2-ancestry mixing, positive discriminant

Percentage Accurate: 44.5% → 95.7%

Time: 22.9s

Alternatives: 14

Speedup: 2.0×

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{2 \cdot a}\\ t_1 := \sqrt{g \cdot g - h \cdot h}\\ \sqrt[3]{t_0 \cdot \left(\left(-g\right) + t_1\right)} + \sqrt[3]{t_0 \cdot \left(\left(-g\right) - t_1\right)} \end{array} \end{array} \]

FPCore

(FPCore (g h a)
 :precision binary64
 (let* ((t_0 (/ 1.0 (* 2.0 a))) (t_1 (sqrt (- (* g g) (* h h)))))
   (+ (cbrt (* t_0 (+ (- g) t_1))) (cbrt (* t_0 (- (- g) t_1))))))

C

double code(double g, double h, double a) {
	double t_0 = 1.0 / (2.0 * a);
	double t_1 = sqrt(((g * g) - (h * h)));
	return cbrt((t_0 * (-g + t_1))) + cbrt((t_0 * (-g - t_1)));
}

Java

public static double code(double g, double h, double a) {
	double t_0 = 1.0 / (2.0 * a);
	double t_1 = Math.sqrt(((g * g) - (h * h)));
	return Math.cbrt((t_0 * (-g + t_1))) + Math.cbrt((t_0 * (-g - t_1)));
}

Julia

function code(g, h, a)
	t_0 = Float64(1.0 / Float64(2.0 * a))
	t_1 = sqrt(Float64(Float64(g * g) - Float64(h * h)))
	return Float64(cbrt(Float64(t_0 * Float64(Float64(-g) + t_1))) + cbrt(Float64(t_0 * Float64(Float64(-g) - t_1))))
end

Wolfram

code[g_, h_, a_] := Block[{t$95$0 = N[(1.0 / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(N[(g * g), $MachinePrecision] - N[(h * h), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, N[(N[Power[N[(t$95$0 * N[((-g) + t$95$1), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] + N[Power[N[(t$95$0 * N[((-g) - t$95$1), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]]]

Initial Program: 44.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{2 \cdot a}\\ t_1 := \sqrt{g \cdot g - h \cdot h}\\ \sqrt[3]{t_0 \cdot \left(\left(-g\right) + t_1\right)} + \sqrt[3]{t_0 \cdot \left(\left(-g\right) - t_1\right)} \end{array} \end{array} \]

FPCore

(FPCore (g h a)
 :precision binary64
 (let* ((t_0 (/ 1.0 (* 2.0 a))) (t_1 (sqrt (- (* g g) (* h h)))))
   (+ (cbrt (* t_0 (+ (- g) t_1))) (cbrt (* t_0 (- (- g) t_1))))))

C

double code(double g, double h, double a) {
	double t_0 = 1.0 / (2.0 * a);
	double t_1 = sqrt(((g * g) - (h * h)));
	return cbrt((t_0 * (-g + t_1))) + cbrt((t_0 * (-g - t_1)));
}

Java

public static double code(double g, double h, double a) {
	double t_0 = 1.0 / (2.0 * a);
	double t_1 = Math.sqrt(((g * g) - (h * h)));
	return Math.cbrt((t_0 * (-g + t_1))) + Math.cbrt((t_0 * (-g - t_1)));
}

Julia

function code(g, h, a)
	t_0 = Float64(1.0 / Float64(2.0 * a))
	t_1 = sqrt(Float64(Float64(g * g) - Float64(h * h)))
	return Float64(cbrt(Float64(t_0 * Float64(Float64(-g) + t_1))) + cbrt(Float64(t_0 * Float64(Float64(-g) - t_1))))
end

Wolfram

code[g_, h_, a_] := Block[{t$95$0 = N[(1.0 / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(N[(g * g), $MachinePrecision] - N[(h * h), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, N[(N[Power[N[(t$95$0 * N[((-g) + t$95$1), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] + N[Power[N[(t$95$0 * N[((-g) - t$95$1), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]]]

Alternative 1: 95.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\sqrt[3]{0.5} \cdot \sqrt[3]{\frac{1}{a}}\right) \cdot \sqrt[3]{g \cdot -2} + \sqrt[3]{\left(g - g\right) \cdot \frac{-0.5}{a}} \end{array} \]

FPCore

(FPCore (g h a)
 :precision binary64
 (+
  (* (* (cbrt 0.5) (cbrt (/ 1.0 a))) (cbrt (* g -2.0)))
  (cbrt (* (- g g) (/ -0.5 a)))))

