac{F}{l_m}}\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot l_m\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
l_s = (copysign.f64 1 l)
(FPCore (l_s F l_m)
 :precision binary64
 (*
  l_s
  (if (<= (* PI l_m) 1e+15) (- (* PI l_m) (/ PI (* F (/ F 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 ((((double) M_PI) * l_m) <= 1e+15) {
		tmp = (((double) M_PI) * l_m) - (((double) M_PI) / (F * (F / 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 ((Math.PI * l_m) <= 1e+15) {
		tmp = (Math.PI * l_m) - (Math.PI / (F * (F / 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 (math.pi * l_m) <= 1e+15:
		tmp = (math.pi * l_m) - (math.pi / (F * (F / 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 (Float64(pi * l_m) <= 1e+15)
		tmp = Float64(Float64(pi * l_m) - Float64(pi / Float64(F * Float64(F / 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 ((pi * l_m) <= 1e+15)
		tmp = (pi * l_m) - (pi / (F * (F / 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[LessEqual[N[(Pi * l$95$m), $MachinePrecision], 1e+15], N[(N[(Pi * l$95$m), $MachinePrecision] - N[(Pi / N[(F * N[(F / l$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(Pi * l$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 4: 72.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ l_s = \mathsf{copysign}\left(1, \ell\right) \\ l_s \cdot \begin{array}{l} \mathbf{if}\;l_m \leq 7.6 \cdot 10^{-209} \lor \neg \left(l_m \leq 5 \cdot 10^{-136} \lor \neg \left(l_m \leq 7.8 \cdot 10^{-66}\right) \land l_m \leq 7.2 \cdot 10^{-12}\right):\\ \;\;\;\;\pi \cdot l_m\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi \cdot \left(-l_m\right)}{{F}^{2}}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
l_s = (copysign.f64 1 l)
(FPCore (l_s F l_m)
 :precision binary64
 (*
  l_s
  (if (or (<= l_m 7.6e-209)
          (not
           (or (<= l_m 5e-136) (and (not (<= l_m 7.8e-66)) (<= l_m 7.2e-12)))))
    (* PI l_m)
    (/ (* PI (- l_m)) (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 ((l_m <= 7.6e-209) || !((l_m <= 5e-136) || (!(l_m <= 7.8e-66) && (l_m <= 7.2e-12)))) {
		tmp = ((double) M_PI) * l_m;
	} else {
		tmp = (((double) M_PI) * -l_m) / 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 ((l_m <= 7.6e-209) || !((l_m <= 5e-136) || (!(l_m <= 7.8e-66) && (l_m <= 7.2e-12)))) {
		tmp = Math.PI * l_m;
	} else {
		tmp = (Math.PI * -l_m) / 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 (l_m <= 7.6e-209) or not ((l_m <= 5e-136) or (not (l_m <= 7.8e-66) and (l_m <= 7.2e-12))):
		tmp = math.pi * l_m
	else:
		tmp = (math.pi * -l_m) / 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 ((l_m <= 7.6e-209) || !((l_m <= 5e-136) || (!(l_m <= 7.8e-66) && (l_m <= 7.2e-12))))
		tmp = Float64(pi * l_m);
	else
		tmp = Float64(Float64(pi * Float64(-l_m)) / (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 ((l_m <= 7.6e-209) || ~(((l_m <= 5e-136) || (~((l_m <= 7.8e-66)) && (l_m <= 7.2e-12)))))
		tmp = pi * l_m;
	else
		tmp = (pi * -l_m) / (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[Or[LessEqual[l$95$m, 7.6e-209], N[Not[Or[LessEqual[l$95$m, 5e-136], And[N[Not[LessEqual[l$95$m, 7.8e-66]], $MachinePrecision], LessEqual[l$95$m, 7.2e-12]]]], $MachinePrecision]], N[(Pi * l$95$m), $MachinePrecision], N[(N[(Pi * (-l$95$m)), $MachinePrecision] / N[Power[F, 2.0], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 5: 72.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ l_s = \mathsf{copysign}\left(1, \ell\right) \\ l_s \cdot \begin{array}{l} \mathbf{if}\;l_m \leq 6.5 \cdot 10^{-210}:\\ \;\;\;\;\pi \cdot l_m\\ \mathbf{elif}\;l_m \leq 8.5 \cdot 10^{-136}:\\ \;\;\;\;\frac{\pi}{{F}^{2}} \cdot \left(-l_m\right)\\ \mathbf{elif}\;l_m \leq 2.45 \cdot 10^{-64} \lor \neg \left(l_m \leq 5 \cdot 10^{-13}\right):\\ \;\;\;\;\pi \cdot l_m\\ \mathbf{else}:\\ \;\;\;\;\frac{\pi \cdot \left(-l_m\right)}{{F}^{2}}\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
l_s = (copysign.f64 1 l)
(FPCore (l_s F l_m)
 :precision binary64
 (*
  l_s
  (if (<= l_m 6.5e-210)
    (* PI l_m)
    (if (<= l_m 8.5e-136)
      (* (/ PI (pow F 2.0)) (- l_m))
      (if (or (<= l_m 2.45e-64) (not (<= l_m 5e-13)))
        (* PI l_m)
        (/ (* PI (- l_m)) (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 (l_m <= 6.5e-210) {
		tmp = ((double) M_PI) * l_m;
	} else if (l_m <= 8.5e-136) {
		tmp = (((double) M_PI) / pow(F, 2.0)) * -l_m;
	} else if ((l_m <= 2.45e-64) || !(l_m <= 5e-13)) {
		tmp = ((double) M_PI) * l_m;
	} else {
		tmp = (((double) M_PI) * -l_m) / 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 (l_m <= 6.5e-210) {
		tmp = Math.PI * l_m;
	} else if (l_m <= 8.5e-136) {
		tmp = (Math.PI / Math.pow(F, 2.0)) * -l_m;
	} else if ((l_m <= 2.45e-64) || !(l_m <= 5e-13)) {
		tmp = Math.PI * l_m;
	} else {
		tmp = (Math.PI * -l_m) / 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 l_m <= 6.5e-210:
		tmp = math.pi * l_m
	elif l_m <= 8.5e-136:
		tmp = (math.pi / math.pow(F, 2.0)) * -l_m
	elif (l_m <= 2.45e-64) or not (l_m <= 5e-13):
		tmp = math.pi * l_m
	else:
		tmp = (math.pi * -l_m) / 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 (l_m <= 6.5e-210)
		tmp = Float64(pi * l_m);
	elseif (l_m <= 8.5e-136)
		tmp = Float64(Float64(pi / (F ^ 2.0)) * Float64(-l_m));
	elseif ((l_m <= 2.45e-64) || !(l_m <= 5e-13))
		tmp = Float64(pi * l_m);
	else
		tmp = Float64(Float64(pi * Float64(-l_m)) / (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 (l_m <= 6.5e-210)
		tmp = pi * l_m;
	elseif (l_m <= 8.5e-136)
		tmp = (pi / (F ^ 2.0)) * -l_m;
	elseif ((l_m <= 2.45e-64) || ~((l_m <= 5e-13)))
		tmp = pi * l_m;
	else
		tmp = (pi * -l_m) / (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[l$95$m, 6.5e-210], N[(Pi * l$95$m), $MachinePrecision], If[LessEqual[l$95$m, 8.5e-136], N[(N[(Pi / N[Power[F, 2.0], $MachinePrecision]), $MachinePrecision] * (-l$95$m)), $MachinePrecision], If[Or[LessEqual[l$95$m, 2.45e-64], N[Not[LessEqual[l$95$m, 5e-13]], $MachinePrecision]], N[(Pi * l$95$m), $MachinePrecision], N[(N[(Pi * (-l$95$m)), $MachinePrecision] / N[Power[F, 2.0], $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 6: 98.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ l_s = \mathsf{copysign}\left(1, \ell\right) \\ l_s \cdot \begin{array}{l} \mathbf{if}\;l_m \leq 2.25 \cdot 10^{+14}:\\ \;\;\;\;\pi \cdot l_m - \frac{\pi}{F} \cdot \frac{l_m}{F}\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot l_m\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
l_s = (copysign.f64 1 l)
(FPCore (l_s F l_m)
 :precision binary64
 (*
  l_s
  (if (<= l_m 2.25e+14) (- (* 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 (l_m <= 2.25e+14) {
		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 (l_m <= 2.25e+14) {
		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 l_m <= 2.25e+14:
		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 (l_m <= 2.25e+14)
		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 (l_m <= 2.25e+14)
		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[l$95$m, 2.25e+14], 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

