2-ancestry mixing, positive discriminant

Percentage Accurate: 43.8% → 76.9%

Time: 24.1s

Alternatives: 2

Speedup: 2.1×

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: 43.8% 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: 76.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{g \cdot g - h \cdot h}\\ t_1 := t\_0 - g\\ t_2 := \sqrt[3]{\frac{1}{2 \cdot a} \cdot t\_1} + \sqrt[3]{\left(g + t\_0\right) \cdot \frac{-1}{2 \cdot a}}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-106}:\\ \;\;\;\;\sqrt[3]{\frac{-0.25}{a} \cdot \frac{{h}^{2}}{g}} + \sqrt[3]{\left(g + g\right) \cdot \frac{-0.5}{a}}\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\sqrt[3]{t\_1 \cdot \frac{0.5}{a}} + \sqrt[3]{\frac{-0.5}{a}} \cdot \sqrt[3]{g + g}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + \sqrt[3]{\frac{-g}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (g h a)
 :precision binary64
 (let* ((t_0 (sqrt (- (* g g) (* h h))))
        (t_1 (- t_0 g))
        (t_2
         (+
          (cbrt (* (/ 1.0 (* 2.0 a)) t_1))
          (cbrt (* (+ g t_0) (/ -1.0 (* 2.0 a)))))))
   (if (<= t_2 -5e-106)
     (+ (cbrt (* (/ -0.25 a) (/ (pow h 2.0) g))) (cbrt (* (+ g g) (/ -0.5 a))))
     (if (<= t_2 0.0)
       (+ (cbrt (* t_1 (/ 0.5 a))) (* (cbrt (/ -0.5 a)) (cbrt (+ g g))))
       (+ (cbrt (* (/ 0.5 a) (- g g))) (cbrt (/ (- g) a)))))))

C

double code(double g, double h, double a) {
	double t_0 = sqrt(((g * g) - (h * h)));
	double t_1 = t_0 - g;
	double t_2 = cbrt(((1.0 / (2.0 * a)) * t_1)) + cbrt(((g + t_0) * (-1.0 / (2.0 * a))));
	double tmp;
	if (t_2 <= -5e-106) {
		tmp = cbrt(((-0.25 / a) * (pow(h, 2.0) / g))) + cbrt(((g + g) * (-0.5 / a)));
	} else if (t_2 <= 0.0) {
		tmp = cbrt((t_1 * (0.5 / a))) + (cbrt((-0.5 / a)) * cbrt((g + g)));
	} else {
		tmp = cbrt(((0.5 / a) * (g - g))) + cbrt((-g / a));
	}
	return tmp;
}

Java

public static double code(double g, double h, double a) {
	double t_0 = Math.sqrt(((g * g) - (h * h)));
	double t_1 = t_0 - g;
	double t_2 = Math.cbrt(((1.0 / (2.0 * a)) * t_1)) + Math.cbrt(((g + t_0) * (-1.0 / (2.0 * a))));
	double tmp;
	if (t_2 <= -5e-106) {
		tmp = Math.cbrt(((-0.25 / a) * (Math.pow(h, 2.0) / g))) + Math.cbrt(((g + g) * (-0.5 / a)));
	} else if (t_2 <= 0.0) {
		tmp = Math.cbrt((t_1 * (0.5 / a))) + (Math.cbrt((-0.5 / a)) * Math.cbrt((g + g)));
	} else {
		tmp = Math.cbrt(((0.5 / a) * (g - g))) + Math.cbrt((-g / a));
	}
	return tmp;
}