C

double code(double g, double h, double a) {
	return ((cbrt(0.5) * cbrt((1.0 / a))) * cbrt((g * -2.0))) + cbrt(((g - g) * (-0.5 / a)));
}

Java

public static double code(double g, double h, double a) {
	return ((Math.cbrt(0.5) * Math.cbrt((1.0 / a))) * Math.cbrt((g * -2.0))) + Math.cbrt(((g - g) * (-0.5 / a)));
}

Julia

function code(g, h, a)
	return Float64(Float64(Float64(cbrt(0.5) * cbrt(Float64(1.0 / a))) * cbrt(Float64(g * -2.0))) + cbrt(Float64(Float64(g - g) * Float64(-0.5 / a))))
end

Wolfram

code[g_, h_, a_] := N[(N[(N[(N[Power[0.5, 1/3], $MachinePrecision] * N[Power[N[(1.0 / a), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision] * N[Power[N[(g * -2.0), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision] + N[Power[N[(N[(g - g), $MachinePrecision] * N[(-0.5 / a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 2: 95.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{\left(g - g\right) \cdot \frac{-0.5}{a}} + \sqrt[3]{g \cdot -2} \cdot \sqrt[3]{\frac{0.5}{a}} \end{array} \]

FPCore

(FPCore (g h a)
 :precision binary64
 (+ (cbrt (* (- g g) (/ -0.5 a))) (* (cbrt (* g -2.0)) (cbrt (/ 0.5 a)))))

C

double code(double g, double h, double a) {
	return cbrt(((g - g) * (-0.5 / a))) + (cbrt((g * -2.0)) * cbrt((0.5 / a)));
}

Java

public static double code(double g, double h, double a) {
	return Math.cbrt(((g - g) * (-0.5 / a))) + (Math.cbrt((g * -2.0)) * Math.cbrt((0.5 / a)));
}

Julia

function code(g, h, a)
	return Float64(cbrt(Float64(Float64(g - g) * Float64(-0.5 / a))) + Float64(cbrt(Float64(g * -2.0)) * cbrt(Float64(0.5 / a))))
end

Wolfram

code[g_, h_, a_] := N[(N[Power[N[(N[(g - g), $MachinePrecision] * N[(-0.5 / a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] + N[(N[Power[N[(g * -2.0), $MachinePrecision], 1/3], $MachinePrecision] * N[Power[N[(0.5 / a), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 3: 95.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{\left(g - g\right) \cdot \frac{-0.5}{a}} + \frac{\sqrt[3]{-g}}{\sqrt[3]{a}} \end{array} \]

FPCore

(FPCore (g h a)
 :precision binary64
 (+ (cbrt (* (- g g) (/ -0.5 a))) (/ (cbrt (- g)) (cbrt a))))

C

double code(double g, double h, double a) {
	return cbrt(((g - g) * (-0.5 / a))) + (cbrt(-g) / cbrt(a));
}

Java

public static double code(double g, double h, double a) {
	return Math.cbrt(((g - g) * (-0.5 / a))) + (Math.cbrt(-g) / Math.cbrt(a));
}

Julia

function code(g, h, a)
	return Float64(cbrt(Float64(Float64(g - g) * Float64(-0.5 / a))) + Float64(cbrt(Float64(-g)) / cbrt(a)))
end

Wolfram

code[g_, h_, a_] := N[(N[Power[N[(N[(g - g), $MachinePrecision] * N[(-0.5 / a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] + N[(N[Power[(-g), 1/3], $MachinePrecision] / N[Power[a, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 4: 89.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt[3]{\left(g - g\right) \cdot \frac{-0.5}{a}}\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{-82}:\\ \;\;\;\;t_0 + \sqrt[3]{-\frac{g}{a}}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-68}:\\ \;\;\;\;\frac{\sqrt[3]{-g}}{\sqrt[3]{a}} + \sqrt[3]{-2}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \sqrt[3]{\left(g \cdot -2\right) \cdot \frac{0.5}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (g h a)
 :precision binary64
 (let* ((t_0 (cbrt (* (- g g) (/ -0.5 a)))))
   (if (<= a -1.2e-82)
     (+ t_0 (cbrt (- (/ g a))))
     (if (<= a 5e-68)
       (+ (/ (cbrt (- g)) (cbrt a)) (cbrt -2.0))
       (+ t_0 (cbrt (* (* g -2.0) (/ 0.5 a))))))))

