2-ancestry mixing, positive discriminant

Percentage Accurate: 44.4% → 95.8%

Time: 28.5s

Alternatives: 4

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: 44.4% 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: 95.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 41.2%

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

3. Simplified 41.2%

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

5. Taylor expanded in g around inf 23.2%

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

6. Taylor expanded in g around inf 72.2%

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

   1. associate-*r/ 72.2%

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

   2. neg-mul-1 72.2%

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

8. Simplified 72.2%

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

   1. frac-2neg 72.2%

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

   2. cbrt-div 96.1%

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

   3. remove-double-neg 96.1%

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

10. Applied egg-rr 96.1%

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

11. Final simplification 96.1%

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

Alternative 2: 73.7% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 41.2%

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

3. Simplified 41.2%

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

5. Taylor expanded in g around inf 23.2%

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

6. Taylor expanded in g around inf 72.2%

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

7. Final simplification 72.2%

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

Alternative 3: 73.8% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

code[g_, h_, a_] := 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. Initial program 41.2%

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

3. Simplified 41.2%

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

5. Taylor expanded in g around inf 23.2%

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

6. Taylor expanded in g around inf 72.2%

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

   1. associate-*r/ 72.2%

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

   2. neg-mul-1 72.2%

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

8. Simplified 72.2%

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

9. Final simplification 72.2%

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

Alternative 4: 2.9% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Java

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

Julia

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

Wolfram

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

Derivation

1. Initial program 41.2%

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

3. Simplified 41.2%

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

5. Taylor expanded in g around inf 23.2%

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

6. Taylor expanded in g around inf 72.2%

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

   1. pow1/3 34.4%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + \color{blue}{{\left(\left(g + g\right) \cdot \frac{-0.5}{a}\right)}^{0.3333333333333333}} \]

   2. add-log-exp 3.7%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + {\color{blue}{\log \left(e^{\left(g + g\right) \cdot \frac{-0.5}{a}}\right)}}^{0.3333333333333333} \]

   3. *-commutative 3.7%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + {\log \left(e^{\color{blue}{\frac{-0.5}{a} \cdot \left(g + g\right)}}\right)}^{0.3333333333333333} \]

   4. exp-prod 2.8%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + {\log \color{blue}{\left({\left(e^{\frac{-0.5}{a}}\right)}^{\left(g + g\right)}\right)}}^{0.3333333333333333} \]

   5. add-sqr-sqrt 1.4%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + {\log \left({\left(e^{\color{blue}{\sqrt{\frac{-0.5}{a}} \cdot \sqrt{\frac{-0.5}{a}}}}\right)}^{\left(g + g\right)}\right)}^{0.3333333333333333} \]

   6. sqrt-unprod 2.8%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + {\log \left({\left(e^{\color{blue}{\sqrt{\frac{-0.5}{a} \cdot \frac{-0.5}{a}}}}\right)}^{\left(g + g\right)}\right)}^{0.3333333333333333} \]

   7. frac-times 2.8%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + {\log \left({\left(e^{\sqrt{\color{blue}{\frac{-0.5 \cdot -0.5}{a \cdot a}}}}\right)}^{\left(g + g\right)}\right)}^{0.3333333333333333} \]

   8. metadata-eval 2.8%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + {\log \left({\left(e^{\sqrt{\frac{\color{blue}{0.25}}{a \cdot a}}}\right)}^{\left(g + g\right)}\right)}^{0.3333333333333333} \]

   9. metadata-eval 2.8%

      \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + {\log \left({\left(e^{\sqrt{\frac{\color{blue}{0.5 \cdot 0.5}}{a \cdot a}}}\right)}^{\left(g + g\right)}\right)}^{0.3333333333333333} \]

   10. frac-times 2.8%

       \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + {\log \left({\left(e^{\sqrt{\color{blue}{\frac{0.5}{a} \cdot \frac{0.5}{a}}}}\right)}^{\left(g + g\right)}\right)}^{0.3333333333333333} \]

   11. sqrt-unprod 1.4%

       \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + {\log \left({\left(e^{\color{blue}{\sqrt{\frac{0.5}{a}} \cdot \sqrt{\frac{0.5}{a}}}}\right)}^{\left(g + g\right)}\right)}^{0.3333333333333333} \]

   12. add-sqr-sqrt 2.8%

       \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + {\log \left({\left(e^{\color{blue}{\frac{0.5}{a}}}\right)}^{\left(g + g\right)}\right)}^{0.3333333333333333} \]

   13. add-sqr-sqrt 2.1%

       \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + {\log \left({\left(e^{\frac{0.5}{a}}\right)}^{\left(g + \color{blue}{\sqrt{g} \cdot \sqrt{g}}\right)}\right)}^{0.3333333333333333} \]

   14. sqrt-prod 2.8%

       \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + {\log \left({\left(e^{\frac{0.5}{a}}\right)}^{\left(g + \color{blue}{\sqrt{g \cdot g}}\right)}\right)}^{0.3333333333333333} \]

   15. sqr-neg 2.8%

       \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + {\log \left({\left(e^{\frac{0.5}{a}}\right)}^{\left(g + \sqrt{\color{blue}{\left(-g\right) \cdot \left(-g\right)}}\right)}\right)}^{0.3333333333333333} \]

   16. sqrt-unprod 2.2%

       \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + {\log \left({\left(e^{\frac{0.5}{a}}\right)}^{\left(g + \color{blue}{\sqrt{-g} \cdot \sqrt{-g}}\right)}\right)}^{0.3333333333333333} \]

   17. add-sqr-sqrt 2.9%

       \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + {\log \left({\left(e^{\frac{0.5}{a}}\right)}^{\left(g + \color{blue}{\left(-g\right)}\right)}\right)}^{0.3333333333333333} \]

   18. sub-neg 2.9%

       \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + {\log \left({\left(e^{\frac{0.5}{a}}\right)}^{\color{blue}{\left(g - g\right)}}\right)}^{0.3333333333333333} \]

   19. +-inverses 2.9%

       \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + {\log \left({\left(e^{\frac{0.5}{a}}\right)}^{\color{blue}{0}}\right)}^{0.3333333333333333} \]

   20. metadata-eval 2.9%

       \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + {\log \color{blue}{1}}^{0.3333333333333333} \]

   21. metadata-eval 2.9%

       \[\leadsto \sqrt[3]{\frac{0.5}{a} \cdot \left(g - g\right)} + {\color{blue}{0}}^{0.3333333333333333} \]

8. Applied egg-rr 2.9%

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

9. Final simplification 2.9%

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

Reproduce

herbie shell --seed 2024044 
(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))))))))