Julia

function code(g, h, a)
	t_0 = sqrt(Float64(Float64(g * g) - Float64(h * h)))
	t_1 = Float64(t_0 - g)
	t_2 = Float64(cbrt(Float64(Float64(1.0 / Float64(2.0 * a)) * t_1)) + cbrt(Float64(Float64(g + t_0) * Float64(-1.0 / Float64(2.0 * a)))))
	tmp = 0.0
	if (t_2 <= -5e-106)
		tmp = Float64(cbrt(Float64(Float64(-0.25 / a) * Float64((h ^ 2.0) / g))) + cbrt(Float64(Float64(g + g) * Float64(-0.5 / a))));
	elseif (t_2 <= 0.0)
		tmp = Float64(cbrt(Float64(t_1 * Float64(0.5 / a))) + Float64(cbrt(Float64(-0.5 / a)) * cbrt(Float64(g + g))));
	else
		tmp = Float64(cbrt(Float64(Float64(0.5 / a) * Float64(g - g))) + cbrt(Float64(Float64(-g) / a)));
	end
	return tmp
end

Wolfram

code[g_, h_, a_] := Block[{t$95$0 = N[Sqrt[N[(N[(g * g), $MachinePrecision] - N[(h * h), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 - g), $MachinePrecision]}, Block[{t$95$2 = N[(N[Power[N[(N[(1.0 / N[(2.0 * a), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision], 1/3], $MachinePrecision] + N[Power[N[(N[(g + t$95$0), $MachinePrecision] * N[(-1.0 / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-106], N[(N[Power[N[(N[(-0.25 / a), $MachinePrecision] * N[(N[Power[h, 2.0], $MachinePrecision] / g), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] + N[Power[N[(N[(g + g), $MachinePrecision] * N[(-0.5 / a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(N[Power[N[(t$95$1 * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] + N[(N[Power[N[(-0.5 / a), $MachinePrecision], 1/3], $MachinePrecision] * N[Power[N[(g + g), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[N[(N[(0.5 / a), $MachinePrecision] * N[(g - g), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] + N[Power[N[((-g) / a), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))) (cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))))) < -4.99999999999999983e-106

   1. Initial program 81.7%

      \[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]

   3. Simplified 81.7%

      \[\leadsto \color{blue}{\sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{g \cdot g - h \cdot h} - g\right)} + \sqrt[3]{\left(g + \sqrt{g \cdot g - h \cdot h}\right) \cdot \frac{-0.5}{a}}} \]
   4. Add Preprocessing

   5. Taylor expanded in g around inf 44.2%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{g \cdot g - h \cdot h} - g\right)} + \sqrt[3]{\left(g + \color{blue}{g}\right) \cdot \frac{-0.5}{a}} \]
   6. Step-by-step derivation

      1. difference-of-squares 44.2%

         \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{\color{blue}{\left(g + h\right) \cdot \left(g - h\right)}} - g\right)} + \sqrt[3]{\left(g + g\right) \cdot \frac{-0.5}{a}} \]

      2. +-commutative 44.2%

         \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{\color{blue}{\left(h + g\right)} \cdot \left(g - h\right)} - g\right)} + \sqrt[3]{\left(g + g\right) \cdot \frac{-0.5}{a}} \]

      3. sqrt-unprod 26.9%

         \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(\color{blue}{\sqrt{h + g} \cdot \sqrt{g - h}} - g\right)} + \sqrt[3]{\left(g + g\right) \cdot \frac{-0.5}{a}} \]

      4. *-commutative 26.9%

         \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(\color{blue}{\sqrt{g - h} \cdot \sqrt{h + g}} - g\right)} + \sqrt[3]{\left(g + g\right) \cdot \frac{-0.5}{a}} \]

      5. fma-neg 17.3%

         \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \color{blue}{\mathsf{fma}\left(\sqrt{g - h}, \sqrt{h + g}, -g\right)}} + \sqrt[3]{\left(g + g\right) \cdot \frac{-0.5}{a}} \]

      6. +-commutative 17.3%

         \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \mathsf{fma}\left(\sqrt{g - h}, \sqrt{\color{blue}{g + h}}, -g\right)} + \sqrt[3]{\left(g + g\right) \cdot \frac{-0.5}{a}} \]

   7. Applied egg-rr 17.3%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \color{blue}{\mathsf{fma}\left(\sqrt{g - h}, \sqrt{g + h}, -g\right)}} + \sqrt[3]{\left(g + g\right) \cdot \frac{-0.5}{a}} \]