C

double code(double g, double h, double a) {
	double t_0 = cbrt(((g - g) * (-0.5 / a)));
	double tmp;
	if (a <= -1.2e-82) {
		tmp = t_0 + cbrt(-(g / a));
	} else if (a <= 5e-68) {
		tmp = (cbrt(-g) / cbrt(a)) + cbrt(-2.0);
	} else {
		tmp = t_0 + cbrt(((g * -2.0) * (0.5 / a)));
	}
	return tmp;
}

Java

public static double code(double g, double h, double a) {
	double t_0 = Math.cbrt(((g - g) * (-0.5 / a)));
	double tmp;
	if (a <= -1.2e-82) {
		tmp = t_0 + Math.cbrt(-(g / a));
	} else if (a <= 5e-68) {
		tmp = (Math.cbrt(-g) / Math.cbrt(a)) + Math.cbrt(-2.0);
	} else {
		tmp = t_0 + Math.cbrt(((g * -2.0) * (0.5 / a)));
	}
	return tmp;
}

Julia

function code(g, h, a)
	t_0 = cbrt(Float64(Float64(g - g) * Float64(-0.5 / a)))
	tmp = 0.0
	if (a <= -1.2e-82)
		tmp = Float64(t_0 + cbrt(Float64(-Float64(g / a))));
	elseif (a <= 5e-68)
		tmp = Float64(Float64(cbrt(Float64(-g)) / cbrt(a)) + cbrt(-2.0));
	else
		tmp = Float64(t_0 + cbrt(Float64(Float64(g * -2.0) * Float64(0.5 / a))));
	end
	return tmp
end

Wolfram

code[g_, h_, a_] := Block[{t$95$0 = N[Power[N[(N[(g - g), $MachinePrecision] * N[(-0.5 / a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]}, If[LessEqual[a, -1.2e-82], N[(t$95$0 + N[Power[(-N[(g / a), $MachinePrecision]), 1/3], $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-68], N[(N[(N[Power[(-g), 1/3], $MachinePrecision] / N[Power[a, 1/3], $MachinePrecision]), $MachinePrecision] + N[Power[-2.0, 1/3], $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[Power[N[(N[(g * -2.0), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 5: 63.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;g \leq -0.00142 \lor \neg \left(g \leq 4 \cdot 10^{-9}\right):\\ \;\;\;\;\sqrt[3]{\frac{-0.25}{a \cdot g}} + \sqrt[3]{\frac{-0.5}{a} \cdot \left(g + g\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left(g \cdot -2\right) \cdot \frac{0.5}{a}} + \frac{\sqrt[3]{g}}{-2}\\ \end{array} \end{array} \]

FPCore

(FPCore (g h a)
 :precision binary64
 (if (or (<= g -0.00142) (not (<= g 4e-9)))
   (+ (cbrt (/ -0.25 (* a g))) (cbrt (* (/ -0.5 a) (+ g g))))
   (+ (cbrt (* (* g -2.0) (/ 0.5 a))) (/ (cbrt g) -2.0))))

C

double code(double g, double h, double a) {
	double tmp;
	if ((g <= -0.00142) || !(g <= 4e-9)) {
		tmp = cbrt((-0.25 / (a * g))) + cbrt(((-0.5 / a) * (g + g)));
	} else {
		tmp = cbrt(((g * -2.0) * (0.5 / a))) + (cbrt(g) / -2.0);
	}
	return tmp;
}

Java

public static double code(double g, double h, double a) {
	double tmp;
	if ((g <= -0.00142) || !(g <= 4e-9)) {
		tmp = Math.cbrt((-0.25 / (a * g))) + Math.cbrt(((-0.5 / a) * (g + g)));
	} else {
		tmp = Math.cbrt(((g * -2.0) * (0.5 / a))) + (Math.cbrt(g) / -2.0);
	}
	return tmp;
}

Julia

function code(g, h, a)
	tmp = 0.0
	if ((g <= -0.00142) || !(g <= 4e-9))
		tmp = Float64(cbrt(Float64(-0.25 / Float64(a * g))) + cbrt(Float64(Float64(-0.5 / a) * Float64(g + g))));
	else
		tmp = Float64(cbrt(Float64(Float64(g * -2.0) * Float64(0.5 / a))) + Float64(cbrt(g) / -2.0));
	end
	return tmp
end