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1. Add Preprocessing

Alternative 7: 92.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} l_m = \left|\ell\right| \\ l_s = \mathsf{copysign}\left(1, \ell\right) \\ l_s \cdot \begin{array}{l} \mathbf{if}\;l_m \leq 2.25 \cdot 10^{+14}:\\ \;\;\;\;\pi \cdot \left(l_m - l_m \cdot {F}^{-2}\right)\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot l_m\\ \end{array} \end{array} \]

FPCore

l_m = (fabs.f64 l)
l_s = (copysign.f64 1 l)
(FPCore (l_s F l_m)
 :precision binary64
 (* l_s (if (<= l_m 2.25e+14) (* PI (- l_m (* l_m (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 (l_m <= 2.25e+14) {
		tmp = ((double) M_PI) * (l_m - (l_m * 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 (l_m <= 2.25e+14) {
		tmp = Math.PI * (l_m - (l_m * 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 l_m <= 2.25e+14:
		tmp = math.pi * (l_m - (l_m * 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 (l_m <= 2.25e+14)
		tmp = Float64(pi * Float64(l_m - Float64(l_m * (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 (l_m <= 2.25e+14)
		tmp = pi * (l_m - (l_m * (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[l$95$m, 2.25e+14], N[(Pi * N[(l$95$m - N[(l$95$m * N[Power[F, -2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(Pi * l$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 8: 74.1% 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

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1. Add Preprocessing

Reproduce

herbie shell --seed 2023350 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  :precision binary64
  (- (* PI l) (* (/ 1.0 (* F F)) (tan (* PI l)))))