   8. Taylor expanded in h around 0 77.9%

      \[\leadsto \sqrt[3]{\color{blue}{-0.25 \cdot \frac{{h}^{2}}{a \cdot g}}} + \sqrt[3]{\left(g + g\right) \cdot \frac{-0.5}{a}} \]
   9. Step-by-step derivation

      1. associate-*r/ 77.9%

         \[\leadsto \sqrt[3]{\color{blue}{\frac{-0.25 \cdot {h}^{2}}{a \cdot g}}} + \sqrt[3]{\left(g + g\right) \cdot \frac{-0.5}{a}} \]

      2. times-frac 91.1%

         \[\leadsto \sqrt[3]{\color{blue}{\frac{-0.25}{a} \cdot \frac{{h}^{2}}{g}}} + \sqrt[3]{\left(g + g\right) \cdot \frac{-0.5}{a}} \]

   10. Simplified 91.1%

       \[\leadsto \sqrt[3]{\color{blue}{\frac{-0.25}{a} \cdot \frac{{h}^{2}}{g}}} + \sqrt[3]{\left(g + g\right) \cdot \frac{-0.5}{a}} \]

   if -4.99999999999999983e-106 < (+.f64 (cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))) (cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))))) < 0.0

   1. Initial program 4.5%

      \[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]

   3. Simplified 4.5%

      \[\leadsto \color{blue}{\sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{g \cdot g - h \cdot h} - g\right)} + \sqrt[3]{\left(g + \sqrt{g \cdot g - h \cdot h}\right) \cdot \frac{-0.5}{a}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 4.5%

         \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{g \cdot g - h \cdot h} - g\right)} + \sqrt[3]{\color{blue}{\frac{-0.5}{a} \cdot \left(g + \sqrt{g \cdot g - h \cdot h}\right)}} \]

      2. cbrt-prod 33.2%

         \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{g \cdot g - h \cdot h} - g\right)} + \color{blue}{\sqrt[3]{\frac{-0.5}{a}} \cdot \sqrt[3]{g + \sqrt{g \cdot g - h \cdot h}}} \]

      3. pow2 33.2%

         \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{g \cdot g - h \cdot h} - g\right)} + \sqrt[3]{\frac{-0.5}{a}} \cdot \sqrt[3]{g + \sqrt{\color{blue}{{g}^{2}} - h \cdot h}} \]

      4. pow2 33.2%

         \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{g \cdot g - h \cdot h} - g\right)} + \sqrt[3]{\frac{-0.5}{a}} \cdot \sqrt[3]{g + \sqrt{{g}^{2} - \color{blue}{{h}^{2}}}} \]

   6. Applied egg-rr 33.2%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{g \cdot g - h \cdot h} - g\right)} + \color{blue}{\sqrt[3]{\frac{-0.5}{a}} \cdot \sqrt[3]{g + \sqrt{{g}^{2} - {h}^{2}}}} \]

   7. Taylor expanded in g around inf 83.2%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{g \cdot g - h \cdot h} - g\right)} + \sqrt[3]{\frac{-0.5}{a}} \cdot \sqrt[3]{g + \color{blue}{g}} \]

   if 0.0 < (+.f64 (cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (+.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))) (cbrt.f64 (*.f64 (/.f64 1 (*.f64 2 a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))))))

   1. Initial program 33.9%

      \[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]

   3. Simplified 33.9%

      \[\leadsto \color{blue}{\sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{g \cdot g - h \cdot h} - g\right)} + \sqrt[3]{\left(g + \sqrt{g \cdot g - h \cdot h}\right) \cdot \frac{-0.5}{a}}} \]
   4. Add Preprocessing

   5. Taylor expanded in g around inf 21.0%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{g \cdot g - h \cdot h} - g\right)} + \sqrt[3]{\left(g + \color{blue}{g}\right) \cdot \frac{-0.5}{a}} \]

   6. Taylor expanded in g around inf 76.3%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(\color{blue}{g} - g\right)} + \sqrt[3]{\left(g + g\right) \cdot \frac{-0.5}{a}} \]