Wolfram

code[g_, h_, a_] := If[Or[LessEqual[g, -0.00142], N[Not[LessEqual[g, 4e-9]], $MachinePrecision]], N[(N[Power[N[(-0.25 / N[(a * g), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] + N[Power[N[(N[(-0.5 / a), $MachinePrecision] * N[(g + g), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], N[(N[Power[N[(N[(g * -2.0), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] + N[(N[Power[g, 1/3], $MachinePrecision] / -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 6: 47.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;g \leq -120000000 \lor \neg \left(g \leq 70\right):\\ \;\;\;\;\sqrt[3]{-\frac{g}{a}} + \sqrt[3]{-2}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left(g \cdot -2\right) \cdot \frac{0.5}{a}} + \frac{\sqrt[3]{g}}{-2}\\ \end{array} \end{array} \]

FPCore

(FPCore (g h a)
 :precision binary64
 (if (or (<= g -120000000.0) (not (<= g 70.0)))
   (+ (cbrt (- (/ g a))) (cbrt -2.0))
   (+ (cbrt (* (* g -2.0) (/ 0.5 a))) (/ (cbrt g) -2.0))))

C

double code(double g, double h, double a) {
	double tmp;
	if ((g <= -120000000.0) || !(g <= 70.0)) {
		tmp = cbrt(-(g / a)) + cbrt(-2.0);
	} else {
		tmp = cbrt(((g * -2.0) * (0.5 / a))) + (cbrt(g) / -2.0);
	}
	return tmp;
}

Java

public static double code(double g, double h, double a) {
	double tmp;
	if ((g <= -120000000.0) || !(g <= 70.0)) {
		tmp = Math.cbrt(-(g / a)) + Math.cbrt(-2.0);
	} else {
		tmp = Math.cbrt(((g * -2.0) * (0.5 / a))) + (Math.cbrt(g) / -2.0);
	}
	return tmp;
}

Julia

function code(g, h, a)
	tmp = 0.0
	if ((g <= -120000000.0) || !(g <= 70.0))
		tmp = Float64(cbrt(Float64(-Float64(g / a))) + cbrt(-2.0));
	else
		tmp = Float64(cbrt(Float64(Float64(g * -2.0) * Float64(0.5 / a))) + Float64(cbrt(g) / -2.0));
	end
	return tmp
end

Wolfram

code[g_, h_, a_] := If[Or[LessEqual[g, -120000000.0], N[Not[LessEqual[g, 70.0]], $MachinePrecision]], N[(N[Power[(-N[(g / a), $MachinePrecision]), 1/3], $MachinePrecision] + N[Power[-2.0, 1/3], $MachinePrecision]), $MachinePrecision], N[(N[Power[N[(N[(g * -2.0), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] + N[(N[Power[g, 1/3], $MachinePrecision] / -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 7: 56.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt[3]{\frac{-0.5}{a} \cdot \left(g + g\right)}\\ \mathbf{if}\;g \leq -2.9 \cdot 10^{-22} \lor \neg \left(g \leq 1.15 \cdot 10^{-5}\right):\\ \;\;\;\;t_0 + \sqrt[3]{\frac{-2}{g}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \sqrt[3]{g}\\ \end{array} \end{array} \]

FPCore

(FPCore (g h a)
 :precision binary64
 (let* ((t_0 (cbrt (* (/ -0.5 a) (+ g g)))))
   (if (or (<= g -2.9e-22) (not (<= g 1.15e-5)))
     (+ t_0 (cbrt (/ -2.0 g)))
     (+ t_0 (cbrt g)))))

C

double code(double g, double h, double a) {
	double t_0 = cbrt(((-0.5 / a) * (g + g)));
	double tmp;
	if ((g <= -2.9e-22) || !(g <= 1.15e-5)) {
		tmp = t_0 + cbrt((-2.0 / g));
	} else {
		tmp = t_0 + cbrt(g);
	}
	return tmp;
}

Java

public static double code(double g, double h, double a) {
	double t_0 = Math.cbrt(((-0.5 / a) * (g + g)));
	double tmp;
	if ((g <= -2.9e-22) || !(g <= 1.15e-5)) {
		tmp = t_0 + Math.cbrt((-2.0 / g));
	} else {
		tmp = t_0 + Math.cbrt(g);
	}
	return tmp;
}

Julia

function code(g, h, a)
	t_0 = cbrt(Float64(Float64(-0.5 / a) * Float64(g + g)))
	tmp = 0.0
	if ((g <= -2.9e-22) || !(g <= 1.15e-5))
		tmp = Float64(t_0 + cbrt(Float64(-2.0 / g)));
	else
		tmp = Float64(t_0 + cbrt(g));
	end
	return tmp
end

Wolfram

code[g_, h_, a_] := Block[{t$95$0 = N[Power[N[(N[(-0.5 / a), $MachinePrecision] * N[(g + g), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]}, If[Or[LessEqual[g, -2.9e-22], N[Not[LessEqual[g, 1.15e-5]], $MachinePrecision]], N[(t$95$0 + N[Power[N[(-2.0 / g), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[Power[g, 1/3], $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 8: 47.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;g \leq -0.76 \lor \neg \left(g \leq 8.5 \cdot 10^{-6}\right):\\ \;\;\;\;\sqrt[3]{-\frac{g}{a}} + \sqrt[3]{-2}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\frac{-0.5}{a} \cdot \left(g + g\right)} + \sqrt[3]{g}\\ \end{array} \end{array} \]

FPCore

(FPCore (g h a)
 :precision binary64
 (if (or (<= g -0.76) (not (<= g 8.5e-6)))
   (+ (cbrt (- (/ g a))) (cbrt -2.0))
   (+ (cbrt (* (/ -0.5 a) (+ g g))) (cbrt g))))

C

double code(double g, double h, double a) {
	double tmp;
	if ((g <= -0.76) || !(g <= 8.5e-6)) {
		tmp = cbrt(-(g / a)) + cbrt(-2.0);
	} else {
		tmp = cbrt(((-0.5 / a) * (g + g))) + cbrt(g);
	}
	return tmp;
}

Java

public static double code(double g, double h, double a) {
	double tmp;
	if ((g <= -0.76) || !(g <= 8.5e-6)) {
		tmp = Math.cbrt(-(g / a)) + Math.cbrt(-2.0);
	} else {
		tmp = Math.cbrt(((-0.5 / a) * (g + g))) + Math.cbrt(g);
	}
	return tmp;
}

Julia

function code(g, h, a)
	tmp = 0.0
	if ((g <= -0.76) || !(g <= 8.5e-6))
		tmp = Float64(cbrt(Float64(-Float64(g / a))) + cbrt(-2.0));
	else
		tmp = Float64(cbrt(Float64(Float64(-0.5 / a) * Float64(g + g))) + cbrt(g));
	end
	return tmp
end

Wolfram

code[g_, h_, a_] := If[Or[LessEqual[g, -0.76], N[Not[LessEqual[g, 8.5e-6]], $MachinePrecision]], N[(N[Power[(-N[(g / a), $MachinePrecision]), 1/3], $MachinePrecision] + N[Power[-2.0, 1/3], $MachinePrecision]), $MachinePrecision], N[(N[Power[N[(N[(-0.5 / a), $MachinePrecision] * N[(g + g), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] + N[Power[g, 1/3], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 9: 47.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;g \leq -800000000 \lor \neg \left(g \leq 2.15\right):\\ \;\;\;\;\sqrt[3]{-\frac{g}{a}} + \sqrt[3]{-2}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left(g \cdot -2\right) \cdot \frac{0.5}{a}} - \sqrt[3]{g}\\ \end{array} \end{array} \]

FPCore

(FPCore (g h a)
 :precision binary64
 (if (or (<= g -800000000.0) (not (<= g 2.15)))
   (+ (cbrt (- (/ g a))) (cbrt -2.0))
   (- (cbrt (* (* g -2.0) (/ 0.5 a))) (cbrt g))))

C

double code(double g, double h, double a) {
	double tmp;
	if ((g <= -800000000.0) || !(g <= 2.15)) {
		tmp = cbrt(-(g / a)) + cbrt(-2.0);
	} else {
		tmp = cbrt(((g * -2.0) * (0.5 / a))) - cbrt(g);
	}
	return tmp;
}

Java

public static double code(double g, double h, double a) {
	double tmp;
	if ((g <= -800000000.0) || !(g <= 2.15)) {
		tmp = Math.cbrt(-(g / a)) + Math.cbrt(-2.0);
	} else {
		tmp = Math.cbrt(((g * -2.0) * (0.5 / a))) - Math.cbrt(g);
	}
	return tmp;
}

Julia

function code(g, h, a)
	tmp = 0.0
	if ((g <= -800000000.0) || !(g <= 2.15))
		tmp = Float64(cbrt(Float64(-Float64(g / a))) + cbrt(-2.0));
	else
		tmp = Float64(cbrt(Float64(Float64(g * -2.0) * Float64(0.5 / a))) - cbrt(g));
	end
	return tmp
end