   7. Taylor expanded in g around 0 76.3%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + \sqrt[3]{\color{blue}{-1 \cdot \frac{g}{a}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 76.3%

         \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + \sqrt[3]{\color{blue}{\frac{-1 \cdot g}{a}}} \]

      2. mul-1-neg 76.3%

         \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + \sqrt[3]{\frac{\color{blue}{-g}}{a}} \]

   9. Simplified 76.3%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + \sqrt[3]{\color{blue}{\frac{-g}{a}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\sqrt{g \cdot g - h \cdot h} - g\right)} + \sqrt[3]{\left(g + \sqrt{g \cdot g - h \cdot h}\right) \cdot \frac{-1}{2 \cdot a}} \leq -5 \cdot 10^{-106}:\\ \;\;\;\;\sqrt[3]{\frac{-0.25}{a} \cdot \frac{{h}^{2}}{g}} + \sqrt[3]{\left(g + g\right) \cdot \frac{-0.5}{a}}\\ \mathbf{elif}\;\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\sqrt{g \cdot g - h \cdot h} - g\right)} + \sqrt[3]{\left(g + \sqrt{g \cdot g - h \cdot h}\right) \cdot \frac{-1}{2 \cdot a}} \leq 0:\\ \;\;\;\;\sqrt[3]{\left(\sqrt{g \cdot g - h \cdot h} - g\right) \cdot \frac{0.5}{a}} + \sqrt[3]{\frac{-0.5}{a}} \cdot \sqrt[3]{g + g}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + \sqrt[3]{\frac{-g}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.2% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{\frac{0.5}{a} \cdot \left(g \cdot -2\right)} + \frac{0}{\sqrt[3]{a}} \end{array} \]

FPCore

(FPCore (g h a)
 :precision binary64
 (+ (cbrt (* (/ 0.5 a) (* g -2.0))) (/ 0.0 (cbrt a))))

C

double code(double g, double h, double a) {
	return cbrt(((0.5 / a) * (g * -2.0))) + (0.0 / cbrt(a));
}

Java

public static double code(double g, double h, double a) {
	return Math.cbrt(((0.5 / a) * (g * -2.0))) + (0.0 / Math.cbrt(a));
}

Julia

function code(g, h, a)
	return Float64(cbrt(Float64(Float64(0.5 / a) * Float64(g * -2.0))) + Float64(0.0 / cbrt(a)))
end

Wolfram

code[g_, h_, a_] := N[(N[Power[N[(N[(0.5 / a), $MachinePrecision] * N[(g * -2.0), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] + N[(0.0 / N[Power[a, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 43.6%

   \[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]

3. Simplified 43.6%

   \[\leadsto \color{blue}{\sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{g \cdot g - h \cdot h} - g\right)} + \sqrt[3]{\left(g + \sqrt{g \cdot g - h \cdot h}\right) \cdot \frac{-0.5}{a}}} \]
4. Add Preprocessing

5. Taylor expanded in g around inf 25.6%

   \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{g \cdot g - h \cdot h} - g\right)} + \sqrt[3]{\left(g + \color{blue}{g}\right) \cdot \frac{-0.5}{a}} \]

6. Taylor expanded in g around -inf 15.6%

   \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \color{blue}{\left(-2 \cdot g\right)}} + \sqrt[3]{\left(g + g\right) \cdot \frac{-0.5}{a}} \]

8. Simplified 15.6%

   \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \color{blue}{\left(g \cdot -2\right)}} + \sqrt[3]{\left(g + g\right) \cdot \frac{-0.5}{a}} \]

10. Applied egg-rr 0.0%

    \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g \cdot -2\right)} + \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{\frac{0}{0}}{\sqrt[3]{a}}\right)} - 1\right)} \]

12. Simplified 75.9%

    \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g \cdot -2\right)} + \color{blue}{\frac{0}{\sqrt[3]{a}}} \]

13. Final simplification 75.9%

    \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g \cdot -2\right)} + \frac{0}{\sqrt[3]{a}} \]
14. Add Preprocessing

Reproduce

herbie shell --seed 2024041 
(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))))))))