Wolfram

code[g_, h_, a_] := If[Or[LessEqual[g, -800000000.0], N[Not[LessEqual[g, 2.15]], $MachinePrecision]], N[(N[Power[(-N[(g / a), $MachinePrecision]), 1/3], $MachinePrecision] + N[Power[-2.0, 1/3], $MachinePrecision]), $MachinePrecision], N[(N[Power[N[(N[(g * -2.0), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] - N[Power[g, 1/3], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 73.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{\left(g - g\right) \cdot \frac{-0.5}{a}} + \sqrt[3]{-\frac{g}{a}} \end{array} \]

FPCore

(FPCore (g h a)
 :precision binary64
 (+ (cbrt (* (- g g) (/ -0.5 a))) (cbrt (- (/ g a)))))

C

double code(double g, double h, double a) {
	return cbrt(((g - g) * (-0.5 / a))) + cbrt(-(g / a));
}

Java

public static double code(double g, double h, double a) {
	return Math.cbrt(((g - g) * (-0.5 / a))) + Math.cbrt(-(g / a));
}

Julia

function code(g, h, a)
	return Float64(cbrt(Float64(Float64(g - g) * Float64(-0.5 / a))) + cbrt(Float64(-Float64(g / a))))
end

Wolfram

code[g_, h_, a_] := N[(N[Power[N[(N[(g - g), $MachinePrecision] * N[(-0.5 / a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] + N[Power[(-N[(g / a), $MachinePrecision]), 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 11: 43.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{-\frac{g}{a}} + \sqrt[3]{-2} \end{array} \]

FPCore

(FPCore (g h a) :precision binary64 (+ (cbrt (- (/ g a))) (cbrt -2.0)))

C

double code(double g, double h, double a) {
	return cbrt(-(g / a)) + cbrt(-2.0);
}

Java

public static double code(double g, double h, double a) {
	return Math.cbrt(-(g / a)) + Math.cbrt(-2.0);
}

Julia

function code(g, h, a)
	return Float64(cbrt(Float64(-Float64(g / a))) + cbrt(-2.0))
end

Wolfram

code[g_, h_, a_] := N[(N[Power[(-N[(g / a), $MachinePrecision]), 1/3], $MachinePrecision] + N[Power[-2.0, 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 12: 4.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{-2} + \frac{\sqrt[3]{g}}{-2} \end{array} \]

FPCore

(FPCore (g h a) :precision binary64 (+ (cbrt -2.0) (/ (cbrt g) -2.0)))

C

double code(double g, double h, double a) {
	return cbrt(-2.0) + (cbrt(g) / -2.0);
}

Java

public static double code(double g, double h, double a) {
	return Math.cbrt(-2.0) + (Math.cbrt(g) / -2.0);
}

Julia

function code(g, h, a)
	return Float64(cbrt(-2.0) + Float64(cbrt(g) / -2.0))
end

Wolfram

code[g_, h_, a_] := N[(N[Power[-2.0, 1/3], $MachinePrecision] + N[(N[Power[g, 1/3], $MachinePrecision] / -2.0), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 13: 4.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{-2} - \sqrt[3]{g} \end{array} \]

FPCore

(FPCore (g h a) :precision binary64 (- (cbrt -2.0) (cbrt g)))

C

double code(double g, double h, double a) {
	return cbrt(-2.0) - cbrt(g);
}

Java

public static double code(double g, double h, double a) {
	return Math.cbrt(-2.0) - Math.cbrt(g);
}

Julia

function code(g, h, a)
	return Float64(cbrt(-2.0) - cbrt(g))
end

Wolfram

code[g_, h_, a_] := N[(N[Power[-2.0, 1/3], $MachinePrecision] - N[Power[g, 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 14: 4.4% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{-2} \end{array} \]

FPCore

(FPCore (g h a) :precision binary64 (cbrt -2.0))

C

double code(double g, double h, double a) {
	return cbrt(-2.0);
}

Java

public static double code(double g, double h, double a) {
	return Math.cbrt(-2.0);
}

Julia

function code(g, h, a)
	return cbrt(-2.0)
end

Wolfram

code[g_, h_, a_] := N[Power[-2.0, 1/3], $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2023346 
(FPCore (g h a)
  :name "2-ancestry mixing, positive discriminant"
  :precision binary64
  (+ (cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))))